Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [216,3,Mod(17,216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(216, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("216.17");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 216 = 2^{3} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 216.m (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: | \(5.88557371018\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 72) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 17.1 | ||
Root | \(-1.22474 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 216.17 |
Dual form | 216.3.m.a.89.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/216\mathbb{Z}\right)^\times\).
\(n\) | \(55\) | \(109\) | \(137\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(5\) | −6.39898 | − | 3.69445i | −1.27980 | − | 0.738891i | −0.302985 | − | 0.952995i | \(-0.597983\pi\) |
−0.976811 | + | 0.214105i | \(0.931317\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.39898 | + | 5.88721i | 0.485568 | + | 0.841029i | 0.999862 | − | 0.0165847i | \(-0.00527930\pi\) |
−0.514294 | + | 0.857614i | \(0.671946\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.29796 | + | 3.05878i | −0.481633 | + | 0.278071i | −0.721097 | − | 0.692835i | \(-0.756362\pi\) |
0.239464 | + | 0.970905i | \(0.423028\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −8.39898 | + | 14.5475i | −0.646075 | + | 1.11904i | 0.337977 | + | 0.941154i | \(0.390257\pi\) |
−0.984052 | + | 0.177881i | \(0.943076\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 25.1701i | 1.48059i | 0.672279 | + | 0.740297i | \(0.265315\pi\) | ||||
−0.672279 | + | 0.740297i | \(0.734685\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −17.5959 | −0.926101 | −0.463050 | − | 0.886332i | \(-0.653245\pi\) | ||||
−0.463050 | + | 0.886332i | \(0.653245\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −12.3990 | − | 7.15855i | −0.539086 | − | 0.311241i | 0.205622 | − | 0.978631i | \(-0.434078\pi\) |
−0.744708 | + | 0.667390i | \(0.767411\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 14.7980 | + | 25.6308i | 0.591918 | + | 1.02523i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −16.1969 | + | 9.35131i | −0.558515 | + | 0.322459i | −0.752549 | − | 0.658536i | \(-0.771176\pi\) |
0.194034 | + | 0.980995i | \(0.437843\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 23.3990 | − | 40.5282i | 0.754806 | − | 1.30736i | −0.190665 | − | 0.981655i | \(-0.561064\pi\) |
0.945471 | − | 0.325707i | \(-0.105602\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 50.2295i | − | 1.43513i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −49.5959 | −1.34043 | −0.670215 | − | 0.742167i | \(-0.733798\pi\) | ||||
−0.670215 | + | 0.742167i | \(0.733798\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 34.5000 | + | 19.9186i | 0.841463 | + | 0.485819i | 0.857761 | − | 0.514048i | \(-0.171855\pi\) |
−0.0162980 | + | 0.999867i | \(0.505188\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 22.0959 | + | 38.2713i | 0.513859 | + | 0.890029i | 0.999871 | + | 0.0160771i | \(0.00511772\pi\) |
−0.486012 | + | 0.873952i | \(0.661549\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −28.8031 | + | 16.6295i | −0.612831 | + | 0.353818i | −0.774073 | − | 0.633097i | \(-0.781784\pi\) |
0.161242 | + | 0.986915i | \(0.448450\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.39388 | − | 2.41427i | 0.0284465 | − | 0.0492707i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.1708i | 0.191902i | 0.995386 | + | 0.0959509i | \(0.0305892\pi\) | ||||
−0.995386 | + | 0.0959509i | \(0.969411\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 45.2020 | 0.821855 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.2980 | + | 8.25493i | 0.242338 | + | 0.139914i | 0.616251 | − | 0.787550i | \(-0.288651\pi\) |
−0.373913 | + | 0.927464i | \(0.621984\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.6010 | − | 18.3615i | −0.173787 | − | 0.301008i | 0.765954 | − | 0.642896i | \(-0.222267\pi\) |
−0.939741 | + | 0.341887i | \(0.888934\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 107.490 | − | 62.0593i | 1.65369 | − | 0.954758i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 43.4898 | − | 75.3265i | 0.649101 | − | 1.12428i | −0.334236 | − | 0.942489i | \(-0.608478\pi\) |
0.983338 | − | 0.181787i | \(-0.0581883\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 30.2555i | − | 0.426134i | −0.977038 | − | 0.213067i | \(-0.931655\pi\) | ||
0.977038 | − | 0.213067i | \(-0.0683453\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −48.7878 | −0.668325 | −0.334163 | − | 0.942515i | \(-0.608454\pi\) | ||||
−0.334163 | + | 0.942515i | \(0.608454\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −36.0153 | − | 20.7934i | −0.467731 | − | 0.270045i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −55.7929 | − | 96.6361i | −0.706239 | − | 1.22324i | −0.966243 | − | 0.257634i | \(-0.917057\pi\) |
0.260004 | − | 0.965608i | \(-0.416276\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 85.0857 | − | 49.1243i | 1.02513 | − | 0.591859i | 0.109544 | − | 0.993982i | \(-0.465061\pi\) |
0.915585 | + | 0.402123i | \(0.131728\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 92.9898 | − | 161.063i | 1.09400 | − | 1.89486i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 75.5103i | 0.848431i | 0.905561 | + | 0.424215i | \(0.139450\pi\) | ||||
−0.905561 | + | 0.424215i | \(0.860550\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −114.192 | −1.25486 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 112.596 | + | 65.0073i | 1.18522 | + | 0.684287i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 70.2980 | + | 121.760i | 0.724721 | + | 1.25525i | 0.959089 | + | 0.283106i | \(0.0913648\pi\) |
−0.234367 | + | 0.972148i | \(0.575302\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −28.1969 | + | 16.2795i | −0.279178 | + | 0.161183i | −0.633051 | − | 0.774110i | \(-0.718198\pi\) |
0.353873 | + | 0.935293i | \(0.384864\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −67.7929 | + | 117.421i | −0.658183 | + | 1.14001i | 0.322903 | + | 0.946432i | \(0.395341\pi\) |
