Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,3,Mod(55,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.55");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.f (of order \(6\), degree \(2\), 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: | \(8.82836056527\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{6}]$ |
Embedding invariants
Embedding label | 55.2 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 324.55 |
Dual form | 324.3.f.k.271.2 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | + | 1.73205i | −0.500000 | + | 0.866025i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | − | 3.46410i | −0.500000 | − | 0.866025i | ||||
\(5\) | 0.598076 | + | 1.03590i | 0.119615 | + | 0.207180i | 0.919615 | − | 0.392820i | \(-0.128501\pi\) |
−0.800000 | + | 0.600000i | \(0.795167\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(8\) | 8.00000 | 1.00000 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.39230 | −0.239230 | ||||||||
\(11\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −12.8923 | − | 22.3301i | −0.991716 | − | 1.71770i | −0.607100 | − | 0.794625i | \(-0.707667\pi\) |
−0.384615 | − | 0.923077i | \(-0.625666\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(17\) | 17.9808 | 1.05769 | 0.528846 | − | 0.848718i | \(-0.322625\pi\) | ||||
0.528846 | + | 0.848718i | \(0.322625\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(20\) | 2.39230 | − | 4.14359i | 0.119615 | − | 0.207180i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 11.7846 | − | 20.4115i | 0.471384 | − | 0.816462i | ||||
\(26\) | 51.5692 | 1.98343 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 28.1865 | − | 48.8205i | 0.971949 | − | 1.68347i | 0.282294 | − | 0.959328i | \(-0.408905\pi\) |
0.689655 | − | 0.724138i | \(-0.257762\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(32\) | −16.0000 | − | 27.7128i | −0.500000 | − | 0.866025i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −17.9808 | + | 31.1436i | −0.528846 | + | 0.915988i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 55.7846 | 1.50769 | 0.753846 | − | 0.657051i | \(-0.228196\pi\) | ||||
0.753846 | + | 0.657051i | \(0.228196\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.78461 | + | 8.28719i | 0.119615 | + | 0.207180i | ||||
\(41\) | 40.0000 | + | 69.2820i | 0.975610 | + | 1.68981i | 0.677908 | + | 0.735147i | \(0.262887\pi\) |
0.297702 | + | 0.954659i | \(0.403780\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −24.5000 | − | 42.4352i | −0.500000 | − | 0.866025i | ||||
\(50\) | 23.5692 | + | 40.8231i | 0.471384 | + | 0.816462i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −51.5692 | + | 89.3205i | −0.991716 | + | 1.71770i | ||||
\(53\) | −56.0000 | −1.05660 | −0.528302 | − | 0.849057i | \(-0.677171\pi\) | ||||
−0.528302 | + | 0.849057i | \(0.677171\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 56.3731 | + | 97.6410i | 0.971949 | + | 1.68347i | ||||
\(59\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 46.4615 | − | 80.4737i | 0.761664 | − | 1.31924i | −0.180328 | − | 0.983607i | \(-0.557716\pi\) |
0.941992 | − | 0.335635i | \(-0.108951\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 1.00000 | ||||||||
\(65\) | 15.4212 | − | 26.7102i | 0.237249 | − | 0.410927i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(68\) | −35.9615 | − | 62.2872i | −0.528846 | − | 0.915988i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 28.1384 | 0.385458 | 0.192729 | − | 0.981252i | \(-0.438266\pi\) | ||||
0.192729 | + | 0.981252i | \(0.438266\pi\) | |||||||
\(74\) | −55.7846 | + | 96.6218i | −0.753846 | + | 1.30570i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(80\) | −19.1384 | −0.239230 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −160.000 | −1.95122 | ||||||||
\(83\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.7539 | + | 18.6262i | 0.126516 | + | 0.219132i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −147.550 | −1.65786 | −0.828932 | − | 0.559349i | \(-0.811051\pi\) | ||||
−0.828932 | + | 0.559349i | \(0.811051\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 65.0000 | − | 112.583i | 0.670103 | − | 1.16065i | −0.307771 | − | 0.951460i | \(-0.599583\pi\) |
