Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,4,Mod(17,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.bl (of order \(6\), degree \(2\), 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: | \(29.7369626429\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 17.2 | ||
Character | \(\chi\) | \(=\) | 504.17 |
Dual form | 504.4.bl.a.89.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | −9.74197 | − | 16.8736i | −0.871348 | − | 1.50922i | −0.860603 | − | 0.509277i | \(-0.829913\pi\) |
−0.0107451 | − | 0.999942i | \(-0.503420\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −18.4446 | + | 1.67197i | −0.995917 | + | 0.0902780i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −15.1087 | − | 8.72302i | −0.414132 | − | 0.239099i | 0.278432 | − | 0.960456i | \(-0.410185\pi\) |
−0.692563 | + | 0.721357i | \(0.743519\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 16.5278i | − | 0.352615i | −0.984335 | − | 0.176308i | \(-0.943585\pi\) | ||
0.984335 | − | 0.176308i | \(-0.0564154\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 68.6466 | − | 118.899i | 0.979368 | − | 1.69632i | 0.314674 | − | 0.949200i | \(-0.398105\pi\) |
0.664694 | − | 0.747115i | \(-0.268562\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −20.6975 | + | 11.9497i | −0.249912 | + | 0.144287i | −0.619724 | − | 0.784820i | \(-0.712756\pi\) |
0.369812 | + | 0.929107i | \(0.379422\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −108.910 | + | 62.8794i | −0.987365 | + | 0.570055i | −0.904486 | − | 0.426504i | \(-0.859745\pi\) |
−0.0828792 | + | 0.996560i | \(0.526412\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −127.312 | + | 220.511i | −1.01849 | + | 1.76408i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 105.188i | 0.673548i | 0.941586 | + | 0.336774i | \(0.109336\pi\) | ||||
−0.941586 | + | 0.336774i | \(0.890664\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −95.0849 | − | 54.8973i | −0.550895 | − | 0.318060i | 0.198588 | − | 0.980083i | \(-0.436365\pi\) |
−0.749483 | + | 0.662024i | \(0.769698\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 207.899 | + | 294.939i | 1.00404 | + | 1.42439i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 58.5919 | + | 101.484i | 0.260336 | + | 0.450916i | 0.966331 | − | 0.257301i | \(-0.0828332\pi\) |
−0.705995 | + | 0.708217i | \(0.749500\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 348.056 | 1.32579 | 0.662893 | − | 0.748714i | \(-0.269328\pi\) | ||||
0.662893 | + | 0.748714i | \(0.269328\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −141.953 | −0.503432 | −0.251716 | − | 0.967801i | \(-0.580995\pi\) | ||||
−0.251716 | + | 0.967801i | \(0.580995\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 172.830 | + | 299.351i | 0.536381 | + | 0.929040i | 0.999095 | + | 0.0425319i | \(0.0135424\pi\) |
−0.462714 | + | 0.886508i | \(0.653124\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 337.409 | − | 61.6778i | 0.983700 | − | 0.179819i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 149.292 | + | 86.1937i | 0.386921 | + | 0.223389i | 0.680825 | − | 0.732446i | \(-0.261621\pi\) |
−0.293904 | + | 0.955835i | \(0.594955\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 339.918i | 0.833354i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −297.569 | + | 515.404i | −0.656613 | + | 1.13729i | 0.324874 | + | 0.945757i | \(0.394678\pi\) |
−0.981487 | + | 0.191530i | \(0.938655\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −561.746 | + | 324.324i | −1.17909 | + | 0.680746i | −0.955803 | − | 0.294008i | \(-0.905011\pi\) |
−0.223283 | + | 0.974754i | \(0.571677\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −278.884 | + | 161.014i | −0.532174 | + | 0.307251i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −64.9996 | + | 112.583i | −0.118522 | + | 0.205286i | −0.919182 | − | 0.393833i | \(-0.871149\pi\) |
0.800660 | + | 0.599119i | \(0.204482\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 908.671i | − | 1.51886i | −0.650586 | − | 0.759432i | \(-0.725477\pi\) | ||
0.650586 | − | 0.759432i | \(-0.274523\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −44.8988 | − | 25.9223i | −0.0719864 | − | 0.0415614i | 0.463575 | − | 0.886058i | \(-0.346567\pi\) |
−0.535561 | + | 0.844496i | \(0.679900\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 293.259 | + | 135.632i | 0.434026 | + | 0.200736i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 474.917 | + | 822.580i | 0.676358 | + | 1.17149i | 0.976070 | + | 0.217457i | \(0.0697761\pi\) |
−0.299712 | + | 0.954030i | \(0.596891\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1302.27 | 1.72220 | 0.861100 | − | 0.508436i | \(-0.169776\pi\) | ||||
