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 | 1873.8 | ||
Character | \(\chi\) | \(=\) | 3024.1873 |
Dual form | 3024.2.t.l.289.8 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.83657 | 0.821340 | 0.410670 | − | 0.911784i | \(-0.365295\pi\) | ||||
0.410670 | + | 0.911784i | \(0.365295\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.45061 | − | 0.997255i | −0.926243 | − | 0.376927i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.09719 | −0.933838 | −0.466919 | − | 0.884300i | \(-0.654636\pi\) | ||||
−0.466919 | + | 0.884300i | \(0.654636\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.40225 | − | 4.16081i | 0.666263 | − | 1.15400i | −0.312678 | − | 0.949859i | \(-0.601226\pi\) |
0.978941 | − | 0.204143i | \(-0.0654406\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.87185 | + | 3.24214i | −0.453990 | + | 0.786333i | −0.998629 | − | 0.0523367i | \(-0.983333\pi\) |
0.544640 | + | 0.838670i | \(0.316666\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.71408 | + | 4.70093i | 0.622654 | + | 1.07847i | 0.988990 | + | 0.147985i | \(0.0472788\pi\) |
−0.366336 | + | 0.930483i | \(0.619388\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.95829 | −1.65942 | −0.829709 | − | 0.558197i | \(-0.811493\pi\) | ||||
−0.829709 | + | 0.558197i | \(0.811493\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.62701 | −0.325401 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.325267 | + | 0.563379i | 0.0604006 | + | 0.104617i | 0.894645 | − | 0.446779i | \(-0.147429\pi\) |
−0.834244 | + | 0.551396i | \(0.814096\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.518342 | + | 0.897795i | 0.0930970 | + | 0.161249i | 0.908813 | − | 0.417204i | \(-0.136990\pi\) |
−0.815716 | + | 0.578453i | \(0.803657\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.50072 | − | 1.83153i | −0.760760 | − | 0.309585i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.873712 | + | 1.51331i | 0.143637 | + | 0.248787i | 0.928864 | − | 0.370422i | \(-0.120787\pi\) |
−0.785226 | + | 0.619209i | \(0.787453\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.52260 | + | 4.36927i | −0.393964 | + | 0.682365i | −0.992968 | − | 0.118381i | \(-0.962230\pi\) |
0.599005 | + | 0.800745i | \(0.295563\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.09645 | + | 10.5594i | 0.929699 | + | 1.61029i | 0.783824 | + | 0.620984i | \(0.213267\pi\) |
0.145876 | + | 0.989303i | \(0.453400\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.30691 | − | 3.99569i | 0.336498 | − | 0.582832i | −0.647273 | − | 0.762258i | \(-0.724091\pi\) |
0.983771 | + | 0.179426i | \(0.0574241\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.01096 | + | 4.88776i | 0.715852 | + | 0.698252i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.55082 | + | 7.88226i | −0.625104 | + | 1.08271i | 0.363417 | + | 0.931626i | \(0.381610\pi\) |
−0.988521 | + | 0.151085i | \(0.951723\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.68821 | −0.766998 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.89863 | + | 5.02058i | 0.377370 | + | 0.653624i | 0.990679 | − | 0.136219i | \(-0.0434952\pi\) |
−0.613309 | + | 0.789843i | \(0.710162\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.40623 | − | 4.16771i | 0.308086 | − | 0.533620i | −0.669858 | − | 0.742489i | \(-0.733645\pi\) |
0.977944 | + | 0.208869i | \(0.0669783\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.41190 | − | 7.64163i | 0.547228 | − | 0.947827i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.23870 | − | 12.5378i | −0.884348 | − | 1.53174i | −0.846459 | − | 0.532454i | \(-0.821270\pi\) |
−0.0378895 | − | 0.999282i | \(-0.512063\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.00714 | −0.594238 | −0.297119 | − | 0.954840i | \(-0.596026\pi\) | ||||
−0.297119 | + | 0.954840i | \(0.596026\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.81364 | + | 3.14131i | −0.212270 | + | 0.367662i | −0.952425 | − | 0.304774i | \(-0.901419\pi\) |
0.740155 | + | 0.672437i | \(0.234752\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.59000 | + | 3.08869i | 0.864961 | + | 0.351989i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.17904 | + | 12.4345i | −0.807705 | + | 1.39899i | 0.106745 | + | 0.994286i | \(0.465957\pi\) |
−0.914450 | + | 0.404699i | \(0.867376\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.83139 | + | 6.63616i | 0.420550 | + | 0.728414i | 0.995993 | − | 0.0894279i | \(-0.0285038\pi\) |
−0.575443 | + | 0.817842i | \(0.695171\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.43778 | + | 5.95441i | −0.372880 | + | 0.645847i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.76798 | + | 9.99043i | 0.611405 | + | 1.05898i | 0.991004 | + | 0.133833i | \(0.0427286\pi\) |
−0.379599 | + | 0.925151i | \(0.623938\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.0364 | + | 7.80087i | −1.05210 | + | 0.817753i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.98461 | + | 8.63360i | 0.511410 | + | 0.885788i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.04480 | − | 1.80964i | −0.106083 | − | 0.183741i | 0.808097 | − | 0.589049i | \(-0.200498\pi\) |
−0.914180 | + | 0.405308i | \(0.867164\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.4532 | 1.63716 | 0.818578 | − | 0.574395i | \(-0.194763\pi\) | ||||
0.818578 | + | 0.574395i | \(0.194763\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.74692 | 0.763327 | 0.381663 | − | 0.924301i | \(-0.375351\pi\) | ||||
0.381663 | + | 0.924301i | \(0.375351\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.74746 | + | 6.49080i | 0.362281 | + | 0.627489i | 0.988336 | − | 0.152290i | \(-0.0486647\pi\) |
−0.626055 | + | 0.779779i | \(0.715331\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.30644 | + | 7.45897i | −0.412482 | + | 0.714440i | −0.995160 | − | 0.0982628i | \(-0.968671\pi\) |
0.582678 | + | 0.812703i | \(0.302005\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.55747 | − | 2.69762i | 0.146514 | − | 0.253771i | −0.783422 | − | 0.621490i | \(-0.786528\pi\) |