−0.981086 | + | 0.193574i | \(0.937992\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 35.3409i | 0.330289i | 0.986269 | + | 0.165144i | \(0.0528090\pi\) | ||||
−0.986269 | + | 0.165144i | \(0.947191\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 53.5959 | 0.491706 | 0.245853 | − | 0.969307i | \(-0.420932\pi\) | ||||
0.245853 | + | 0.969307i | \(0.420932\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −143.076 | − | 82.6047i | −1.26615 | − | 0.731015i | −0.291897 | − | 0.956450i | \(-0.594286\pi\) |
−0.974258 | + | 0.225435i | \(0.927620\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 52.8939 | + | 91.6149i | 0.459947 | + | 0.796651i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −148.182 | + | 85.5527i | −1.24522 | + | 0.718930i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −41.7878 | + | 72.3785i | −0.345353 | + | 0.598170i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 33.9588i | − | 0.271670i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.9796 | 0.0943275 | 0.0471637 | − | 0.998887i | \(-0.484982\pi\) | ||||
0.0471637 | + | 0.998887i | \(0.484982\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.3082 | + | 7.68347i | 0.101589 | + | 0.0586525i | 0.549934 | − | 0.835208i | \(-0.314653\pi\) |
−0.448345 | + | 0.893861i | \(0.647986\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −59.8082 | − | 103.591i | −0.449685 | − | 0.778878i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 47.7122 | − | 27.5467i | 0.348265 | − | 0.201071i | −0.315656 | − | 0.948874i | \(-0.602225\pi\) |
0.663921 | + | 0.747803i | \(0.268891\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −50.4898 | + | 87.4509i | −0.363236 | + | 0.629143i | −0.988491 | − | 0.151277i | \(-0.951661\pi\) |
0.625255 | + | 0.780420i | \(0.284995\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 102.762i | − | 0.718619i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 138.192 | 0.953047 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −187.389 | − | 108.189i | −1.25764 | − | 0.726100i | −0.285027 | − | 0.958519i | \(-0.592003\pi\) |
−0.972616 | + | 0.232419i | \(0.925336\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 76.7929 | + | 133.009i | 0.508562 | + | 0.880855i | 0.999951 | + | 0.00991488i | \(0.00315606\pi\) |
−0.491389 | + | 0.870940i | \(0.663511\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −299.459 | + | 172.893i | −1.93199 | + | 1.11544i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −40.9847 | + | 70.9876i | −0.261049 | + | 0.452150i | −0.966521 | − | 0.256588i | \(-0.917402\pi\) |
0.705472 | + | 0.708738i | \(0.250735\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 97.3271i | − | 0.604516i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 55.2122 | 0.338725 | 0.169363 | − | 0.985554i | \(-0.445829\pi\) | ||||
0.169363 | + | 0.985554i | \(0.445829\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 133.803 | + | 77.2512i | 0.801216 | + | 0.462582i | 0.843896 | − | 0.536507i | \(-0.180256\pi\) |
−0.0426802 | + | 0.999089i | \(0.513590\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −56.5857 | − | 98.0093i | −0.334827 | − | 0.579937i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −22.8031 | + | 13.1654i | −0.131810 | + | 0.0761003i | −0.564455 | − | 0.825464i | \(-0.690914\pi\) |
0.432645 | + | 0.901564i | \(0.357580\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −100.596 | + | 174.237i | −0.574834 | + | 0.995641i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 266.700i | 1.48995i | 0.667094 | + | 0.744973i | \(0.267538\pi\) | ||||
−0.667094 | + | 0.744973i | \(0.732462\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −58.4041 | −0.322674 | −0.161337 | − | 0.986899i | \(-0.551581\pi\) | ||||
−0.161337 | + | 0.986899i | \(0.551581\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 317.363 | + | 183.230i | 1.71548 | + | 0.990431i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −76.9898 | − | 133.350i | −0.411710 | − | 0.713103i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 99.5602 | − | 57.4811i | 0.521258 | − | 0.300948i | −0.216191 | − | 0.976351i | \(-0.569364\pi\) |
0.737449 | + | 0.675403i | \(0.236030\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −108.490 | + | 187.910i | −0.562123 | + | 0.973626i | 0.435188 | + | 0.900340i | \(0.356682\pi\) |
−0.997311 | + | 0.0732863i | \(0.976651\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 171.105i | 0.868555i | 0.900779 | + | 0.434278i | \(0.142996\pi\) | ||||
−0.900779 | + | 0.434278i | \(0.857004\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −62.0000 | −0.311558 | −0.155779 | − | 0.987792i | \(-0.549789\pi\) | ||||
−0.155779 | + | 0.987792i | \(0.549789\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −110.106 | − | 63.5698i | −0.542395 | − | 0.313152i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −147.177 | − | 254.917i | −0.717934 | − | 1.24350i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 93.2225 | − | 53.8220i | 0.446040 | − | 0.257522i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 64.7020 | − | 112.067i | 0.306645 | − | 0.531124i | −0.670981 | − | 0.741474i | \(-0.734127\pi\) |
0.977626 | + | 0.210350i | \(0.0674603\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 326.529i | − | 1.51874i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 318.131 | 1.46604 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −366.161 | − | 211.403i | −1.65684 | − | 0.956576i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −49.1867 | − | 85.1939i | −0.220568 | − | 0.382036i | 0.734412 | − | 0.678704i | \(-0.237458\pi\) |
−0.954981 | + | 0.296668i | \(0.904125\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 383.651 | − | 221.501i | 1.69009 | − | 0.975775i | 0.735659 | − | 0.677352i | \(-0.236873\pi\) |
0.954434 | − | 0.298423i | \(-0.0964607\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 56.0051 | − | 97.0037i | 0.244564 | − | 0.423597i | −0.717445 | − | 0.696615i | \(-0.754689\pi\) |