0.977875 | − | 0.209192i | \(-0.0670835\pi\) | |||||||
\(98\) | 98.0000 | 1.00000 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −94.2769 | −0.942769 | ||||||||
\(101\) | −20.0000 | + | 34.6410i | −0.198020 | + | 0.342980i | −0.947886 | − | 0.318609i | \(-0.896784\pi\) |
0.749866 | + | 0.661589i | \(0.230118\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(104\) | −103.138 | − | 178.641i | −0.991716 | − | 1.71770i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 56.0000 | − | 96.9948i | 0.528302 | − | 0.915046i | ||||
\(107\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −194.923 | −1.78828 | −0.894142 | − | 0.447783i | \(-0.852214\pi\) | ||||
−0.894142 | + | 0.447783i | \(0.852214\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −68.9904 | − | 119.495i | −0.610534 | − | 1.05748i | −0.991150 | − | 0.132743i | \(-0.957621\pi\) |
0.380616 | − | 0.924733i | \(-0.375712\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −225.492 | −1.94390 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −60.5000 | − | 104.789i | −0.500000 | − | 0.866025i | ||||
\(122\) | 92.9230 | + | 160.947i | 0.761664 | + | 1.31924i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 58.0962 | 0.464770 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(128\) | −64.0000 | + | 110.851i | −0.500000 | + | 0.866025i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 30.8423 | + | 53.4205i | 0.237249 | + | 0.410927i | ||||
\(131\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 143.846 | 1.05769 | ||||||||
\(137\) | −134.933 | + | 233.710i | −0.984910 | + | 1.70591i | −0.342574 | + | 0.939491i | \(0.611299\pi\) |
−0.642336 | + | 0.766423i | \(0.722035\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 67.4308 | 0.465040 | ||||||||
\(146\) | −28.1384 | + | 48.7372i | −0.192729 | + | 0.333816i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −111.569 | − | 193.244i | −0.753846 | − | 1.30570i | ||||
\(149\) | 25.8327 | + | 44.7436i | 0.173374 | + | 0.300292i | 0.939597 | − | 0.342282i | \(-0.111200\pi\) |
−0.766223 | + | 0.642574i | \(0.777866\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 156.815 | + | 271.612i | 0.998824 | + | 1.73001i | 0.541401 | + | 0.840764i | \(0.317894\pi\) |
0.457423 | + | 0.889249i | \(0.348773\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 19.1384 | − | 33.1487i | 0.119615 | − | 0.207180i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(164\) | 160.000 | − | 277.128i | 0.975610 | − | 1.68981i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −247.923 | + | 429.415i | −1.46700 | + | 2.54092i | ||||
\(170\) | −43.0155 | −0.253032 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 116.894 | − | 202.467i | 0.675689 | − | 1.17033i | −0.300578 | − | 0.953757i | \(-0.597180\pi\) |
0.976267 | − | 0.216570i | \(-0.0694871\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 147.550 | − | 255.564i | 0.828932 | − | 1.43575i | ||||
\(179\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 38.0000 | 0.209945 | 0.104972 | − | 0.994475i | \(-0.466525\pi\) | ||||
0.104972 | + | 0.994475i | \(0.466525\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 33.3634 | + | 57.7872i | 0.180343 | + | 0.312363i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 97.9923 | + | 169.728i | 0.507732 | + | 0.879418i | 0.999960 | + | 0.00895123i | \(0.00284930\pi\) |
−0.492228 | + | 0.870466i | \(0.663817\pi\) | |||||||
\(194\) | 130.000 | + | 225.167i | 0.670103 | + | 1.16065i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −98.0000 | + | 169.741i | −0.500000 | + | 0.866025i | ||||
\(197\) | 365.750 | 1.85660 | 0.928299 | − | 0.371834i | \(-0.121271\pi\) | ||||
0.928299 | + | 0.371834i | \(0.121271\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | 94.2769 | − | 163.292i | 0.471384 | − | 0.816462i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −40.0000 | − | 69.2820i | −0.198020 | − | 0.342980i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −47.8461 | + | 82.8719i | −0.233396 | + | 0.404253i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 412.554 | 1.98343 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(212\) | 112.000 | + | 193.990i | 0.528302 | + | 0.915046i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 194.923 | − | 337.617i | 0.894142 | − | 1.54870i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −231.813 | − | 401.513i | −1.04893 | − | 1.81680i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 275.962 | 1.22107 | ||||||||