0.929937 | + | 0.367719i | \(0.119861\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −14.6160 | −1.36295 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.82040 | − | 6.07850i | 0.716895 | − | 0.557215i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.40741 | −0.127946 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.1710 | −1.08860 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.8866 | −0.966033 | −0.483017 | − | 0.875611i | \(-0.660459\pi\) | ||||
−0.483017 | + | 0.875611i | \(0.660459\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.0558 | −1.40280 | −0.701401 | − | 0.712767i | \(-0.747442\pi\) | ||||
−0.701401 | + | 0.712767i | \(0.747442\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.96313 | − | 14.2268i | −0.170225 | − | 1.23362i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.4406 | −1.14831 | −0.574155 | − | 0.818747i | \(-0.694669\pi\) | ||||
−0.574155 | + | 0.818747i | \(0.694669\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.06953 | − | 7.04863i | 0.345173 | − | 0.597857i | −0.640212 | − | 0.768198i | \(-0.721154\pi\) |
0.985385 | + | 0.170341i | \(0.0544869\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.44022 | + | 12.8868i | −0.622182 | + | 1.07765i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.597376 | + | 1.03469i | 0.0496094 | + | 0.0859260i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.52958 | −0.616847 | −0.308424 | − | 0.951249i | \(-0.599801\pi\) | ||||
−0.308424 | + | 0.951249i | \(0.599801\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.67232 | 0.461607 | 0.230803 | − | 0.973000i | \(-0.425865\pi\) | ||||
0.230803 | + | 0.973000i | \(0.425865\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.951973 | + | 1.64886i | 0.0764643 | + | 0.132440i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.218381 | − | 0.378248i | −0.0174287 | − | 0.0301875i | 0.857179 | − | 0.515018i | \(-0.172215\pi\) |
−0.874608 | + | 0.484830i | \(0.838881\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 19.5026 | + | 7.93644i | 1.53702 | + | 0.625479i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.12649 | − | 15.8076i | −0.714842 | − | 1.23814i | −0.963020 | − | 0.269429i | \(-0.913165\pi\) |
0.248178 | − | 0.968714i | \(-0.420168\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.765108 | − | 1.32521i | 0.0592058 | − | 0.102548i | −0.834903 | − | 0.550397i | \(-0.814477\pi\) |
0.894109 | + | 0.447849i | \(0.147810\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.04157 | − | 8.73226i | −0.387813 | − | 0.671713i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.08474 | − | 1.87883i | 0.0824716 | − | 0.142845i | −0.821839 | − | 0.569719i | \(-0.807052\pi\) |
0.904311 | + | 0.426874i | \(0.140385\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.98716 | + | 1.62254i | 0.301401 | + | 0.122653i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.08263 | + | 1.87517i | −0.0809195 | + | 0.140157i | −0.903645 | − | 0.428282i | \(-0.859119\pi\) |
0.822726 | + | 0.568439i | \(0.192452\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.557838 | 0.0414638 | 0.0207319 | − | 0.999785i | \(-0.493400\pi\) | ||||
0.0207319 | + | 0.999785i | \(0.493400\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.60463 | + | 2.77931i | 0.117975 | + | 0.204339i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.79747 | − | 10.0415i | 0.423953 | − | 0.734308i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.9998 | − | 20.7843i | 0.868277 | − | 1.50390i | 0.00452179 | − | 0.999990i | \(-0.498561\pi\) |
0.863756 | − | 0.503911i | \(-0.168106\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.6397 | + | 18.4285i | 0.765862 | + | 1.32651i | 0.939790 | + | 0.341753i | \(0.111021\pi\) |
−0.173928 | + | 0.984758i | \(0.555646\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.8768 | 1.05993 | 0.529964 | − | 0.848020i | \(-0.322205\pi\) | ||||
0.529964 | + | 0.848020i | \(0.322205\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.17884 | + | 10.7021i | −0.438006 | + | 0.758649i | −0.997536 | − | 0.0701616i | \(-0.977649\pi\) |
0.559530 | + | 0.828810i | \(0.310982\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.235270 | − | 1.70500i | −0.0165127 | − | 0.119667i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.63293 | + | 8.02447i | −0.323578 | + | 0.560453i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.40604 | − | 14.5597i | −0.581458 | − | 1.00711i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.65802 | + | 14.9961i | −0.596043 | + | 1.03238i | 0.397356 | + | 0.917664i | \(0.369928\pi\) |
−0.993399 | + | 0.114712i | \(0.963406\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.1966 | + | 19.3930i | 0.763599 | + | 1.32259i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.374923 | − | 2.71706i | −0.0254514 | − | 0.184446i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.99328 | + | 15.5768i | 0.604953 | + | 1.04781i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.14489 | − | 1.98301i | −0.0766677 | − | 0.132792i | 0.825143 | − | 0.564925i | \(-0.191095\pi\) |
−0.901810 | + | 0.432132i | \(0.857761\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.56026 | −0.236303 | −0.118152 | − | 0.992996i | \(-0.537697\pi\) | ||||
−0.118152 | + | 0.992996i | \(0.537697\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −26.9597 | −1.78155 | −0.890775 | − | 0.454445i | \(-0.849837\pi\) | ||||
−0.890775 | + | 0.454445i | \(0.849837\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.7321 | − | 18.5885i | −0.703081 | − | 1.21777i | −0.967380 | − | 0.253332i | \(-0.918474\pi\) |
0.264298 | − | 0.964441i | \(-0.414860\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.23681 | − | 7.33837i | 0.276379 | − | 0.478703i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.65970 | − | 8.07083i | 0.301411 | − | 0.522059i | −0.675045 | − | 0.737777i | \(-0.735876\pi\) |