0.962009 | + | 0.273018i | \(0.0880219\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 80.8526i | 0.347007i | 0.984833 | + | 0.173503i | \(0.0555088\pi\) | ||||
−0.984833 | + | 0.173503i | \(0.944491\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 245.747 | 1.04573 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −37.3888 | − | 21.5864i | −0.156438 | − | 0.0903197i | 0.419737 | − | 0.907646i | \(-0.362122\pi\) |
−0.576176 | + | 0.817326i | \(0.695456\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 140.904 | + | 244.053i | 0.584664 | + | 1.01267i | 0.994917 | + | 0.100696i | \(0.0321071\pi\) |
−0.410253 | + | 0.911972i | \(0.634560\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −17.8388 | + | 10.2992i | −0.0728113 | + | 0.0420376i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 147.788 | − | 255.976i | 0.598331 | − | 1.03634i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.5131i | 0.0618050i | 0.999522 | + | 0.0309025i | \(0.00983814\pi\) | ||||
−0.999522 | + | 0.0309025i | \(0.990162\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 87.5857 | 0.346189 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 312.035 | + | 180.153i | 1.21414 | + | 0.700986i | 0.963659 | − | 0.267135i | \(-0.0860770\pi\) |
0.250484 | + | 0.968121i | \(0.419410\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −168.576 | − | 291.981i | −0.650871 | − | 1.12734i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 42.4296 | − | 24.4967i | 0.161329 | − | 0.0931435i | −0.417162 | − | 0.908832i | \(-0.636975\pi\) |
0.578491 | + | 0.815689i | \(0.303642\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 37.5755 | − | 65.0827i | 0.141794 | − | 0.245595i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 281.700i | − | 1.04721i | −0.851961 | − | 0.523606i | \(-0.824587\pi\) | ||
0.851961 | − | 0.523606i | \(-0.175413\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −89.5959 | −0.330612 | −0.165306 | − | 0.986242i | \(-0.552861\pi\) | ||||
−0.165306 | + | 0.986242i | \(0.552861\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −156.798 | − | 90.5273i | −0.570174 | − | 0.329190i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −42.1969 | − | 73.0872i | −0.152336 | − | 0.263853i | 0.779750 | − | 0.626091i | \(-0.215346\pi\) |
−0.932086 | + | 0.362238i | \(0.882013\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.2673 | − | 13.4334i | 0.0828019 | − | 0.0478057i | −0.458027 | − | 0.888938i | \(-0.651444\pi\) |
0.540829 | + | 0.841132i | \(0.318110\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −90.4898 | + | 156.733i | −0.319752 | + | 0.553827i | −0.980436 | − | 0.196837i | \(-0.936933\pi\) |
0.660684 | + | 0.750664i | \(0.270266\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 270.811i | 0.943594i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −344.535 | −1.19216 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 407.985 | + | 235.550i | 1.39244 | + | 0.803925i | 0.993585 | − | 0.113089i | \(-0.0360746\pi\) |
0.398854 | + | 0.917014i | \(0.369408\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −60.9949 | − | 105.646i | −0.206762 | − | 0.358123i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 208.278 | − | 120.249i | 0.696580 | − | 0.402171i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −150.207 | + | 260.166i | −0.499027 | + | 0.864340i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 156.660i | 0.513639i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 464.747 | 1.51383 | 0.756917 | − | 0.653511i | \(-0.226705\pi\) | ||||
0.756917 | + | 0.653511i | \(0.226705\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 218.348 | + | 126.063i | 0.702083 | + | 0.405348i | 0.808123 | − | 0.589014i | \(-0.200484\pi\) |
−0.106039 | + | 0.994362i | \(0.533817\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −98.1061 | − | 169.925i | −0.313438 | − | 0.542891i | 0.665666 | − | 0.746250i | \(-0.268147\pi\) |
−0.979104 | + | 0.203359i | \(0.934814\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −98.9847 | + | 57.1488i | −0.312255 | + | 0.180280i | −0.647935 | − | 0.761696i | \(-0.724367\pi\) |
0.335680 | + | 0.941976i | \(0.391034\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 57.2071 | − | 99.0857i | 0.179333 | − | 0.310613i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 442.891i | − | 1.37118i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −497.151 | −1.52970 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −195.802 | − | 113.046i | −0.595143 | − | 0.343606i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.2980 | − | 47.2815i | −0.0824712 | − | 0.142844i | 0.821840 | − | 0.569719i | \(-0.192948\pi\) |
−0.904311 | + | 0.426875i | \(0.859615\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −556.581 | + | 321.342i | −1.66143 | + | 0.959230i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 118.884 | − | 205.913i | 0.352771 | − | 0.611016i | −0.633963 | − | 0.773363i | \(-0.718573\pi\) |
0.986734 | + | 0.162347i | \(0.0519063\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 286.289i | 0.839558i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 352.051 | 1.02639 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −108.349 | − | 62.5553i | −0.312245 | − | 0.180275i | 0.335686 | − | 0.941974i | \(-0.391032\pi\) |
−0.647931 | + | 0.761699i | \(0.724365\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 269.985 | + | 467.627i | 0.773595 | + | 1.33991i | 0.935581 | + | 0.353113i | \(0.114877\pi\) |
−0.161986 | + | 0.986793i | \(0.551790\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −254.490 | + | 146.930i | −0.720934 | + | 0.416232i | −0.815096 | − | 0.579325i | \(-0.803316\pi\) |
0.0941622 | + | 0.995557i | \(0.469983\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −111.778 | + | 193.604i | −0.314866 | + | 0.545364i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 422.550i | − | 1.17702i | −0.808490 | − | 0.588509i | \(-0.799715\pi\) | ||
