Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,3,Mod(557,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 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("1764.557");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.bk (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: | \(48.0655186332\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.12745506816.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 8x^{6} + 55x^{4} - 72x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 557.2 | ||
Root | \(-1.00781 + 0.581861i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.557 |
Dual form | 1764.3.bk.d.1745.2 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.01563 | + | 1.16372i | −0.403125 | + | 0.232744i | −0.687832 | − | 0.725870i | \(-0.741437\pi\) |
0.284706 | + | 0.958615i | \(0.408104\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 7.70549 | + | 4.44876i | 0.700499 | + | 0.404433i | 0.807533 | − | 0.589822i | \(-0.200802\pi\) |
−0.107034 | + | 0.994255i | \(0.534136\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 8.58301 | 0.660231 | 0.330116 | − | 0.943941i | \(-0.392912\pi\) | ||||
0.330116 | + | 0.943941i | \(0.392912\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 17.4266 | + | 10.0613i | 1.02509 | + | 0.591838i | 0.915575 | − | 0.402146i | \(-0.131736\pi\) |
0.109519 | + | 0.993985i | \(0.465069\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.93725 | − | 5.08747i | −0.154592 | − | 0.267762i | 0.778318 | − | 0.627870i | \(-0.216073\pi\) |
−0.932911 | + | 0.360108i | \(0.882740\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −15.0540 | + | 8.69140i | −0.654520 | + | 0.377887i | −0.790186 | − | 0.612867i | \(-0.790016\pi\) |
0.135666 | + | 0.990755i | \(0.456683\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −9.79150 | + | 16.9594i | −0.391660 | + | 0.678375i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 19.0318i | − | 0.656269i | −0.944631 | − | 0.328134i | \(-0.893580\pi\) | ||
0.944631 | − | 0.328134i | \(-0.106420\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.35425 | + | 4.07768i | −0.0759435 | + | 0.131538i | −0.901496 | − | 0.432787i | \(-0.857530\pi\) |
0.825553 | + | 0.564325i | \(0.190864\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −19.8745 | − | 34.4237i | −0.537149 | − | 0.930369i | −0.999056 | − | 0.0434408i | \(-0.986168\pi\) |
0.461907 | − | 0.886928i | \(-0.347165\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 6.98233i | − | 0.170301i | −0.996368 | − | 0.0851504i | \(-0.972863\pi\) | ||
0.996368 | − | 0.0851504i | \(-0.0271371\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −35.7490 | −0.831372 | −0.415686 | − | 0.909508i | \(-0.636459\pi\) | ||||
−0.415686 | + | 0.909508i | \(0.636459\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 63.5330 | − | 36.6808i | 1.35177 | − | 0.780443i | 0.363270 | − | 0.931684i | \(-0.381660\pi\) |
0.988497 | + | 0.151241i | \(0.0483270\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 40.4166 | + | 23.3345i | 0.762577 | + | 0.440274i | 0.830220 | − | 0.557436i | \(-0.188215\pi\) |
−0.0676432 | + | 0.997710i | \(0.521548\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −20.7085 | −0.376518 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −20.8703 | − | 12.0495i | −0.353734 | − | 0.204228i | 0.312595 | − | 0.949887i | \(-0.398802\pi\) |
−0.666328 | + | 0.745658i | \(0.732135\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 36.6458 | + | 63.4723i | 0.600750 | + | 1.04053i | 0.992708 | + | 0.120546i | \(0.0384646\pi\) |
−0.391958 | + | 0.919983i | \(0.628202\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −17.3001 | + | 9.98823i | −0.266156 | + | 0.153665i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 16.0405 | − | 27.7830i | 0.239411 | − | 0.414672i | −0.721135 | − | 0.692795i | \(-0.756379\pi\) |
0.960545 | + | 0.278123i | \(0.0897124\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 114.843i | 1.61751i | 0.588144 | + | 0.808756i | \(0.299859\pi\) | ||||
−0.588144 | + | 0.808756i | \(0.700141\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −20.6458 | + | 35.7595i | −0.282819 | + | 0.489856i | −0.972078 | − | 0.234659i | \(-0.924603\pi\) |
0.689259 | + | 0.724515i | \(0.257936\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.3320 | + | 23.0917i | 0.168760 | + | 0.292300i | 0.937984 | − | 0.346678i | \(-0.112690\pi\) |
−0.769224 | + | 0.638979i | \(0.779357\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 136.057i | 1.63924i | 0.572910 | + | 0.819618i | \(0.305814\pi\) | ||||
−0.572910 | + | 0.819618i | \(0.694186\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −46.8340 | −0.550988 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 126.226 | − | 72.8764i | 1.41826 | − | 0.818836i | 0.422118 | − | 0.906541i | \(-0.361287\pi\) |
0.996146 | + | 0.0877052i | \(0.0279533\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 11.8408 | + | 6.83629i | 0.124640 | + | 0.0719610i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −65.9555 | −0.679954 | −0.339977 | − | 0.940434i | \(-0.610419\pi\) | ||||
−0.339977 | + | 0.940434i | \(0.610419\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 80.2456 | + | 46.3298i | 0.794511 | + | 0.458711i | 0.841548 | − | 0.540182i | \(-0.181645\pi\) |
−0.0470373 | + | 0.998893i | \(0.514978\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 96.5608 | + | 167.248i | 0.937483 | + | 1.62377i | 0.770145 | + | 0.637869i | \(0.220184\pi\) |