0.976456 | + | 0.215718i | \(0.0692091\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.2007 | −1.30124 | −0.650620 | − | 0.759404i | \(-0.725491\pi\) | ||||
−0.650620 | + | 0.759404i | \(0.725491\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.20299 | + | 8.97673i | 0.587958 | + | 0.573502i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26.0796 | 1.65940 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 27.1837 | 1.71582 | 0.857910 | − | 0.513800i | \(-0.171762\pi\) | ||||
0.857910 | + | 0.513800i | \(0.171762\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 24.6483 | 1.54963 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −28.4821 | −1.77667 | −0.888333 | − | 0.459200i | \(-0.848136\pi\) | ||||
−0.888333 | + | 0.459200i | \(0.848136\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.631966 | − | 4.57985i | −0.0392685 | − | 0.284578i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.59814 | 0.221871 | 0.110935 | − | 0.993828i | \(-0.464615\pi\) | ||||
0.110935 | + | 0.993828i | \(0.464615\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.35791 | + | 14.4763i | −0.513422 | + | 0.889274i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.2261 | + | 19.4443i | −0.684470 | + | 1.18554i | 0.289133 | + | 0.957289i | \(0.406633\pi\) |
−0.973603 | + | 0.228248i | \(0.926700\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.7935 | + | 25.6231i | 0.898642 | + | 1.55649i | 0.829231 | + | 0.558906i | \(0.188779\pi\) |
0.0694115 | + | 0.997588i | \(0.477888\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.03915 | 0.303872 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.3867 | −1.22492 | −0.612459 | − | 0.790503i | \(-0.709819\pi\) | ||||
−0.612459 | + | 0.790503i | \(0.709819\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.23968 | + | 3.87924i | 0.133608 | + | 0.231416i | 0.925065 | − | 0.379809i | \(-0.124010\pi\) |
−0.791457 | + | 0.611225i | \(0.790677\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.03840 | + | 1.79856i | 0.0617264 | + | 0.106913i | 0.895237 | − | 0.445590i | \(-0.147006\pi\) |
−0.833511 | + | 0.552503i | \(0.813673\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.5392 | − | 8.19169i | 0.622108 | − | 0.483540i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.49237 | + | 2.58486i | 0.0877865 | + | 0.152051i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.887340 | − | 1.53692i | 0.0518389 | − | 0.0897877i | −0.838942 | − | 0.544222i | \(-0.816825\pi\) |
0.890780 | + | 0.454434i | \(0.150158\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.32355 | + | 9.22066i | 0.309949 | + | 0.536847i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −19.1178 | + | 33.1129i | −1.10561 | + | 1.91497i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.40963 | − | 31.9566i | −0.254167 | − | 1.84195i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.41921 | − | 7.65429i | 0.253043 | − | 0.438283i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.6315 | −1.12043 | −0.560215 | − | 0.828347i | \(-0.689282\pi\) | ||||
−0.560215 | + | 0.828347i | \(0.689282\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.65795 | + | 11.5319i | 0.377538 | + | 0.653915i | 0.990703 | − | 0.136040i | \(-0.0434375\pi\) |
−0.613166 | + | 0.789954i | \(0.710104\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.32641 | + | 4.02945i | −0.131496 | + | 0.227758i | −0.924254 | − | 0.381779i | \(-0.875311\pi\) |
0.792757 | + | 0.609537i | \(0.208645\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.06276 | + | 3.57281i | −0.115856 | + | 0.200669i | −0.918122 | − | 0.396299i | \(-0.870295\pi\) |
0.802265 | + | 0.596967i | \(0.203628\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.00741 | − | 1.74489i | −0.0564044 | − | 0.0976953i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −20.3214 | −1.13071 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.90847 | + | 6.76967i | −0.216803 | + | 0.375514i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.63807 | + | 7.49130i | −0.531364 | + | 0.413009i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.0220297 | − | 0.0381566i | 0.00121086 | − | 0.00209727i | −0.865419 | − | 0.501048i | \(-0.832948\pi\) |
0.866630 | + | 0.498951i | \(0.166281\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −13.2944 | − | 23.0266i | −0.726350 | − | 1.25808i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.3351 | + | 23.0970i | −0.726407 | + | 1.25817i | 0.231986 | + | 0.972719i | \(0.425478\pi\) |
−0.958392 | + | 0.285454i | \(0.907856\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.60541 | − | 2.78064i | −0.0869376 | − | 0.150580i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.40556 | − | 16.9752i | −0.399863 | − | 0.916575i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.41259 | − | 9.37488i | −0.290563 | − | 0.503270i | 0.683380 | − | 0.730063i | \(-0.260509\pi\) |
−0.973943 | + | 0.226793i | \(0.927176\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.69555 | − | 4.66884i | −0.144290 | − | 0.249917i | 0.784818 | − | 0.619726i | \(-0.212756\pi\) |
−0.929108 | + | 0.369809i | \(0.879423\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.94614 | 0.476155 | 0.238078 | − | 0.971246i | \(-0.423483\pi\) | ||||
0.238078 | + | 0.971246i | \(0.423483\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.19596 | −0.488071 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.84157 | + | 3.18969i | 0.0971942 | + | 0.168345i | 0.910522 | − | 0.413460i | \(-0.135680\pi\) |
−0.813328 | + | 0.581805i | \(0.802347\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.23251 | + | 9.06297i | −0.275395 | + | 0.476998i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.33087 | + | 5.76924i | −0.174346 | + | 0.301976i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.49976 | 0.391484 | 0.195742 | − | 0.980655i | \(-0.437288\pi\) | ||||