\(227\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −58.5385 | − | 101.392i | −0.255627 | − | 0.442758i | 0.709439 | − | 0.704767i | \(-0.248948\pi\) |
−0.965066 | + | 0.262009i | \(0.915615\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 225.492 | − | 390.564i | 0.971949 | − | 1.68347i | ||||
\(233\) | 389.865 | 1.67324 | 0.836621 | − | 0.547782i | \(-0.184528\pi\) | ||||
0.836621 | + | 0.547782i | \(0.184528\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −208.423 | + | 360.999i | −0.864826 | + | 1.49792i | 0.00239399 | + | 0.999997i | \(0.499238\pi\) |
−0.867220 | + | 0.497925i | \(0.834095\pi\) | |||||||
\(242\) | 242.000 | 1.00000 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −371.692 | −1.52333 | ||||||||
\(245\) | 29.3057 | − | 50.7590i | 0.119615 | − | 0.207180i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −58.0962 | + | 100.626i | −0.232385 | + | 0.402502i | ||||
\(251\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | − | 221.703i | −0.500000 | − | 0.866025i | ||||
\(257\) | 236.836 | + | 410.213i | 0.921543 | + | 1.59616i | 0.797029 | + | 0.603941i | \(0.206404\pi\) |
0.124514 | + | 0.992218i | \(0.460263\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −123.369 | −0.474497 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −33.4923 | − | 58.0103i | −0.126386 | − | 0.218907i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −140.488 | −0.522262 | −0.261131 | − | 0.965303i | \(-0.584095\pi\) | ||||
−0.261131 | + | 0.965303i | \(0.584095\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | −143.846 | + | 249.149i | −0.528846 | + | 0.915988i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −269.865 | − | 467.420i | −0.984910 | − | 1.70591i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −115.000 | + | 199.186i | −0.415162 | + | 0.719082i | −0.995445 | − | 0.0953324i | \(-0.969609\pi\) |
0.580283 | + | 0.814415i | \(0.302942\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −280.052 | + | 485.064i | −0.996626 | + | 1.72621i | −0.427231 | + | 0.904143i | \(0.640511\pi\) |
−0.569395 | + | 0.822064i | \(0.692822\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 34.3078 | 0.118712 | ||||||||
\(290\) | −67.4308 | + | 116.794i | −0.232520 | + | 0.402736i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −56.2769 | − | 97.4744i | −0.192729 | − | 0.333816i | ||||
\(293\) | −212.817 | − | 368.610i | −0.726339 | − | 1.25806i | −0.958421 | − | 0.285359i | \(-0.907887\pi\) |
0.232082 | − | 0.972696i | \(-0.425446\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 446.277 | 1.50769 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −103.331 | −0.346748 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 111.150 | 0.364427 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 282.700 | − | 489.651i | 0.903195 | − | 1.56438i | 0.0798722 | − | 0.996805i | \(-0.474549\pi\) |
0.823322 | − | 0.567574i | \(-0.192118\pi\) | |||||||
\(314\) | −627.261 | −1.99765 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 218.952 | − | 379.236i | 0.690700 | − | 1.19633i | −0.280909 | − | 0.959734i | \(-0.590636\pi\) |
0.971609 | − | 0.236593i | \(-0.0760308\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 38.2769 | + | 66.2975i | 0.119615 | + | 0.207180i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −607.723 | −1.86992 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 320.000 | + | 554.256i | 0.975610 | + | 1.68981i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −175.000 | − | 303.109i | −0.519288 | − | 0.899433i | −0.999749 | − | 0.0224168i | \(-0.992864\pi\) |
0.480461 | − | 0.877016i | \(-0.340469\pi\) | |||||||
\(338\) | −495.846 | − | 858.831i | −1.46700 | − | 2.54092i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 43.0155 | − | 74.5050i | 0.126516 | − | 0.219132i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 233.788 | + | 404.933i | 0.675689 | + | 1.17033i | ||||