0.167339 | + | 0.985899i | \(0.446483\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −40.8777 | + | 23.6007i | −0.382034 | + | 0.220568i | −0.678703 | − | 0.734413i | \(-0.737458\pi\) |
0.296669 | + | 0.954980i | \(0.404124\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −104.081 | + | 180.274i | −0.954872 | + | 1.65389i | −0.220211 | + | 0.975452i | \(0.570675\pi\) |
−0.734661 | + | 0.678434i | \(0.762659\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 124.686i | 1.10341i | 0.834039 | + | 0.551706i | \(0.186023\pi\) | ||||
−0.834039 | + | 0.551706i | \(0.813977\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 20.2288 | − | 35.0372i | 0.175902 | − | 0.304672i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −20.9170 | − | 36.2293i | −0.172868 | − | 0.299416i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 103.764i | − | 0.830116i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 51.5791 | 0.406134 | 0.203067 | − | 0.979165i | \(-0.434909\pi\) | ||||
0.203067 | + | 0.979165i | \(0.434909\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 153.604 | − | 88.6832i | 1.17255 | − | 0.676971i | 0.218269 | − | 0.975889i | \(-0.429959\pi\) |
0.954279 | + | 0.298918i | \(0.0966255\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 139.264 | + | 80.4040i | 1.01652 | + | 0.586891i | 0.913095 | − | 0.407746i | \(-0.133685\pi\) |
0.103429 | + | 0.994637i | \(0.467018\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −74.8340 | −0.538374 | −0.269187 | − | 0.963088i | \(-0.586755\pi\) | ||||
−0.269187 | + | 0.963088i | \(0.586755\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 66.1362 | + | 38.1838i | 0.462491 | + | 0.267019i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 22.1477 | + | 38.3610i | 0.152743 | + | 0.264558i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −227.490 | + | 131.342i | −1.52678 | + | 0.881487i | −0.527286 | + | 0.849688i | \(0.676791\pi\) |
−0.999494 | + | 0.0317997i | \(0.989876\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.9595 | + | 29.3747i | −0.112314 | + | 0.194534i | −0.916703 | − | 0.399569i | \(-0.869160\pi\) |
0.804389 | + | 0.594104i | \(0.202493\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 10.9588i | − | 0.0707017i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −81.8118 | + | 141.702i | −0.521094 | + | 0.902561i | 0.478605 | + | 0.878030i | \(0.341143\pi\) |
−0.999699 | + | 0.0245310i | \(0.992191\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −140.373 | − | 243.132i | −0.861181 | − | 1.49161i | −0.870790 | − | 0.491656i | \(-0.836392\pi\) |
0.00960841 | − | 0.999954i | \(-0.496942\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 76.0755i | 0.455542i | 0.973715 | + | 0.227771i | \(0.0731437\pi\) | ||||
−0.973715 | + | 0.227771i | \(0.926856\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −95.3320 | −0.564095 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 133.321 | − | 76.9730i | 0.770642 | − | 0.444930i | −0.0624615 | − | 0.998047i | \(-0.519895\pi\) |
0.833104 | + | 0.553117i | \(0.186562\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 230.094 | + | 132.845i | 1.28544 | + | 0.742148i | 0.977837 | − | 0.209367i | \(-0.0671403\pi\) |
0.307601 | + | 0.951515i | \(0.400474\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 203.328 | 1.12336 | 0.561680 | − | 0.827355i | \(-0.310155\pi\) | ||||
0.561680 | + | 0.827355i | \(0.310155\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 80.1191 | + | 46.2568i | 0.433076 | + | 0.250037i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 89.5203 | + | 155.054i | 0.478718 | + | 0.829164i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −184.783 | + | 106.684i | −0.967449 | + | 0.558557i | −0.898458 | − | 0.439060i | \(-0.855311\pi\) |
−0.0689915 | + | 0.997617i | \(0.521978\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.25098 | + | 14.2911i | −0.0427512 | + | 0.0740473i | −0.886609 | − | 0.462519i | \(-0.846946\pi\) |
0.843858 | + | 0.536567i | \(0.180279\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 57.0437i | 0.289562i | 0.989464 | + | 0.144781i | \(0.0462477\pi\) | ||||
−0.989464 | + | 0.144781i | \(0.953752\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −151.122 | + | 261.750i | −0.759405 | + | 1.31533i | 0.183750 | + | 0.982973i | \(0.441176\pi\) |
−0.943154 | + | 0.332355i | \(0.892157\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.12549 | + | 14.0738i | 0.0396365 | + | 0.0686525i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 52.2686i | − | 0.250089i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −142.996 | −0.677706 | −0.338853 | − | 0.940839i | \(-0.610039\pi\) | ||||
−0.338853 | + | 0.940839i | \(0.610039\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 72.0566 | − | 41.6019i | 0.335147 | − | 0.193497i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 149.573 | + | 86.3558i | 0.676799 | + | 0.390750i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −167.749 | −0.752238 | −0.376119 | − | 0.926571i | \(-0.622742\pi\) | ||||
−0.376119 | + | 0.926571i | \(0.622742\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 53.1203 | + | 30.6690i | 0.234010 | + | 0.135106i | 0.612421 | − | 0.790532i | \(-0.290196\pi\) |
−0.378411 | + | 0.925638i | \(0.623529\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.7935 | + | 39.4795i | 0.0995348 | + | 0.172399i | 0.911492 | − | 0.411317i | \(-0.134931\pi\) |
−0.811957 | + | 0.583717i | \(0.801598\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 259.279 | − | 149.695i | 1.11279 | − | 0.642468i | 0.173237 | − | 0.984880i | \(-0.444577\pi\) |