0.195742 | + | 0.980655i | \(0.437288\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 19.0129 | − | 14.7780i | 0.987101 | − | 0.767235i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.23833 | 0.426565 | 0.213282 | − | 0.976991i | \(-0.431585\pi\) | ||||
0.213282 | + | 0.976991i | \(0.431585\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.12549 | 0.160971 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.92853 | 0.201795 | 0.100897 | − | 0.994897i | \(-0.467829\pi\) | ||||
0.100897 | + | 0.994897i | \(0.467829\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 23.9265 | 1.22259 | 0.611293 | − | 0.791404i | \(-0.290650\pi\) | ||||
0.611293 | + | 0.791404i | \(0.290650\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.9396 | + | 5.67260i | 0.710427 | + | 0.289102i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.6575 | −0.641761 | −0.320881 | − | 0.947120i | \(-0.603979\pi\) | ||||
−0.320881 | + | 0.947120i | \(0.603979\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.8967 | − | 25.8018i | 0.753359 | − | 1.30486i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.1848 | + | 22.8368i | −0.663400 | + | 1.14904i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.7703 | − | 30.7791i | −0.891866 | − | 1.54476i | −0.837636 | − | 0.546229i | \(-0.816063\pi\) |
−0.0542297 | − | 0.998528i | \(-0.517270\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.32332 | 0.165959 | 0.0829794 | − | 0.996551i | \(-0.473556\pi\) | ||||
0.0829794 | + | 0.996551i | \(0.473556\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.98074 | 0.248109 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.70605 | − | 4.68702i | −0.134134 | − | 0.232327i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.2564 | − | 19.4967i | −0.556595 | − | 0.964051i | −0.997777 | − | 0.0666338i | \(-0.978774\pi\) |
0.441182 | − | 0.897418i | \(-0.354559\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.09662 | − | 15.1942i | −0.103168 | − | 0.747656i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.03662 | + | 12.1878i | 0.345414 | + | 0.598275i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.59772 | + | 6.23144i | −0.175760 | + | 0.304426i | −0.940424 | − | 0.340004i | \(-0.889572\pi\) |
0.764664 | + | 0.644429i | \(0.222905\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.8121 | + | 29.1193i | 0.819370 | + | 1.41919i | 0.906147 | + | 0.422962i | \(0.139010\pi\) |
−0.0867773 | + | 0.996228i | \(0.527657\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.04551 | − | 5.27498i | 0.147729 | − | 0.255874i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.0530 | + | 7.81380i | −0.486498 | + | 0.378136i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.4871 | − | 28.5565i | 0.794156 | − | 1.37552i | −0.129217 | − | 0.991616i | \(-0.541246\pi\) |
0.923373 | − | 0.383903i | \(-0.125420\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.8977 | 0.956221 | 0.478110 | − | 0.878300i | \(-0.341322\pi\) | ||||
0.478110 | + | 0.878300i | \(0.341322\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −21.5995 | − | 37.4114i | −1.03324 | − | 1.78963i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.5634 | − | 25.2246i | 0.695074 | − | 1.20390i | −0.275082 | − | 0.961421i | \(-0.588705\pi\) |
0.970156 | − | 0.242482i | \(-0.0779617\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.88317 | + | 11.9220i | −0.327029 | + | 0.566431i | −0.981921 | − | 0.189292i | \(-0.939381\pi\) |
0.654892 | + | 0.755723i | \(0.272714\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.5933 | + | 18.3481i | 0.502171 | + | 0.869785i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.0958 | 0.570838 | 0.285419 | − | 0.958403i | \(-0.407867\pi\) | ||||
0.285419 | + | 0.958403i | \(0.407867\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.81297 | − | 13.5325i | 0.367898 | − | 0.637218i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −18.4325 | + | 14.3269i | −0.864128 | + | 0.671653i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.17738 | − | 7.23544i | 0.195410 | − | 0.338459i | −0.751625 | − | 0.659591i | \(-0.770730\pi\) |
0.947035 | + | 0.321131i | \(0.104063\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.1673 | − | 19.3423i | −0.520112 | − | 0.900860i | −0.999727 | − | 0.0233807i | \(-0.992557\pi\) |
0.479615 | − | 0.877479i | \(-0.340776\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.0370790 | − | 0.0642228i | 0.00172321 | − | 0.00298469i | −0.865163 | − | 0.501492i | \(-0.832785\pi\) |
0.866886 | + | 0.498507i | \(0.166118\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.5828 | + | 25.2581i | 0.674810 | + | 1.16880i | 0.976524 | + | 0.215407i | \(0.0691077\pi\) |
−0.301715 | + | 0.953398i | \(0.597559\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.23584 | + | 37.9441i | 0.241769 | + | 1.75209i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −18.8819 | − | 32.7043i | −0.868189 | − | 1.50375i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.41583 | − | 7.64845i | −0.202612 | − | 0.350935i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 27.9103 | 1.27525 | 0.637626 | − | 0.770346i | \(-0.279917\pi\) | ||||
0.637626 | + | 0.770346i | \(0.279917\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.39548 | 0.382801 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.91884 | − | 3.32353i | −0.0871301 | − | 0.150914i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.14409 | − | 3.71367i | 0.0971580 | − | 0.168283i | −0.813349 | − | 0.581776i | \(-0.802358\pi\) |
0.910507 | + | 0.413493i | \(0.135691\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.22215 | + | 9.04503i | −0.235672 | + | 0.408196i | −0.959468 | − | 0.281818i | \(-0.909063\pi\) |
0.723796 | + | 0.690015i | \(0.242396\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.43540 | −0.109685 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.2705 | + | 4.99339i | 0.550409 | + | 0.223984i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.12624 | 0.274248 | 0.137124 | − | 0.990554i | \(-0.456214\pi\) | ||||