0.808490 | − | 0.588509i | \(-0.200285\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −51.3837 | −0.142337 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 312.192 | + | 180.244i | 0.855320 | + | 0.493819i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 131.358 | + | 227.519i | 0.357924 | + | 0.619943i | 0.987614 | − | 0.156904i | \(-0.0501513\pi\) |
−0.629690 | + | 0.776847i | \(0.716818\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −59.8775 | + | 34.5703i | −0.161395 | + | 0.0931814i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −60.9847 | + | 105.629i | −0.163498 | + | 0.283187i | −0.936121 | − | 0.351679i | \(-0.885611\pi\) |
0.772623 | + | 0.634865i | \(0.218944\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 314.166i | − | 0.833331i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −641.151 | −1.69169 | −0.845846 | − | 0.533428i | \(-0.820904\pi\) | ||||
−0.845846 | + | 0.533428i | \(0.820904\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −640.681 | − | 369.897i | −1.67280 | − | 0.965789i | −0.966063 | − | 0.258308i | \(-0.916835\pi\) |
−0.706733 | − | 0.707481i | \(-0.749832\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 153.641 | + | 266.114i | 0.399067 | + | 0.691204i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −75.7520 | + | 43.7355i | −0.194735 | + | 0.112430i | −0.594197 | − | 0.804319i | \(-0.702530\pi\) |
0.399462 | + | 0.916750i | \(0.369197\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 180.182 | − | 312.084i | 0.460823 | − | 0.798168i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 824.496i | 2.08733i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 483.090 | 1.21685 | 0.608425 | − | 0.793611i | \(-0.291801\pi\) | ||||
0.608425 | + | 0.793611i | \(0.291801\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −317.682 | − | 183.414i | −0.792224 | − | 0.457390i | 0.0485212 | − | 0.998822i | \(-0.484549\pi\) |
−0.840745 | + | 0.541432i | \(0.817882\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 393.055 | + | 680.791i | 0.975323 | + | 1.68931i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 262.757 | − | 151.703i | 0.645595 | − | 0.372734i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −267.641 | + | 463.567i | −0.654379 | + | 1.13342i | 0.327671 | + | 0.944792i | \(0.393736\pi\) |
−0.982049 | + | 0.188625i | \(0.939597\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 112.233i | 0.271751i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −725.949 | −1.74927 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −605.620 | − | 349.655i | −1.44539 | − | 0.834499i | −0.447193 | − | 0.894438i | \(-0.647576\pi\) |
−0.998202 | + | 0.0599386i | \(0.980910\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 180.772 | + | 313.107i | 0.429388 | + | 0.743722i | 0.996819 | − | 0.0796989i | \(-0.0253959\pi\) |
−0.567431 | + | 0.823421i | \(0.692063\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −645.131 | + | 372.466i | −1.51795 | + | 0.876391i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 72.0653 | − | 124.821i | 0.168771 | − | 0.292320i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 463.747i | 1.07598i | 0.842952 | + | 0.537989i | \(0.180816\pi\) | ||||
−0.842952 | + | 0.537989i | \(0.819184\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −689.514 | −1.59241 | −0.796206 | − | 0.605026i | \(-0.793163\pi\) | ||||
−0.796206 | + | 0.605026i | \(0.793163\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 218.171 | + | 125.961i | 0.499248 | + | 0.288241i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 310.772 | + | 538.274i | 0.707910 | + | 1.22614i | 0.965631 | + | 0.259917i | \(0.0836951\pi\) |
−0.257721 | + | 0.966219i | \(0.582972\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 698.843 | − | 403.477i | 1.57752 | − | 0.910784i | 0.582320 | − | 0.812960i | \(-0.302145\pi\) |
0.995204 | − | 0.0978236i | \(-0.0311881\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 278.969 | − | 483.189i | 0.626897 | − | 1.08582i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 317.554i | − | 0.707248i | −0.935388 | − | 0.353624i | \(-0.884949\pi\) | ||
0.935388 | − | 0.353624i | \(-0.115051\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −243.706 | −0.540368 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 730.711 | + | 421.876i | 1.60596 | + | 0.927201i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −285.843 | − | 495.094i | −0.625477 | − | 1.08336i | −0.988448 | − | 0.151557i | \(-0.951571\pi\) |
0.362972 | − | 0.931800i | \(-0.381762\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 478.550 | − | 276.291i | 1.03807 | − | 0.599330i | 0.118784 | − | 0.992920i | \(-0.462101\pi\) |
0.919286 | + | 0.393591i | \(0.128767\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 60.1663 | − | 104.211i | 0.129949 | − | 0.225078i | −0.793708 | − | 0.608299i | \(-0.791852\pi\) |
0.923657 | + | 0.383221i | \(0.125185\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 880.440i | 1.88531i | 0.333767 | + | 0.942656i | \(0.391680\pi\) | ||||
−0.333767 | + | 0.942656i | \(0.608320\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 591.284 | 1.26073 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −234.127 | − | 135.173i | −0.494982 | − | 0.285778i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −260.384 | − | 450.998i | −0.548176 | − | 0.949469i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −593.793 | + | 342.826i | −1.23965 | + | 0.715713i | −0.969023 | − | 0.246971i | \(-0.920565\pi\) |
−0.270628 | + | 0.962684i | \(0.587231\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 416.555 | − | 721.495i | 0.866019 | − | 1.49999i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 1038.85i | − | 2.14196i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 391.131 | 0.803143 | 0.401571 | − | 0.915828i | \(-0.368464\pi\) | ||||
0.401571 | + | 0.915828i | \(0.368464\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −166.469 | − | 96.1111i | −0.339042 | − | 0.195746i | 0.320807 | − | 0.947145i | \(-0.396046\pi\) |
