Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(289,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.t (of order \(3\), 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: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 289.2 | ||
Character | \(\chi\) | \(=\) | 3024.289 |
Dual form | 3024.2.t.k.1873.2 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.19500 | −1.42885 | −0.714423 | − | 0.699714i | \(-0.753311\pi\) | ||||
−0.714423 | + | 0.699714i | \(0.753311\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.61289 | − | 0.415693i | −0.987580 | − | 0.157117i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.28279 | −0.688286 | −0.344143 | − | 0.938917i | \(-0.611830\pi\) | ||||
−0.344143 | + | 0.938917i | \(0.611830\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.675051 | − | 1.16922i | −0.187225 | − | 0.324284i | 0.757099 | − | 0.653300i | \(-0.226616\pi\) |
−0.944324 | + | 0.329017i | \(0.893283\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.21425 | − | 3.83519i | −0.537033 | − | 0.930169i | −0.999062 | − | 0.0433042i | \(-0.986212\pi\) |
0.462028 | − | 0.886865i | \(-0.347122\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.69214 | − | 6.39497i | 0.847034 | − | 1.46711i | −0.0368084 | − | 0.999322i | \(-0.511719\pi\) |
0.883843 | − | 0.467784i | \(-0.154948\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.46959 | −1.34900 | −0.674501 | − | 0.738274i | \(-0.735641\pi\) | ||||
−0.674501 | + | 0.738274i | \(0.735641\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.20800 | 1.04160 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.06167 | − | 1.83887i | 0.197148 | − | 0.341470i | −0.750455 | − | 0.660922i | \(-0.770166\pi\) |
0.947602 | + | 0.319452i | \(0.103499\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.316154 | + | 0.547595i | −0.0567830 | + | 0.0983510i | −0.893020 | − | 0.450018i | \(-0.851418\pi\) |
0.836237 | + | 0.548369i | \(0.184751\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.34818 | + | 1.32814i | 1.41110 | + | 0.224496i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.92885 | − | 3.34087i | 0.317102 | − | 0.549236i | −0.662780 | − | 0.748814i | \(-0.730624\pi\) |
0.979882 | + | 0.199578i | \(0.0639570\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.05124 | + | 8.74900i | 0.788871 | + | 1.36636i | 0.926659 | + | 0.375903i | \(0.122667\pi\) |
−0.137788 | + | 0.990462i | \(0.543999\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.24701 | + | 7.35603i | −0.647663 | + | 1.12178i | 0.336017 | + | 0.941856i | \(0.390920\pi\) |
−0.983680 | + | 0.179929i | \(0.942413\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.26587 | − | 5.65664i | −0.476375 | − | 0.825106i | 0.523258 | − | 0.852174i | \(-0.324716\pi\) |
−0.999634 | + | 0.0270678i | \(0.991383\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.65440 | + | 2.17232i | 0.950628 | + | 0.310332i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.39950 | − | 4.15606i | −0.329597 | − | 0.570879i | 0.652835 | − | 0.757500i | \(-0.273580\pi\) |
−0.982432 | + | 0.186621i | \(0.940246\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.29349 | 0.983454 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.10191 | + | 5.37267i | −0.403835 | + | 0.699463i | −0.994185 | − | 0.107685i | \(-0.965656\pi\) |
0.590350 | + | 0.807147i | \(0.298990\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.45546 | + | 7.71709i | 0.570464 | + | 0.988072i | 0.996518 | + | 0.0833747i | \(0.0265698\pi\) |
−0.426055 | + | 0.904697i | \(0.640097\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.15679 | + | 3.73566i | 0.267516 | + | 0.463352i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.50785 | + | 2.61167i | −0.184213 | + | 0.319067i | −0.943311 | − | 0.331910i | \(-0.892307\pi\) |
0.759098 | + | 0.650976i | \(0.225640\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15.3791 | −1.82516 | −0.912580 | − | 0.408899i | \(-0.865913\pi\) | ||||
−0.912580 | + | 0.408899i | \(0.865913\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.36577 | + | 7.56173i | 0.510974 | + | 0.885033i | 0.999919 | + | 0.0127186i | \(0.00404857\pi\) |
−0.488945 | + | 0.872315i | \(0.662618\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.96467 | + | 0.948938i | 0.679737 | + | 0.108142i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.938050 | − | 1.62475i | −0.105539 | − | 0.182799i | 0.808419 | − | 0.588607i | \(-0.200323\pi\) |
−0.913958 | + | 0.405808i | \(0.866990\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.00140 | + | 5.19857i | −0.329446 | + | 0.570617i | −0.982402 | − | 0.186779i | \(-0.940195\pi\) |
0.652956 | + | 0.757396i | \(0.273529\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.07451 | + | 12.2534i | 0.767338 | + | 1.32907i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.65390 | + | 4.59668i | −0.281313 | + | 0.487248i | −0.971708 | − | 0.236184i | \(-0.924103\pi\) |
0.690396 | + | 0.723432i | \(0.257436\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.27780 | + | 3.33566i | 0.133949 | + | 0.349673i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −11.7964 | + | 20.4319i | −1.21028 | + | 2.09627i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.44539 | − | 12.8958i | 0.755965 | − | 1.30937i | −0.188929 | − | 0.981991i | \(-0.560502\pi\) |
0.944893 | − | 0.327378i | \(-0.106165\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.0060 | 1.39365 | 0.696824 | − | 0.717242i | \(-0.254596\pi\) | ||||
0.696824 | + | 0.717242i | \(0.254596\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.0611 | −1.58255 | −0.791274 | − | 0.611462i | \(-0.790582\pi\) | ||||
−0.791274 | + | 0.611462i | \(0.790582\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.26820 | − | 2.19658i | 0.122601 | − | 0.212352i | −0.798191 | − | 0.602404i | \(-0.794210\pi\) |
0.920793 | + | 0.390052i | \(0.127543\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.10946 | + | 14.0460i | 0.776746 | + | 1.34536i | 0.933808 | + | 0.357775i | \(0.116464\pi\) |