0.939550 | + | 0.342413i | \(0.111244\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −85.3725 | + | 147.870i | −0.363287 | + | 0.629232i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 146.895i | − | 0.614624i | −0.951609 | − | 0.307312i | \(-0.900570\pi\) | ||
0.951609 | − | 0.307312i | \(-0.0994295\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 176.808 | − | 306.240i | 0.733642 | − | 1.27071i | −0.221674 | − | 0.975121i | \(-0.571152\pi\) |
0.955316 | − | 0.295585i | \(-0.0955146\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −25.2105 | − | 43.6658i | −0.102067 | − | 0.176785i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 289.908i | 1.15501i | 0.816386 | + | 0.577506i | \(0.195974\pi\) | ||||
−0.816386 | + | 0.577506i | \(0.804026\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −154.664 | −0.611320 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 420.001 | − | 242.488i | 1.63425 | − | 0.943532i | 0.651482 | − | 0.758664i | \(-0.274148\pi\) |
0.982763 | − | 0.184867i | \(-0.0591856\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −181.719 | − | 104.915i | −0.690945 | − | 0.398917i | 0.113021 | − | 0.993593i | \(-0.463947\pi\) |
−0.803966 | + | 0.594675i | \(0.797281\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −108.620 | −0.409885 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 135.969 | + | 78.5018i | 0.505461 | + | 0.291828i | 0.730966 | − | 0.682414i | \(-0.239070\pi\) |
−0.225505 | + | 0.974242i | \(0.572403\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −79.6013 | − | 137.873i | −0.293732 | − | 0.508758i | 0.680957 | − | 0.732323i | \(-0.261564\pi\) |
−0.974689 | + | 0.223565i | \(0.928231\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −150.897 | + | 87.1202i | −0.548715 | + | 0.316801i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.7530 | + | 23.8208i | −0.0496496 | + | 0.0859957i | −0.889782 | − | 0.456385i | \(-0.849144\pi\) |
0.840133 | + | 0.542381i | \(0.182477\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 503.037i | 1.79017i | 0.445900 | + | 0.895083i | \(0.352884\pi\) | ||||
−0.445900 | + | 0.895083i | \(0.647116\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 101.225 | − | 175.327i | 0.357685 | − | 0.619528i | −0.629889 | − | 0.776685i | \(-0.716900\pi\) |
0.987574 | + | 0.157157i | \(0.0502329\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 57.9575 | + | 100.385i | 0.200545 | + | 0.347354i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.3969i | 0.0388972i | 0.999811 | + | 0.0194486i | \(0.00619107\pi\) | ||||
−0.999811 | + | 0.0194486i | \(0.993809\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 56.0889 | 0.190132 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −129.208 | + | 74.5984i | −0.432134 | + | 0.249493i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −147.728 | − | 85.2909i | −0.484355 | − | 0.279642i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.96342 | −0.0324541 | −0.0162271 | − | 0.999868i | \(-0.505165\pi\) | ||||
−0.0162271 | + | 0.999868i | \(0.505165\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −132.317 | − | 76.3934i | −0.425457 | − | 0.245638i | 0.271952 | − | 0.962311i | \(-0.412331\pi\) |
−0.697410 | + | 0.716673i | \(0.745664\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 254.535 | + | 440.867i | 0.813210 | + | 1.40852i | 0.910606 | + | 0.413275i | \(0.135615\pi\) |
−0.0973968 | + | 0.995246i | \(0.531052\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 228.413 | − | 131.874i | 0.720544 | − | 0.416006i | −0.0944088 | − | 0.995534i | \(-0.530096\pi\) |
0.814953 | + | 0.579527i | \(0.196763\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 84.6680 | − | 146.649i | 0.265417 | − | 0.459715i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 118.210i | − | 0.365975i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −84.0405 | + | 145.562i | −0.258586 | + | 0.447884i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 48.2510 | + | 83.5732i | 0.145773 | + | 0.252487i | 0.929661 | − | 0.368416i | \(-0.120100\pi\) |
−0.783888 | + | 0.620902i | \(0.786766\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 74.6668i | 0.222886i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −213.417 | −0.633285 | −0.316642 | − | 0.948545i | \(-0.602556\pi\) | ||||
−0.316642 | + | 0.948545i | \(0.602556\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −36.2813 | + | 20.9470i | −0.106397 | + | 0.0614281i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −111.298 | − | 64.2580i | −0.320744 | − | 0.185182i | 0.330980 | − | 0.943638i | \(-0.392621\pi\) |
−0.651724 | + | 0.758456i | \(0.725954\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 373.041 | 1.06888 | 0.534442 | − | 0.845205i | \(-0.320522\pi\) | ||||
0.534442 | + | 0.845205i | \(0.320522\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −348.658 | − | 201.298i | −0.987701 | − | 0.570249i | −0.0831146 | − | 0.996540i | \(-0.526487\pi\) |
−0.904586 | + | 0.426291i | \(0.859820\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −133.646 | − | 231.481i | −0.376467 | − | 0.652060i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −328.480 | + | 189.648i | −0.914985 | + | 0.528267i | −0.882032 | − | 0.471190i | \(-0.843825\pi\) |
−0.0329535 | + | 0.999457i | \(0.510491\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 163.245 | − | 282.749i | 0.452202 | − | 0.783238i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 96.1037i | − | 0.263298i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 82.8784 | − | 143.550i | 0.225827 | − | 0.391144i | −0.730740 | − | 0.682655i | \(-0.760825\pi\) |