0.137124 | + | 0.990554i | \(0.456214\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.4469 | −0.554982 | −0.277491 | − | 0.960728i | \(-0.589503\pi\) | ||||
−0.277491 | + | 0.960728i | \(0.589503\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 30.2175 | 1.34466 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.8090 | −0.523425 | −0.261712 | − | 0.965146i | \(-0.584287\pi\) | ||||
−0.261712 | + | 0.965146i | \(0.584287\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.57720 | − | 5.88946i | 0.335195 | − | 0.260534i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 14.2278 | 0.626950 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.14495 | + | 12.3754i | −0.314235 | + | 0.544271i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.54828 | + | 9.60991i | −0.243075 | + | 0.421018i | −0.961589 | − | 0.274495i | \(-0.911489\pi\) |
0.718514 | + | 0.695513i | \(0.244823\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.6209 | − | 18.3960i | −0.464421 | − | 0.804401i | 0.534754 | − | 0.845008i | \(-0.320404\pi\) |
−0.999175 | + | 0.0406065i | \(0.987071\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.88103 | −0.169060 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 40.3343 | 1.75367 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.1198 | + | 20.9921i | 0.524967 | + | 0.909269i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.88248 | + | 11.9208i | 0.297556 | + | 0.515382i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −15.5199 | − | 15.1383i | −0.668490 | − | 0.652054i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.33567 | − | 10.9737i | −0.272392 | − | 0.471796i | 0.697082 | − | 0.716991i | \(-0.254481\pi\) |
−0.969474 | + | 0.245195i | \(0.921148\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.90908 | + | 13.6989i | −0.338788 | + | 0.586798i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.4805 | + | 37.2053i | 0.918438 | + | 1.59078i | 0.801788 | + | 0.597609i | \(0.203883\pi\) |
0.116651 | + | 0.993173i | \(0.462784\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.76560 | + | 3.05812i | −0.0752173 | + | 0.130280i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 29.9933 | − | 23.3126i | 1.27545 | − | 0.991355i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16.5129 | + | 28.6012i | −0.699673 | + | 1.21187i | 0.268906 | + | 0.963166i | \(0.413338\pi\) |
−0.968580 | + | 0.248703i | \(0.919996\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 58.5807 | 2.47770 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.4066 | − | 31.8812i | −0.775746 | − | 1.34363i | −0.934374 | − | 0.356293i | \(-0.884041\pi\) |
0.158629 | − | 0.987338i | \(-0.449293\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.86040 | − | 4.95437i | 0.120338 | − | 0.208432i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 22.1786 | − | 38.4144i | 0.929774 | − | 1.61042i | 0.146075 | − | 0.989273i | \(-0.453336\pi\) |
0.783698 | − | 0.621142i | \(-0.213331\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.2936 | − | 36.8816i | −0.891110 | − | 1.54345i | −0.838546 | − | 0.544831i | \(-0.816594\pi\) |
−0.0525644 | − | 0.998618i | \(-0.516739\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.9482 | 0.539977 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.3209 | − | 28.2687i | 0.679450 | − | 1.17684i | −0.295697 | − | 0.955282i | \(-0.595552\pi\) |
0.975147 | − | 0.221559i | \(-0.0711147\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.77129 | − | 20.0835i | −0.114973 | − | 0.833205i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.0948 | − | 24.4129i | 0.583746 | − | 1.01108i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.1270 | − | 22.7366i | −0.541809 | − | 0.938441i | −0.998800 | − | 0.0489701i | \(-0.984406\pi\) |
0.456991 | − | 0.889471i | \(-0.348927\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.81365 | + | 4.87338i | −0.115934 | + | 0.200804i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.59998 | + | 4.50330i | 0.106768 | + | 0.184928i | 0.914459 | − | 0.404678i | \(-0.132616\pi\) |
−0.807691 | + | 0.589606i | \(0.799283\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14.3627 | − | 11.1636i | 0.588814 | − | 0.457663i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.1837 | − | 22.8349i | −0.538673 | − | 0.933008i | −0.998976 | − | 0.0452465i | \(-0.985593\pi\) |
0.460303 | − | 0.887762i | \(-0.347741\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.4505 | − | 26.7611i | −0.630239 | − | 1.09161i | −0.987503 | − | 0.157603i | \(-0.949623\pi\) |
0.357263 | − | 0.934004i | \(-0.383710\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.58480 | −0.105087 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.67321 | −0.311446 | −0.155723 | − | 0.987801i | \(-0.549771\pi\) | ||||
−0.155723 | + | 0.987801i | \(0.549771\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11.0836 | − | 19.1973i | −0.448393 | − | 0.776639i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.97498 | − | 13.8131i | 0.322106 | − | 0.557905i | −0.658816 | − | 0.752304i | \(-0.728942\pi\) |
0.980922 | + | 0.194399i | \(0.0622758\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.67011 | − | 6.35682i | 0.147753 | − | 0.255916i | −0.782644 | − | 0.622470i | \(-0.786129\pi\) |
0.930397 | + | 0.366554i | \(0.119463\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.5684 | −0.826713 | −0.413357 | − | 0.910569i | \(-0.635644\pi\) | ||||
−0.413357 | + | 0.910569i | \(0.635644\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.17205 | − | 30.2348i | −0.167150 | − | 1.21133i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14.2178 | −0.568713 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.54182 | −0.260840 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.09394 | 0.202787 | 0.101393 | − | 0.994846i | \(-0.467670\pi\) | ||||