−0.659848 | + | 0.751399i | \(0.729379\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −235.373 | − | 407.679i | −0.477431 | − | 0.826935i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 178.120 | − | 102.838i | 0.358391 | − | 0.206917i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −304.692 | + | 527.742i | −0.610605 | + | 1.05760i | 0.380534 | + | 0.924767i | \(0.375740\pi\) |
−0.991139 | + | 0.132832i | \(0.957593\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 232.130i | − | 0.461491i | −0.973014 | − | 0.230746i | \(-0.925883\pi\) | ||
0.973014 | − | 0.230746i | \(-0.0741165\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 240.576 | 0.476387 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 223.136 | + | 128.827i | 0.438381 | + | 0.253099i | 0.702910 | − | 0.711278i | \(-0.251883\pi\) |
−0.264530 | + | 0.964377i | \(0.585217\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −165.829 | − | 287.224i | −0.324518 | − | 0.562081i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 867.610 | − | 500.915i | 1.68468 | − | 0.972650i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 101.732 | − | 176.204i | 0.196773 | − | 0.340821i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 484.088i | − | 0.929152i | −0.885533 | − | 0.464576i | \(-0.846207\pi\) | ||
0.885533 | − | 0.464576i | \(-0.153793\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −644.384 | −1.23209 | −0.616046 | − | 0.787711i | \(-0.711266\pi\) | ||||
−0.616046 | + | 0.787711i | \(0.711266\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1020.10 | + | 588.955i | 1.93567 | + | 1.11756i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −162.010 | − | 280.610i | −0.306257 | − | 0.530454i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −579.530 | + | 334.592i | −1.08730 | + | 0.627752i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 130.565 | − | 226.146i | 0.244047 | − | 0.422702i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 17.0542i | 0.0316405i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −332.302 | −0.614237 | −0.307118 | − | 0.951671i | \(-0.599365\pi\) | ||||
−0.307118 | + | 0.951671i | \(0.599365\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −342.959 | − | 198.008i | −0.629283 | − | 0.363317i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 157.329 | + | 272.501i | 0.287621 | + | 0.498174i | 0.973241 | − | 0.229785i | \(-0.0738024\pi\) |
−0.685621 | + | 0.727959i | \(0.740469\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 285.000 | − | 164.545i | 0.517241 | − | 0.298629i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 379.278 | − | 656.928i | 0.685855 | − | 1.18793i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 664.080i | 1.19224i | 0.802894 | + | 0.596122i | \(0.203293\pi\) | ||||
−0.802894 | + | 0.596122i | \(0.796707\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −742.333 | −1.32797 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 211.024 | + | 121.835i | 0.374821 | + | 0.216403i | 0.675563 | − | 0.737302i | \(-0.263901\pi\) |
−0.300741 | + | 0.953706i | \(0.597234\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 610.358 | + | 1057.17i | 1.08028 | + | 1.87110i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 502.155 | − | 289.919i | 0.882522 | − | 0.509524i | 0.0110330 | − | 0.999939i | \(-0.496488\pi\) |
0.871489 | + | 0.490415i | \(0.163155\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 356.843 | − | 618.070i | 0.624944 | − | 1.08243i | −0.363608 | − | 0.931552i | \(-0.618455\pi\) |
0.988552 | − | 0.150882i | \(-0.0482114\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 423.728i | − | 0.736918i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 829.433 | 1.43749 | 0.718746 | − | 0.695273i | \(-0.244717\pi\) | ||||
0.718746 | + | 0.695273i | \(0.244717\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 578.409 | + | 333.945i | 0.995541 | + | 0.574776i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −31.1102 | − | 53.8844i | −0.0533623 | − | 0.0924261i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −777.480 | + | 448.878i | −1.32450 | + | 0.764699i | −0.984442 | − | 0.175707i | \(-0.943779\pi\) |
−0.340054 | + | 0.940406i | \(0.610445\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −411.727 | + | 713.131i | −0.699026 | + | 1.21075i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 378.065i | 0.637547i | 0.947831 | + | 0.318774i | \(0.103271\pi\) | ||||
−0.947831 | + | 0.318774i | \(0.896729\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1264.28 | 2.12484 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −822.438 | − | 474.835i | −1.37302 | − | 0.792712i | −0.381711 | − | 0.924282i | \(-0.624665\pi\) |
−0.991307 | + | 0.131569i | \(0.957998\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −252.308 | − | 437.011i | −0.419814 | − | 0.727139i | 0.576107 | − | 0.817375i | \(-0.304571\pi\) |
−0.995920 | + | 0.0902356i | \(0.971238\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 534.798 | − | 308.766i | 0.883964 | − | 0.510357i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −429.954 | + | 744.702i | −0.708326 | + | 1.22686i | 0.257151 | + | 0.966371i | \(0.417216\pi\) |
−0.965478 | + | 0.260486i | \(0.916117\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 558.682i | − | 0.914373i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −655.253 | −1.06893 | −0.534464 | − | 0.845191i | \(-0.679487\pi\) | ||||
−0.534464 | + | 0.845191i | \(0.679487\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 147.227 | + | 85.0013i | 0.238617 | + | 0.137765i | 0.614541 | − | 0.788885i | \(-0.289341\pi\) |
−0.375924 | + | 0.926650i | \(0.622675\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −270.531 | − | 468.573i | −0.437045 | − | 0.756983i | 0.560415 | − | 0.828212i | \(-0.310641\pi\) |
−0.997460 | + | 0.0712282i | \(0.977308\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −444.545 | + | 256.658i | −0.713555 | + | 0.411971i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 244.490 | − | 423.469i | 0.391184 | − | 0.677550i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1248.33i | − | 1.98463i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 260.788 | 0.413293 | 0.206646 | − | 0.978416i | \(-0.433745\pi\) | ||||
