Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,3,Mod(17,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 11]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.17");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.k (of order \(18\), degree \(6\), 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: | \(8.82836056527\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 108) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 17.4 | ||
Character | \(\chi\) | \(=\) | 324.17 |
Dual form | 324.3.k.a.305.4 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{11}{18}\right)\) |
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 | ||||||||
\(5\) | 4.32861 | + | 0.763252i | 0.865723 | + | 0.152650i | 0.588836 | − | 0.808252i | \(-0.299586\pi\) |
0.276887 | + | 0.960903i | \(0.410697\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.73772 | + | 2.29722i | −0.391103 | + | 0.328175i | −0.817043 | − | 0.576577i | \(-0.804388\pi\) |
0.425939 | + | 0.904752i | \(0.359944\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 14.4582 | − | 2.54938i | 1.31438 | − | 0.231762i | 0.527866 | − | 0.849328i | \(-0.322992\pi\) |
0.786519 | + | 0.617566i | \(0.211881\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.67778 | + | 1.33860i | −0.282906 | + | 0.102969i | −0.479576 | − | 0.877500i | \(-0.659209\pi\) |
0.196670 | + | 0.980470i | \(0.436987\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.96626 | + | 3.44462i | 0.350956 | + | 0.202625i | 0.665106 | − | 0.746749i | \(-0.268386\pi\) |
−0.314150 | + | 0.949373i | \(0.601720\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 14.1412 | + | 24.4932i | 0.744272 | + | 1.28912i | 0.950534 | + | 0.310620i | \(0.100537\pi\) |
−0.206263 | + | 0.978497i | \(0.566130\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.832583 | + | 0.992234i | −0.0361993 | + | 0.0431406i | −0.783840 | − | 0.620962i | \(-0.786742\pi\) |
0.747641 | + | 0.664103i | \(0.231186\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.33796 | − | 1.94286i | −0.213519 | − | 0.0777144i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 12.9959 | − | 35.7059i | 0.448134 | − | 1.23124i | −0.485887 | − | 0.874021i | \(-0.661504\pi\) |
0.934021 | − | 0.357217i | \(-0.116274\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 41.7175 | + | 35.0052i | 1.34573 | + | 1.12920i | 0.980115 | + | 0.198431i | \(0.0635846\pi\) |
0.365612 | + | 0.930767i | \(0.380860\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −13.6039 | + | 7.85422i | −0.388683 | + | 0.224406i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 18.5334 | − | 32.1007i | 0.500902 | − | 0.867588i | −0.499097 | − | 0.866546i | \(-0.666335\pi\) |
0.999999 | − | 0.00104187i | \(-0.000331638\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 14.0768 | + | 38.6757i | 0.343336 | + | 0.943309i | 0.984419 | + | 0.175837i | \(0.0562632\pi\) |
−0.641083 | + | 0.767472i | \(0.721515\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.615899 | − | 3.49294i | −0.0143232 | − | 0.0812311i | 0.976808 | − | 0.214116i | \(-0.0686870\pi\) |
−0.991131 | + | 0.132885i | \(0.957576\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 27.5222 | + | 32.7997i | 0.585578 | + | 0.697865i | 0.974750 | − | 0.223300i | \(-0.0716830\pi\) |
−0.389171 | + | 0.921165i | \(0.627239\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.29086 | + | 35.6773i | −0.128385 | + | 0.728107i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 47.8007i | − | 0.901900i | −0.892549 | − | 0.450950i | \(-0.851085\pi\) | ||
0.892549 | − | 0.450950i | \(-0.148915\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 64.5299 | 1.17327 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 61.1091 | + | 10.7752i | 1.03575 | + | 0.182630i | 0.665574 | − | 0.746332i | \(-0.268187\pi\) |
0.370174 | + | 0.928962i | \(0.379298\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.50896 | + | 7.13987i | −0.139491 | + | 0.117047i | −0.709863 | − | 0.704339i | \(-0.751243\pi\) |
0.570372 | + | 0.821386i | \(0.306799\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −16.9414 | + | 2.98722i | −0.260636 | + | 0.0459572i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −105.153 | + | 38.2727i | −1.56945 | + | 0.571235i | −0.972877 | − | 0.231321i | \(-0.925695\pi\) |
−0.596577 | + | 0.802556i | \(0.703473\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −90.9885 | − | 52.5322i | −1.28153 | − | 0.739890i | −0.304400 | − | 0.952544i | \(-0.598456\pi\) |
−0.977128 | + | 0.212654i | \(0.931789\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −48.5118 | − | 84.0248i | −0.664545 | − | 1.15102i | −0.979409 | − | 0.201888i | \(-0.935292\pi\) |
0.314864 | − | 0.949137i | \(-0.398041\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −33.7262 | + | 40.1933i | −0.438002 | + | 0.521991i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −104.299 | − | 37.9616i | −1.32024 | − | 0.480527i | −0.416702 | − | 0.909043i | \(-0.636814\pi\) |
−0.903534 | + | 0.428516i | \(0.859037\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 44.8984 | − | 123.357i | 0.540945 | − | 1.48623i | −0.304679 | − | 0.952455i | \(-0.598549\pi\) |
0.845624 | − | 0.533779i | \(-0.179229\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 23.1965 | + | 19.4642i | 0.272900 | + | 0.228990i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −87.8638 | + | 50.7282i | −0.987233 | + | 0.569979i | −0.904446 | − | 0.426588i | \(-0.859715\pi\) |
−0.0827871 | + | 0.996567i | \(0.526382\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.99367 | − | 12.1134i | 0.0768535 | − | 0.133114i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 42.5172 | + | 116.815i | 0.447549 | + | 1.22963i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −28.7527 | − | 163.065i | −0.296420 | − | 1.68108i | −0.661376 | − | 0.750055i | \(-0.730027\pi\) |
0.364956 | − | 0.931025i | \(-0.381084\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.2076 | − | 16.9319i | −0.140669 | − | 0.167643i | 0.691110 | − | 0.722749i | \(-0.257122\pi\) |
−0.831779 | + | 0.555107i | \(0.812677\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.91300 | + | 27.8630i | −0.0476991 | + | 0.270515i | −0.999325 | − | 0.0367451i | \(-0.988301\pi\) |