\(347\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 299.000 | − | 517.883i | 0.856734 | − | 1.48391i | −0.0182939 | − | 0.999833i | \(-0.505823\pi\) |
0.875027 | − | 0.484073i | \(-0.160843\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −272.000 | + | 471.118i | −0.770538 | + | 1.33461i | 0.166730 | + | 0.986003i | \(0.446679\pi\) |
−0.937268 | + | 0.348609i | \(0.886654\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 295.100 | + | 511.128i | 0.828932 | + | 1.43575i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 361.000 | 1.00000 | ||||||||
\(362\) | −38.0000 | + | 65.8179i | −0.104972 | + | 0.181817i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.8289 | + | 29.1486i | 0.0461067 | + | 0.0798591i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −133.454 | −0.360686 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 275.000 | + | 476.314i | 0.737265 | + | 1.27698i | 0.953722 | + | 0.300689i | \(0.0972166\pi\) |
−0.216457 | + | 0.976292i | \(0.569450\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1453.56 | −3.85559 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −391.969 | −1.01546 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −520.000 | −1.34021 | ||||||||
\(389\) | 340.000 | − | 588.897i | 0.874036 | − | 1.51387i | 0.0162499 | − | 0.999868i | \(-0.494827\pi\) |
0.857786 | − | 0.514007i | \(-0.171839\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −196.000 | − | 339.482i | −0.500000 | − | 0.866025i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −365.750 | + | 633.497i | −0.928299 | + | 1.60786i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 69.9076 | 0.176090 | 0.0880448 | − | 0.996117i | \(-0.471938\pi\) | ||||
0.0880448 | + | 0.996117i | \(0.471938\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 188.554 | + | 326.585i | 0.471384 | + | 0.816462i | ||||
\(401\) | 325.544 | + | 563.859i | 0.811831 | + | 1.40613i | 0.911581 | + | 0.411120i | \(0.134862\pi\) |
−0.0997506 | + | 0.995012i | \(0.531805\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 160.000 | 0.396040 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 91.5770 | + | 158.616i | 0.223905 | + | 0.387814i | 0.955990 | − | 0.293399i | \(-0.0947863\pi\) |
−0.732086 | + | 0.681213i | \(0.761453\pi\) | |||||||
\(410\) | −95.6922 | − | 165.744i | −0.233396 | − | 0.404253i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −412.554 | + | 714.564i | −0.991716 | + | 1.71770i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 349.231 | − | 604.885i | 0.829527 | − | 1.43678i | −0.0688836 | − | 0.997625i | \(-0.521944\pi\) |
0.898410 | − | 0.439157i | \(-0.144723\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −448.000 | −1.05660 | ||||||||
\(425\) | 211.896 | − | 367.015i | 0.498579 | − | 0.863565i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 561.677 | 1.29717 | 0.648587 | − | 0.761140i | \(-0.275360\pi\) | ||||
0.648587 | + | 0.761140i | \(0.275360\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 389.846 | + | 675.233i | 0.894142 | + | 1.54870i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 927.254 | 2.09786 | ||||||||
\(443\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −88.2461 | − | 152.847i | −0.198306 | − | 0.343476i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −560.000 | −1.24722 | −0.623608 | − | 0.781737i | \(-0.714334\pi\) | ||||
−0.623608 | + | 0.781737i | \(0.714334\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −275.962 | + | 477.979i | −0.610534 | + | 1.05748i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −67.0077 | + | 116.061i | −0.146625 | + | 0.253962i | −0.929978 | − | 0.367615i | \(-0.880174\pi\) |
0.783353 | + | 0.621577i | \(0.213508\pi\) | |||||||
\(458\) | 234.154 | 0.511253 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −380.000 | + | 658.179i | −0.824295 | + | 1.42772i | 0.0781619 | + | 0.996941i | \(0.475095\pi\) |
−0.902457 | + | 0.430780i | \(0.858238\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(464\) | 450.985 | + | 781.128i | 0.971949 | + | 1.68347i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −389.865 | + | 675.267i | −0.836621 | + | 1.44907i | ||||