0.206646 | + | 0.978416i | \(0.433745\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −76.6571 | − | 44.2580i | −0.120720 | − | 0.0696977i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 23.4143 | + | 40.5547i | 0.0367571 | + | 0.0636652i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −585.418 | + | 337.991i | −0.913289 | + | 0.527288i | −0.881488 | − | 0.472206i | \(-0.843458\pi\) |
−0.0318012 | + | 0.999494i | \(0.510124\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 378.318 | − | 655.267i | 0.588364 | − | 1.01908i | −0.406082 | − | 0.913837i | \(-0.633105\pi\) |
0.994447 | − | 0.105241i | \(-0.0335613\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 554.770i | − | 0.857450i | −0.903435 | − | 0.428725i | \(-0.858963\pi\) | ||
0.903435 | − | 0.428725i | \(-0.141037\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −101.000 | −0.155624 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −174.499 | − | 100.747i | −0.267227 | − | 0.154283i | 0.360400 | − | 0.932798i | \(-0.382640\pi\) |
−0.627627 | + | 0.778514i | \(0.715974\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −56.7724 | − | 98.3328i | −0.0866755 | − | 0.150126i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 89.7122 | − | 51.7954i | 0.136134 | − | 0.0785969i | −0.430386 | − | 0.902645i | \(-0.641623\pi\) |
0.566520 | + | 0.824048i | \(0.308289\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −109.207 | + | 189.152i | −0.165215 | + | 0.286161i | −0.936732 | − | 0.350048i | \(-0.886165\pi\) |
0.771517 | + | 0.636209i | \(0.219498\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 883.834i | 1.32907i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 267.767 | 0.401450 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 112.328 | + | 64.8523i | 0.167403 | + | 0.0966503i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −394.429 | − | 683.170i | −0.586075 | − | 1.01511i | −0.994740 | − | 0.102428i | \(-0.967339\pi\) |
0.408665 | − | 0.912684i | \(-0.365994\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 634.550 | − | 366.358i | 0.937297 | − | 0.541149i | 0.0481850 | − | 0.998838i | \(-0.484656\pi\) |
0.889112 | + | 0.457690i | \(0.151323\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −477.883 | + | 827.717i | −0.703804 | + | 1.21902i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1353.33i | 1.98145i | 0.135883 | + | 0.990725i | \(0.456613\pi\) | ||||
−0.135883 | + | 0.990725i | \(0.543387\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −407.080 | −0.594277 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −147.959 | − | 85.4243i | −0.214745 | − | 0.123983i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 368.257 | + | 637.840i | 0.532934 | + | 0.923068i | 0.999260 | + | 0.0384555i | \(0.0122438\pi\) |
−0.466327 | + | 0.884613i | \(0.654423\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 646.166 | − | 373.064i | 0.929736 | − | 0.536783i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −501.353 | + | 868.369i | −0.719301 | + | 1.24587i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1068.34i | 1.52403i | 0.647561 | + | 0.762014i | \(0.275789\pi\) | ||||
−0.647561 | + | 0.762014i | \(0.724211\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 872.686 | 1.24137 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −191.682 | − | 110.667i | −0.271120 | − | 0.156531i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −136.944 | − | 237.194i | −0.193151 | − | 0.334547i | 0.753142 | − | 0.657858i | \(-0.228537\pi\) |
−0.946293 | + | 0.323311i | \(0.895204\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −580.247 | + | 335.006i | −0.813811 | + | 0.469854i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −379.651 | + | 657.575i | −0.530980 | + | 0.919685i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 654.423i | 0.910185i | 0.890444 | + | 0.455092i | \(0.150394\pi\) | ||||
−0.890444 | + | 0.455092i | \(0.849606\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −921.706 | −1.27837 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −479.363 | − | 276.761i | −0.661191 | − | 0.381739i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −583.166 | − | 1010.07i | −0.802155 | − | 1.38937i | −0.918195 | − | 0.396128i | \(-0.870354\pi\) |
0.116041 | − | 0.993244i | \(-0.462980\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −963.292 | + | 556.157i | −1.31777 | + | 0.760816i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −439.146 | + | 760.623i | −0.599108 | + | 1.03768i | 0.393845 | + | 0.919177i | \(0.371145\pi\) |
−0.992953 | + | 0.118508i | \(0.962189\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 532.103i | 0.721984i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −593.151 | −0.802640 | −0.401320 | − | 0.915938i | \(-0.631448\pi\) | ||||
−0.401320 | + | 0.915938i | \(0.631448\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 47.0561 | + | 27.1679i | 0.0633326 | + | 0.0365651i | 0.531332 | − | 0.847164i | \(-0.321692\pi\) |
−0.467999 | + | 0.883729i | \(0.655025\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 799.398 | + | 1384.60i | 1.07302 | + | 1.85852i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −208.059 | + | 120.123i | −0.277783 | + | 0.160378i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −455.570 | + | 789.071i | −0.606618 | + | 1.05069i | 0.385175 | + | 0.922844i | \(0.374141\pi\) |
−0.991793 | + | 0.127850i | \(0.959192\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 1134.83i | − | 1.50309i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1272.22 | 1.68061 | 0.840304 | − | 0.542115i | \(-0.182376\pi\) | ||||
0.840304 | + | 0.542115i | \(0.182376\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −399.480 | − | 230.640i | −0.524940 | − | 0.303074i | 0.214013 | − | 0.976831i | \(-0.431346\pi\) |