0.951626 | + | 0.307260i | \(0.0994121\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 67.0830i | 0.626944i | 0.949597 | + | 0.313472i | \(0.101492\pi\) | ||||
−0.949597 | + | 0.313472i | \(0.898508\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 82.0479 | 0.752733 | 0.376367 | − | 0.926471i | \(-0.377173\pi\) | ||||
0.376367 | + | 0.926471i | \(0.377173\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −139.573 | − | 24.6104i | −1.23516 | − | 0.217791i | −0.482317 | − | 0.875997i | \(-0.660205\pi\) |
−0.752839 | + | 0.658205i | \(0.771316\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.36126 | + | 3.65953i | −0.0379240 | + | 0.0318220i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −24.2470 | + | 4.27540i | −0.203757 | + | 0.0359278i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 88.8384 | − | 32.3345i | 0.734202 | − | 0.267228i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −116.786 | − | 67.4265i | −0.934289 | − | 0.539412i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 36.1258 | + | 62.5718i | 0.284455 | + | 0.492691i | 0.972477 | − | 0.232999i | \(-0.0748539\pi\) |
−0.688022 | + | 0.725690i | \(0.741521\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −80.4893 | + | 95.9234i | −0.614422 | + | 0.732239i | −0.980101 | − | 0.198502i | \(-0.936392\pi\) |
0.365679 | + | 0.930741i | \(0.380837\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −94.9809 | − | 34.5702i | −0.714142 | − | 0.259927i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 44.4879 | − | 122.229i | 0.324729 | − | 0.892186i | −0.664693 | − | 0.747117i | \(-0.731437\pi\) |
0.989422 | − | 0.145069i | \(-0.0463403\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −64.7192 | − | 54.3058i | −0.465606 | − | 0.390689i | 0.379583 | − | 0.925158i | \(-0.376067\pi\) |
−0.845189 | + | 0.534468i | \(0.820512\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −49.7615 | + | 28.7298i | −0.347983 | + | 0.200908i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 83.5068 | − | 144.638i | 0.575909 | − | 0.997503i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −48.8305 | − | 134.161i | −0.327722 | − | 0.900408i | −0.988687 | − | 0.149992i | \(-0.952075\pi\) |
0.660966 | − | 0.750416i | \(-0.270147\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.41354 | + | 42.0443i | 0.0490963 | + | 0.278439i | 0.999466 | − | 0.0326849i | \(-0.0104058\pi\) |
−0.950369 | + | 0.311124i | \(0.899295\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 153.861 | + | 183.365i | 0.992654 | + | 1.18300i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.8042 | + | 66.9447i | −0.0751857 | + | 0.426399i | 0.923860 | + | 0.382730i | \(0.125016\pi\) |
−0.999046 | + | 0.0436696i | \(0.986095\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 4.62909i | − | 0.0287521i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −52.2555 | −0.320586 | −0.160293 | − | 0.987069i | \(-0.551244\pi\) | ||||
−0.160293 | + | 0.987069i | \(0.551244\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 205.761 | + | 36.2813i | 1.23210 | + | 0.217253i | 0.751529 | − | 0.659700i | \(-0.229317\pi\) |
0.480575 | + | 0.876953i | \(0.340428\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −117.727 | + | 98.7850i | −0.696611 | + | 0.584526i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −285.514 | + | 50.3439i | −1.65037 | + | 0.291005i | −0.919963 | − | 0.392005i | \(-0.871782\pi\) |
−0.730409 | + | 0.683010i | \(0.760671\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 19.0771 | − | 6.94348i | 0.109012 | − | 0.0396770i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 84.3915 | + | 48.7235i | 0.471461 | + | 0.272198i | 0.716851 | − | 0.697226i | \(-0.245583\pi\) |
−0.245390 | + | 0.969424i | \(0.578916\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.6602 | + | 32.3205i | 0.103095 | + | 0.178566i | 0.912958 | − | 0.408053i | \(-0.133792\pi\) |
−0.809863 | + | 0.586619i | \(0.800459\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 104.725 | − | 124.806i | 0.566080 | − | 0.674628i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 95.0432 | + | 34.5929i | 0.508252 | + | 0.184989i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 119.816 | − | 329.191i | 0.627307 | − | 1.72351i | −0.0610446 | − | 0.998135i | \(-0.519443\pi\) |
0.688352 | − | 0.725377i | \(-0.258335\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.46714 | + | 7.10477i | 0.0438712 | + | 0.0368123i | 0.664460 | − | 0.747324i | \(-0.268662\pi\) |
−0.620588 | + | 0.784136i | \(0.713106\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 275.483 | − | 159.050i | 1.39839 | − | 0.807362i | 0.404167 | − | 0.914685i | \(-0.367561\pi\) |
0.994224 | + | 0.107323i | \(0.0342280\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −88.3486 | + | 153.024i | −0.443963 | + | 0.768966i | −0.997979 | − | 0.0635397i | \(-0.979761\pi\) |
0.554017 | + | 0.832506i | \(0.313094\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 46.4453 | + | 127.607i | 0.228794 | + | 0.628608i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 31.4137 | + | 178.156i | 0.153238 | + | 0.869054i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 266.899 | + | 318.077i | 1.27703 | + | 1.52190i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −36.0058 | + | 204.199i | −0.170644 | + | 0.967768i | 0.772409 | + | 0.635125i | \(0.219051\pi\) |
−0.943053 | + | 0.332643i | \(0.892060\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 15.5897i | − | 0.0725100i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −194.626 | −0.896893 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −26.5535 | − | 4.68210i | −0.120152 | − | 0.0211860i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 316.844 | − | 265.863i | 1.42082 | − | 1.19221i | 0.469926 | − | 0.882706i | \(-0.344281\pi\) |
0.950897 | − | 0.309506i | \(-0.100164\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −94.9127 | + | 16.7357i | −0.418117 | + | 0.0737254i | −0.378749 | − | 0.925499i | \(-0.623646\pi\) |
−0.0393683 | + | 0.999225i | \(0.512535\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 189.133 | − | 68.8386i | 0.825906 | − | 0.300605i | 0.105729 | − | 0.994395i | \(-0.466283\pi\) |
