Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,3,Mod(449,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, 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("1728.449");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.q (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: | \(47.0845896815\) |
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 | 449.2 | ||
Root | \(-1.22474 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.449 |
Dual form | 1728.3.q.f.1601.2 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | 0.976811 | − | 0.214105i | \(-0.0686834\pi\) |
0.302985 | + | 0.952995i | \(0.402017\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.39898 | − | 5.88721i | −0.485568 | − | 0.841029i | 0.514294 | − | 0.857614i | \(-0.328054\pi\) |
−0.999862 | + | 0.0165847i | \(0.994721\pi\) | |||||||
\(8\) | 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 | \(-0.609743\pi\) |
0.984052 | − | 0.177881i | \(-0.0569242\pi\) | |||||||
\(14\) | 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 | 0.744708 | − | 0.667390i | \(-0.232589\pi\) |
−0.205622 | + | 0.978631i | \(0.565922\pi\) | |||||||
\(24\) | 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 | −0.194034 | − | 0.980995i | \(-0.562157\pi\) |
0.752549 | + | 0.658536i | \(0.228824\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −23.3990 | + | 40.5282i | −0.754806 | + | 1.30736i | 0.190665 | + | 0.981655i | \(0.438936\pi\) |
−0.945471 | + | 0.325707i | \(0.894398\pi\) | |||||||
\(32\) | 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 | \(-0.266202\pi\) | ||||
0.670215 | + | 0.742167i | \(0.266202\pi\) | |||||||
\(38\) | 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 | −0.161242 | − | 0.986915i | \(-0.551550\pi\) |
0.774073 | + | 0.633097i | \(0.218216\pi\) | |||||||
\(48\) | 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 | \(-0.969411\pi\) | ||
0.995386 | − | 0.0959509i | \(-0.0305892\pi\) | |||||||
\(54\) | 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 | 0.939741 | − | 0.341887i | \(-0.111066\pi\) |
−0.765954 | + | 0.642896i | \(0.777733\pi\) | |||||||
\(62\) | 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 | \(0.0683453\pi\) | ||||
−0.977038 | + | 0.213067i | \(0.931655\pi\) | |||||||
\(72\) | 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 | \(0.0829428\pi\) |
−0.260004 | + | 0.965608i | \(0.583724\pi\) | |||||||
\(80\) | 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 | −0.353873 | − | 0.935293i | \(-0.615136\pi\) |
0.633051 | + | 0.774110i | \(0.281802\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 67.7929 | − | 117.421i | 0.658183 | − | 1.14001i | −0.322903 | − | 0.946432i | \(-0.604659\pi\) |
0.981086 | − | 0.193574i | \(-0.0620081\pi\) | |||||||
\(104\) | 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 | \(-0.579068\pi\) | ||||
−0.245853 | + | 0.969307i | \(0.579068\pi\) | |||||||
\(110\) | 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 | \(-0.515018\pi\) | ||||
−0.0471637 | + | 0.998887i | \(0.515018\pi\) | |||||||
\(128\) | 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 | 0.972616 | − | 0.232419i | \(-0.0746641\pi\) |
0.285027 | + | 0.958519i | \(0.407997\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −76.7929 | − | 133.009i | −0.508562 | − | 0.880855i | −0.999951 | − | 0.00991488i | \(-0.996844\pi\) |
0.491389 | − | 0.870940i | \(-0.336489\pi\) | |||||||
\(152\) | 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 | −0.705472 | − | 0.708738i | \(-0.749265\pi\) |
0.966521 | + | 0.256588i | \(0.0825983\pi\) | |||||||
\(158\) | 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 | 0.0426802 | − | 0.999089i | \(-0.486410\pi\) |
−0.843896 | + | 0.536507i | \(0.819744\pi\) | |||||||
\(168\) | 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 | −0.432645 | − | 0.901564i | \(-0.642420\pi\) |
0.564455 | + | 0.825464i | \(0.309086\pi\) | |||||||
\(174\) | 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 | \(-0.448419\pi\) | ||||