0.956567 | + | 0.291512i | \(0.0941583\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 42.1660 | + | 73.0337i | 0.113046 | + | 0.195801i | 0.916997 | − | 0.398895i | \(-0.130606\pi\) |
−0.803951 | + | 0.594695i | \(0.797273\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 163.350i | − | 0.433289i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 537.652 | 1.41861 | 0.709304 | − | 0.704903i | \(-0.249009\pi\) | ||||
0.709304 | + | 0.704903i | \(0.249009\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −364.567 | + | 210.483i | −0.951873 | + | 0.549564i | −0.893662 | − | 0.448740i | \(-0.851873\pi\) |
−0.0582107 | + | 0.998304i | \(0.518540\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 276.118 | + | 159.417i | 0.709816 | + | 0.409812i | 0.810993 | − | 0.585056i | \(-0.198928\pi\) |
−0.101177 | + | 0.994868i | \(0.532261\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −349.786 | −0.894592 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −53.7447 | − | 31.0295i | −0.136063 | − | 0.0785558i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −67.8562 | − | 117.530i | −0.170922 | − | 0.296046i | 0.767820 | − | 0.640665i | \(-0.221341\pi\) |
−0.938743 | + | 0.344619i | \(0.888008\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 369.417 | − | 213.283i | 0.921239 | − | 0.531877i | 0.0372086 | − | 0.999308i | \(-0.488153\pi\) |
0.884030 | + | 0.467430i | \(0.154820\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.2065 | + | 34.9987i | −0.0501403 | + | 0.0868455i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 353.668i | − | 0.868963i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −270.557 | + | 468.618i | −0.661508 | + | 1.14577i | 0.318711 | + | 0.947852i | \(0.396750\pi\) |
−0.980219 | + | 0.197914i | \(0.936583\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −158.332 | − | 274.239i | −0.381523 | − | 0.660817i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 337.625i | − | 0.805789i | −0.915247 | − | 0.402894i | \(-0.868004\pi\) | ||
0.915247 | − | 0.402894i | \(-0.131996\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 366.324 | 0.870129 | 0.435064 | − | 0.900399i | \(-0.356726\pi\) | ||||
0.435064 | + | 0.900399i | \(0.356726\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −341.265 | + | 197.030i | −0.802977 | + | 0.463599i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −261.332 | − | 150.880i | −0.606338 | − | 0.350069i | 0.165193 | − | 0.986261i | \(-0.447175\pi\) |
−0.771531 | + | 0.636192i | \(0.780509\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −40.2431 | −0.0929402 | −0.0464701 | − | 0.998920i | \(-0.514797\pi\) | ||||
−0.0464701 | + | 0.998920i | \(0.514797\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 88.4346 | + | 51.0577i | 0.202367 | + | 0.116837i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −395.409 | − | 684.869i | −0.900704 | − | 1.56007i | −0.826582 | − | 0.562816i | \(-0.809718\pi\) |
−0.0741221 | − | 0.997249i | \(-0.523615\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 166.813 | − | 96.3098i | 0.376554 | − | 0.217404i | −0.299764 | − | 0.954013i | \(-0.596908\pi\) |
0.676318 | + | 0.736610i | \(0.263575\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −169.616 | + | 293.783i | −0.381159 | + | 0.660186i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 196.690i | − | 0.438063i | −0.975718 | − | 0.219032i | \(-0.929710\pi\) | ||
0.975718 | − | 0.219032i | \(-0.0702897\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 31.0627 | − | 53.8023i | 0.0688753 | − | 0.119295i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 324.664 | + | 562.335i | 0.710425 | + | 1.23049i | 0.964698 | + | 0.263359i | \(0.0848304\pi\) |
−0.254273 | + | 0.967132i | \(0.581836\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 846.252i | − | 1.83569i | −0.396941 | − | 0.917844i | \(-0.629928\pi\) | ||
0.396941 | − | 0.917844i | \(-0.370072\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.91896 | 0.00846428 | 0.00423214 | − | 0.999991i | \(-0.498653\pi\) | ||||
0.00423214 | + | 0.999991i | \(0.498653\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −723.304 | + | 417.600i | −1.54883 | + | 0.894218i | −0.550599 | + | 0.834770i | \(0.685601\pi\) |
−0.998231 | + | 0.0594479i | \(0.981066\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −275.464 | − | 159.039i | −0.582375 | − | 0.336235i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 115.041 | 0.242191 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 353.530 | + | 204.111i | 0.738059 | + | 0.426118i | 0.821363 | − | 0.570406i | \(-0.193214\pi\) |
−0.0833043 | + | 0.996524i | \(0.526547\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −170.583 | − | 295.458i | −0.354642 | − | 0.614259i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 132.942 | − | 76.7539i | 0.274107 | − | 0.158255i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 186.627 | − | 323.248i | 0.383219 | − | 0.663754i | −0.608302 | − | 0.793706i | \(-0.708149\pi\) |
0.991520 | + | 0.129952i | \(0.0414823\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 328.281i | − | 0.668596i | −0.942467 | − | 0.334298i | \(-0.891501\pi\) | ||
0.942467 | − | 0.334298i | \(-0.108499\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 191.484 | − | 331.659i | 0.388405 | − | 0.672737i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −143.203 | − | 248.034i | −0.286979 | − | 0.497062i | 0.686108 | − | 0.727500i | \(-0.259318\pi\) |