0.720178 | + | 0.693790i | \(0.244060\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 303.285 | + | 175.101i | 1.30165 | + | 0.751508i | 0.980687 | − | 0.195583i | \(-0.0626600\pi\) |
0.320964 | + | 0.947092i | \(0.395993\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 94.0985 | + | 162.983i | 0.400419 | + | 0.693547i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 100.663 | − | 119.965i | 0.421183 | − | 0.501947i | −0.513174 | − | 0.858285i | \(-0.671530\pi\) |
0.934357 | + | 0.356338i | \(0.115975\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 324.419 | + | 118.079i | 1.34614 | + | 0.489954i | 0.911740 | − | 0.410768i | \(-0.134739\pi\) |
0.434397 | + | 0.900721i | \(0.356961\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −54.4614 | + | 149.632i | −0.222292 | + | 0.610741i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −84.7946 | − | 71.1512i | −0.343298 | − | 0.288061i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.8819 | + | 13.2109i | −0.0911628 | + | 0.0526329i | −0.544888 | − | 0.838509i | \(-0.683428\pi\) |
0.453726 | + | 0.891141i | \(0.350095\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.50810 | + | 16.4685i | −0.0375814 | + | 0.0650930i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −40.6520 | − | 111.691i | −0.158179 | − | 0.434593i | 0.835134 | − | 0.550047i | \(-0.185390\pi\) |
−0.993313 | + | 0.115453i | \(0.963168\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 23.0033 | + | 130.458i | 0.0888159 | + | 0.503700i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −110.151 | − | 131.272i | −0.418823 | − | 0.499134i | 0.514840 | − | 0.857286i | \(-0.327851\pi\) |
−0.933663 | + | 0.358152i | \(0.883407\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 36.4840 | − | 206.911i | 0.137675 | − | 0.780796i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 147.131i | − | 0.546957i | −0.961878 | − | 0.273478i | \(-0.911826\pi\) | ||
0.961878 | − | 0.273478i | \(-0.0881742\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 42.2256 | 0.155814 | 0.0779071 | − | 0.996961i | \(-0.475176\pi\) | ||||
0.0779071 | + | 0.996961i | \(0.475176\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −82.1306 | − | 14.4818i | −0.298657 | − | 0.0526612i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −241.990 | + | 203.054i | −0.873611 | + | 0.733046i | −0.964855 | − | 0.262782i | \(-0.915360\pi\) |
0.0912446 | + | 0.995829i | \(0.470916\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −425.296 | + | 74.9912i | −1.51351 | + | 0.266872i | −0.867878 | − | 0.496777i | \(-0.834517\pi\) |
−0.645631 | + | 0.763650i | \(0.723406\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −51.4917 | + | 18.7414i | −0.181949 | + | 0.0662242i | −0.431388 | − | 0.902166i | \(-0.641976\pi\) |
0.249439 | + | 0.968391i | \(0.419754\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −127.385 | − | 73.5457i | −0.443850 | − | 0.256257i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −120.769 | − | 209.178i | −0.417886 | − | 0.723801i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 90.3507 | − | 107.676i | 0.308364 | − | 0.367494i | −0.589499 | − | 0.807769i | \(-0.700675\pi\) |
0.897863 | + | 0.440275i | \(0.145119\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 256.294 | + | 93.2833i | 0.868792 | + | 0.316214i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.73385 | − | 4.76371i | 0.00579883 | − | 0.0159321i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.71021 | + | 8.14784i | 0.0322598 | + | 0.0270692i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −42.2815 | + | 24.4113i | −0.138628 | + | 0.0800369i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −213.941 | + | 370.556i | −0.696876 | + | 1.20702i | 0.272669 | + | 0.962108i | \(0.412094\pi\) |
−0.969544 | + | 0.244916i | \(0.921240\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −142.432 | − | 391.327i | −0.457979 | − | 1.25829i | −0.926987 | − | 0.375094i | \(-0.877611\pi\) |
0.469008 | − | 0.883194i | \(-0.344612\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.1171 | + | 142.446i | 0.0802462 | + | 0.455099i | 0.998282 | + | 0.0586003i | \(0.0186638\pi\) |
−0.918035 | + | 0.396499i | \(0.870225\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 348.939 | + | 415.849i | 1.10075 | + | 1.31183i | 0.946106 | + | 0.323858i | \(0.104980\pi\) |
0.154648 | + | 0.987970i | \(0.450576\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 96.8698 | − | 549.376i | 0.303667 | − | 1.72218i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 194.844i | 0.603231i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 22.2325 | 0.0684078 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −150.696 | − | 26.5718i | −0.458043 | − | 0.0807654i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 169.745 | − | 142.433i | 0.512825 | − | 0.430311i | −0.349297 | − | 0.937012i | \(-0.613580\pi\) |
0.862122 | + | 0.506701i | \(0.169135\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −484.380 | + | 85.4093i | −1.44591 | + | 0.254953i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 36.2922 | − | 13.2093i | 0.107692 | − | 0.0391967i | −0.287612 | − | 0.957747i | \(-0.592861\pi\) |
0.395304 | + | 0.918550i | \(0.370639\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 692.403 | + | 399.759i | 2.03051 | + | 1.17231i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −152.295 | − | 263.783i | −0.444009 | − | 0.769046i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −134.499 | + | 160.290i | −0.387607 | + | 0.461932i | −0.924200 | − | 0.381910i | \(-0.875267\pi\) |
0.536593 | + | 0.843841i | \(0.319711\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −262.851 | − | 95.6701i | −0.753156 | − | 0.274126i | −0.0632228 | − | 0.997999i | \(-0.520138\pi\) |
−0.689933 | + | 0.723873i | \(0.742360\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.7312 | − | 78.9384i | 0.0813916 | − | 0.223622i | −0.892321 | − | 0.451401i | \(-0.850924\pi\) |