0.861100 | + | 0.508436i | \(0.169776\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2675.01 | −3.41348 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −210.570 | − | 364.719i | −0.250791 | − | 0.434383i | 0.712953 | − | 0.701212i | \(-0.247357\pi\) |
−0.963744 | + | 0.266829i | \(0.914024\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 27.6341 | + | 304.850i | 0.0318334 | + | 0.351175i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 403.269 | + | 232.827i | 0.435521 | + | 0.251448i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 553.292i | − | 0.579158i | −0.957154 | − | 0.289579i | \(-0.906485\pi\) | ||
0.957154 | − | 0.289579i | \(-0.0935153\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −115.951 | + | 200.833i | −0.114233 | + | 0.197858i | −0.917473 | − | 0.397798i | \(-0.869774\pi\) |
0.803240 | + | 0.595656i | \(0.203108\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1674.49 | + | 966.766i | −1.60187 | + | 0.924837i | −0.610751 | + | 0.791823i | \(0.709132\pi\) |
−0.991114 | + | 0.133015i | \(0.957534\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −769.974 | + | 444.544i | −0.695665 | + | 0.401642i | −0.805731 | − | 0.592282i | \(-0.798227\pi\) |
0.110066 | + | 0.993924i | \(0.464894\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −961.155 | + | 1664.77i | −0.844605 | + | 1.46290i | 0.0413585 | + | 0.999144i | \(0.486831\pi\) |
−0.885964 | + | 0.463755i | \(0.846502\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 2070.45i | − | 1.72365i | −0.507210 | − | 0.861823i | \(-0.669323\pi\) | ||
0.507210 | − | 0.861823i | \(-0.330677\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2122.00 | + | 1225.14i | 1.72068 | + | 0.993433i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1067.37 | + | 2307.83i | −0.822229 | + | 1.77780i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −513.318 | − | 889.092i | −0.385663 | − | 0.667988i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2525.58 | 1.80716 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1508.37 | 1.05391 | 0.526955 | − | 0.849893i | \(-0.323334\pi\) | ||||
0.526955 | + | 0.849893i | \(0.323334\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1067.52 | + | 1848.99i | 0.711979 | + | 1.23318i | 0.964113 | + | 0.265491i | \(0.0855342\pi\) |
−0.252134 | + | 0.967692i | \(0.581132\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 361.778 | − | 255.014i | 0.235866 | − | 0.166259i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −494.811 | − | 285.679i | −0.308574 | − | 0.178155i | 0.337714 | − | 0.941249i | \(-0.390346\pi\) |
−0.646288 | + | 0.763094i | \(0.723680\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 3003.94i | − | 1.83302i | −0.400006 | − | 0.916512i | \(-0.630992\pi\) | ||
0.400006 | − | 0.916512i | \(-0.369008\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −144.173 | + | 249.714i | −0.0843100 | + | 0.146029i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1774.89 | − | 1024.74i | 1.01653 | − | 0.586894i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1433.52 | + | 827.646i | −0.788180 | + | 0.455056i | −0.839322 | − | 0.543635i | \(-0.817047\pi\) |
0.0511412 | + | 0.998691i | \(0.483714\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 396.703 | − | 687.109i | 0.213796 | − | 0.370306i | −0.739103 | − | 0.673592i | \(-0.764750\pi\) |
0.952899 | + | 0.303286i | \(0.0980838\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2139.23i | 1.10856i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −621.514 | − | 358.831i | −0.315938 | − | 0.182407i | 0.333643 | − | 0.942700i | \(-0.391722\pi\) |
−0.649580 | + | 0.760293i | \(0.725055\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1903.68 | − | 1341.88i | 0.931869 | − | 0.656865i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1038.88 | + | 1799.39i | 0.499211 | + | 0.864659i | 1.00000 | 0.000910600i | \(-0.000289853\pi\) | |
−0.500788 | + | 0.865570i | \(0.666957\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1017.38 | −0.471420 | −0.235710 | − | 0.971823i | \(-0.575742\pi\) | ||||
−0.235710 | + | 0.971823i | \(0.575742\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1923.83 | 0.875662 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1498.46 | − | 2595.42i | −0.658533 | − | 1.14061i | −0.980996 | − | 0.194030i | \(-0.937844\pi\) |
0.322463 | − | 0.946582i | \(-0.395489\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1979.53 | − | 4280.10i | 0.855078 | − | 1.84883i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3473.51 | − | 2005.43i | −1.45040 | − | 0.837391i | −0.451900 | − | 0.892068i | \(-0.649254\pi\) |
−0.998504 | + | 0.0546769i | \(0.982587\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2885.89i | 1.18512i | 0.805527 | + | 0.592559i | \(0.201882\pi\) | ||||