0.161337 | + | 0.986899i | \(0.448419\pi\) | |||||||
\(182\) | 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 | −0.737449 | − | 0.675403i | \(-0.763970\pi\) |
0.216191 | + | 0.976351i | \(0.430636\pi\) | |||||||
\(192\) | 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 | \(-0.857004\pi\) | ||
0.900779 | − | 0.434278i | \(-0.142996\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 62.0000 | 0.311558 | 0.155779 | − | 0.987792i | \(-0.450211\pi\) | ||||
0.155779 | + | 0.987792i | \(0.450211\pi\) | |||||||
\(200\) | 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 | 0.954981 | − | 0.296668i | \(-0.0958755\pi\) |
−0.734412 | + | 0.678704i | \(0.762542\pi\) | |||||||
\(224\) | 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 | −0.962009 | − | 0.273018i | \(-0.911978\pi\) |
0.717445 | + | 0.696615i | \(0.245311\pi\) | |||||||
\(230\) | 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 | 0.576176 | − | 0.817326i | \(-0.304544\pi\) |
−0.419737 | + | 0.907646i | \(0.637878\pi\) | |||||||
\(240\) | 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 | −0.578491 | − | 0.815689i | \(-0.696358\pi\) |
0.417162 | + | 0.908832i | \(0.363025\pi\) | |||||||
\(264\) | 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 | \(0.175413\pi\) | ||||
−0.851961 | + | 0.523606i | \(0.824587\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 89.5959 | 0.330612 | 0.165306 | − | 0.986242i | \(-0.447139\pi\) | ||||
0.165306 | + | 0.986242i | \(0.447139\pi\) | |||||||
\(272\) | 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 | 0.932086 | − | 0.362238i | \(-0.117987\pi\) |
−0.779750 | + | 0.626091i | \(0.784654\pi\) | |||||||
\(278\) | 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 | −0.398854 | − | 0.917014i | \(-0.630592\pi\) |
−0.993585 | + | 0.113089i | \(0.963925\pi\) | |||||||
\(294\) | 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 | 0.106039 | − | 0.994362i | \(-0.466183\pi\) |
−0.808123 | + | 0.589014i | \(0.799516\pi\) | |||||||
\(312\) | 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 | −0.335680 | − | 0.941976i | \(-0.608966\pi\) |
0.647935 | + | 0.761696i | \(0.275633\pi\) | |||||||
\(318\) | 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 | \(-0.885123\pi\) |
0.161986 | − | 0.986793i | \(-0.448210\pi\) | |||||||
\(350\) | 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 | \(0.200285\pi\) | ||||
−0.808490 | + | 0.588509i | \(0.799715\pi\) | |||||||
\(360\) | 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 | 0.629690 | − | 0.776847i | \(-0.283182\pi\) |
−0.987614 | + | 0.156904i | \(0.949849\pi\) | |||||||
\(368\) | 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 | −0.772623 | − | 0.634865i | \(-0.781056\pi\) |
0.936121 | + | 0.351679i | \(0.114389\pi\) | |||||||
\(374\) | 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 | \(0.0831650\pi\) |
0.706733 | + | 0.707481i | \(0.250168\pi\) | |||||||
\(384\) | 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 | −0.399462 | − | 0.916750i | \(-0.630803\pi\) |
0.594197 | + | 0.804319i | \(0.297470\pi\) | |||||||
\(390\) | 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 | \(-0.708199\pi\) | ||||
−0.608425 | + | 0.793611i | \(0.708199\pi\) | |||||||
\(398\) | 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 | 0.567431 | − | 0.823421i | \(-0.307937\pi\) |
−0.996819 | + | 0.0796989i | \(0.974604\pi\) | |||||||
\(422\) | 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 | \(-0.819184\pi\) | ||
0.842952 | − | 0.537989i | \(-0.180816\pi\) | |||||||
\(432\) | 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 | \(-0.916305\pi\) |
0.257721 | − | 0.966219i | \(-0.417028\pi\) | |||||||
\(440\) | 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 | −0.919286 | − | 0.393591i | \(-0.871233\pi\) |
−0.118784 | + | 0.992920i | \(0.537899\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −60.1663 | + | 104.211i | −0.129949 | + | 0.225078i | −0.923657 | − | 0.383221i | \(-0.874815\pi\) |