0.973713 | + | 0.227780i | \(0.0731466\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −353.759 | − | 296.839i | −0.996503 | − | 0.836166i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 221.262 | − | 127.746i | 0.616330 | − | 0.355838i | −0.159109 | − | 0.987261i | \(-0.550862\pi\) |
0.775439 | + | 0.631423i | \(0.217529\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −219.445 | + | 380.090i | −0.607880 | + | 1.05288i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −145.857 | − | 400.738i | −0.399607 | − | 1.09791i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −44.7221 | − | 253.632i | −0.121859 | − | 0.691095i | −0.983124 | − | 0.182940i | \(-0.941439\pi\) |
0.861265 | − | 0.508155i | \(-0.169672\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 109.809 | + | 130.865i | 0.295981 | + | 0.352736i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 83.5846 | − | 474.032i | 0.224087 | − | 1.27086i | −0.640335 | − | 0.768096i | \(-0.721204\pi\) |
0.864422 | − | 0.502767i | \(-0.167684\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 148.715i | 0.394469i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −370.571 | −0.977759 | −0.488880 | − | 0.872351i | \(-0.662594\pi\) | ||||
−0.488880 | + | 0.872351i | \(0.662594\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −481.807 | − | 84.9556i | −1.25798 | − | 0.221816i | −0.495375 | − | 0.868679i | \(-0.664969\pi\) |
−0.762606 | + | 0.646863i | \(0.776081\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −176.665 | + | 148.240i | −0.458870 | + | 0.385038i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −309.685 | + | 54.6057i | −0.796104 | + | 0.140375i | −0.556884 | − | 0.830591i | \(-0.688003\pi\) |
−0.239221 | + | 0.970965i | \(0.576892\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.38528 | + | 3.05199i | −0.0214457 | + | 0.00780560i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −422.495 | − | 243.927i | −1.06961 | − | 0.617538i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −44.8022 | − | 77.5996i | −0.112852 | − | 0.195465i | 0.804067 | − | 0.594538i | \(-0.202665\pi\) |
−0.916919 | + | 0.399073i | \(0.869332\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 55.2456 | − | 65.8392i | 0.137770 | − | 0.164187i | −0.692748 | − | 0.721180i | \(-0.743600\pi\) |
0.830518 | + | 0.556992i | \(0.188045\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −200.286 | − | 72.8980i | −0.496987 | − | 0.180888i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 186.123 | − | 511.369i | 0.457305 | − | 1.25643i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 479.987 | + | 402.757i | 1.17356 | + | 0.984736i | 1.00000 | 8.63705e-5i | \(-2.74926e-5\pi\) | |
0.173563 | + | 0.984823i | \(0.444472\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −192.053 | + | 110.882i | −0.465019 | + | 0.268479i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 288.501 | − | 499.698i | 0.695183 | − | 1.20409i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 120.491 | + | 331.047i | 0.287569 | + | 0.790089i | 0.996405 | + | 0.0847157i | \(0.0269982\pi\) |
−0.708836 | + | 0.705373i | \(0.750780\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.8471 | + | 152.258i | 0.0637699 | + | 0.361657i | 0.999949 | + | 0.0101329i | \(0.00322545\pi\) |
−0.936179 | + | 0.351524i | \(0.885663\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −25.1553 | − | 29.9789i | −0.0591888 | − | 0.0705385i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.89332 | − | 39.0940i | 0.0161436 | − | 0.0915549i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 226.253i | 0.524949i | 0.964939 | + | 0.262474i | \(0.0845386\pi\) | ||||
−0.964939 | + | 0.262474i | \(0.915461\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −648.539 | −1.49778 | −0.748890 | − | 0.662695i | \(-0.769413\pi\) | ||||
−0.748890 | + | 0.662695i | \(0.769413\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −36.0767 | − | 6.36129i | −0.0825553 | − | 0.0145567i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 231.313 | − | 194.095i | 0.526909 | − | 0.442129i | −0.340123 | − | 0.940381i | \(-0.610469\pi\) |
0.867032 | + | 0.498252i | \(0.166024\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −458.869 | + | 80.9110i | −1.03582 | + | 0.182643i | −0.665606 | − | 0.746303i | \(-0.731827\pi\) |
−0.370215 | + | 0.928946i | \(0.620716\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −419.047 | + | 152.521i | −0.941678 | + | 0.342743i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −35.8903 | − | 20.7213i | −0.0799339 | − | 0.0461498i | 0.459500 | − | 0.888178i | \(-0.348029\pi\) |
−0.539434 | + | 0.842028i | \(0.681362\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 302.124 | + | 523.295i | 0.669899 | + | 1.16030i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 39.5185 | − | 47.0963i | 0.0868538 | − | 0.103508i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 405.966 | + | 147.760i | 0.888329 | + | 0.323325i | 0.745566 | − | 0.666432i | \(-0.232179\pi\) |
0.142763 | + | 0.989757i | \(0.454401\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −224.994 | + | 618.167i | −0.488057 | + | 1.34093i | 0.414380 | + | 0.910104i | \(0.363998\pi\) |
−0.902437 | + | 0.430822i | \(0.858224\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −415.550 | − | 348.688i | −0.897516 | − | 0.753105i | 0.0721872 | − | 0.997391i | \(-0.477002\pi\) |
−0.969703 | + | 0.244286i | \(0.921447\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 71.4291 | − | 41.2396i | 0.152953 | − | 0.0883075i | −0.421570 | − | 0.906796i | \(-0.638521\pi\) |
0.574523 | + | 0.818488i | \(0.305188\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 199.960 | − | 346.341i | 0.426354 | − | 0.738467i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −17.8096 | − | 48.9315i | −0.0376525 | − | 0.103449i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −27.8981 | − | 158.218i | −0.0587329 | − | 0.333091i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −54.1626 | − | 64.5485i | −0.113074 | − | 0.134757i | 0.706538 | − | 0.707675i | \(-0.250256\pi\) |
−0.819613 | + | 0.572918i | \(0.805811\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −25.1915 | + | 142.868i | −0.0523732 | + | 0.297023i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 727.790i | − | 1.50060i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 566.361 | 1.16296 | 0.581479 | − | 0.813561i | \(-0.302474\pi\) | ||||