\(467\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −719.192 | − | 1245.68i | −1.49520 | − | 2.58977i | ||||
\(482\) | −416.846 | − | 721.999i | −0.864826 | − | 1.49792i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −242.000 | + | 419.156i | −0.500000 | + | 0.866025i | ||||
\(485\) | 155.500 | 0.320618 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(488\) | 371.692 | − | 643.790i | 0.761664 | − | 1.31924i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 58.6115 | + | 101.518i | 0.119615 | + | 0.207180i | ||||
\(491\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 506.815 | − | 877.830i | 1.02802 | − | 1.78059i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(500\) | −116.192 | − | 201.251i | −0.232385 | − | 0.402502i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −47.8461 | −0.0947447 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 220.000 | + | 381.051i | 0.432220 | + | 0.748627i | 0.997064 | − | 0.0765706i | \(-0.0243970\pi\) |
−0.564844 | + | 0.825198i | \(0.691064\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 512.000 | 1.00000 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −947.346 | −1.84309 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 123.369 | − | 213.682i | 0.237249 | − | 0.410927i | ||||
\(521\) | 880.000 | 1.68906 | 0.844530 | − | 0.535509i | \(-0.179880\pi\) | ||||
0.844530 | + | 0.535509i | \(0.179880\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −264.500 | + | 458.127i | −0.500000 | + | 0.866025i | ||||
\(530\) | 133.969 | 0.252772 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1031.38 | − | 1786.41i | 1.93506 | − | 3.35161i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 140.488 | − | 243.333i | 0.261131 | − | 0.452292i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −386.461 | −0.714346 | −0.357173 | − | 0.934038i | \(-0.616259\pi\) | ||||
−0.357173 | + | 0.934038i | \(0.616259\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −287.692 | − | 498.297i | −0.528846 | − | 0.915988i | ||||
\(545\) | −116.579 | − | 201.920i | −0.213906 | − | 0.370496i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(548\) | 1079.46 | 1.96982 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −230.000 | − | 398.372i | −0.415162 | − | 0.719082i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 246.212 | 0.442032 | 0.221016 | − | 0.975270i | \(-0.429063\pi\) | ||||
0.221016 | + | 0.975270i | \(0.429063\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −560.104 | − | 970.128i | −0.996626 | − | 1.72621i | ||||
\(563\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 82.5230 | − | 142.934i | 0.146058 | − | 0.252981i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −460.052 | + | 796.833i | −0.808527 | + | 1.40041i | 0.105357 | + | 0.994434i | \(0.466401\pi\) |
−0.913884 | + | 0.405975i | \(0.866932\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 658.138 | 1.14062 | 0.570311 | − | 0.821429i | \(-0.306823\pi\) | ||||
0.570311 | + | 0.821429i | \(0.306823\pi\) | |||||||
\(578\) | −34.3078 | + | 59.4229i | −0.0593561 | + | 0.102808i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −134.862 | − | 233.587i | −0.232520 | − | 0.402736i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 225.108 | 0.385458 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 851.269 | 1.45268 | ||||||||
\(587\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −446.277 | + | 772.974i | −0.753846 | + | 1.30570i | ||||
\(593\) | 437.404 | 0.737612 | 0.368806 | − | 0.929506i | \(-0.379767\pi\) | ||||
0.368806 | + | 0.929506i | \(0.379767\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 103.331 | − | 178.974i | 0.173374 | − | 0.300292i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −67.6539 | + | 117.180i | −0.112569 | + | 0.194975i | −0.916805 | − | 0.399334i | \(-0.869241\pi\) |
0.804236 | + | 0.594309i | \(0.202575\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 72.3672 | − | 125.344i | 0.119615 | − | 0.207180i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −111.150 | + | 192.518i | −0.182213 | + | 0.315603i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −70.0000 | −0.114192 | −0.0570962 | − | 0.998369i | \(-0.518184\pi\) | ||||