−0.157062 | + | 0.987589i | \(0.550202\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.61499 | − | 2.79725i | −0.151926 | − | 0.263143i | 0.780010 | − | 0.625767i | \(-0.215214\pi\) |
−0.931935 | + | 0.362625i | \(0.881881\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 20.6703 | 1.92752 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.19132 | + | 10.9414i | 0.384218 | + | 1.00299i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.78889 | −0.526263 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.664575 | −0.0594414 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.6429 | 1.12187 | 0.560936 | − | 0.827859i | \(-0.310441\pi\) | ||||
0.560936 | + | 0.827859i | \(0.310441\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.0686 | 1.66603 | 0.833015 | − | 0.553250i | \(-0.186613\pi\) | ||||
0.833015 | + | 0.553250i | \(0.186613\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.3055 | + | 15.1746i | −1.06702 | + | 1.31580i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.76473 | −0.577949 | −0.288975 | − | 0.957337i | \(-0.593314\pi\) | ||||
−0.288975 | + | 0.957337i | \(0.593314\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.57218 | + | 11.3834i | 0.557445 | + | 0.965524i | 0.997709 | + | 0.0676550i | \(0.0215517\pi\) |
−0.440263 | + | 0.897869i | \(0.645115\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.54100 | + | 2.66908i | 0.128865 | + | 0.223200i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.39204 | + | 5.87518i | −0.281693 | + | 0.487907i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.280514 | −0.0229806 | −0.0114903 | − | 0.999934i | \(-0.503658\pi\) | ||||
−0.0114903 | + | 0.999934i | \(0.503658\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.85798 | −0.720852 | −0.360426 | − | 0.932788i | \(-0.617369\pi\) | ||||
−0.360426 | + | 0.932788i | \(0.617369\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.01011 | − | 1.74956i | 0.0811341 | − | 0.140528i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.964471 | − | 1.67051i | 0.0769731 | − | 0.133321i | −0.824969 | − | 0.565177i | \(-0.808808\pi\) |
0.901943 | + | 0.431856i | \(0.142141\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.9043 | + | 2.68936i | 1.33225 | + | 0.211952i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.1983 | − | 21.1281i | 0.955446 | − | 1.65488i | 0.222100 | − | 0.975024i | \(-0.428709\pi\) |
0.733345 | − | 0.679856i | \(-0.237958\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.75658 | + | 4.77453i | 0.213310 | + | 0.369464i | 0.952749 | − | 0.303760i | \(-0.0982421\pi\) |
−0.739438 | + | 0.673224i | \(0.764909\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.58861 | − | 9.67976i | 0.429893 | − | 0.744597i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.30260 | + | 10.9164i | 0.479178 | + | 0.829960i | 0.999715 | − | 0.0238790i | \(-0.00760165\pi\) |
−0.520537 | + | 0.853839i | \(0.674268\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −13.6079 | − | 2.16493i | −1.02866 | − | 0.163653i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.10472 | + | 8.84164i | 0.381545 | + | 0.660855i | 0.991283 | − | 0.131747i | \(-0.0420588\pi\) |
−0.609738 | + | 0.792603i | \(0.708725\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.2398 | −1.20710 | −0.603548 | − | 0.797327i | \(-0.706247\pi\) | ||||
−0.603548 | + | 0.797327i | \(0.706247\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.16268 | + | 10.6741i | −0.453089 | + | 0.784774i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.05465 | + | 8.75491i | 0.369632 | + | 0.640222i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.97060 | + | 3.41318i | 0.142587 | + | 0.246969i | 0.928470 | − | 0.371407i | \(-0.121124\pi\) |
−0.785883 | + | 0.618375i | \(0.787791\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.87056 | − | 4.97196i | 0.206627 | − | 0.357889i | −0.744023 | − | 0.668154i | \(-0.767085\pi\) |
0.950650 | + | 0.310265i | \(0.100418\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.67480 | 0.546807 | 0.273403 | − | 0.961899i | \(-0.411851\pi\) | ||||
0.273403 | + | 0.961899i | \(0.411851\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.26928 | + | 3.93050i | 0.160865 | + | 0.278626i | 0.935179 | − | 0.354175i | \(-0.115238\pi\) |
−0.774314 | + | 0.632801i | \(0.781905\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.53844 | + | 4.36344i | −0.248350 | + | 0.306253i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −16.1387 | − | 27.9530i | −1.12718 | − | 1.95232i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.42836 | + | 14.5983i | −0.583002 | + | 1.00979i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.84097 | − | 17.0451i | −0.677480 | − | 1.17343i | −0.975737 | − | 0.218944i | \(-0.929739\pi\) |
0.298257 | − | 0.954486i | \(-0.403595\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.5692 | − | 23.5025i | 0.925410 | − | 1.60286i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.05371 | − | 1.29938i | 0.0715304 | − | 0.0882079i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.98946 | + | 5.17789i | −0.201093 | + | 0.348303i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.63518 | + | 11.4925i | −0.444324 | + | 0.769592i | −0.998005 | − | 0.0631368i | \(-0.979890\pi\) |
0.553681 | + | 0.832729i | \(0.313223\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 22.0610 | 1.46424 | 0.732118 | − | 0.681177i | \(-0.238532\pi\) | ||||
0.732118 | + | 0.681177i | \(0.238532\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.8472 | −1.17938 | −0.589688 | − | 0.807631i | \(-0.700749\pi\) | ||||
−0.589688 | + | 0.807631i | \(0.700749\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.84409 | − | 13.5864i | 0.513883 | − | 0.890072i | −0.485987 | − | 0.873966i | \(-0.661540\pi\) |