0.101393 | + | 0.994846i | \(0.467670\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −19.9941 | −0.793442 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 32.3746 | − | 9.10807i | 1.28273 | − | 0.360875i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.6372 | −0.499140 | −0.249570 | − | 0.968357i | \(-0.580289\pi\) | ||||
−0.249570 | + | 0.968357i | \(0.580289\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.4329 | + | 21.5344i | −0.490306 | + | 0.849235i | −0.999938 | − | 0.0111579i | \(-0.996448\pi\) |
0.509632 | + | 0.860393i | \(0.329782\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.12339 | − | 1.94577i | 0.0441650 | − | 0.0764960i | −0.843098 | − | 0.537760i | \(-0.819271\pi\) |
0.887263 | + | 0.461264i | \(0.152604\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.97762 | − | 15.5497i | −0.352403 | − | 0.610379i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.05762 | −0.0805207 | −0.0402604 | − | 0.999189i | \(-0.512819\pi\) | ||||
−0.0402604 | + | 0.999189i | \(0.512819\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −29.4876 | −1.15218 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.16599 | − | 7.21571i | −0.162284 | − | 0.281084i | 0.773403 | − | 0.633914i | \(-0.218553\pi\) |
−0.935687 | + | 0.352830i | \(0.885219\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.0463 | − | 29.5251i | −0.663024 | − | 1.14839i | −0.979817 | − | 0.199897i | \(-0.935939\pi\) |
0.316793 | − | 0.948495i | \(-0.397394\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.60543 | − | 26.1285i | −0.139812 | − | 1.01322i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.58857 | − | 4.48353i | −0.100230 | − | 0.173603i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.45255 | + | 12.9082i | −0.287702 | + | 0.498315i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.571008 | + | 0.989016i | 0.0220108 | + | 0.0381237i | 0.876821 | − | 0.480817i | \(-0.159660\pi\) |
−0.854810 | + | 0.518941i | \(0.826327\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.1906 | − | 31.5070i | 0.699121 | − | 1.21091i | −0.269651 | − | 0.962958i | \(-0.586908\pi\) |
0.968772 | − | 0.247955i | \(-0.0797584\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.755713 | + | 5.47665i | 0.0290016 | + | 0.210174i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.11274 | − | 5.39142i | 0.119106 | − | 0.206297i | −0.800308 | − | 0.599589i | \(-0.795331\pi\) |
0.919414 | + | 0.393292i | \(0.128664\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −24.6846 | −0.943152 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 21.8644 | + | 37.8702i | 0.832967 | + | 1.44274i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.9130 | + | 34.4903i | −0.757525 | + | 1.31207i | 0.186584 | + | 0.982439i | \(0.440258\pi\) |
−0.944109 | + | 0.329633i | \(0.893075\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.47398 | − | 12.9453i | 0.283504 | − | 0.491044i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.44384 | − | 16.3572i | −0.357711 | − | 0.619573i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 48.3337 | 1.82554 | 0.912769 | − | 0.408477i | \(-0.133940\pi\) | ||||
0.912769 | + | 0.408477i | \(0.133940\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.74265 | + | 8.21452i | −0.178873 | + | 0.309816i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −40.3204 | − | 16.4081i | −1.51640 | − | 0.617088i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.04198 | − | 13.9291i | 0.302023 | − | 0.523119i | −0.674571 | − | 0.738210i | \(-0.735671\pi\) |
0.976594 | + | 0.215091i | \(0.0690048\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.12512 | − | 7.14491i | −0.154487 | − | 0.267579i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13.6645 | + | 23.6676i | −0.511023 | + | 0.885117i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 21.0734 | + | 36.5002i | 0.785906 | + | 1.36123i | 0.928456 | + | 0.371442i | \(0.121136\pi\) |
−0.142550 | + | 0.989788i | \(0.545530\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −18.9847 | − | 7.72566i | −0.707026 | − | 0.287718i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.529212 | − | 0.916622i | −0.0196544 | − | 0.0340425i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.9548 | + | 22.4384i | 0.480467 | + | 0.832192i | 0.999749 | − | 0.0224103i | \(-0.00713401\pi\) |
−0.519282 | + | 0.854603i | \(0.673801\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −45.6465 | −1.68830 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.4054 | 0.753692 | 0.376846 | − | 0.926276i | \(-0.377009\pi\) | ||||
0.376846 | + | 0.926276i | \(0.377009\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 22.4196 | + | 38.8320i | 0.825838 | + | 1.43039i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.8953 | − | 20.6033i | 0.437576 | − | 0.757903i | −0.559926 | − | 0.828542i | \(-0.689171\pi\) |
0.997502 | + | 0.0706392i | \(0.0225039\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.6320 | − | 37.4678i | 0.793603 | − | 1.37456i | −0.130120 | − | 0.991498i | \(-0.541536\pi\) |
0.923723 | − | 0.383062i | \(-0.125130\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13.8286 | −0.506641 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.71058 | − | 19.6436i | −0.0990426 | − | 0.717761i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.3693 | 0.524343 | 0.262172 | − | 0.965021i | \(-0.415561\pi\) | ||||
0.262172 | + | 0.965021i | \(0.415561\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.4176 | 0.379136 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39.7854 | 1.44603 | 0.723013 | − | 0.690835i | \(-0.242757\pi\) | ||||
0.723013 | + | 0.690835i | \(0.242757\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.3933 | 0.811756 | 0.405878 | − | 0.913927i | \(-0.366966\pi\) | ||||
0.405878 | + | 0.913927i | \(0.366966\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.9919 | − | 13.9844i | 0.651350 | − | 0.506269i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 27.8529 | 1.00571 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.45546 | + | 2.52093i | −0.0524853 | + | 0.0909071i | −0.891074 | − | 0.453857i | \(-0.850048\pi\) |