−0.0570962 | + | 0.998369i | \(0.518184\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 213.067 | + | 369.043i | 0.345328 | + | 0.598126i | 0.985413 | − | 0.170178i | \(-0.0544344\pi\) |
−0.640085 | + | 0.768304i | \(0.721101\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −259.869 | − | 450.107i | −0.415791 | − | 0.720171i | ||||
\(626\) | 565.400 | + | 979.301i | 0.903195 | + | 1.56438i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 627.261 | − | 1086.45i | 0.998824 | − | 1.73001i | ||||
\(629\) | 1003.05 | 1.59467 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 437.904 | + | 758.472i | 0.690700 | + | 1.19633i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −631.723 | + | 1094.18i | −0.991716 | + | 1.71770i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −153.108 | −0.239230 | ||||||||
\(641\) | −427.409 | + | 740.295i | −0.666785 | + | 1.15491i | 0.312012 | + | 0.950078i | \(0.398997\pi\) |
−0.978798 | + | 0.204828i | \(0.934336\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 607.723 | − | 1052.61i | 0.934959 | − | 1.61940i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −572.000 | − | 990.733i | −0.875957 | − | 1.51720i | −0.855740 | − | 0.517407i | \(-0.826897\pi\) |
−0.0202175 | − | 0.999796i | \(-0.506436\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1280.00 | −1.95122 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.6924 | + | 60.0890i | 0.0524847 | + | 0.0909061i | 0.891074 | − | 0.453858i | \(-0.149953\pi\) |
−0.838589 | + | 0.544764i | \(0.816619\pi\) | |||||||
\(662\) | 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 | ||||||||
\(673\) | −285.546 | + | 494.580i | −0.424288 | + | 0.734889i | −0.996354 | − | 0.0853191i | \(-0.972809\pi\) |
0.572065 | + | 0.820208i | \(0.306142\pi\) | |||||||
\(674\) | 700.000 | 1.03858 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1983.38 | 2.93400 | ||||||||
\(677\) | 52.0000 | − | 90.0666i | 0.0768095 | − | 0.133038i | −0.825062 | − | 0.565042i | \(-0.808860\pi\) |
0.901872 | + | 0.432004i | \(0.142193\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 86.0309 | + | 149.010i | 0.126516 | + | 0.219132i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −322.800 | −0.471241 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 721.969 | + | 1250.49i | 1.04785 | + | 1.81493i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(692\) | −935.154 | −1.35138 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 719.230 | + | 1245.74i | 1.03189 | + | 1.78729i | ||||
\(698\) | 598.000 | + | 1035.77i | 0.856734 | + | 1.48391i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1387.57 | −1.97941 | −0.989704 | − | 0.143129i | \(-0.954284\pi\) | ||||
−0.989704 | + | 0.143129i | \(0.954284\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −544.000 | − | 942.236i | −0.770538 | − | 1.33461i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −442.077 | + | 765.699i | −0.623522 | + | 1.07997i | 0.365303 | + | 0.930889i | \(0.380965\pi\) |
−0.988825 | + | 0.149082i | \(0.952368\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1180.40 | −1.65786 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −361.000 | + | 625.270i | −0.500000 | + | 0.866025i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −76.0000 | − | 131.636i | −0.104972 | − | 0.181817i | ||||
\(725\) | −664.335 | − | 1150.66i | −0.916324 | − | 1.58712i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −67.3157 | −0.0922133 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 725.000 | + | 1255.74i | 0.989086 | + | 1.71315i | 0.622143 | + | 0.782904i | \(0.286262\pi\) |
0.366943 | + | 0.930243i | \(0.380404\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(740\) | 133.454 | − | 231.149i | 0.180343 | − | 0.312363i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −30.8999 | + | 53.5201i | −0.0414763 | + | 0.0718391i | ||||