0.999870 | − | 0.0161061i | \(-0.00512696\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.4344 | + | 18.0730i | 0.680667 | + | 1.17895i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.0639656 | − | 0.110792i | −0.00413759 | − | 0.00716652i | 0.863949 | − | 0.503579i | \(-0.167984\pi\) |
−0.868087 | + | 0.496412i | \(0.834650\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.0869 | 0.971830 | 0.485915 | − | 0.874006i | \(-0.338486\pi\) | ||||
0.485915 | + | 0.874006i | \(0.338486\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −21.2608 | − | 6.94056i | −1.35830 | − | 0.443416i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.96952 | −0.634345 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.3738 | 0.781030 | 0.390515 | − | 0.920596i | \(-0.372297\pi\) | ||||
0.390515 | + | 0.920596i | \(0.372297\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.7687 | 0.928499 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −22.0867 | −1.37773 | −0.688865 | − | 0.724890i | \(-0.741891\pi\) | ||||
−0.688865 | + | 0.724890i | \(0.741891\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.42866 | + | 7.92752i | −0.399458 | + | 0.492592i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.79357 | −0.480572 | −0.240286 | − | 0.970702i | \(-0.577241\pi\) | ||||
−0.240286 | + | 0.970702i | \(0.577241\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.66641 | + | 13.2786i | 0.470944 | + | 0.815698i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.85738 | + | 6.68119i | 0.235189 | + | 0.407359i | 0.959328 | − | 0.282295i | \(-0.0910958\pi\) |
−0.724139 | + | 0.689654i | \(0.757762\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.5744 | + | 21.7795i | −0.763839 | + | 1.32301i | 0.177019 | + | 0.984207i | \(0.443355\pi\) |
−0.940858 | + | 0.338801i | \(0.889979\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −11.8888 | −0.716919 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.96273 | −0.478434 | −0.239217 | − | 0.970966i | \(-0.576891\pi\) | ||||
−0.239217 | + | 0.970966i | \(0.576891\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.3385 | + | 23.1030i | −0.795710 | + | 1.37821i | 0.126678 | + | 0.991944i | \(0.459569\pi\) |
−0.922388 | + | 0.386266i | \(0.873765\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.21996 | − | 12.5053i | 0.429182 | − | 0.743365i | −0.567619 | − | 0.823292i | \(-0.692135\pi\) |
0.996801 | + | 0.0799265i | \(0.0254686\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.56144 | − | 24.9600i | −0.564394 | − | 1.47334i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.30577 | + | 2.26166i | −0.0768099 | + | 0.133039i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.27703 | + | 14.3362i | 0.483549 | + | 0.837532i | 0.999822 | − | 0.0188927i | \(-0.00601408\pi\) |
−0.516272 | + | 0.856424i | \(0.672681\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.91061 | − | 17.1657i | 0.577018 | − | 0.999424i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.36730 | + | 7.56439i | 0.252568 | + | 0.437460i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 14.1548 | − | 17.4551i | 0.815870 | − | 1.00609i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −14.2352 | − | 24.6561i | −0.815105 | − | 1.41180i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.9233 | −0.623425 | −0.311713 | − | 0.950176i | \(-0.600903\pi\) | ||||
−0.311713 | + | 0.950176i | \(0.600903\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.62680 | − | 4.54975i | 0.148952 | − | 0.257992i | −0.781888 | − | 0.623418i | \(-0.785743\pi\) |
0.930840 | + | 0.365426i | \(0.119077\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.7592 | − | 18.6354i | −0.608145 | − | 1.05334i | −0.991546 | − | 0.129756i | \(-0.958581\pi\) |
0.383401 | − | 0.923582i | \(-0.374753\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.76613 | − | 15.1834i | −0.492355 | − | 0.852784i | 0.507606 | − | 0.861589i | \(-0.330530\pi\) |
−0.999961 | + | 0.00880525i | \(0.997197\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.42357 | + | 4.19774i | −0.135694 | + | 0.235029i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −32.7012 | −1.81954 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.51567 | − | 6.08932i | −0.195014 | − | 0.337774i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.18192 | + | 16.1378i | 0.340820 | + | 0.889705i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.13795 | + | 5.43508i | 0.172477 | + | 0.298739i | 0.939285 | − | 0.343137i | \(-0.111490\pi\) |
−0.766808 | + | 0.641876i | \(0.778156\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.81757 | − | 8.34428i | 0.263212 | − | 0.455897i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.5924 | + | 23.5427i | 0.740426 | + | 1.28246i | 0.952302 | + | 0.305159i | \(0.0987095\pi\) |
−0.211876 | + | 0.977297i | \(0.567957\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.721712 | − | 1.25004i | 0.0390829 | − | 0.0676936i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.4842 | − | 8.44222i | −0.890063 | − | 0.455837i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.59040 | − | 16.6111i | 0.514840 | − | 0.891728i | −0.485012 | − | 0.874507i | \(-0.661185\pi\) |
0.999852 | − | 0.0172210i | \(-0.00548188\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.1028 | − | 17.4985i | 0.540789 | − | 0.936675i | −0.458069 | − | 0.888916i | \(-0.651459\pi\) |
0.998859 | − | 0.0477584i | \(-0.0152078\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.4999 | 1.51690 | 0.758448 | − | 0.651733i | \(-0.225958\pi\) | ||||
0.758448 | + | 0.651733i | \(0.225958\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 49.1361 | 2.60787 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.4572 | − | 26.7727i | 0.815802 | − | 1.41301i | −0.0929489 | − | 0.995671i | \(-0.529629\pi\) |
0.908751 | − | 0.417339i | \(-0.137037\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.7638 | − | 30.7677i | −0.934934 | − | 1.61935i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.9486 | − | 24.1597i | −0.730103 | − | 1.26458i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.83095 | 0.356573 | 0.178286 | − | 0.983979i | \(-0.442945\pi\) | ||||