−0.973087 | + | 0.230437i | \(0.925984\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 798.493i | 1.58746i | 0.608270 | + | 0.793730i | \(0.291864\pi\) | ||||
−0.608270 | + | 0.793730i | \(0.708136\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −215.660 | −0.427050 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −732.921 | + | 423.152i | −1.43992 | + | 0.831340i | −0.997844 | − | 0.0656358i | \(-0.979092\pi\) |
−0.442080 | + | 0.896976i | \(0.645759\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −389.261 | − | 224.740i | −0.755846 | − | 0.436388i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 652.737 | 1.26255 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −222.515 | − | 128.469i | −0.427091 | − | 0.246581i | 0.271015 | − | 0.962575i | \(-0.412641\pi\) |
−0.698107 | + | 0.715994i | \(0.745974\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.7569 | − | 37.6840i | −0.0416002 | − | 0.0720536i | 0.844476 | − | 0.535594i | \(-0.179912\pi\) |
−0.886076 | + | 0.463540i | \(0.846579\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −82.0531 | + | 47.3734i | −0.155698 | + | 0.0898925i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −113.419 | + | 196.447i | −0.214403 | + | 0.371356i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 59.9294i | − | 0.112438i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 54.9294 | − | 95.1405i | 0.102672 | − | 0.177833i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 304.830 | + | 527.981i | 0.563457 | + | 0.975936i | 0.997191 | + | 0.0748950i | \(0.0238622\pi\) |
−0.433735 | + | 0.901041i | \(0.642805\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 484.486i | − | 0.888964i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1003.83 | 1.83516 | 0.917578 | − | 0.397556i | \(-0.130142\pi\) | ||||
0.917578 | + | 0.397556i | \(0.130142\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −96.8238 | + | 55.9012i | −0.175724 | + | 0.101454i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.08875 | − | 5.24739i | −0.0163173 | − | 0.00942081i | 0.491819 | − | 0.870697i | \(-0.336332\pi\) |
−0.508136 | + | 0.861277i | \(0.669665\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −306.834 | −0.548898 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −833.992 | − | 481.505i | −1.48134 | − | 0.855250i | −0.481560 | − | 0.876413i | \(-0.659930\pi\) |
−0.999776 | + | 0.0211638i | \(0.993263\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −145.099 | − | 251.319i | −0.256813 | − | 0.444813i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 381.972 | − | 220.531i | 0.671303 | − | 0.387577i | −0.125267 | − | 0.992123i | \(-0.539979\pi\) |
0.796570 | + | 0.604546i | \(0.206645\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 481.575 | − | 834.113i | 0.843389 | − | 1.46079i | −0.0436239 | − | 0.999048i | \(-0.513890\pi\) |
0.887013 | − | 0.461745i | \(-0.152776\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 340.408i | − | 0.592013i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 204.033 | − | 353.395i | 0.353609 | − | 0.612470i | −0.633270 | − | 0.773931i | \(-0.718288\pi\) |
0.986879 | + | 0.161462i | \(0.0516209\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 207.620 | + | 359.608i | 0.356123 | + | 0.616823i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 643.388i | 1.09606i | 0.836458 | + | 0.548030i | \(0.184622\pi\) | ||||
−0.836458 | + | 0.548030i | \(0.815378\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27.6601 | 0.0469611 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −82.7592 | + | 47.7810i | −0.139560 | + | 0.0805751i | −0.568154 | − | 0.822922i | \(-0.692342\pi\) |
0.428594 | + | 0.903497i | \(0.359009\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −627.833 | − | 362.480i | −1.04814 | − | 0.605141i | −0.126009 | − | 0.992029i | \(-0.540217\pi\) |
−0.922127 | + | 0.386888i | \(0.873550\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 999.239 | 1.66263 | 0.831314 | − | 0.555803i | \(-0.187589\pi\) | ||||
0.831314 | + | 0.555803i | \(0.187589\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 84.3217 | + | 48.6831i | 0.139375 | + | 0.0804680i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −231.793 | − | 401.478i | −0.381867 | − | 0.661414i | 0.609462 | − | 0.792815i | \(-0.291386\pi\) |
−0.991329 | + | 0.131402i | \(0.958052\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 545.304 | − | 314.832i | 0.892479 | − | 0.515273i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 472.697 | − | 818.735i | 0.771120 | − | 1.33562i | −0.165829 | − | 0.986154i | \(-0.553030\pi\) |
0.936949 | − | 0.349465i | \(-0.113637\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 346.419i | 0.561458i | 0.959787 | + | 0.280729i | \(0.0905762\pi\) | ||||
−0.959787 | + | 0.280729i | \(0.909424\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 569.292 | − | 986.042i | 0.919695 | − | 1.59296i | 0.119818 | − | 0.992796i | \(-0.461769\pi\) |
0.799877 | − | 0.600163i | \(-0.204898\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −124.035 | − | 214.834i | −0.198455 | − | 0.343735i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 799.850i | − | 1.27162i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1006.22 | −1.59464 | −0.797321 | − | 0.603555i | \(-0.793750\pi\) | ||||
−0.797321 | + | 0.603555i | \(0.793750\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −103.964 | + | 60.0237i | −0.163723 | + | 0.0945255i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −103.741 | − | 59.8952i | −0.161843 | − | 0.0934402i | 0.416891 | − | 0.908957i | \(-0.363120\pi\) |