\(746\) | −1100.00 | −1.47453 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1453.56 | − | 2517.64i | 1.92780 | − | 3.33904i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1190.00 | 1.57199 | 0.785997 | − | 0.618230i | \(-0.212150\pi\) | ||||
0.785997 | + | 0.618230i | \(0.212150\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −346.225 | − | 599.679i | −0.454961 | − | 0.788015i | 0.543725 | − | 0.839263i | \(-0.317013\pi\) |
−0.998686 | + | 0.0512484i | \(0.983680\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 760.115 | + | 1316.56i | 0.988446 | + | 1.71204i | 0.625488 | + | 0.780234i | \(0.284900\pi\) |
0.362959 | + | 0.931805i | \(0.381767\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 391.969 | − | 678.910i | 0.507732 | − | 0.879418i | ||||
\(773\) | 1085.75 | 1.40459 | 0.702296 | − | 0.711885i | \(-0.252158\pi\) | ||||
0.702296 | + | 0.711885i | \(0.252158\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 520.000 | − | 900.666i | 0.670103 | − | 1.16065i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 680.000 | + | 1177.79i | 0.874036 | + | 1.51387i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 784.000 | 1.00000 | ||||||||
\(785\) | −187.575 | + | 324.890i | −0.238949 | + | 0.413872i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(788\) | −731.500 | − | 1266.99i | −0.928299 | − | 1.60786i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2395.98 | −3.02142 | ||||||||
\(794\) | −69.9076 | + | 121.083i | −0.0880448 | + | 0.152498i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −194.644 | − | 337.133i | −0.244221 | − | 0.423003i | 0.717691 | − | 0.696361i | \(-0.245199\pi\) |
−0.961912 | + | 0.273358i | \(0.911866\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −754.215 | −0.942769 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1302.18 | −1.62366 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −160.000 | + | 277.128i | −0.198020 | + | 0.342980i | ||||
\(809\) | −1034.63 | −1.27890 | −0.639448 | − | 0.768835i | \(-0.720837\pi\) | ||||
−0.639448 | + | 0.768835i | \(0.720837\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −366.308 | −0.447809 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 382.769 | 0.466791 | ||||||||
\(821\) | −721.525 | + | 1249.72i | −0.878837 | + | 1.52219i | −0.0262179 | + | 0.999656i | \(0.508346\pi\) |
−0.852619 | + | 0.522533i | \(0.824987\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1258.00 | −1.51749 | −0.758745 | − | 0.651387i | \(-0.774187\pi\) | ||||
−0.758745 | + | 0.651387i | \(0.774187\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −825.108 | − | 1429.13i | −0.991716 | − | 1.71770i | ||||
\(833\) | −440.529 | − | 763.018i | −0.528846 | − | 0.915988i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1168.46 | − | 2023.83i | −1.38937 | − | 2.40646i | ||||
\(842\) | 698.461 | + | 1209.77i | 0.829527 | + | 1.43678i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −593.108 | −0.701902 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 448.000 | − | 775.959i | 0.528302 | − | 0.915046i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 423.793 | + | 734.030i | 0.498579 | + | 0.863565i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −205.000 | + | 355.070i | −0.240328 | + | 0.416261i | −0.960808 | − | 0.277215i | \(-0.910588\pi\) |
0.720480 | + | 0.693476i | \(0.243922\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −830.471 | + | 1438.42i | −0.969044 | + | 1.67843i | −0.270712 | + | 0.962660i | \(0.587259\pi\) |
−0.698333 | + | 0.715774i | \(0.746074\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 279.647 | 0.323291 | ||||||||
\(866\) | −561.677 | + | 972.853i | −0.648587 | + | 1.12339i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −1559.38 | −1.78828 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 703.877 | + | 1219.15i | 0.802596 | + | 1.39014i | 0.917902 | + | 0.396807i | \(0.129882\pi\) |
−0.115306 | + | 0.993330i | \(0.536785\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1600.00 | 1.81612 | 0.908059 | − | 0.418842i | \(-0.137564\pi\) | ||||