0.178286 | + | 0.983979i | \(0.442945\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.54199 | + | 11.8568i | 0.235809 | + | 0.615574i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.76490 | 0.350273 | 0.175137 | − | 0.984544i | \(-0.443963\pi\) | ||||
0.175137 | + | 0.984544i | \(0.443963\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.86673 | −0.147644 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.62967 | 0.391910 | 0.195955 | − | 0.980613i | \(-0.437219\pi\) | ||||
0.195955 | + | 0.980613i | \(0.437219\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.42264 | −0.328181 | −0.164091 | − | 0.986445i | \(-0.552469\pi\) | ||||
−0.164091 | + | 0.986445i | \(0.552469\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −19.0571 | − | 3.03185i | −0.971240 | − | 0.154518i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.8535 | 0.803804 | 0.401902 | − | 0.915683i | \(-0.368349\pi\) | ||||
0.401902 | + | 0.915683i | \(0.368349\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.3253 | + | 24.8121i | 0.724460 | + | 1.25480i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.99707 | + | 5.19107i | 0.150799 | + | 0.261191i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.56287 | + | 14.8313i | −0.429758 | + | 0.744363i | −0.996852 | − | 0.0792903i | \(-0.974735\pi\) |
0.567093 | + | 0.823654i | \(0.308068\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −23.7691 | −1.18697 | −0.593486 | − | 0.804844i | \(-0.702249\pi\) | ||||
−0.593486 | + | 0.804844i | \(0.702249\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.853681 | 0.0425249 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.40316 | + | 7.62649i | −0.218256 | + | 0.378031i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.55946 | + | 13.0934i | −0.373791 | + | 0.647425i | −0.990145 | − | 0.140044i | \(-0.955276\pi\) |
0.616354 | + | 0.787469i | \(0.288609\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.3383 | − | 12.7488i | 0.508717 | − | 0.627326i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.58945 | − | 16.6094i | 0.470728 | − | 0.815324i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.82673 | + | 4.89604i | 0.138095 | + | 0.239187i | 0.926775 | − | 0.375616i | \(-0.122569\pi\) |
−0.788681 | + | 0.614803i | \(0.789236\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.5088 | + | 21.6658i | −0.609640 | + | 1.05593i | 0.381660 | + | 0.924303i | \(0.375353\pi\) |
−0.991300 | + | 0.131625i | \(0.957981\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.5318 | − | 19.9737i | −0.559375 | − | 0.968865i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.43370 | − | 22.0160i | −0.408135 | − | 1.06543i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.4514 | + | 18.1024i | 0.503428 | + | 0.871962i | 0.999992 | + | 0.00396247i | \(0.00126130\pi\) |
−0.496564 | + | 0.868000i | \(0.665405\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −21.2708 | −1.02221 | −0.511104 | − | 0.859519i | \(-0.670763\pi\) | ||||
−0.511104 | + | 0.859519i | \(0.670763\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −23.8866 | + | 41.3728i | −1.14265 | + | 1.97913i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.59087 | + | 14.8798i | 0.410020 | + | 0.710176i | 0.994891 | − | 0.100951i | \(-0.0321884\pi\) |
−0.584871 | + | 0.811126i | \(0.698855\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.37181 | + | 11.0363i | 0.302734 | + | 0.524350i | 0.976754 | − | 0.214363i | \(-0.0687674\pi\) |
−0.674020 | + | 0.738713i | \(0.735434\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.47919 | − | 14.6864i | 0.401952 | − | 0.696202i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −31.5913 | −1.49088 | −0.745442 | − | 0.666570i | \(-0.767762\pi\) | ||||
−0.745442 | + | 0.666570i | \(0.767762\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.5309 | − | 19.9721i | −0.542969 | − | 0.940449i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.08256 | − | 10.6574i | −0.191393 | − | 0.499628i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.65243 | + | 6.32619i | 0.170853 | + | 0.295927i | 0.938718 | − | 0.344685i | \(-0.112014\pi\) |
−0.767865 | + | 0.640612i | \(0.778681\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.3651 | − | 23.1491i | 0.622477 | − | 1.07816i | −0.366546 | − | 0.930400i | \(-0.619460\pi\) |
0.989023 | − | 0.147761i | \(-0.0472068\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.75608 | + | 3.04161i | 0.0816117 | + | 0.141356i | 0.903942 | − | 0.427654i | \(-0.140660\pi\) |
−0.822331 | + | 0.569010i | \(0.807327\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.80239 | + | 13.5141i | −0.361052 | + | 0.625360i | −0.988134 | − | 0.153593i | \(-0.950915\pi\) |
0.627083 | + | 0.778953i | \(0.284249\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.02550 | − | 6.19721i | 0.232056 | − | 0.286161i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.69501 | − | 16.7922i | 0.445777 | − | 0.772108i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 19.2287 | − | 33.3050i | 0.882272 | − | 1.52814i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.0889 | −0.780811 | −0.390405 | − | 0.920643i | \(-0.627665\pi\) | ||||
−0.390405 | + | 0.920643i | \(0.627665\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.20830 | −0.237478 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −23.7880 | + | 41.2020i | −1.08016 | + | 1.87089i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.9335 | + | 22.4014i | 0.586072 | + | 1.01511i | 0.994741 | + | 0.102423i | \(0.0326597\pi\) |
−0.408669 | + | 0.912683i | \(0.634007\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.51452 | − | 13.0155i | −0.339126 | − | 0.587383i | 0.645143 | − | 0.764062i | \(-0.276798\pi\) |
−0.984269 | + | 0.176679i | \(0.943465\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.40321 | −0.423499 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 40.1838 | + | 6.39297i | 1.80249 | + | 0.286764i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.2419 | −0.682321 | −0.341160 | − | 0.940005i | \(-0.610820\pi\) | ||||