−0.805527 | + | 0.592559i | \(0.798118\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1141.60 | − | 1977.31i | 0.453687 | − | 0.785809i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2074.33 | + | 1197.61i | −0.811175 | + | 0.468332i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1169.89 | + | 675.436i | −0.443195 | + | 0.255879i | −0.704952 | − | 0.709255i | \(-0.749031\pi\) |
0.261757 | + | 0.965134i | \(0.415698\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −315.843 | + | 547.055i | −0.117797 | + | 0.204031i | −0.918894 | − | 0.394504i | \(-0.870917\pi\) |
0.801097 | + | 0.598534i | \(0.204250\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 2350.91i | − | 0.850232i | −0.905139 | − | 0.425116i | \(-0.860233\pi\) | ||
0.905139 | − | 0.425116i | \(-0.139767\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −970.169 | − | 560.127i | −0.345595 | − | 0.199530i | 0.317148 | − | 0.948376i | \(-0.397275\pi\) |
−0.662744 | + | 0.748846i | \(0.730608\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −175.871 | − | 1940.15i | −0.0608066 | − | 0.670797i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3390.75 | − | 5872.95i | −1.15522 | − | 2.00090i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 416.950 | 0.137996 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −396.657 | −0.129417 | −0.0647085 | − | 0.997904i | \(-0.520612\pi\) | ||||
−0.0647085 | + | 0.997904i | \(0.520612\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1382.90 | + | 2395.25i | 0.438664 | + | 0.759789i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1845.59 | + | 853.581i | 0.577360 | + | 0.267027i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1965.15 | − | 1134.58i | −0.598147 | − | 0.345340i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2574.52i | 0.773106i | 0.922267 | + | 0.386553i | \(0.126334\pi\) | ||||
−0.922267 | + | 0.386553i | \(0.873666\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1165.21 | − | 2018.20i | 0.340694 | − | 0.590100i | −0.643868 | − | 0.765137i | \(-0.722671\pi\) |
0.984562 | + | 0.175037i | \(0.0560046\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1211.86 | − | 699.668i | 0.349703 | − | 0.201901i | −0.314852 | − | 0.949141i | \(-0.601955\pi\) |
0.664554 | + | 0.747240i | \(0.268621\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1950.66 | + | 1126.21i | −0.548463 | + | 0.316655i | −0.748502 | − | 0.663133i | \(-0.769227\pi\) |
0.200039 | + | 0.979788i | \(0.435893\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3367.42 | − | 5832.54i | 0.934749 | − | 1.61903i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 3423.46i | − | 0.926549i | −0.886215 | − | 0.463275i | \(-0.846674\pi\) | ||
0.886215 | − | 0.463275i | \(-0.153326\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1997.78 | + | 1153.42i | 0.533977 | + | 0.308292i | 0.742635 | − | 0.669697i | \(-0.233576\pi\) |
−0.208657 | + | 0.977989i | \(0.566909\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4327.75 | − | 5092.43i | −1.12853 | − | 1.32793i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 197.503 | + | 342.085i | 0.0508778 | + | 0.0881229i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7897.26 | −1.98594 | −0.992970 | − | 0.118368i | \(-0.962234\pi\) | ||||
−0.992970 | + | 0.118368i | \(0.962234\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2194.00 | 0.545199 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 217.517 | + | 376.750i | 0.0527950 | + | 0.0914437i | 0.891215 | − | 0.453581i | \(-0.149854\pi\) |
−0.838420 | + | 0.545025i | \(0.816520\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1250.38 | − | 1773.87i | −0.299981 | − | 0.425572i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5144.46 | + | 2970.16i | 1.20616 | + | 0.696379i | 0.961919 | − | 0.273335i | \(-0.0881266\pi\) |
0.244245 | + | 0.969714i | \(0.421460\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 3358.78i | − | 0.778598i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 915.170 | − | 1585.12i | 0.207431 | − | 0.359281i | −0.743474 | − | 0.668765i | \(-0.766823\pi\) |
0.950905 | + | 0.309484i | \(0.100156\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2605.49 | − | 1504.28i | 0.584030 | − | 0.337190i | −0.178703 | − | 0.983903i | \(-0.557190\pi\) |
0.762733 | + | 0.646713i | \(0.223857\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3847.04 | − | 2221.09i | 0.843582 | − | 0.487042i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 147.124 | − | 254.826i | 0.0319127 | − | 0.0552744i | −0.849628 | − | 0.527383i | \(-0.823173\pi\) |
0.881541 | + | 0.472108i | \(0.156507\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8000.78i | 1.69853i | 0.527967 | + | 0.849265i | \(0.322954\pi\) | ||||