0.838589 | + | 0.544764i | \(0.183381\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.68612 | − | 11.5807i | 0.240483 | − | 0.416529i | −0.720369 | − | 0.693591i | \(-0.756028\pi\) |
0.960852 | + | 0.277062i | \(0.0893609\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.843347 | − | 1.46072i | −0.0302939 | − | 0.0524706i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −27.3862 | −0.981211 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.5081 | 0.554922 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.401073 | − | 0.694679i | −0.0143149 | − | 0.0247941i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.9264 | − | 20.6571i | −0.425130 | − | 0.736347i | 0.571302 | − | 0.820740i | \(-0.306438\pi\) |
−0.996433 | + | 0.0843925i | \(0.973105\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.50696 | + | 5.05761i | −0.231361 | + | 0.179828i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.5607 | − | 20.0237i | −0.410533 | − | 0.711063i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.10559 | − | 10.5752i | 0.216271 | − | 0.374593i | −0.737394 | − | 0.675463i | \(-0.763944\pi\) |
0.953665 | + | 0.300870i | \(0.0972772\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.63639 | + | 14.9587i | 0.305533 | + | 0.529199i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.61718 | − | 9.72923i | 0.198226 | − | 0.343337i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 35.8180 | + | 14.5758i | 1.26242 | + | 0.513731i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −26.7838 | + | 46.3910i | −0.941669 | + | 1.63102i | −0.179383 | + | 0.983779i | \(0.557410\pi\) |
−0.762287 | + | 0.647240i | \(0.775923\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.81310 | −0.0636667 | −0.0318334 | − | 0.999493i | \(-0.510135\pi\) | ||||
−0.0318334 | + | 0.999493i | \(0.510135\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.7615 | − | 29.0317i | −0.587128 | − | 1.01694i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −33.0925 | + | 57.3180i | −1.15776 | + | 2.00530i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.8371 | + | 34.3589i | −0.692321 | + | 1.19913i | 0.278755 | + | 0.960362i | \(0.410078\pi\) |
−0.971076 | + | 0.238772i | \(0.923255\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.40656 | + | 14.5606i | 0.293034 | + | 0.507550i | 0.974526 | − | 0.224276i | \(-0.0720016\pi\) |
−0.681491 | + | 0.731826i | \(0.738668\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37.2198 | 1.29426 | 0.647130 | − | 0.762379i | \(-0.275969\pi\) | ||||
0.647130 | + | 0.762379i | \(0.275969\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.4365 | + | 19.8086i | −0.397206 | + | 0.687981i | −0.993380 | − | 0.114874i | \(-0.963354\pi\) |
0.596174 | + | 0.802855i | \(0.296687\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −25.2266 | + | 7.09707i | −0.874048 | + | 0.245899i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.40518 | − | 2.43384i | 0.0486281 | − | 0.0842263i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 18.4071 | + | 31.8820i | 0.635484 | + | 1.10069i | 0.986412 | + | 0.164288i | \(0.0525326\pi\) |
−0.350929 | + | 0.936402i | \(0.614134\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.2884 | − | 24.7482i | 0.492704 | − | 0.853388i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.25921 | − | 16.0374i | −0.318527 | − | 0.551704i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.44901 | + | 1.40354i | 0.118509 | + | 0.0482264i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.95325 | − | 12.0434i | −0.238354 | − | 0.412842i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.98355 | + | 12.0959i | 0.239112 | + | 0.414155i | 0.960460 | − | 0.278419i | \(-0.0898102\pi\) |
−0.721347 | + | 0.692573i | \(0.756477\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −17.5677 | −0.600102 | −0.300051 | − | 0.953923i | \(-0.597004\pi\) | ||||
−0.300051 | + | 0.953923i | \(0.597004\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.84577 | −0.0970963 | −0.0485482 | − | 0.998821i | \(-0.515459\pi\) | ||||
−0.0485482 | + | 0.998821i | \(0.515459\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −27.7115 | − | 47.9977i | −0.943310 | − | 1.63386i | −0.759100 | − | 0.650974i | \(-0.774361\pi\) |
−0.184210 | − | 0.982887i | \(-0.558973\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.99221 | − | 3.45061i | 0.0677372 | − | 0.117324i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 22.2348 | − | 38.5119i | 0.754265 | − | 1.30643i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −69.5566 | −2.35684 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 29.8263 | + | 12.1376i | 1.00831 | + | 0.410324i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 54.8689 | 1.85279 | 0.926396 | − | 0.376552i | \(-0.122890\pi\) | ||||
0.926396 | + | 0.376552i | \(0.122890\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 51.1572 | 1.72353 | 0.861765 | − | 0.507307i | \(-0.169359\pi\) | ||||
0.861765 | + | 0.507307i | \(0.169359\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −38.6438 | −1.30047 | −0.650234 | − | 0.759734i | \(-0.725329\pi\) | ||||
−0.650234 | + | 0.759734i | \(0.725329\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.8525 | −0.599429 | −0.299714 | − | 0.954029i | \(-0.596891\pi\) | ||||
−0.299714 | + | 0.954029i | \(0.596891\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 26.6789 | + | 10.8568i | 0.894782 | + | 0.364124i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 25.0446 | 0.838087 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.98833 | + | 3.44388i | −0.0664624 | + | 0.115116i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.337199 | + | 0.584047i | −0.0112462 | + | 0.0194790i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.0369 | − | 29.5088i | −0.567581 | − | 0.983080i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.02451 | 0.0340559 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36.4663 | 1.21084 | 0.605422 | − | 0.795905i | \(-0.293004\pi\) | ||||