−0.341160 | + | 0.940005i | \(0.610820\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.6284 | 0.830599 | 0.415299 | − | 0.909685i | \(-0.363677\pi\) | ||||
0.415299 | + | 0.909685i | \(0.363677\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −44.7491 | −1.99131 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.44665 | 0.330067 | 0.165034 | − | 0.986288i | \(-0.447227\pi\) | ||||
0.165034 | + | 0.986288i | \(0.447227\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.26391 | − | 21.5728i | −0.365574 | − | 0.954324i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 51.3152 | 2.26122 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.45527 | + | 12.9129i | 0.327882 | + | 0.567909i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.3853 | + | 19.7200i | 0.498800 | + | 0.863947i | 0.999999 | − | 0.00138491i | \(-0.000440830\pi\) |
−0.501199 | + | 0.865332i | \(0.667107\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.5092 | + | 28.5949i | −0.721899 | + | 1.25037i | 0.238339 | + | 0.971182i | \(0.423397\pi\) |
−0.960238 | + | 0.279184i | \(0.909936\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.80017 | 0.121977 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.8556 | 0.819808 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.81969 | − | 11.8120i | 0.295393 | − | 0.511636i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.05189 | + | 7.01808i | −0.175179 | + | 0.303418i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −15.1906 | − | 4.95894i | −0.654304 | − | 0.213597i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.53464 | − | 14.7824i | 0.366933 | − | 0.635546i | −0.622151 | − | 0.782897i | \(-0.713741\pi\) |
0.989084 | + | 0.147351i | \(0.0470745\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −25.9097 | − | 44.8769i | −1.10985 | − | 1.92232i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.3574 | + | 28.3318i | −0.699390 | + | 1.21138i | 0.269288 | + | 0.963060i | \(0.413212\pi\) |
−0.968678 | + | 0.248319i | \(0.920122\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.83968 | − | 13.5787i | −0.333981 | − | 0.578473i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.77563 | + | 4.63524i | 0.0755073 | + | 0.197110i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17.0783 | − | 29.5806i | −0.723633 | − | 1.25337i | −0.959534 | − | 0.281592i | \(-0.909138\pi\) |
0.235902 | − | 0.971777i | \(-0.424196\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.4678 | 0.485036 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.83537 | − | 8.37510i | 0.203786 | − | 0.352969i | −0.745959 | − | 0.665992i | \(-0.768009\pi\) |
0.949745 | + | 0.313023i | \(0.101342\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.15989 | + | 8.93720i | 0.217078 | + | 0.375991i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.56369 | + | 9.63659i | 0.233242 | + | 0.403987i | 0.958760 | − | 0.284216i | \(-0.0917333\pi\) |
−0.725518 | + | 0.688203i | \(0.758400\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.364653 | − | 0.631597i | 0.0152602 | − | 0.0264315i | −0.858294 | − | 0.513158i | \(-0.828476\pi\) |
0.873555 | + | 0.486726i | \(0.161809\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −33.6937 | −1.40512 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.49359 | + | 16.4434i | 0.395223 | + | 0.684547i | 0.993130 | − | 0.117019i | \(-0.0373338\pi\) |
−0.597906 | + | 0.801566i | \(0.704001\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.0033 | − | 12.3356i | 0.415008 | − | 0.511769i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.47755 | + | 9.48740i | 0.226857 | + | 0.392928i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.30535 | + | 2.26093i | −0.0538775 | + | 0.0933185i | −0.891706 | − | 0.452615i | \(-0.850491\pi\) |
0.837829 | + | 0.545933i | \(0.183825\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.33457 | + | 4.04359i | 0.0961942 | + | 0.166613i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.92622 | − | 13.7286i | 0.325491 | − | 0.563767i | −0.656121 | − | 0.754656i | \(-0.727804\pi\) |
0.981612 | + | 0.190889i | \(0.0611371\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13.3913 | − | 34.9576i | −0.548988 | − | 1.43312i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.93051 | + | 13.7360i | −0.324032 | + | 0.561239i | −0.981316 | − | 0.192403i | \(-0.938372\pi\) |
0.657284 | + | 0.753643i | \(0.271705\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.834141 | − | 1.44477i | 0.0340253 | − | 0.0589336i | −0.848511 | − | 0.529177i | \(-0.822501\pi\) |
0.882537 | + | 0.470244i | \(0.155834\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 18.4955 | 0.751949 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 36.5110 | 1.48194 | 0.740968 | − | 0.671541i | \(-0.234367\pi\) | ||||
0.740968 | + | 0.671541i | \(0.234367\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.40925 | + | 7.63705i | −0.178379 | + | 0.308962i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.2957 | + | 31.6891i | 0.738958 | + | 1.27991i | 0.952965 | + | 0.303080i | \(0.0980150\pi\) |
−0.214007 | + | 0.976832i | \(0.568652\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.10936 | + | 8.84967i | 0.205695 | + | 0.356274i | 0.950354 | − | 0.311171i | \(-0.100721\pi\) |
−0.744659 | + | 0.667445i | \(0.767388\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.7329 | 0.994098 | 0.497049 | − | 0.867723i | \(-0.334417\pi\) | ||||
0.497049 | + | 0.867723i | \(0.334417\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.84515 | − | 10.9074i | 0.354374 | − | 0.436997i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.9167 | −0.956668 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −17.0838 | −0.681177 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −42.1420 | −1.67765 | −0.838823 | − | 0.544404i | \(-0.816756\pi\) | ||||