−0.527967 | + | 0.849265i | \(0.677046\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7523.20 | + | 4343.52i | 1.58024 | + | 0.912352i | 0.994823 | + | 0.101619i | \(0.0324023\pi\) |
0.585416 | + | 0.810733i | \(0.300931\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6419.77 | + | 581.940i | −1.32037 | + | 0.119689i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6968.22 | − | 12069.3i | −1.41832 | − | 2.45661i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4055.18 | −0.808554 | −0.404277 | − | 0.914637i | \(-0.632477\pi\) | ||||
−0.404277 | + | 0.914637i | \(0.632477\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11595.6 | 2.28855 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1039.26 | + | 1800.05i | 0.201010 | + | 0.348160i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2618.26 | − | 237.341i | 0.501376 | − | 0.0454488i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10945.0 | + | 6319.11i | 2.05479 | + | 1.18633i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4591.37i | 0.853562i | 0.904355 | + | 0.426781i | \(0.140352\pi\) | ||||
−0.904355 | + | 0.426781i | \(0.859648\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2849.94 | − | 4936.24i | 0.519631 | − | 0.900028i | −0.480108 | − | 0.877209i | \(-0.659403\pi\) |
0.999740 | − | 0.0228187i | \(-0.00726406\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3909.34 | + | 2257.06i | −0.705971 | + | 0.407593i | −0.809568 | − | 0.587027i | \(-0.800298\pi\) |
0.103596 | + | 0.994619i | \(0.466965\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1819.78 | + | 1050.65i | −0.322427 | + | 0.186153i | −0.652474 | − | 0.757811i | \(-0.726269\pi\) |
0.330047 | + | 0.943965i | \(0.392935\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 917.555 | − | 1589.25i | 0.161045 | − | 0.278937i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3281.23i | 0.565240i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3644.56 | + | 2104.19i | 0.622043 | + | 0.359137i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3688.30 | − | 5232.46i | −0.618063 | − | 0.876822i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3111.81 | − | 5389.81i | −0.516739 | − | 0.895018i | −0.999811 | − | 0.0194375i | \(-0.993812\pi\) |
0.483072 | − | 0.875581i | \(-0.339521\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2532.89 | 0.413095 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1599.77 | 0.258591 | 0.129295 | − | 0.991606i | \(-0.458728\pi\) | ||||
0.129295 | + | 0.991606i | \(0.458728\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 957.741 | + | 1658.86i | 0.152096 | + | 0.263437i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6120.26 | + | 1701.76i | −0.963449 | + | 0.267891i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2237.47 | + | 1291.80i | 0.346149 | + | 0.199849i | 0.662988 | − | 0.748630i | \(-0.269288\pi\) |
−0.316839 | + | 0.948479i | \(0.602621\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6406.75i | 0.982652i | 0.870976 | + | 0.491326i | \(0.163488\pi\) | ||||
−0.870976 | + | 0.491326i | \(0.836512\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3536.88 | + | 6126.05i | −0.533283 | + | 0.923673i | 0.465961 | + | 0.884805i | \(0.345709\pi\) |
−0.999244 | + | 0.0388682i | \(0.987625\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15332.5 | + | 8852.24i | −2.29230 | + | 1.32346i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1355.38 | − | 782.532i | 0.199260 | − | 0.115043i | −0.397050 | − | 0.917797i | \(-0.629966\pi\) |
0.596310 | + | 0.802754i | \(0.296633\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3143.91 | + | 5445.41i | −0.458363 | + | 0.793907i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1010.14i | 0.144858i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8459.40 | − | 4884.03i | −1.20321 | − | 0.694672i | −0.241940 | − | 0.970291i | \(-0.577784\pi\) |
−0.961267 | + | 0.275620i | \(0.911117\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2897.75 | − | 1340.20i | −0.405508 | − | 0.187546i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3840.66 | + | 6652.21i | 0.533141 | + | 0.923427i | 0.999251 | + | 0.0387005i | \(0.0123218\pi\) |
−0.466110 | + | 0.884727i | \(0.654345\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1738.53 | 0.237503 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6320.25 | −0.856595 | −0.428297 | − | 0.903638i | \(-0.640886\pi\) | ||||
−0.428297 | + | 0.903638i | \(0.640886\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −91.9525 | − | 159.266i | −0.0122678 | − | 0.0212484i | 0.859826 | − | 0.510587i | \(-0.170572\pi\) |
−0.872094 | + | 0.489338i | \(0.837238\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −568.333 | − | 6269.65i | −0.0752336 | − | 0.829951i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9127.81 | − | 5269.94i | −1.18971 | − | 0.686881i | −0.231471 | − | 0.972842i | \(-0.574354\pi\) |