0.793708 | + | 0.608299i | \(0.208148\pi\) | |||||||
\(464\) | 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 | 0.270628 | − | 0.962684i | \(-0.412769\pi\) |
0.969023 | + | 0.246971i | \(0.0794353\pi\) | |||||||
\(480\) | 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 | \(-0.631536\pi\) | ||||
−0.401571 | + | 0.915828i | \(0.631536\pi\) | |||||||
\(488\) | 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 | \(0.0741165\pi\) | ||||
−0.973014 | + | 0.230746i | \(0.925883\pi\) | |||||||
\(504\) | 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 | 0.264530 | − | 0.964377i | \(-0.414783\pi\) |
−0.702910 | + | 0.711278i | \(0.748117\pi\) | |||||||
\(510\) | 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 | \(-0.400635\pi\) | ||||
0.307118 | + | 0.951671i | \(0.400635\pi\) | |||||||
\(542\) | 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 | \(-0.796707\pi\) | ||
0.802894 | − | 0.596122i | \(-0.203293\pi\) | |||||||
\(558\) | 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 | 0.991307 | − | 0.131569i | \(-0.0420016\pi\) |
0.381711 | + | 0.924282i | \(0.375335\pi\) | |||||||
\(600\) | 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 | \(-0.582784\pi\) |
0.965478 | − | 0.260486i | \(-0.0838828\pi\) | |||||||
\(608\) | 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 | \(-0.320513\pi\) | ||||
0.534464 | + | 0.845191i | \(0.320513\pi\) | |||||||
\(614\) | 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 | \(-0.566255\pi\) | ||||
−0.206646 | + | 0.978416i | \(0.566255\pi\) | |||||||
\(632\) | 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 | \(0.141037\pi\) | ||||
−0.903435 | + | 0.428725i | \(0.858963\pi\) | |||||||
\(648\) | 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 | 0.627627 | − | 0.778514i | \(-0.284026\pi\) |
−0.360400 | + | 0.932798i | \(0.617360\pi\) | |||||||
\(654\) | 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 | −0.771517 | − | 0.636209i | \(-0.780502\pi\) |
0.936732 | + | 0.350048i | \(0.113835\pi\) | |||||||
\(662\) | 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 | −0.889112 | − | 0.457690i | \(-0.848677\pi\) |
−0.0481850 | + | 0.998838i | \(0.515344\pi\) | |||||||
\(678\) | 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 | \(-0.724211\pi\) | ||
0.647561 | − | 0.762014i | \(-0.275789\pi\) | |||||||
\(702\) | 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 | 0.946293 | − | 0.323311i | \(-0.104796\pi\) |
−0.753142 | + | 0.657858i | \(0.771463\pi\) | |||||||
\(710\) | 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 | \(-0.849606\pi\) | ||
0.890444 | − | 0.455092i | \(-0.150394\pi\) | |||||||
\(720\) | 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 | \(0.129646\pi\) |
−0.116041 | + | 0.993244i | \(0.537020\pi\) | |||||||
\(728\) | 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 | \(-0.628855\pi\) |
0.992953 | − | 0.118508i | \(-0.0378112\pi\) | |||||||
\(734\) | 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 | 0.467999 | − | 0.883729i | \(-0.344975\pi\) |
−0.531332 | + | 0.847164i | \(0.678308\pi\) | |||||||
\(744\) | 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 | \(-0.625859\pi\) |
0.991793 | − | 0.127850i | \(-0.0408077\pi\) | |||||||
\(752\) | 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 | \(-0.817624\pi\) | ||||
−0.840304 | + | 0.542115i | \(0.817624\pi\) | |||||||
\(758\) | 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 | \(-0.766164\pi\) | ||
0.742087 | − | 0.670304i | \(-0.233836\pi\) | |||||||
\(774\) | 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 | 0.537450 | − | 0.843296i | \(-0.319388\pi\) |
−0.461590 | + | 0.887093i | \(0.652721\pi\) | |||||||
\(798\) | 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 | −0.164991 | − | 0.986295i | \(-0.552759\pi\) |
0.771661 | + | 0.636034i | \(0.219426\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.6214 | + | 20.1289i | −0.0141208 | + | 0.0244580i | −0.872999 | − | 0.487721i | \(-0.837828\pi\) |