−0.838823 | + | 0.544404i | \(0.816756\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −40.3939 | −1.60298 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.95213 | − | 9.24690i | −0.0773463 | − | 0.366375i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.33038 | 0.0920444 | 0.0460222 | − | 0.998940i | \(-0.485346\pi\) | ||||
0.0460222 | + | 0.998940i | \(0.485346\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.5035 | − | 28.5850i | −0.650836 | − | 1.12728i | −0.982920 | − | 0.184031i | \(-0.941085\pi\) |
0.332085 | − | 0.943250i | \(-0.392248\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.4187 | − | 18.0458i | −0.409603 | − | 0.709452i | 0.585243 | − | 0.810858i | \(-0.300999\pi\) |
−0.994845 | + | 0.101406i | \(0.967666\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.08101 | − | 12.2647i | 0.277954 | − | 0.481430i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 48.8352 | 1.91107 | 0.955534 | − | 0.294882i | \(-0.0952805\pi\) | ||||
0.955534 | + | 0.294882i | \(0.0952805\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −60.9241 | −2.38050 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.272662 | − | 0.472265i | 0.0106214 | − | 0.0183968i | −0.860666 | − | 0.509170i | \(-0.829952\pi\) |
0.871287 | + | 0.490773i | \(0.163286\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.2125 | − | 40.2052i | 0.902861 | − | 1.56380i | 0.0790978 | − | 0.996867i | \(-0.474796\pi\) |
0.823763 | − | 0.566934i | \(-0.191871\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 39.3160 | − | 48.4827i | 1.52461 | − | 1.88008i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.86858 | + | 11.8967i | −0.265953 | + | 0.460643i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.1709 | − | 17.6165i | −0.392642 | − | 0.680076i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.9838 | + | 29.4168i | −0.654677 | + | 1.13393i | 0.327298 | + | 0.944921i | \(0.393862\pi\) |
−0.981975 | + | 0.189013i | \(0.939471\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.6425 | + | 27.0936i | 0.601191 | + | 1.04129i | 0.992641 | + | 0.121094i | \(0.0386403\pi\) |
−0.391450 | + | 0.920199i | \(0.628026\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −24.8147 | + | 30.6003i | −0.952300 | + | 1.17433i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.289712 | + | 0.501795i | 0.0110855 | + | 0.0192007i | 0.871515 | − | 0.490369i | \(-0.163138\pi\) |
−0.860429 | + | 0.509570i | \(0.829805\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.6133 | 0.825801 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.23957 | + | 5.61111i | −0.123418 | + | 0.213766i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.10782 | + | 1.91881i | 0.0421436 | + | 0.0729948i | 0.886328 | − | 0.463058i | \(-0.153248\pi\) |
−0.844184 | + | 0.536053i | \(0.819915\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −20.9981 | − | 36.3698i | −0.796504 | − | 1.37958i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22.3694 | − | 38.7449i | 0.847300 | − | 1.46757i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.74299 | −0.179140 | −0.0895702 | − | 0.995981i | \(-0.528549\pi\) | ||||
−0.0895702 | + | 0.995981i | \(0.528549\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.2432 | − | 24.6699i | −0.537192 | − | 0.930444i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −36.5961 | − | 5.82219i | −1.37634 | − | 0.218966i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.6883 | + | 20.2446i | 0.438962 | + | 0.760304i | 0.997610 | − | 0.0691011i | \(-0.0220131\pi\) |
−0.558648 | + | 0.829405i | \(0.688680\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.04539 | − | 3.54272i | 0.0766004 | − | 0.132676i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.92348 | − | 8.52771i | −0.184128 | − | 0.318918i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.0256 | − | 22.5610i | 0.485772 | − | 0.841382i | −0.514094 | − | 0.857734i | \(-0.671872\pi\) |
0.999866 | + | 0.0163516i | \(0.00520511\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 41.9659 | + | 6.67649i | 1.56289 | + | 0.248645i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.52919 | − | 9.57684i | 0.205349 | − | 0.355675i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.79712 | + | 10.0409i | −0.215003 | + | 0.372396i | −0.953274 | − | 0.302108i | \(-0.902310\pi\) |
0.738270 | + | 0.674505i | \(0.235643\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 37.6157 | 1.39127 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −35.3487 | −1.30563 | −0.652816 | − | 0.757516i | \(-0.726413\pi\) | ||||
−0.652816 | + | 0.757516i | \(0.726413\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.44210 | − | 5.96189i | 0.126791 | − | 0.219609i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.66968 | − | 8.08812i | −0.171777 | − | 0.297526i | 0.767264 | − | 0.641331i | \(-0.221617\pi\) |
−0.939041 | + | 0.343805i | \(0.888284\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.6308 | − | 25.3412i | −0.536750 | − | 0.929679i | −0.999076 | − | 0.0429687i | \(-0.986318\pi\) |
0.462326 | − | 0.886710i | \(-0.347015\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.896240 | 0.0328357 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.22677 | + | 5.21225i | −0.154443 | + | 0.190452i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.6213 | −0.971424 | −0.485712 | − | 0.874119i | \(-0.661440\pi\) | ||||
−0.485712 | + | 0.874119i | \(0.661440\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 28.3012 | 1.02999 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −35.3183 | −1.28367 | −0.641833 | − | 0.766845i | \(-0.721826\pi\) | ||||
−0.641833 | + | 0.766845i | \(0.721826\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.5648 | −1.14422 | −0.572112 | − | 0.820175i | \(-0.693876\pi\) | ||||