0.581479 | + | 0.813561i | \(0.302474\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 754.890 | + | 133.107i | 1.53745 | + | 0.271095i | 0.877266 | − | 0.480005i | \(-0.159365\pi\) |
0.660188 | + | 0.751100i | \(0.270476\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 200.530 | − | 168.265i | 0.406755 | − | 0.341308i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 369.779 | − | 65.2021i | 0.744023 | − | 0.131191i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −207.387 | + | 75.4828i | −0.415606 | + | 0.151268i | −0.541355 | − | 0.840794i | \(-0.682089\pi\) |
0.125750 | + | 0.992062i | \(0.459866\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −783.399 | − | 452.296i | −1.55745 | − | 0.899196i | −0.997500 | − | 0.0706721i | \(-0.977486\pi\) |
−0.559954 | − | 0.828524i | \(-0.689181\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −48.5757 | − | 84.1357i | −0.0961896 | − | 0.166605i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −220.212 | + | 262.439i | −0.432637 | + | 0.515596i | −0.937681 | − | 0.347497i | \(-0.887032\pi\) |
0.505044 | + | 0.863093i | \(0.331476\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 325.835 | + | 118.594i | 0.637643 | + | 0.232083i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −42.5330 | + | 116.858i | −0.0825884 | + | 0.226910i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 481.541 | + | 404.061i | 0.931414 | + | 0.781549i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 120.568 | − | 69.6099i | 0.231416 | − | 0.133608i | −0.379809 | − | 0.925065i | \(-0.624010\pi\) |
0.611225 | + | 0.791457i | \(0.290677\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.3821 | + | 21.4464i | −0.0236751 | + | 0.0410065i | −0.877620 | − | 0.479357i | \(-0.840870\pi\) |
0.853945 | + | 0.520363i | \(0.174203\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 128.318 | + | 352.551i | 0.243488 | + | 0.668977i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 91.5686 | + | 519.311i | 0.173097 | + | 0.981684i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −103.543 | − | 123.397i | −0.194264 | − | 0.231514i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −51.2012 | + | 290.376i | −0.0957032 | + | 0.542760i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 531.868i | 0.986768i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 476.086 | 0.880011 | 0.440006 | − | 0.897995i | \(-0.354976\pi\) | ||||
0.440006 | + | 0.897995i | \(0.354976\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 355.154 | + | 62.6232i | 0.651658 | + | 0.114905i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −225.822 | + | 189.487i | −0.412836 | + | 0.346411i | −0.825430 | − | 0.564504i | \(-0.809067\pi\) |
0.412594 | + | 0.910915i | \(0.364623\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1058.33 | − | 186.612i | 1.92074 | − | 0.338679i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 372.747 | − | 135.669i | 0.674046 | − | 0.245333i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 756.664 | + | 436.860i | 1.35846 | + | 0.784309i | 0.989417 | − | 0.145101i | \(-0.0463509\pi\) |
0.369047 | + | 0.929411i | \(0.379684\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.94078 | + | 12.0218i | 0.0124164 | + | 0.0215059i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 327.795 | − | 390.651i | 0.582230 | − | 0.693874i | −0.391863 | − | 0.920024i | \(-0.628169\pi\) |
0.974093 | + | 0.226149i | \(0.0726137\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −585.372 | − | 213.058i | −1.03606 | − | 0.377094i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 303.435 | − | 833.680i | 0.533277 | − | 1.46517i | −0.321871 | − | 0.946784i | \(-0.604312\pi\) |
0.855148 | − | 0.518384i | \(-0.173466\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 403.162 | + | 338.293i | 0.706063 | + | 0.592457i | 0.923491 | − | 0.383619i | \(-0.125323\pi\) |
−0.217429 | + | 0.976076i | \(0.569767\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.37207 | − | 3.67892i | 0.0110819 | − | 0.00639812i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 68.5779 | − | 118.780i | 0.118853 | − | 0.205859i | −0.800461 | − | 0.599385i | \(-0.795412\pi\) |
0.919313 | + | 0.393527i | \(0.128745\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 160.460 | + | 440.860i | 0.276179 | + | 0.758796i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −121.862 | − | 691.114i | −0.209026 | − | 1.18544i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 115.043 | + | 137.103i | 0.195985 | + | 0.233566i | 0.855083 | − | 0.518491i | \(-0.173506\pi\) |
−0.659098 | + | 0.752057i | \(0.729062\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −267.454 | + | 1516.81i | −0.454082 | + | 2.57523i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 52.0285i | − | 0.0877377i | −0.999037 | − | 0.0438689i | \(-0.986032\pi\) | ||
0.999037 | − | 0.0438689i | \(-0.0139684\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −108.219 | −0.181881 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −114.494 | − | 20.1884i | −0.191142 | − | 0.0337035i | 0.0772575 | − | 0.997011i | \(-0.475384\pi\) |
−0.268400 | + | 0.963308i | \(0.586495\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −402.677 | + | 337.886i | −0.670011 | + | 0.562206i | −0.913069 | − | 0.407806i | \(-0.866294\pi\) |
0.243057 | + | 0.970012i | \(0.421850\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 409.227 | − | 72.1577i | 0.676408 | − | 0.119269i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 80.4769 | − | 29.2912i | 0.132581 | − | 0.0482557i | −0.274877 | − | 0.961479i | \(-0.588637\pi\) |
0.407459 | + | 0.913224i | \(0.366415\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −145.126 | − | 83.7886i | −0.237522 | − | 0.137134i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 81.6463 | + | 141.416i | 0.133191 | + | 0.230694i | 0.924905 | − | 0.380198i | \(-0.124144\pi\) |
−0.791714 | + | 0.610892i | \(0.790811\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −179.054 | + | 213.388i | −0.290200 | + | 0.345847i | −0.891372 | − | 0.453273i | \(-0.850256\pi\) |