0.605422 | + | 0.795905i | \(0.293004\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.9847 | + | 32.8825i | 0.628993 | + | 1.08945i | 0.987754 | + | 0.156018i | \(0.0498658\pi\) |
−0.358762 | + | 0.933429i | \(0.616801\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.8666 | − | 20.5535i | −0.392726 | − | 0.680221i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 39.3465 | + | 16.0117i | 1.29934 | + | 0.528754i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.21770 | + | 2.10911i | 0.0401681 | + | 0.0695732i | 0.885411 | − | 0.464810i | \(-0.153877\pi\) |
−0.845242 | + | 0.534383i | \(0.820544\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −12.0284 | + | 20.8338i | −0.395919 | + | 0.685752i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.42153 | − | 2.46217i | −0.0467398 | − | 0.0809557i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17.7404 | + | 30.7273i | −0.582044 | + | 1.00813i | 0.413193 | + | 0.910644i | \(0.364414\pi\) |
−0.995237 | + | 0.0974863i | \(0.968920\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.37687 | + | 36.8220i | −0.307314 | + | 1.20679i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10.6475 | − | 18.4420i | 0.348209 | − | 0.603116i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30.0427 | −0.981452 | −0.490726 | − | 0.871314i | \(-0.663268\pi\) | ||||
−0.490726 | + | 0.871314i | \(0.663268\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.1250 | − | 26.1972i | −0.493060 | − | 0.854004i | 0.506908 | − | 0.862000i | \(-0.330788\pi\) |
−0.999968 | + | 0.00799565i | \(0.997455\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20.0756 | − | 34.7719i | 0.653750 | − | 1.13233i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.9944 | + | 29.4352i | −0.552245 | + | 0.956516i | 0.445868 | + | 0.895099i | \(0.352895\pi\) |
−0.998112 | + | 0.0614168i | \(0.980438\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.71360 | + | 15.0924i | 0.282855 | + | 0.489920i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.4324 | 0.694265 | 0.347132 | − | 0.937816i | \(-0.387155\pi\) | ||||
0.347132 | + | 0.937816i | \(0.387155\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.0385 | − | 38.1719i | 0.713151 | − | 1.23521i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 32.9377 | + | 13.4037i | 1.06361 | + | 0.432829i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.9626 | − | 25.9161i | 0.482666 | − | 0.836002i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 19.5406 | + | 33.8452i | 0.629033 | + | 1.08952i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.4095 | + | 21.4938i | −0.399061 | + | 0.691194i | −0.993610 | − | 0.112865i | \(-0.963997\pi\) |
0.594549 | + | 0.804059i | \(0.297331\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13.9437 | − | 24.1512i | −0.447475 | − | 0.775050i | 0.550746 | − | 0.834673i | \(-0.314343\pi\) |
−0.998221 | + | 0.0596234i | \(0.981010\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17.0021 | + | 13.2151i | −0.545062 | + | 0.423656i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13.6237 | + | 23.5969i | 0.435859 | + | 0.754930i | 0.997365 | − | 0.0725422i | \(-0.0231112\pi\) |
−0.561506 | + | 0.827473i | \(0.689778\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17.8645 | − | 30.9423i | −0.570953 | − | 0.988920i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13.8908 | −0.443047 | −0.221523 | − | 0.975155i | \(-0.571103\pi\) | ||||
−0.221523 | + | 0.975155i | \(0.571103\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27.3223 | 0.870561 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −48.5173 | − | 84.0344i | −1.54276 | − | 2.67214i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.3271 | + | 36.9397i | −0.677479 | + | 1.17343i | 0.298259 | + | 0.954485i | \(0.403594\pi\) |
−0.975738 | + | 0.218942i | \(0.929739\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −11.3479 | + | 19.6551i | −0.359752 | + | 0.623108i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 43.1810 | 1.36756 | 0.683779 | − | 0.729690i | \(-0.260335\pi\) | ||||
0.683779 | + | 0.729690i | \(0.260335\pi\) | |||||||
\(998\) | 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.l.1873.8 | 22 | ||
3.2 | odd | 2 | 1008.2.t.k.193.11 | 22 | |||
4.3 | odd | 2 | 1512.2.t.d.361.8 | 22 | |||
7.2 | even | 3 | 3024.2.q.k.2305.4 | 22 | |||
9.2 | odd | 6 | 1008.2.q.k.529.3 | 22 | |||
9.7 | even | 3 | 3024.2.q.k.2881.4 | 22 | |||
12.11 | even | 2 | 504.2.t.d.193.1 | yes | 22 | ||
21.2 | odd | 6 | 1008.2.q.k.625.3 | 22 | |||
28.23 | odd | 6 | 1512.2.q.c.793.4 | 22 | |||
36.7 | odd | 6 | 1512.2.q.c.1369.4 | 22 | |||
36.11 | even | 6 | 504.2.q.d.25.9 | ✓ | 22 | ||
63.2 | odd | 6 | 1008.2.t.k.961.11 | 22 | |||
63.16 | even | 3 | inner | 3024.2.t.l.289.8 | 22 | ||
84.23 | even | 6 | 504.2.q.d.121.9 | yes | 22 | ||
252.79 | odd | 6 | 1512.2.t.d.289.8 | 22 | |||
252.191 | even | 6 | 504.2.t.d.457.1 | yes | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.d.25.9 | ✓ | 22 | 36.11 | even | 6 | ||
504.2.q.d.121.9 | yes | 22 | 84.23 | even | 6 | ||
504.2.t.d.193.1 | yes | 22 | 12.11 | even | 2 | ||
504.2.t.d.457.1 | yes | 22 | 252.191 | even | 6 | ||
1008.2.q.k.529.3 | 22 | 9.2 | odd | 6 | |||
1008.2.q.k.625.3 | 22 | 21.2 | odd | 6 | |||
1008.2.t.k.193.11 | 22 | 3.2 | odd | 2 | |||
1008.2.t.k.961.11 | 22 | 63.2 | odd | 6 | |||
1512.2.q.c.793.4 | 22 | 28.23 | odd | 6 | |||
1512.2.q.c.1369.4 | 22 | 36.7 | odd | 6 | |||
1512.2.t.d.289.8 | 22 | 252.79 | odd | 6 | |||
1512.2.t.d.361.8 | 22 | 4.3 | odd | 2 | |||
3024.2.q.k.2305.4 | 22 | 7.2 | even | 3 | |||
3024.2.q.k.2881.4 | 22 | 9.7 | even | 3 | |||
3024.2.t.l.289.8 | 22 | 63.16 | even | 3 | inner | ||
3024.2.t.l.1873.8 | 22 | 1.1 | even | 1 | trivial |