−0.572112 | + | 0.820175i | \(0.693876\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.3503 | − | 40.0717i | −0.555719 | − | 1.45069i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.37580 | 0.302433 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23.8477 | − | 41.3055i | −0.859972 | − | 1.48951i | −0.871955 | − | 0.489587i | \(-0.837148\pi\) |
0.0119829 | − | 0.999928i | \(-0.496186\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20.7219 | − | 35.8914i | −0.745314 | − | 1.29092i | −0.950048 | − | 0.312105i | \(-0.898966\pi\) |
0.204733 | − | 0.978818i | \(-0.434367\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.64653 | + | 2.85188i | −0.0591452 | + | 0.102442i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 74.5995 | 2.67280 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 35.1071 | 1.25623 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.08148 | + | 5.33728i | −0.109983 | + | 0.190496i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.1589 | + | 22.7918i | −0.469063 | + | 0.812440i | −0.999375 | − | 0.0353624i | \(-0.988741\pi\) |
0.530312 | + | 0.847803i | \(0.322075\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.05700 | + | 7.98024i | 0.108694 | + | 0.283745i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.01533 | − | 10.4189i | 0.213611 | − | 0.369984i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.42109 | − | 14.5858i | −0.298290 | − | 0.516654i | 0.677455 | − | 0.735565i | \(-0.263083\pi\) |
−0.975745 | + | 0.218911i | \(0.929750\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.4629 | + | 25.0504i | −0.511659 | + | 0.886220i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.96611 | − | 17.2618i | −0.351696 | − | 0.609156i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −54.0093 | − | 8.59251i | −1.90358 | − | 0.302846i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.8734 | + | 20.5653i | 0.417445 | + | 0.723036i | 0.995682 | − | 0.0928330i | \(-0.0295923\pi\) |
−0.578237 | + | 0.815869i | \(0.696259\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.9596 | −0.771107 | −0.385553 | − | 0.922686i | \(-0.625989\pi\) | ||||
−0.385553 | + | 0.922686i | \(0.625989\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −38.9736 | + | 67.5042i | −1.36518 | + | 2.36457i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 31.3611 | + | 54.3190i | 1.09718 | + | 1.90038i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.6104 | − | 18.3777i | −0.370305 | − | 0.641387i | 0.619307 | − | 0.785149i | \(-0.287413\pi\) |
−0.989612 | + | 0.143762i | \(0.954080\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.53927 | − | 11.3264i | 0.227945 | − | 0.394812i | −0.729254 | − | 0.684243i | \(-0.760133\pi\) |
0.957199 | + | 0.289431i | \(0.0934661\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25.8079 | −0.897427 | −0.448714 | − | 0.893676i | \(-0.648118\pi\) | ||||
−0.448714 | + | 0.893676i | \(0.648118\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.21392 | − | 10.7628i | −0.215818 | − | 0.373808i | 0.737707 | − | 0.675121i | \(-0.235909\pi\) |
−0.953525 | + | 0.301313i | \(0.902575\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.40322 | − | 30.3309i | −0.221858 | − | 1.05090i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.80725 | − | 15.2546i | −0.304788 | − | 0.527908i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.492155 | − | 0.852437i | 0.0169911 | − | 0.0294294i | −0.857405 | − | 0.514643i | \(-0.827925\pi\) |
0.874396 | + | 0.485213i | \(0.161258\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.2457 | + | 21.2102i | 0.422266 | + | 0.731386i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −17.8556 | + | 30.9268i | −0.614251 | + | 1.06391i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.1257 | + | 2.40640i | 0.519727 | + | 0.0826849i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.4789 | + | 21.6141i | −0.427771 | + | 0.740921i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.66990 | + | 8.08850i | −0.159894 | + | 0.276945i | −0.934830 | − | 0.355095i | \(-0.884449\pi\) |
0.774936 | + | 0.632040i | \(0.217782\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.5798 | 0.395559 | 0.197779 | − | 0.980247i | \(-0.436627\pi\) | ||||
0.197779 | + | 0.980247i | \(0.436627\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 53.6428 | 1.83027 | 0.915134 | − | 0.403150i | \(-0.132085\pi\) | ||||
0.915134 | + | 0.403150i | \(0.132085\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.80485 | + | 8.32225i | −0.163559 | + | 0.283293i | −0.936143 | − | 0.351620i | \(-0.885631\pi\) |
0.772584 | + | 0.634913i | \(0.218964\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20.1368 | − | 34.8779i | −0.684671 | − | 1.18588i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.14137 | + | 3.70896i | 0.0726409 | + | 0.125818i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.07150 | 0.137958 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.73646 | + | 0.276259i | 0.0587031 | + | 0.00933926i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.06483 | −0.0359568 | −0.0179784 | − | 0.999838i | \(-0.505723\pi\) | ||||
−0.0179784 | + | 0.999838i | \(0.505723\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.7526 | 0.699171 | 0.349586 | − | 0.936904i | \(-0.386322\pi\) | ||||
0.349586 | + | 0.936904i | \(0.386322\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.80560 | 0.296332 | 0.148166 | − | 0.988963i | \(-0.452663\pi\) | ||||
0.148166 | + | 0.988963i | \(0.452663\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.0149 | 0.672033 | 0.336017 | − | 0.941856i | \(-0.390920\pi\) | ||||
0.336017 | + | 0.941856i | \(0.390920\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −33.0344 | − | 5.25554i | −1.10794 | − | 0.176265i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −48.2321 | −1.61403 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.3096 | − | 28.2490i | −0.545169 | − | 0.944260i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.671304 | + | 1.16273i | 0.0223892 | + | 0.0387793i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.6262 | + | 18.4051i | −0.354009 | + | 0.613162i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 51.8861 | 1.72475 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25.0615 | −0.832152 | −0.416076 | − | 0.909330i | \(-0.636595\pi\) | ||||