0.601171 | + | 0.799120i | \(0.294701\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −669.731 | − | 243.762i | −1.08196 | − | 0.393800i | −0.261321 | − | 0.965252i | \(-0.584158\pi\) |
−0.820636 | + | 0.571452i | \(0.806380\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 124.013 | − | 340.722i | 0.199057 | − | 0.546906i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −345.270 | − | 289.716i | −0.552432 | − | 0.463545i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 221.150 | − | 127.681i | 0.351590 | − | 0.202990i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −311.029 | + | 538.718i | −0.492914 | + | 0.853753i | −0.999967 | − | 0.00816241i | \(-0.997402\pi\) |
0.507052 | + | 0.861915i | \(0.330735\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 108.617 | + | 298.422i | 0.171050 | + | 0.469956i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −24.6212 | − | 139.634i | −0.0386518 | − | 0.219206i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −163.405 | − | 194.738i | −0.254921 | − | 0.303804i | 0.623372 | − | 0.781925i | \(-0.285762\pi\) |
−0.878294 | + | 0.478122i | \(0.841318\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36.8378 | − | 208.917i | 0.0572905 | − | 0.324910i | −0.942671 | − | 0.333724i | \(-0.891695\pi\) |
0.999961 | + | 0.00881399i | \(0.00280562\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 330.267i | − | 0.510459i | −0.966880 | − | 0.255230i | \(-0.917849\pi\) | ||
0.966880 | − | 0.255230i | \(-0.0821511\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 911.000 | 1.40370 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −329.228 | − | 58.0518i | −0.504178 | − | 0.0889002i | −0.0842262 | − | 0.996447i | \(-0.526842\pi\) |
−0.419952 | + | 0.907546i | \(0.637953\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −421.621 | + | 353.782i | −0.643696 | + | 0.540125i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1021.20 | − | 180.064i | 1.54962 | − | 0.273239i | 0.667622 | − | 0.744501i | \(-0.267312\pi\) |
0.881993 | + | 0.471262i | \(0.156201\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 397.057 | − | 144.517i | 0.600692 | − | 0.218634i | −0.0237335 | − | 0.999718i | \(-0.507555\pi\) |
0.624426 | + | 0.781084i | \(0.285333\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −384.750 | − | 222.136i | −0.578572 | − | 0.334038i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 24.6085 | + | 42.6231i | 0.0368942 | + | 0.0639027i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −104.822 | + | 124.922i | −0.156218 | + | 0.186173i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.3659 | − | 5.22876i | −0.0213460 | − | 0.00776932i | 0.331325 | − | 0.943517i | \(-0.392504\pi\) |
−0.352671 | + | 0.935747i | \(0.614727\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −103.653 | + | 284.784i | −0.153106 | + | 0.420655i | −0.992405 | − | 0.123015i | \(-0.960744\pi\) |
0.839299 | + | 0.543670i | \(0.182966\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 453.313 | + | 380.375i | 0.667618 | + | 0.560198i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −688.686 | + | 397.613i | −1.00833 | + | 0.582157i | −0.910701 | − | 0.413067i | \(-0.864458\pi\) |
−0.0976243 | + | 0.995223i | \(0.531124\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 285.863 | − | 495.129i | 0.417318 | − | 0.722816i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 63.9861 | + | 175.800i | 0.0928680 | + | 0.255153i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.31097 | + | 47.1339i | 0.0120275 | + | 0.0682111i | 0.990231 | − | 0.139438i | \(-0.0445297\pi\) |
−0.978203 | + | 0.207650i | \(0.933419\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −238.695 | − | 284.466i | −0.343447 | − | 0.409304i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −49.2372 | + | 279.238i | −0.0706416 | + | 0.400629i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32.9301i | 0.0469759i | 0.999724 | + | 0.0234880i | \(0.00747714\pi\) | ||||
−0.999724 | + | 0.0234880i | \(0.992523\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1048.33 | 1.49123 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 77.7927 | + | 13.7170i | 0.110032 | + | 0.0194016i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 705.725 | − | 592.173i | 0.995380 | − | 0.835223i | 0.00904260 | − | 0.999959i | \(-0.497122\pi\) |
0.986338 | + | 0.164736i | \(0.0526772\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −69.4666 | + | 12.2488i | −0.0974286 | + | 0.0171793i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −237.327 | + | 86.3798i | −0.331925 | + | 0.120811i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −406.335 | − | 234.597i | −0.565139 | − | 0.326283i | 0.190067 | − | 0.981771i | \(-0.439130\pi\) |
−0.755205 | + | 0.655488i | \(0.772463\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −50.5571 | − | 87.5675i | −0.0701209 | − | 0.121453i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −138.743 | + | 165.348i | −0.191370 | + | 0.228066i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 53.3053 | + | 19.4016i | 0.0733223 | + | 0.0266871i | 0.378421 | − | 0.925634i | \(-0.376467\pi\) |
−0.305099 | + | 0.952321i | \(0.598689\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.35723 | − | 22.9613i | 0.0114326 | − | 0.0314108i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −773.970 | − | 649.438i | −1.05589 | − | 0.886000i | −0.0621924 | − | 0.998064i | \(-0.519809\pi\) |
−0.993701 | + | 0.112064i | \(0.964254\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1422.76 | + | 821.432i | −1.93048 | + | 1.11456i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 368.682 | − | 638.576i | 0.498893 | − | 0.864108i | −0.501106 | − | 0.865386i | \(-0.667073\pi\) |
0.999999 | + | 0.00127777i | \(0.000406727\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.4911 | + | 86.5211i | 0.0423837 | + | 0.116448i | 0.959079 | − | 0.283139i | \(-0.0913757\pi\) |
−0.916695 | + | 0.399587i | \(0.869153\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −108.970 | − | 618.000i | −0.146269 | − | 0.829531i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −154.105 | − | 183.655i | −0.205747 | − | 0.245200i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −65.4270 | + | 371.055i | −0.0871199 | + | 0.494081i | 0.909759 | + | 0.415137i | \(0.136266\pi\) |