−0.578734 | + | 0.815516i | \(0.696453\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −935.616 | −1.45508 | −0.727539 | − | 0.686066i | \(-0.759336\pi\) | ||||
−0.727539 | + | 0.686066i | \(0.759336\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −494.624 | − | 285.571i | −0.764488 | − | 0.441378i | 0.0664166 | − | 0.997792i | \(-0.478843\pi\) |
−0.830905 | + | 0.556414i | \(0.812177\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −107.210 | − | 185.694i | −0.165193 | − | 0.286123i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 532.601 | − | 307.497i | 0.815621 | − | 0.470899i | −0.0332829 | − | 0.999446i | \(-0.510596\pi\) |
0.848904 | + | 0.528547i | \(0.177263\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −206.405 | + | 357.504i | −0.315122 | + | 0.545808i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 958.528i | − | 1.45452i | −0.686363 | − | 0.727259i | \(-0.740794\pi\) | ||
0.686363 | − | 0.727259i | \(-0.259206\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −397.893 | + | 689.171i | −0.601956 | + | 1.04262i | 0.390569 | + | 0.920574i | \(0.372278\pi\) |
−0.992525 | + | 0.122044i | \(0.961055\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 165.413 | + | 286.504i | 0.247996 | + | 0.429541i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 652.113i | 0.971853i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 127.514 | 0.189471 | 0.0947353 | − | 0.995502i | \(-0.469800\pi\) | ||||
0.0947353 | + | 0.995502i | \(0.469800\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −26.4113 | + | 15.2486i | −0.0390122 | + | 0.0225237i | −0.519379 | − | 0.854544i | \(-0.673837\pi\) |
0.480367 | + | 0.877068i | \(0.340503\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −947.477 | − | 547.026i | −1.38723 | − | 0.800917i | −0.394226 | − | 0.919013i | \(-0.628987\pi\) |
−0.993002 | + | 0.118097i | \(0.962321\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −374.272 | −0.546382 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 346.896 | + | 200.280i | 0.503477 | + | 0.290683i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −55.8745 | − | 96.7775i | −0.0808604 | − | 0.140054i | 0.822759 | − | 0.568390i | \(-0.192433\pi\) |
−0.903620 | + | 0.428336i | \(0.859100\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 150.837 | − | 87.0860i | 0.217032 | − | 0.125304i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 70.2510 | − | 121.678i | 0.100791 | − | 0.174574i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 71.8328i | 0.102472i | 0.998687 | + | 0.0512360i | \(0.0163161\pi\) | ||||
−0.998687 | + | 0.0512360i | \(0.983684\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −116.753 | + | 202.222i | −0.166078 | + | 0.287656i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −90.9882 | − | 157.596i | −0.128333 | − | 0.222280i | 0.794698 | − | 0.607005i | \(-0.207629\pi\) |
−0.923031 | + | 0.384726i | \(0.874296\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 81.8469i | − | 0.114792i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −177.741 | −0.248589 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −635.330 | + | 366.808i | −0.883631 | + | 0.510164i | −0.871854 | − | 0.489766i | \(-0.837082\pi\) |
−0.0117768 | + | 0.999931i | \(0.503749\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 322.767 | + | 186.350i | 0.445197 | + | 0.257034i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −130.450 | −0.179436 | −0.0897178 | − | 0.995967i | \(-0.528597\pi\) | ||||
−0.0897178 | + | 0.995967i | \(0.528597\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −622.984 | − | 359.680i | −0.852235 | − | 0.492038i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −419.907 | − | 727.301i | −0.572861 | − | 0.992224i | −0.996270 | − | 0.0862860i | \(-0.972500\pi\) |
0.423409 | − | 0.905938i | \(-0.360833\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 247.200 | − | 142.721i | 0.335414 | − | 0.193651i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 130.454 | − | 225.952i | 0.176527 | − | 0.305754i | −0.764162 | − | 0.645025i | \(-0.776847\pi\) |
0.940689 | + | 0.339271i | \(0.110180\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 143.701i | 0.193406i | 0.995313 | + | 0.0967030i | \(0.0308297\pi\) | ||||
−0.995313 | + | 0.0967030i | \(0.969170\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 305.690 | − | 529.471i | 0.410322 | − | 0.710699i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 44.0732 | + | 76.3370i | 0.0586860 | + | 0.101647i | 0.893876 | − | 0.448315i | \(-0.147976\pi\) |
−0.835190 | + | 0.549962i | \(0.814642\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 78.9445i | − | 0.104562i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −519.660 | −0.686473 | −0.343237 | − | 0.939249i | \(-0.611523\pi\) | ||||
−0.343237 | + | 0.939249i | \(0.611523\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −221.637 | + | 127.962i | −0.291245 | + | 0.168150i | −0.638503 | − | 0.769619i | \(-0.720446\pi\) |
0.347258 | + | 0.937769i | \(0.387113\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −179.130 | − | 103.421i | −0.233546 | − | 0.134838i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1202.63 | 1.56389 | 0.781946 | − | 0.623347i | \(-0.214227\pi\) | ||||
0.781946 | + | 0.623347i | \(0.214227\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 87.1330 | + | 50.3063i | 0.112721 | + | 0.0650792i | 0.555300 | − | 0.831650i | \(-0.312603\pi\) |