0.858879 | + | 0.512179i | \(0.171162\pi\) | |||||||
\(824\) | 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 | \(-0.746595\pi\) | ||||
−0.699503 | + | 0.714630i | \(0.746595\pi\) | |||||||
\(830\) | 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 | −0.190553 | − | 0.981677i | \(-0.561028\pi\) |
0.754880 | + | 0.655862i | \(0.227695\pi\) | |||||||
\(840\) | 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 | 0.922507 | − | 0.385981i | \(-0.126137\pi\) |
−0.795523 | + | 0.605924i | \(0.792804\pi\) | |||||||
\(854\) | 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 | \(0.310596\pi\) | ||||
−0.560534 | + | 0.828131i | \(0.689404\pi\) | |||||||
\(864\) | 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 | −0.999732 | − | 0.0231327i | \(-0.992636\pi\) |
0.519900 | + | 0.854227i | \(0.325969\pi\) | |||||||
\(878\) | 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 | \(-0.986848\pi\) |
−0.535346 | − | 0.844633i | \(-0.679819\pi\) | |||||||
\(888\) | 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 | −0.538188 | − | 0.842825i | \(-0.680891\pi\) |
0.460813 | + | 0.887497i | \(0.347558\pi\) | |||||||
\(912\) | 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 | \(-0.439249\pi\) | ||||
0.189698 | + | 0.981842i | \(0.439249\pi\) | |||||||
\(920\) | 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 | 0.397568 | − | 0.917573i | \(-0.369854\pi\) |
−0.595858 | + | 0.803090i | \(0.703188\pi\) | |||||||
\(942\) | 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 | −0.911551 | − | 0.411186i | \(-0.865115\pi\) |
0.811873 | + | 0.583834i | \(0.198448\pi\) | |||||||
\(968\) | 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 | −0.143373 | − | 0.989669i | \(-0.545795\pi\) |
0.785392 | + | 0.618999i | \(0.212461\pi\) | |||||||
\(984\) | 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 | \(-0.622925\pi\) | ||||
−0.376653 | + | 0.926354i | \(0.622925\pi\) | |||||||
\(992\) | 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 | 0.919532 | − | 0.393016i | \(-0.128568\pi\) |
−0.800128 | + | 0.599830i | \(0.795235\pi\) | |||||||
\(998\) | 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 | 1728.3.q.f.449.2 | 4 | ||
3.2 | odd | 2 | 576.3.q.c.257.1 | 4 | |||
4.3 | odd | 2 | 1728.3.q.e.449.2 | 4 | |||
8.3 | odd | 2 | 216.3.m.a.17.1 | 4 | |||
8.5 | even | 2 | 432.3.q.c.17.1 | 4 | |||
9.2 | odd | 6 | inner | 1728.3.q.f.1601.2 | 4 | ||
9.7 | even | 3 | 576.3.q.c.65.1 | 4 | |||
12.11 | even | 2 | 576.3.q.h.257.1 | 4 | |||
24.5 | odd | 2 | 144.3.q.d.113.2 | 4 | |||
24.11 | even | 2 | 72.3.m.a.41.2 | ✓ | 4 | ||
36.7 | odd | 6 | 576.3.q.h.65.1 | 4 | |||
36.11 | even | 6 | 1728.3.q.e.1601.2 | 4 | |||
72.5 | odd | 6 | 1296.3.e.c.161.1 | 4 | |||
72.11 | even | 6 | 216.3.m.a.89.1 | 4 | |||
72.13 | even | 6 | 1296.3.e.c.161.4 | 4 | |||
72.29 | odd | 6 | 432.3.q.c.305.1 | 4 | |||
72.43 | odd | 6 | 72.3.m.a.65.2 | yes | 4 | ||
72.59 | even | 6 | 648.3.e.b.161.1 | 4 | |||
72.61 | even | 6 | 144.3.q.d.65.2 | 4 | |||
72.67 | odd | 6 | 648.3.e.b.161.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.3.m.a.41.2 | ✓ | 4 | 24.11 | even | 2 | ||
72.3.m.a.65.2 | yes | 4 | 72.43 | odd | 6 | ||
144.3.q.d.65.2 | 4 | 72.61 | even | 6 | |||
144.3.q.d.113.2 | 4 | 24.5 | odd | 2 | |||
216.3.m.a.17.1 | 4 | 8.3 | odd | 2 | |||
216.3.m.a.89.1 | 4 | 72.11 | even | 6 | |||
432.3.q.c.17.1 | 4 | 8.5 | even | 2 | |||
432.3.q.c.305.1 | 4 | 72.29 | odd | 6 | |||
576.3.q.c.65.1 | 4 | 9.7 | even | 3 | |||
576.3.q.c.257.1 | 4 | 3.2 | odd | 2 | |||
576.3.q.h.65.1 | 4 | 36.7 | odd | 6 | |||
576.3.q.h.257.1 | 4 | 12.11 | even | 2 | |||
648.3.e.b.161.1 | 4 | 72.59 | even | 6 | |||
648.3.e.b.161.4 | 4 | 72.67 | odd | 6 | |||
1296.3.e.c.161.1 | 4 | 72.5 | odd | 6 | |||
1296.3.e.c.161.4 | 4 | 72.13 | even | 6 | |||
1728.3.q.e.449.2 | 4 | 4.3 | odd | 2 | |||
1728.3.q.e.1601.2 | 4 | 36.11 | even | 6 | |||
1728.3.q.f.449.2 | 4 | 1.1 | even | 1 | trivial | ||
1728.3.q.f.1601.2 | 4 | 9.2 | odd | 6 | inner |