−0.996879 | + | 0.0789448i | \(0.974845\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 187.652i | 0.248545i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 98.9786 | 0.130751 | 0.0653755 | − | 0.997861i | \(-0.479175\pi\) | ||||
0.0653755 | + | 0.997861i | \(0.479175\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1035.32 | + | 182.555i | 1.36047 | + | 0.239888i | 0.805804 | − | 0.592183i | \(-0.201734\pi\) |
0.554669 | + | 0.832071i | \(0.312845\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −224.625 | + | 188.482i | −0.294396 | + | 0.247028i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −239.169 | + | 42.1720i | −0.311824 | + | 0.0549830i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.0610 | − | 5.11778i | 0.0182848 | − | 0.00665511i | −0.332862 | − | 0.942976i | \(-0.608014\pi\) |
0.351146 | + | 0.936321i | \(0.385792\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −453.509 | − | 261.834i | −0.586687 | − | 0.338724i | 0.177099 | − | 0.984193i | \(-0.443329\pi\) |
−0.763787 | + | 0.645469i | \(0.776662\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −154.677 | − | 267.908i | −0.199583 | − | 0.345687i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −748.229 | + | 891.705i | −0.960499 | + | 1.14468i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1449.46 | − | 527.559i | −1.85590 | − | 0.675492i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −102.191 | + | 280.768i | −0.130180 | + | 0.357667i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 120.730 | + | 101.305i | 0.153406 | + | 0.128723i | 0.716260 | − | 0.697833i | \(-0.245852\pi\) |
−0.562854 | + | 0.826556i | \(0.690297\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 438.647 | − | 253.253i | 0.554547 | − | 0.320168i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21.7366 | − | 37.6489i | 0.0274106 | − | 0.0474766i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.59137 | − | 15.3622i | −0.00701552 | − | 0.0192750i | 0.936135 | − | 0.351640i | \(-0.114376\pi\) |
−0.943151 | + | 0.332365i | \(0.892154\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 51.2221 | + | 290.495i | 0.0641077 | + | 0.363573i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −915.605 | − | 1091.18i | −1.14023 | − | 1.35887i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.53316 | − | 20.0376i | 0.00438902 | − | 0.0248914i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 1248.37i | − | 1.54310i | −0.636168 | − | 0.771551i | \(-0.719481\pi\) | ||
0.636168 | − | 0.771551i | \(-0.280519\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −796.242 | −0.981803 | −0.490901 | − | 0.871215i | \(-0.663332\pi\) | ||||
−0.490901 | + | 0.871215i | \(0.663332\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −226.194 | − | 39.8841i | −0.277538 | − | 0.0489375i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 76.8437 | − | 64.4795i | 0.0940559 | − | 0.0789223i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1369.41 | − | 241.464i | 1.66798 | − | 0.294110i | 0.741640 | − | 0.670798i | \(-0.234048\pi\) |
0.926340 | + | 0.376688i | \(0.122937\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21.0770 | + | 7.67138i | −0.0256099 | + | 0.00932124i | −0.354793 | − | 0.934945i | \(-0.615449\pi\) |
0.329183 | + | 0.944266i | \(0.393227\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −79.4904 | − | 45.8938i | −0.0961190 | − | 0.0554943i | 0.451170 | − | 0.892438i | \(-0.351007\pi\) |
−0.547289 | + | 0.836944i | \(0.684340\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −398.805 | − | 690.751i | −0.481068 | − | 0.833234i | 0.518696 | − | 0.854959i | \(-0.326418\pi\) |
−0.999764 | + | 0.0217246i | \(0.993084\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −160.428 | + | 191.190i | −0.192590 | + | 0.229520i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 862.970 | + | 314.095i | 1.03350 | + | 0.376162i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −566.496 | + | 1556.43i | −0.675203 | + | 1.85511i | −0.187045 | + | 0.982351i | \(0.559891\pi\) |
−0.488158 | + | 0.872755i | \(0.662331\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −461.775 | − | 387.476i | −0.549079 | − | 0.460732i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −584.994 | + | 337.746i | −0.692301 | + | 0.399700i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −168.935 | + | 292.605i | −0.199451 | + | 0.345460i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.4209 | + | 45.1160i | 0.0192960 | + | 0.0530153i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −215.597 | − | 1222.71i | −0.252752 | − | 1.43343i | −0.801779 | − | 0.597621i | \(-0.796113\pi\) |
0.549027 | − | 0.835805i | \(-0.314998\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −949.464 | − | 1131.53i | −1.10789 | − | 1.32033i | −0.942537 | − | 0.334101i | \(-0.891567\pi\) |
−0.165355 | − | 0.986234i | \(-0.552877\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −173.038 | + | 981.345i | −0.201441 | + | 1.14243i | 0.701503 | + | 0.712667i | \(0.252513\pi\) |
−0.902943 | + | 0.429760i | \(0.858598\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 671.209i | 0.777763i | 0.921288 | + | 0.388881i | \(0.127138\pi\) | ||||
−0.921288 | + | 0.388881i | \(0.872862\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1274.31 | −1.47319 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1604.75 | − | 282.961i | −1.84667 | − | 0.325617i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 335.499 | − | 281.517i | 0.385188 | − | 0.323211i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 474.622 | − | 83.6886i | 0.542425 | − | 0.0956441i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −610.614 | + | 222.245i | −0.696253 | + | 0.253415i | −0.665810 | − | 0.746121i | \(-0.731914\pi\) |
−0.0304427 | + | 0.999537i | \(0.509692\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 196.446 | + | 113.418i | 0.222980 | + | 0.128738i | 0.607330 | − | 0.794450i | \(-0.292241\pi\) |