−0.442580 | + | 0.896729i | \(0.645937\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −46.1033 | − | 79.8532i | −0.0594881 | − | 0.103036i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −35.5224 | + | 20.5089i | −0.0456000 | + | 0.0263272i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −510.911 | + | 884.924i | −0.654176 | + | 1.13307i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 380.825i | − | 0.485127i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −368.907 | + | 638.966i | −0.468751 | + | 0.811901i | −0.999362 | − | 0.0357147i | \(-0.988629\pi\) |
0.530611 | + | 0.847616i | \(0.321963\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 314.531 | + | 544.783i | 0.396634 | + | 0.686990i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 747.143i | − | 0.937444i | −0.883346 | − | 0.468722i | \(-0.844715\pi\) | ||
0.883346 | − | 0.468722i | \(-0.155285\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1476.22 | 1.84758 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −318.171 | + | 183.696i | −0.396228 | + | 0.228762i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1001.31 | + | 578.107i | 1.23771 | + | 0.714595i | 0.968627 | − | 0.248521i | \(-0.0799443\pi\) |
0.269088 | + | 0.963116i | \(0.413278\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −194.081 | −0.239311 | −0.119655 | − | 0.992815i | \(-0.538179\pi\) | ||||
−0.119655 | + | 0.992815i | \(0.538179\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 565.877 | + | 326.709i | 0.694328 | + | 0.400870i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 105.004 | + | 181.872i | 0.128524 | + | 0.222610i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −93.8794 | + | 54.2013i | −0.114348 | + | 0.0660187i | −0.556083 | − | 0.831127i | \(-0.687696\pi\) |
0.441735 | + | 0.897145i | \(0.354363\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 546.409 | − | 946.408i | 0.663924 | − | 1.14995i | −0.315652 | − | 0.948875i | \(-0.602223\pi\) |
0.979576 | − | 0.201074i | \(-0.0644433\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 18.9283i | − | 0.0228879i | −0.999935 | − | 0.0114440i | \(-0.996357\pi\) | ||
0.999935 | − | 0.0114440i | \(-0.00364281\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.08891 | + | 15.7425i | −0.0109637 | + | 0.0189897i | −0.871455 | − | 0.490475i | \(-0.836823\pi\) |
0.860492 | + | 0.509465i | \(0.170157\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −88.5307 | − | 153.340i | −0.106025 | − | 0.183640i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 297.466i | 0.354548i | 0.984162 | + | 0.177274i | \(0.0567278\pi\) | ||||
−0.984162 | + | 0.177274i | \(0.943272\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 478.791 | 0.569311 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 192.154 | − | 110.940i | 0.227401 | − | 0.131290i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 598.380 | + | 345.475i | 0.703149 | + | 0.405963i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 280.125 | 0.328400 | 0.164200 | − | 0.986427i | \(-0.447496\pi\) | ||||
0.164200 | + | 0.986427i | \(0.447496\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 370.867 | + | 214.120i | 0.432750 | + | 0.249849i | 0.700518 | − | 0.713635i | \(-0.252952\pi\) |
−0.267767 | + | 0.963484i | \(0.586286\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 267.549 | + | 463.408i | 0.311466 | + | 0.539474i | 0.978680 | − | 0.205392i | \(-0.0658468\pi\) |
−0.667214 | + | 0.744866i | \(0.732513\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1410.52 | + | 814.364i | −1.63444 | + | 0.943643i | −0.651737 | + | 0.758445i | \(0.725959\pi\) |
−0.982701 | + | 0.185198i | \(0.940707\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −179.150 | + | 310.297i | −0.207110 | + | 0.358725i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 237.244i | 0.273008i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 137.676 | − | 238.462i | 0.158066 | − | 0.273779i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −310.705 | − | 538.156i | −0.354281 | − | 0.613633i | 0.632714 | − | 0.774386i | \(-0.281941\pi\) |
−0.986995 | + | 0.160753i | \(0.948608\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1011.60i | − | 1.14824i | −0.818773 | − | 0.574118i | \(-0.805345\pi\) | ||
0.818773 | − | 0.574118i | \(-0.194655\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 400.235 | 0.453268 | 0.226634 | − | 0.973980i | \(-0.427228\pi\) | ||||
0.226634 | + | 0.973980i | \(0.427228\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −396.030 | + | 228.648i | −0.446482 | + | 0.257777i | −0.706343 | − | 0.707869i | \(-0.749656\pi\) |
0.259861 | + | 0.965646i | \(0.416323\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −373.225 | − | 215.482i | −0.417945 | − | 0.241301i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −618.376 | −0.690923 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 77.6055 | + | 44.8056i | 0.0863243 | + | 0.0498394i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 469.549 | + | 813.283i | 0.521142 | + | 0.902644i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −409.833 | + | 236.617i | −0.452854 | + | 0.261456i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −543.793 | + | 941.878i | −0.599552 | + | 1.03845i | 0.393335 | + | 0.919395i | \(0.371321\pi\) |
−0.992887 | + | 0.119059i | \(0.962012\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 740.521i | 0.812866i | 0.913681 | + | 0.406433i | \(0.133228\pi\) | ||||