−0.738954 | + | 0.673756i | \(0.764680\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 182.171 | + | 315.530i | 0.238757 | + | 0.413539i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −240.177 | + | 138.666i | −0.313138 | + | 0.180790i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −269.439 | + | 466.682i | −0.350376 | + | 0.606868i | −0.986315 | − | 0.164871i | \(-0.947279\pi\) |
0.635940 | + | 0.771739i | \(0.280613\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1036.29i | 1.34061i | 0.742087 | + | 0.670304i | \(0.233836\pi\) | ||||
−0.742087 | + | 0.670304i | \(0.766164\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1385.03 | 1.78713 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −607.059 | − | 350.486i | −0.779280 | − | 0.449918i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 92.5449 | + | 160.292i | 0.118495 | + | 0.205240i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 524.520 | − | 302.832i | 0.668179 | − | 0.385773i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 706.096 | − | 1222.99i | 0.897199 | − | 1.55399i | 0.0661406 | − | 0.997810i | \(-0.478931\pi\) |
0.831059 | − | 0.556185i | \(-0.187735\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1123.09i | − | 1.41983i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 356.151 | 0.449119 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −60.4602 | − | 34.9067i | −0.0758597 | − | 0.0437976i | 0.461590 | − | 0.887093i | \(-0.347279\pi\) |
−0.537450 | + | 0.843296i | \(0.680612\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −418.565 | − | 724.976i | −0.523861 | − | 0.907355i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 258.476 | − | 149.231i | 0.321887 | − | 0.185842i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −359.570 | + | 622.794i | −0.446671 | + | 0.773657i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 1263.33i | − | 1.56160i | −0.624781 | − | 0.780800i | \(-0.714812\pi\) | ||
0.624781 | − | 0.780800i | \(-0.285188\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −442.241 | −0.545303 | −0.272652 | − | 0.962113i | \(-0.587901\pi\) | ||||
−0.272652 | + | 0.962113i | \(0.587901\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −353.302 | − | 203.979i | −0.433499 | − | 0.250281i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −388.798 | − | 673.418i | −0.475885 | − | 0.824257i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −498.077 | + | 287.565i | −0.606671 | + | 0.350261i | −0.771661 | − | 0.636034i | \(-0.780574\pi\) |
0.164991 | + | 0.986295i | \(0.447241\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.6214 | − | 20.1289i | 0.0141208 | − | 0.0244580i | −0.858879 | − | 0.512179i | \(-0.828838\pi\) |
0.872999 | + | 0.487721i | \(0.162172\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 790.958i | − | 0.956418i | −0.878246 | − | 0.478209i | \(-0.841286\pi\) | ||
0.878246 | − | 0.478209i | \(-0.158714\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1159.78 | 1.39901 | 0.699503 | − | 0.714630i | \(-0.253405\pi\) | ||||
0.699503 | + | 0.714630i | \(0.253405\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 60.7673 | + | 35.0840i | 0.0729500 | + | 0.0421177i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −570.802 | − | 988.658i | −0.683595 | − | 1.18402i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −473.470 | + | 273.358i | −0.564327 | + | 0.325814i | −0.754880 | − | 0.655862i | \(-0.772305\pi\) |
0.190553 | + | 0.981677i | \(0.438972\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −245.606 | + | 425.402i | −0.292041 | + | 0.505829i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 836.213i | 0.989601i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −568.143 | −0.670771 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 614.939 | + | 355.035i | 0.722607 | + | 0.417197i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −108.317 | − | 187.611i | −0.126984 | − | 0.219943i | 0.795523 | − | 0.605924i | \(-0.207196\pi\) |
−0.922507 | + | 0.385981i | \(0.873863\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −489.741 | + | 282.752i | −0.571460 | + | 0.329932i | −0.757732 | − | 0.652566i | \(-0.773693\pi\) |
0.186273 | + | 0.982498i | \(0.440359\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −187.884 | + | 325.424i | −0.218724 | + | 0.378841i | −0.954418 | − | 0.298473i | \(-0.903523\pi\) |
0.735694 | + | 0.677314i | \(0.236856\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1429.35i | − | 1.65626i | −0.560534 | − | 0.828131i | \(-0.689404\pi\) | ||
0.560534 | − | 0.828131i | \(-0.310596\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 194.555 | 0.224919 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 591.177 | + | 341.316i | 0.680295 | + | 0.392769i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 730.540 | + | 1265.33i | 0.838737 | + | 1.45273i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 199.922 | − | 115.425i | 0.228483 | − | 0.131915i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 420.813 | − | 728.870i | 0.479833 | − | 0.831095i | −0.519900 | − | 0.854227i | \(-0.674031\pi\) |
0.999732 | + | 0.0231327i | \(0.00736403\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 449.261i | 0.509944i | 0.966948 | + | 0.254972i | \(0.0820663\pi\) | ||||
−0.966948 | + | 0.254972i | \(0.917934\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 122.445 | 0.138669 | 0.0693346 | − | 0.997593i | \(-0.477912\pi\) | ||||
0.0693346 | + | 0.997593i | \(0.477912\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1361.09 | + | 785.828i | 1.53449 | + | 0.885940i | 0.999147 | + | 0.0413069i | \(0.0131521\pi\) |
0.535346 | + | 0.844633i | \(0.320181\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 40.7184 | + | 70.5263i | 0.0458025 | + | 0.0793322i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 506.816 | − | 292.611i | 0.567543 | − | 0.327671i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 985.312 | − | 1706.61i | 1.10091 | − | 1.90683i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 875.244i | 0.973575i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −256.000 | −0.284129 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 373.727 | + | 215.771i | 0.412957 | + | 0.238421i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 349.288 | + | 604.984i | 0.385102 | + | 0.667017i | 0.991783 | − | 0.127929i | \(-0.0408328\pi\) |