−0.958241 | + | 0.285961i | \(0.907687\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17265.9i | 2.23318i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9253.24 | − | 16027.1i | 1.17869 | − | 2.04154i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4797.29 | + | 2769.72i | −0.606471 | + | 0.350146i | −0.771583 | − | 0.636129i | \(-0.780535\pi\) |
0.165112 | + | 0.986275i | \(0.447201\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3816.52 | − | 2203.47i | 0.475282 | − | 0.274404i | −0.243166 | − | 0.969985i | \(-0.578186\pi\) |
0.718448 | + | 0.695580i | \(0.244853\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −907.334 | + | 1571.55i | −0.112153 | + | 0.194254i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 2044.39i | − | 0.248985i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8336.94 | + | 4813.33i | 1.00791 | + | 0.581917i | 0.910579 | − | 0.413335i | \(-0.135636\pi\) |
0.0973306 | + | 0.995252i | \(0.468970\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4626.81 | − | 10004.0i | 0.551260 | − | 1.19192i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12686.7 | − | 21973.9i | −1.50063 | − | 2.59918i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3095.82 | 0.360957 | 0.180478 | − | 0.983579i | \(-0.442235\pi\) | ||||
0.180478 | + | 0.983579i | \(0.442235\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4652.51 | 0.538598 | 0.269299 | − | 0.963057i | \(-0.413208\pi\) | ||||
0.269299 | + | 0.963057i | \(0.413208\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 17479.1 | + | 30274.6i | 1.99496 | + | 3.45538i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9818.94 | − | 6921.27i | 1.11281 | − | 0.784411i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6562.34 | − | 3788.77i | −0.733404 | − | 0.423431i | 0.0862625 | − | 0.996272i | \(-0.472508\pi\) |
−0.819666 | + | 0.572842i | \(0.805841\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10028.8i | 1.11305i | 0.830829 | + | 0.556527i | \(0.187867\pi\) | ||||
−0.830829 | + | 0.556527i | \(0.812133\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1502.78 | − | 2602.90i | 0.164503 | − | 0.284928i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12522.8 | + | 7230.07i | −1.36146 | + | 0.786042i | −0.989819 | − | 0.142333i | \(-0.954540\pi\) |
−0.371646 | + | 0.928375i | \(0.621206\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12101.9 | + | 6987.05i | −1.29792 | + | 0.749356i | −0.980045 | − | 0.198775i | \(-0.936304\pi\) |
−0.317878 | + | 0.948132i | \(0.602970\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4102.74 | + | 7106.15i | −0.437053 | + | 0.756998i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12850.1i | 1.35064i | 0.737527 | + | 0.675318i | \(0.235993\pi\) | ||||
−0.737527 | + | 0.675318i | \(0.764007\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5258.68 | − | 3036.10i | −0.549050 | − | 0.316994i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4874.70 | − | 3436.12i | 0.502263 | − | 0.354040i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4530.38 | + | 7846.86i | 0.463725 | + | 0.803196i | 0.999143 | − | 0.0413917i | \(-0.0131792\pi\) |
−0.535418 | + | 0.844587i | \(0.679846\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3390.73 | −0.342564 | −0.171282 | − | 0.985222i | \(-0.554791\pi\) | ||||
−0.171282 | + | 0.985222i | \(0.554791\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 707.176 | 0.0709833 | 0.0354916 | − | 0.999370i | \(-0.488700\pi\) | ||||
0.0354916 | + | 0.999370i | \(0.488700\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2360.37 | + | 4088.28i | 0.233886 | + | 0.405103i | 0.958948 | − | 0.283581i | \(-0.0915224\pi\) |
−0.725062 | + | 0.688683i | \(0.758189\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1010.66 | − | 2185.22i | 0.0995050 | − | 0.215147i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2144.72 | + | 1238.26i | 0.208487 | + | 0.120370i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 6085.36i | − | 0.587822i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2300.35 | + | 3984.32i | −0.219427 | + | 0.380059i | −0.954633 | − | 0.297785i | \(-0.903752\pi\) |
0.735206 | + | 0.677844i | \(0.237085\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1677.31 | − | 968.398i | 0.159000 | − | 0.0917986i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9336.02 | + | 5390.15i | −0.874076 | + | 0.504648i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8189.27 | + | 14184.2i | −0.761994 | + | 1.31981i | 0.179827 | + | 0.983698i | \(0.442446\pi\) |
−0.941821 | + | 0.336115i | \(0.890887\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 4293.59i | − | 0.394637i | −0.980339 | − | 0.197319i | \(-0.936777\pi\) | ||