−0.416076 | + | 0.909330i | \(0.636595\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.86265 | − | 8.42236i | 0.161107 | − | 0.279045i | −0.774159 | − | 0.632991i | \(-0.781827\pi\) |
0.935266 | + | 0.353946i | \(0.115160\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.85154 | − | 11.8672i | 0.226753 | − | 0.392748i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −49.8241 | − | 7.92668i | −1.64534 | − | 0.261762i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23.2582 | − | 40.2844i | 0.767217 | − | 1.32886i | −0.171849 | − | 0.985123i | \(-0.554974\pi\) |
0.939066 | − | 0.343736i | \(-0.111692\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.3817 | + | 17.9815i | 0.341716 | + | 0.591870i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.0455 | − | 17.3993i | 0.330293 | − | 0.572085i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17.2340 | + | 29.8501i | 0.565429 | + | 0.979351i | 0.997010 | + | 0.0772768i | \(0.0246225\pi\) |
−0.431581 | + | 0.902074i | \(0.642044\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 38.4609 | − | 34.5342i | 1.26050 | − | 1.13181i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −16.1496 | − | 27.9719i | −0.528148 | − | 0.914779i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.1376 | 0.886547 | 0.443274 | − | 0.896386i | \(-0.353817\pi\) | ||||
0.443274 | + | 0.896386i | \(0.353817\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.01950 | + | 8.69403i | −0.163631 | + | 0.283417i | −0.936168 | − | 0.351552i | \(-0.885654\pi\) |
0.772537 | + | 0.634969i | \(0.218987\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −32.6794 | − | 56.6025i | −1.06419 | − | 1.84323i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.54883 | + | 14.8070i | 0.277800 | + | 0.481163i | 0.970838 | − | 0.239738i | \(-0.0770615\pi\) |
−0.693038 | + | 0.720901i | \(0.743728\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.89423 | − | 10.2091i | 0.191335 | − | 0.331401i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.79843 | 0.0906500 | 0.0453250 | − | 0.998972i | \(-0.485568\pi\) | ||||
0.0453250 | + | 0.998972i | \(0.485568\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.29605 | − | 10.9051i | −0.203736 | − | 0.352880i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17.6755 | + | 2.81205i | 0.570771 | + | 0.0908058i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.3001 | + | 26.5005i | 0.493551 | + | 0.854856i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.17143 | + | 15.8854i | −0.295239 | + | 0.511369i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.97799 | − | 8.62213i | −0.160081 | − | 0.277269i | 0.774816 | − | 0.632186i | \(-0.217842\pi\) |
−0.934898 | + | 0.354917i | \(0.884509\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.13634 | + | 1.96819i | −0.0364668 | + | 0.0631623i | −0.883683 | − | 0.468086i | \(-0.844944\pi\) |
0.847216 | + | 0.531249i | \(0.178277\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.4404 | − | 32.4755i | −0.398822 | − | 1.04112i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8.42330 | − | 14.5896i | 0.269485 | − | 0.466762i | −0.699244 | − | 0.714883i | \(-0.746480\pi\) |
0.968729 | + | 0.248121i | \(0.0798131\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.05828 | − | 10.4932i | 0.193623 | − | 0.335366i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21.5322 | −0.686772 | −0.343386 | − | 0.939194i | \(-0.611574\pi\) | ||||
−0.343386 | + | 0.939194i | \(0.611574\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24.5210 | −0.781303 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 27.4764 | − | 47.5905i | 0.873699 | − | 1.51329i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.8227 | + | 29.1378i | 0.534392 | + | 0.925594i | 0.999193 | + | 0.0401785i | \(0.0127927\pi\) |
−0.464801 | + | 0.885415i | \(0.653874\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.25033 | − | 12.5579i | −0.229851 | − | 0.398113i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.9881 | 0.443008 | 0.221504 | − | 0.975159i | \(-0.428903\pi\) | ||||
0.221504 | + | 0.975159i | \(0.428903\pi\) | |||||||
\(998\) | 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 | 3024.2.t.k.289.2 | 22 | ||
3.2 | odd | 2 | 1008.2.t.l.961.3 | 22 | |||
4.3 | odd | 2 | 1512.2.t.c.289.2 | 22 | |||
7.4 | even | 3 | 3024.2.q.l.2881.10 | 22 | |||
9.4 | even | 3 | 3024.2.q.l.2305.10 | 22 | |||
9.5 | odd | 6 | 1008.2.q.l.625.10 | 22 | |||
12.11 | even | 2 | 504.2.t.c.457.9 | yes | 22 | ||
21.11 | odd | 6 | 1008.2.q.l.529.10 | 22 | |||
28.11 | odd | 6 | 1512.2.q.d.1369.10 | 22 | |||
36.23 | even | 6 | 504.2.q.c.121.2 | yes | 22 | ||
36.31 | odd | 6 | 1512.2.q.d.793.10 | 22 | |||
63.4 | even | 3 | inner | 3024.2.t.k.1873.2 | 22 | ||
63.32 | odd | 6 | 1008.2.t.l.193.3 | 22 | |||
84.11 | even | 6 | 504.2.q.c.25.2 | ✓ | 22 | ||
252.67 | odd | 6 | 1512.2.t.c.361.2 | 22 | |||
252.95 | even | 6 | 504.2.t.c.193.9 | yes | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.c.25.2 | ✓ | 22 | 84.11 | even | 6 | ||
504.2.q.c.121.2 | yes | 22 | 36.23 | even | 6 | ||
504.2.t.c.193.9 | yes | 22 | 252.95 | even | 6 | ||
504.2.t.c.457.9 | yes | 22 | 12.11 | even | 2 | ||
1008.2.q.l.529.10 | 22 | 21.11 | odd | 6 | |||
1008.2.q.l.625.10 | 22 | 9.5 | odd | 6 | |||
1008.2.t.l.193.3 | 22 | 63.32 | odd | 6 | |||
1008.2.t.l.961.3 | 22 | 3.2 | odd | 2 | |||
1512.2.q.d.793.10 | 22 | 36.31 | odd | 6 | |||
1512.2.q.d.1369.10 | 22 | 28.11 | odd | 6 | |||
1512.2.t.c.289.2 | 22 | 4.3 | odd | 2 | |||
1512.2.t.c.361.2 | 22 | 252.67 | odd | 6 | |||
3024.2.q.l.2305.10 | 22 | 9.4 | even | 3 | |||
3024.2.q.l.2881.10 | 22 | 7.4 | even | 3 | |||
3024.2.t.k.289.2 | 22 | 1.1 | even | 1 | trivial | ||
3024.2.t.k.1873.2 | 22 | 63.4 | even | 3 | inner |