−0.606681 | + | 0.794945i | \(0.707500\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 70.4888 | − | 40.6967i | 0.0773752 | − | 0.0446726i | −0.460813 | − | 0.887497i | \(-0.652442\pi\) |
0.538188 | + | 0.842825i | \(0.319109\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −300.520 | + | 520.517i | −0.329157 | + | 0.570117i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 104.464i | 0.113919i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −348.665 | −0.379396 | −0.189698 | − | 0.981842i | \(-0.560751\pi\) | ||||
−0.189698 | + | 0.981842i | \(0.560751\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 440.141 | + | 254.115i | 0.476859 | + | 0.275315i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −733.918 | − | 1271.18i | −0.793425 | − | 1.37425i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 932.298 | − | 538.262i | 1.00355 | − | 0.579400i | 0.0942533 | − | 0.995548i | \(-0.469954\pi\) |
0.909297 | + | 0.416148i | \(0.136620\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −24.5265 | + | 42.4812i | −0.0263443 | + | 0.0456297i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1137.74i | 1.21683i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1437.39 | −1.53404 | −0.767018 | − | 0.641626i | \(-0.778260\pi\) | ||||
−0.767018 | + | 0.641626i | \(0.778260\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 186.591 | + | 107.728i | 0.198290 | + | 0.114483i | 0.595858 | − | 0.803090i | \(-0.296812\pi\) |
−0.397568 | + | 0.917573i | \(0.630146\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −285.177 | − | 493.940i | −0.302414 | − | 0.523797i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 407.651 | − | 235.357i | 0.430466 | − | 0.248529i | −0.269079 | − | 0.963118i | \(-0.586719\pi\) |
0.699545 | + | 0.714589i | \(0.253386\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 409.767 | − | 709.738i | 0.431789 | − | 0.747880i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1192.14i | − | 1.25093i | −0.780251 | − | 0.625466i | \(-0.784909\pi\) | ||
0.780251 | − | 0.625466i | \(-0.215091\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −849.445 | −0.889471 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 324.346 | + | 187.261i | 0.338213 | + | 0.195267i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −614.524 | − | 1064.39i | −0.639464 | − | 1.10758i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1388.45 | − | 801.621i | 1.43881 | − | 0.830695i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 96.3888 | − | 166.950i | 0.0996782 | − | 0.172648i | −0.811873 | − | 0.583834i | \(-0.801552\pi\) |
0.911551 | + | 0.411186i | \(0.134885\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 202.388i | − | 0.208433i | −0.994555 | − | 0.104216i | \(-0.966767\pi\) | ||
0.994555 | − | 0.104216i | \(-0.0332335\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −686.455 | −0.705504 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −35.1980 | − | 20.3216i | −0.0360266 | − | 0.0208000i | 0.481879 | − | 0.876238i | \(-0.339955\pi\) |
−0.517905 | + | 0.855438i | \(0.673288\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −230.969 | − | 400.051i | −0.235924 | − | 0.408632i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −631.105 | + | 364.369i | −0.642019 | + | 0.370670i | −0.785392 | − | 0.618999i | \(-0.787539\pi\) |
0.143373 | + | 0.989669i | \(0.454205\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 632.141 | − | 1094.90i | 0.641767 | − | 1.11157i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 632.699i | − | 0.639736i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 746.527 | 0.753306 | 0.376653 | − | 0.926354i | \(-0.377075\pi\) | ||||
0.376653 | + | 0.926354i | \(0.377075\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 396.737 | + | 229.056i | 0.398730 | + | 0.230207i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −119.046 | − | 206.194i | −0.119404 | − | 0.206814i | 0.800128 | − | 0.599830i | \(-0.204765\pi\) |
−0.919532 | + | 0.393016i | \(0.871432\pi\) | |||||||
\(998\) | 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 | 216.3.m.a.17.1 | 4 | ||
3.2 | odd | 2 | 72.3.m.a.41.2 | ✓ | 4 | ||
4.3 | odd | 2 | 432.3.q.c.17.1 | 4 | |||
8.3 | odd | 2 | 1728.3.q.f.449.2 | 4 | |||
8.5 | even | 2 | 1728.3.q.e.449.2 | 4 | |||
9.2 | odd | 6 | inner | 216.3.m.a.89.1 | 4 | ||
9.4 | even | 3 | 648.3.e.b.161.4 | 4 | |||
9.5 | odd | 6 | 648.3.e.b.161.1 | 4 | |||
9.7 | even | 3 | 72.3.m.a.65.2 | yes | 4 | ||
12.11 | even | 2 | 144.3.q.d.113.2 | 4 | |||
24.5 | odd | 2 | 576.3.q.h.257.1 | 4 | |||
24.11 | even | 2 | 576.3.q.c.257.1 | 4 | |||
36.7 | odd | 6 | 144.3.q.d.65.2 | 4 | |||
36.11 | even | 6 | 432.3.q.c.305.1 | 4 | |||
36.23 | even | 6 | 1296.3.e.c.161.1 | 4 | |||
36.31 | odd | 6 | 1296.3.e.c.161.4 | 4 | |||
72.11 | even | 6 | 1728.3.q.f.1601.2 | 4 | |||
72.29 | odd | 6 | 1728.3.q.e.1601.2 | 4 | |||
72.43 | odd | 6 | 576.3.q.c.65.1 | 4 | |||
72.61 | even | 6 | 576.3.q.h.65.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.3.m.a.41.2 | ✓ | 4 | 3.2 | odd | 2 | ||
72.3.m.a.65.2 | yes | 4 | 9.7 | even | 3 | ||
144.3.q.d.65.2 | 4 | 36.7 | odd | 6 | |||
144.3.q.d.113.2 | 4 | 12.11 | even | 2 | |||
216.3.m.a.17.1 | 4 | 1.1 | even | 1 | trivial | ||
216.3.m.a.89.1 | 4 | 9.2 | odd | 6 | inner | ||
432.3.q.c.17.1 | 4 | 4.3 | odd | 2 | |||
432.3.q.c.305.1 | 4 | 36.11 | even | 6 | |||
576.3.q.c.65.1 | 4 | 72.43 | odd | 6 | |||
576.3.q.c.257.1 | 4 | 24.11 | even | 2 | |||
576.3.q.h.65.1 | 4 | 72.61 | even | 6 | |||
576.3.q.h.257.1 | 4 | 24.5 | odd | 2 | |||
648.3.e.b.161.1 | 4 | 9.5 | odd | 6 | |||
648.3.e.b.161.4 | 4 | 9.4 | even | 3 | |||
1296.3.e.c.161.1 | 4 | 36.23 | even | 6 | |||
1296.3.e.c.161.4 | 4 | 36.31 | odd | 6 | |||
1728.3.q.e.449.2 | 4 | 8.5 | even | 2 | |||
1728.3.q.e.1601.2 | 4 | 72.29 | odd | 6 | |||
1728.3.q.f.449.2 | 4 | 8.3 | odd | 2 | |||
1728.3.q.f.1601.2 | 4 | 72.11 | even | 6 |