0.980339 | − | 0.197319i | \(-0.0632234\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12506.8 | + | 7220.79i | 1.14255 | + | 0.659651i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1519.27 | + | 16760.1i | 0.137120 | + | 1.51266i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2603.39 | + | 4509.21i | 0.233555 | + | 0.404529i | 0.958852 | − | 0.283907i | \(-0.0916309\pi\) |
−0.725297 | + | 0.688436i | \(0.758298\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16409.4 | 1.45459 | 0.727295 | − | 0.686325i | \(-0.240777\pi\) | ||||
0.727295 | + | 0.686325i | \(0.240777\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4518.37 | 0.398148 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 992.966 | + | 1719.87i | 0.0864685 | + | 0.149768i | 0.906016 | − | 0.423243i | \(-0.139108\pi\) |
−0.819548 | + | 0.573011i | \(0.805775\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 871.483 | + | 403.058i | 0.0754445 | + | 0.0348929i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 32625.6 | + | 18836.4i | 2.79156 | + | 1.61171i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 6030.42i | − | 0.512993i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1336.56 | + | 2315.00i | −0.112391 | + | 0.194668i | −0.916734 | − | 0.399498i | \(-0.869184\pi\) |
0.804343 | + | 0.594166i | \(0.202518\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1236.34 | + | 713.801i | −0.103368 | + | 0.0596794i | −0.550793 | − | 0.834642i | \(-0.685675\pi\) |
0.447425 | + | 0.894322i | \(0.352341\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −13054.5 | + | 7537.03i | −1.07906 | + | 0.622995i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1824.15 | − | 3159.52i | 0.149926 | − | 0.259679i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 5752.62i | − | 0.467493i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15002.1 | + | 8661.47i | 1.21233 | + | 0.699941i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5635.83 | − | 2011.35i | −0.450376 | − | 0.160733i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10091.7 | − | 17479.3i | −0.801985 | − | 1.38908i | −0.918308 | − | 0.395868i | \(-0.870444\pi\) |
0.116322 | − | 0.993211i | \(-0.462889\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 37454.2 | 2.94378 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21275.8 | −1.66305 | −0.831524 | − | 0.555488i | \(-0.812531\pi\) | ||||
−0.831524 | + | 0.555488i | \(0.812531\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1256.96 | − | 2177.13i | −0.0971842 | − | 0.168328i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10135.0 | − | 14378.1i | −0.779356 | − | 1.10564i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15295.5 | − | 8830.84i | −1.16354 | − | 0.671768i | −0.211388 | − | 0.977402i | \(-0.567798\pi\) |
−0.952149 | + | 0.305634i | \(0.901132\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2346.17i | 0.177518i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7447.80 | − | 12900.0i | 0.557527 | − | 0.965665i | −0.440175 | − | 0.897912i | \(-0.645084\pi\) |
0.997702 | − | 0.0677527i | \(-0.0215829\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −34936.0 | + | 20170.3i | −2.60136 | + | 1.50189i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11813.4 | + | 6820.47i | −0.870375 | + | 0.502511i | −0.867473 | − | 0.497485i | \(-0.834257\pi\) |
−0.00290206 | + | 0.999996i | \(0.500924\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7222.20 | + | 12509.2i | −0.529317 | + | 0.916803i | 0.470099 | + | 0.882614i | \(0.344218\pi\) |
−0.999415 | + | 0.0341895i | \(0.989115\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 32021.2i | − | 2.32239i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19780.9 | + | 11420.5i | 1.42719 | + | 0.823989i | 0.996898 | − | 0.0787009i | \(-0.0250772\pi\) |
0.430292 | + | 0.902690i | \(0.358411\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −24019.9 | + | 2177.36i | −1.71517 | + | 0.155477i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1503.74 | − | 2604.55i | −0.106824 | − | 0.185025i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −21564.8 | −1.51631 | −0.758156 | − | 0.652073i | \(-0.773900\pi\) | ||||
−0.758156 | + | 0.652073i | \(0.773900\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2624.03 | 0.183567 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4857.29 | − | 8413.08i | −0.336366 | − | 0.582603i | 0.647380 | − | 0.762167i | \(-0.275865\pi\) |
−0.983746 | + | 0.179564i | \(0.942531\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 49339.6 | − | 4472.55i | 3.39954 | − | 0.308162i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5905.86 | − | 3409.75i | −0.402849 | − | 0.232585i | 0.284863 | − | 0.958568i | \(-0.408052\pi\) |