−0.913681 | + | 0.406433i | \(0.866772\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −605.284 | + | 1048.38i | −0.662961 | + | 1.14828i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −539.956 | − | 935.230i | −0.587547 | − | 1.01766i | −0.994553 | − | 0.104235i | \(-0.966760\pi\) |
0.407006 | − | 0.913426i | \(-0.366573\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 985.701i | 1.06793i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 778.405 | 0.841519 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 126.389 | − | 72.9707i | 0.136048 | − | 0.0785475i | −0.430431 | − | 0.902623i | \(-0.641638\pi\) |
0.566479 | + | 0.824076i | \(0.308305\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −360.879 | − | 208.353i | −0.385966 | − | 0.222838i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −406.972 | −0.434336 | −0.217168 | − | 0.976134i | \(-0.569682\pi\) | ||||
−0.217168 | + | 0.976134i | \(0.569682\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 359.026 | + | 207.284i | 0.381537 | + | 0.220281i | 0.678487 | − | 0.734613i | \(-0.262636\pi\) |
−0.296950 | + | 0.954893i | \(0.595969\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 60.6863 | + | 105.112i | 0.0643545 | + | 0.111465i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −582.910 | + | 336.543i | −0.615533 | + | 0.355378i | −0.775128 | − | 0.631805i | \(-0.782315\pi\) |
0.159595 | + | 0.987183i | \(0.448981\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −177.203 | + | 306.924i | −0.186726 | + | 0.323418i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 68.0024i | 0.0713562i | 0.999363 | + | 0.0356781i | \(0.0113591\pi\) | ||||
−0.999363 | + | 0.0356781i | \(0.988641\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 248.302 | − | 430.072i | 0.260002 | − | 0.450337i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 469.415 | + | 813.051i | 0.488465 | + | 0.846046i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 38.4074i | − | 0.0398004i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1209.25 | −1.25051 | −0.625257 | − | 0.780419i | \(-0.715006\pi\) | ||||
−0.625257 | + | 0.780419i | \(0.715006\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1248.15 | − | 720.622i | 1.28543 | − | 0.742144i | 0.307596 | − | 0.951517i | \(-0.400476\pi\) |
0.977836 | + | 0.209373i | \(0.0671422\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 41.7998 | + | 24.1332i | 0.0427839 | + | 0.0247013i | 0.521239 | − | 0.853411i | \(-0.325470\pi\) |
−0.478456 | + | 0.878112i | \(0.658803\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1296.84 | 1.32466 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.0513 | − | 9.26720i | −0.0163289 | − | 0.00942747i | 0.491813 | − | 0.870701i | \(-0.336334\pi\) |
−0.508142 | + | 0.861273i | \(0.669668\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −66.3830 | − | 114.979i | −0.0673939 | − | 0.116730i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 538.164 | − | 310.709i | 0.544150 | − | 0.314165i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −38.6275 | + | 66.9047i | −0.0389783 | + | 0.0675123i | −0.884856 | − | 0.465864i | \(-0.845744\pi\) |
0.845878 | + | 0.533376i | \(0.179077\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 703.454i | − | 0.706989i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 758.674 | − | 1314.06i | 0.760957 | − | 1.31802i | −0.181400 | − | 0.983409i | \(-0.558063\pi\) |
0.942358 | − | 0.334607i | \(-0.108604\pi\) | |||||||
\(998\) | 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 | 1764.3.bk.d.557.2 | 8 | ||
3.2 | odd | 2 | inner | 1764.3.bk.d.557.3 | 8 | ||
7.2 | even | 3 | inner | 1764.3.bk.d.1745.3 | 8 | ||
7.3 | odd | 6 | 1764.3.c.f.197.3 | 4 | |||
7.4 | even | 3 | 252.3.c.a.197.2 | ✓ | 4 | ||
7.5 | odd | 6 | 1764.3.bk.e.1745.2 | 8 | |||
7.6 | odd | 2 | 1764.3.bk.e.557.3 | 8 | |||
21.2 | odd | 6 | inner | 1764.3.bk.d.1745.2 | 8 | ||
21.5 | even | 6 | 1764.3.bk.e.1745.3 | 8 | |||
21.11 | odd | 6 | 252.3.c.a.197.3 | yes | 4 | ||
21.17 | even | 6 | 1764.3.c.f.197.2 | 4 | |||
21.20 | even | 2 | 1764.3.bk.e.557.2 | 8 | |||
28.11 | odd | 6 | 1008.3.d.c.449.2 | 4 | |||
56.11 | odd | 6 | 4032.3.d.e.449.3 | 4 | |||
56.53 | even | 6 | 4032.3.d.h.449.3 | 4 | |||
63.4 | even | 3 | 2268.3.bg.c.2213.2 | 8 | |||
63.11 | odd | 6 | 2268.3.bg.c.701.2 | 8 | |||
63.25 | even | 3 | 2268.3.bg.c.701.3 | 8 | |||
63.32 | odd | 6 | 2268.3.bg.c.2213.3 | 8 | |||
84.11 | even | 6 | 1008.3.d.c.449.3 | 4 | |||
168.11 | even | 6 | 4032.3.d.e.449.2 | 4 | |||
168.53 | odd | 6 | 4032.3.d.h.449.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.3.c.a.197.2 | ✓ | 4 | 7.4 | even | 3 | ||
252.3.c.a.197.3 | yes | 4 | 21.11 | odd | 6 | ||
1008.3.d.c.449.2 | 4 | 28.11 | odd | 6 | |||
1008.3.d.c.449.3 | 4 | 84.11 | even | 6 | |||
1764.3.c.f.197.2 | 4 | 21.17 | even | 6 | |||
1764.3.c.f.197.3 | 4 | 7.3 | odd | 6 | |||
1764.3.bk.d.557.2 | 8 | 1.1 | even | 1 | trivial | ||
1764.3.bk.d.557.3 | 8 | 3.2 | odd | 2 | inner | ||
1764.3.bk.d.1745.2 | 8 | 21.2 | odd | 6 | inner | ||
1764.3.bk.d.1745.3 | 8 | 7.2 | even | 3 | inner | ||
1764.3.bk.e.557.2 | 8 | 21.20 | even | 2 | |||
1764.3.bk.e.557.3 | 8 | 7.6 | odd | 2 | |||
1764.3.bk.e.1745.2 | 8 | 7.5 | odd | 6 | |||
1764.3.bk.e.1745.3 | 8 | 21.5 | even | 6 | |||
2268.3.bg.c.701.2 | 8 | 63.11 | odd | 6 | |||
2268.3.bg.c.701.3 | 8 | 63.25 | even | 3 | |||
2268.3.bg.c.2213.2 | 8 | 63.4 | even | 3 | |||
2268.3.bg.c.2213.3 | 8 | 63.32 | odd | 6 | |||
4032.3.d.e.449.2 | 4 | 168.11 | even | 6 | |||
4032.3.d.e.449.3 | 4 | 56.11 | odd | 6 | |||
4032.3.d.h.449.2 | 4 | 168.53 | odd | 6 | |||
4032.3.d.h.449.3 | 4 | 56.53 | even | 6 |