0.908059 | + | 0.418842i | \(0.137564\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(884\) | −927.254 | + | 1606.05i | −1.04893 | + | 1.81680i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 352.985 | 0.396612 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 560.000 | − | 969.948i | 0.623608 | − | 1.08012i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1006.92 | −1.11756 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −551.923 | − | 955.959i | −0.610534 | − | 1.05748i | ||||
\(905\) | 22.7269 | + | 39.3641i | 0.0251126 | + | 0.0434963i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −134.015 | − | 232.122i | −0.146625 | − | 0.253962i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −234.154 | + | 405.566i | −0.255627 | + | 0.442758i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −760.000 | − | 1316.36i | −0.824295 | − | 1.42772i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 657.400 | − | 1138.65i | 0.710703 | − | 1.23097i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1803.94 | −1.94390 | ||||||||
\(929\) | 571.717 | − | 990.243i | 0.615411 | − | 1.06592i | −0.374901 | − | 0.927065i | \(-0.622323\pi\) |
0.990312 | − | 0.138859i | \(-0.0443435\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −779.731 | − | 1350.53i | −0.836621 | − | 1.44907i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1794.63 | 1.91529 | 0.957647 | − | 0.287945i | \(-0.0929721\pi\) | ||||
0.957647 | + | 0.287945i | \(0.0929721\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 351.725 | + | 609.205i | 0.373778 | + | 0.647402i | 0.990143 | − | 0.140058i | \(-0.0447290\pi\) |
−0.616366 | + | 0.787460i | \(0.711396\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −362.769 | − | 628.335i | −0.382265 | − | 0.662102i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1793.21 | −1.88165 | −0.940824 | − | 0.338895i | \(-0.889947\pi\) | ||||
−0.940824 | + | 0.338895i | \(0.889947\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −480.500 | + | 832.250i | −0.500000 | + | 0.866025i | ||||
\(962\) | 2876.77 | 2.99040 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1667.38 | 1.72965 | ||||||||
\(965\) | −117.214 | + | 203.020i | −0.121465 | + | 0.210383i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(968\) | −484.000 | − | 838.313i | −0.500000 | − | 0.866025i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −155.500 | + | 269.334i | −0.160309 | + | 0.277663i | ||||
\(971\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 743.384 | + | 1287.58i | 0.761664 | + | 1.31924i | ||||
\(977\) | −248.000 | − | 429.549i | −0.253838 | − | 0.439661i | 0.710741 | − | 0.703454i | \(-0.248360\pi\) |
−0.964579 | + | 0.263793i | \(0.915026\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −234.446 | −0.239230 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 218.746 | + | 378.880i | 0.222077 | + | 0.384649i | ||||
\(986\) | 1013.63 | + | 1755.66i | 1.02802 | + | 1.78059i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 140.339 | − | 243.073i | 0.140761 | − | 0.243805i | −0.787023 | − | 0.616924i | \(-0.788378\pi\) |
0.927783 | + | 0.373119i | \(0.121712\pi\) | |||||||
\(998\) | 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 | 324.3.f.k.55.2 | 4 | ||
3.2 | odd | 2 | 324.3.f.n.55.1 | 4 | |||
4.3 | odd | 2 | CM | 324.3.f.k.55.2 | 4 | ||
9.2 | odd | 6 | 324.3.d.a.163.2 | ✓ | 2 | ||
9.4 | even | 3 | inner | 324.3.f.k.271.2 | 4 | ||
9.5 | odd | 6 | 324.3.f.n.271.1 | 4 | |||
9.7 | even | 3 | 324.3.d.d.163.1 | yes | 2 | ||
12.11 | even | 2 | 324.3.f.n.55.1 | 4 | |||
36.7 | odd | 6 | 324.3.d.d.163.1 | yes | 2 | ||
36.11 | even | 6 | 324.3.d.a.163.2 | ✓ | 2 | ||
36.23 | even | 6 | 324.3.f.n.271.1 | 4 | |||
36.31 | odd | 6 | inner | 324.3.f.k.271.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
324.3.d.a.163.2 | ✓ | 2 | 9.2 | odd | 6 | ||
324.3.d.a.163.2 | ✓ | 2 | 36.11 | even | 6 | ||
324.3.d.d.163.1 | yes | 2 | 9.7 | even | 3 | ||
324.3.d.d.163.1 | yes | 2 | 36.7 | odd | 6 | ||
324.3.f.k.55.2 | 4 | 1.1 | even | 1 | trivial | ||
324.3.f.k.55.2 | 4 | 4.3 | odd | 2 | CM | ||
324.3.f.k.271.2 | 4 | 9.4 | even | 3 | inner | ||
324.3.f.k.271.2 | 4 | 36.31 | odd | 6 | inner | ||
324.3.f.n.55.1 | 4 | 3.2 | odd | 2 | |||
324.3.f.n.55.1 | 4 | 12.11 | even | 2 | |||
324.3.f.n.271.1 | 4 | 9.5 | odd | 6 | |||
324.3.f.n.271.1 | 4 | 36.23 | even | 6 |