−0.687713 | + | 0.725983i | \(0.741385\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 23101.9i | − | 1.56796i | −0.620783 | − | 0.783982i | \(-0.713185\pi\) | ||
0.620783 | − | 0.783982i | \(-0.286815\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10001.4 | + | 17323.0i | −0.672094 | + | 1.16410i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 734.613 | − | 424.129i | 0.0491219 | − | 0.0283606i | −0.475238 | − | 0.879857i | \(-0.657638\pi\) |
0.524360 | + | 0.851497i | \(0.324305\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4947.63 | − | 2856.52i | 0.327594 | − | 0.189136i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7859.10 | + | 13612.4i | −0.517824 | + | 0.896897i | 0.481962 | + | 0.876192i | \(0.339924\pi\) |
−0.999786 | + | 0.0207049i | \(0.993409\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 24534.6i | − | 1.60086i | −0.599429 | − | 0.800428i | \(-0.704606\pi\) | ||
0.599429 | − | 0.800428i | \(-0.295394\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1330.23 | + | 768.007i | 0.0863754 | + | 0.0498689i | 0.542566 | − | 0.840013i | \(-0.317453\pi\) |
−0.456190 | + | 0.889882i | \(0.650786\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4493.69 | + | 6375.03i | 0.288982 | + | 0.409968i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8690.12 | − | 15051.7i | −0.556168 | − | 0.963311i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16088.5 | 1.01986 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14860.1 | −0.937515 | −0.468758 | − | 0.883327i | \(-0.655298\pi\) | ||||
−0.468758 | + | 0.883327i | \(0.655298\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14694.5 | − | 25451.7i | −0.918322 | − | 1.59058i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1019.40 | − | 5576.64i | −0.0634069 | − | 0.346868i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17466.3 | − | 10084.2i | −1.07625 | − | 0.621373i | −0.146368 | − | 0.989230i | \(-0.546758\pi\) |
−0.929882 | + | 0.367857i | \(0.880092\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 3124.44i | − | 0.191627i | −0.995399 | − | 0.0958133i | \(-0.969455\pi\) | ||
0.995399 | − | 0.0958133i | \(-0.0305452\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10143.8 | − | 17569.5i | 0.616372 | − | 1.06759i | −0.373770 | − | 0.927521i | \(-0.621935\pi\) |
0.990142 | − | 0.140066i | \(-0.0447316\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8991.77 | − | 5191.40i | 0.543848 | − | 0.313991i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2651.27 | + | 1530.71i | −0.158885 | + | 0.0917325i | −0.577335 | − | 0.816508i | \(-0.695907\pi\) |
0.418449 | + | 0.908240i | \(0.362574\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20799.4 | − | 36025.6i | 1.24076 | − | 2.14906i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3017.77i | 0.178385i | 0.996014 | + | 0.0891924i | \(0.0284286\pi\) | ||||
−0.996014 | + | 0.0891924i | \(0.971571\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4671.67 | − | 2697.19i | −0.274897 | − | 0.158712i | 0.356214 | − | 0.934404i | \(-0.384067\pi\) |
−0.631111 | + | 0.775693i | \(0.717401\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7827.43 | − | 3620.16i | −0.456443 | − | 0.211104i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6614.15 | − | 11456.0i | −0.383959 | − | 0.665037i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11316.4 | 0.651063 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21062.8 | 1.20641 | 0.603204 | − | 0.797587i | \(-0.293890\pi\) | ||||
0.603204 | + | 0.797587i | \(0.293890\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13505.8 | + | 23392.7i | 0.766718 | + | 1.32800i | 0.939333 | + | 0.343006i | \(0.111445\pi\) |
−0.172615 | + | 0.984989i | \(0.555222\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 925.089 | + | 10205.3i | 0.0522852 | + | 0.576793i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12369.6 | + | 7141.59i | 0.692986 | + | 0.400095i | 0.804730 | − | 0.593642i | \(-0.202310\pi\) |
−0.111744 | + | 0.993737i | \(0.535644\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11132.3i | 0.620940i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1424.60 | − | 2467.47i | 0.0787704 | − | 0.136434i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2246.31 | − | 1296.91i | 0.123666 | − | 0.0713989i | −0.436891 | − | 0.899515i | \(-0.643920\pi\) |
0.560557 | + | 0.828116i | \(0.310587\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −50687.1 | + | 29264.2i | −2.76644 | + | 1.59720i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 23892.9 | − | 41383.7i | 1.29843 | − | 2.24895i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 30185.3i | − | 1.62637i | −0.582009 | − | 0.813183i | \(-0.697733\pi\) | ||