−0.384349 | + | 0.923188i | \(0.625574\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34.4995 | + | 59.7548i | 0.0390707 | + | 0.0676725i | 0.884900 | − | 0.465782i | \(-0.154227\pi\) |
−0.845829 | + | 0.533454i | \(0.820894\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 581.417 | − | 692.906i | 0.655488 | − | 0.781180i | −0.331243 | − | 0.943545i | \(-0.607468\pi\) |
0.986731 | + | 0.162366i | \(0.0519125\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −242.644 | − | 88.3151i | −0.272940 | − | 0.0993421i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −414.173 | + | 1137.93i | −0.463800 | + | 1.27428i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 328.110 | + | 275.317i | 0.366603 | + | 0.307617i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1792.05 | − | 1034.64i | 1.99338 | − | 1.15088i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 164.655 | − | 285.191i | 0.182747 | − | 0.316528i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 56.1043 | + | 154.145i | 0.0619937 | + | 0.170326i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28.0243 | − | 158.934i | −0.0308978 | − | 0.175230i | 0.965454 | − | 0.260575i | \(-0.0839120\pi\) |
−0.996352 | + | 0.0853445i | \(0.972801\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −51.9472 | − | 61.9082i | −0.0570221 | − | 0.0679563i | 0.736779 | − | 0.676133i | \(-0.236346\pi\) |
−0.793802 | + | 0.608177i | \(0.791901\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 334.668 | − | 1897.99i | 0.366558 | − | 2.07885i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 447.513i | − | 0.488019i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −656.985 | −0.714891 | −0.357445 | − | 0.933934i | \(-0.616352\pi\) | ||||
−0.357445 | + | 0.933934i | \(0.616352\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 404.955 | + | 71.4045i | 0.438738 | + | 0.0773613i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −161.298 | + | 135.345i | −0.174376 | + | 0.146319i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 244.546 | − | 43.1200i | 0.263235 | − | 0.0464155i | −0.0404727 | − | 0.999181i | \(-0.512886\pi\) |
0.303708 | + | 0.952765i | \(0.401775\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −962.811 | + | 350.434i | −1.03417 | + | 0.376406i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 385.002 | + | 222.281i | 0.411767 | + | 0.237734i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 468.473 | + | 811.418i | 0.499971 | + | 0.865975i | 1.00000 | 3.38875e-5i | \(-1.07867e-5\pi\) | |
−0.500029 | + | 0.866008i | \(0.666677\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 899.429 | − | 1071.90i | 0.955823 | − | 1.13911i | −0.0343714 | − | 0.999409i | \(-0.510943\pi\) |
0.990194 | − | 0.139696i | \(-0.0446127\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −50.0954 | − | 18.2332i | −0.0531234 | − | 0.0193354i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −249.635 | + | 685.866i | −0.263606 | + | 0.724252i | 0.735311 | + | 0.677730i | \(0.237036\pi\) |
−0.998917 | + | 0.0465220i | \(0.985186\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 290.891 | + | 244.087i | 0.306524 | + | 0.257204i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1167.46 | + | 674.032i | −1.22503 | + | 0.707274i | −0.965987 | − | 0.258591i | \(-0.916742\pi\) |
−0.259047 | + | 0.965865i | \(0.583409\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 769.891 | − | 1333.49i | 0.806169 | − | 1.39633i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 158.993 | + | 436.829i | 0.165790 | + | 0.455505i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 348.115 | + | 1974.26i | 0.362242 | + | 2.05438i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 31.2283 | + | 37.2164i | 0.0323609 | + | 0.0385662i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 124.207 | − | 704.414i | 0.128446 | − | 0.728453i | −0.850755 | − | 0.525562i | \(-0.823855\pi\) |
0.979201 | − | 0.202891i | \(-0.0650337\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1288.41i | 1.32689i | 0.748226 | + | 0.663444i | \(0.230906\pi\) | ||||
−0.748226 | + | 0.663444i | \(0.769094\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 301.936 | 0.310314 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 830.119 | + | 146.372i | 0.849661 | + | 0.149818i | 0.581491 | − | 0.813553i | \(-0.302470\pi\) |
0.268171 | + | 0.963371i | \(0.413581\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1141.03 | + | 957.437i | −1.16551 | + | 0.977975i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −502.601 | + | 88.6222i | −0.511293 | + | 0.0901548i | −0.423342 | − | 0.905970i | \(-0.639143\pi\) |
−0.0879514 | + | 0.996125i | \(0.528032\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1313.86 | − | 478.204i | 1.33386 | − | 0.485487i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.97860 | + | 2.29704i | 0.00402285 | + | 0.00232259i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −186.798 | − | 323.544i | −0.188495 | − | 0.326483i | 0.756254 | − | 0.654278i | \(-0.227028\pi\) |
−0.944749 | + | 0.327796i | \(0.893694\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −499.223 | + | 594.951i | −0.501732 | + | 0.597940i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1763.31 | + | 641.793i | 1.76862 | + | 0.643724i | 0.999992 | + | 0.00402483i | \(0.00128115\pi\) |
0.768625 | + | 0.639699i | \(0.220941\pi\) | |||||||
\(998\) | 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 | 324.3.k.a.17.4 | 36 | ||
3.2 | odd | 2 | 108.3.k.a.77.2 | ✓ | 36 | ||
12.11 | even | 2 | 432.3.bc.b.401.5 | 36 | |||
27.7 | even | 9 | 108.3.k.a.101.2 | yes | 36 | ||
27.13 | even | 9 | 2916.3.c.b.1457.28 | 36 | |||
27.14 | odd | 18 | 2916.3.c.b.1457.9 | 36 | |||
27.20 | odd | 18 | inner | 324.3.k.a.305.4 | 36 | ||
108.7 | odd | 18 | 432.3.bc.b.209.5 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.3.k.a.77.2 | ✓ | 36 | 3.2 | odd | 2 | ||
108.3.k.a.101.2 | yes | 36 | 27.7 | even | 9 | ||
324.3.k.a.17.4 | 36 | 1.1 | even | 1 | trivial | ||
324.3.k.a.305.4 | 36 | 27.20 | odd | 18 | inner | ||
432.3.bc.b.209.5 | 36 | 108.7 | odd | 18 | |||
432.3.bc.b.401.5 | 36 | 12.11 | even | 2 | |||
2916.3.c.b.1457.9 | 36 | 27.14 | odd | 18 | |||
2916.3.c.b.1457.28 | 36 | 27.13 | even | 9 |