0.582009 | − | 0.813183i | \(-0.302267\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2425.41 | − | 1400.31i | −0.130123 | − | 0.0751263i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1802.89 | − | 3898.16i | 0.0959047 | − | 0.207363i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15514.3 | + | 26871.5i | 0.821793 | + | 1.42339i | 0.904345 | + | 0.426801i | \(0.140360\pi\) |
−0.0825520 | + | 0.996587i | \(0.526307\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13807.7 | 0.725246 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5618.10 | 0.293853 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5323.93 | + | 9221.32i | 0.276146 | + | 0.478299i | 0.970424 | − | 0.241408i | \(-0.0776093\pi\) |
−0.694277 | + | 0.719707i | \(0.744276\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 29268.9 | − | 20631.3i | 1.51183 | − | 1.06567i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −23195.0 | − | 13391.6i | −1.18819 | − | 0.686005i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11374.6i | 0.580278i | 0.956985 | + | 0.290139i | \(0.0937015\pi\) | ||||
−0.956985 | + | 0.290139i | \(0.906299\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9744.57 | + | 16878.1i | −0.493045 | + | 0.853979i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19102.2 | + | 11028.7i | −0.962559 | + | 0.555734i | −0.896960 | − | 0.442113i | \(-0.854229\pi\) |
−0.0655991 | + | 0.997846i | \(0.520896\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1964.12 | − | 1133.99i | 0.0981673 | − | 0.0566769i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13160.9 | + | 22795.4i | −0.655119 | + | 1.13470i | 0.326745 | + | 0.945113i | \(0.394048\pi\) |
−0.981864 | + | 0.189587i | \(0.939285\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4269.63i | 0.210818i | 0.994429 | + | 0.105409i | \(0.0336151\pi\) | ||||
−0.994429 | + | 0.105409i | \(0.966385\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 27930.7 | + | 16125.8i | 1.37356 | + | 0.793025i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13458.6 | − | 9486.83i | 0.656565 | − | 0.462806i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14942.7 | − | 25881.5i | −0.726054 | − | 1.25756i | −0.958539 | − | 0.284963i | \(-0.908019\pi\) |
0.232484 | − | 0.972600i | \(-0.425315\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15458.7 | −0.745163 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12658.2 | −0.607756 | −0.303878 | − | 0.952711i | \(-0.598281\pi\) | ||||
−0.303878 | + | 0.952711i | \(0.598281\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13590.3 | + | 23539.0i | 0.647367 | + | 1.12127i | 0.983749 | + | 0.179548i | \(0.0574634\pi\) |
−0.336382 | + | 0.941726i | \(0.609203\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14944.7 | − | 32313.1i | 0.709089 | − | 1.53317i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8518.52 | + | 4918.17i | 0.401025 | + | 0.231532i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 21028.3i | − | 0.986087i | −0.870005 | − | 0.493044i | \(-0.835884\pi\) | ||
0.870005 | − | 0.493044i | \(-0.164116\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7220.65 | − | 12506.5i | 0.335975 | − | 0.581926i | −0.647697 | − | 0.761898i | \(-0.724268\pi\) |
0.983672 | + | 0.179972i | \(0.0576009\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 24210.9 | − | 13978.2i | 1.12217 | − | 0.647884i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7203.90 | + | 4159.17i | −0.331330 | + | 0.191294i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7926.36 | + | 13728.9i | −0.363159 | + | 0.629010i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13982.9i | 0.635759i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17907.5 | − | 10338.9i | −0.811098 | − | 0.468288i | 0.0362388 | − | 0.999343i | \(-0.488462\pi\) |
−0.847337 | + | 0.531055i | \(0.821796\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3461.74 | + | 38188.8i | 0.155607 | + | 1.71661i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5360.38 | + | 9284.45i | 0.240041 | + | 0.415764i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21175.0 | −0.941099 | −0.470550 | − | 0.882374i | \(-0.655944\pi\) | ||||
−0.470550 | + | 0.882374i | \(0.655944\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 47456.9 | 2.10126 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 452.242 | + | 783.306i | 0.0198746 | + | 0.0344238i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −41188.0 | − | 19049.3i | −1.80334 | − | 0.834037i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10628.5 | − | 6136.39i | −0.461903 | − | 0.266680i | 0.250941 | − | 0.968002i | \(-0.419260\pi\) |
−0.712844 | + | 0.701323i | \(0.752593\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 12975.7i | − | 0.561821i | −0.959734 | − | 0.280910i | \(-0.909364\pi\) | ||
0.959734 | − | 0.280910i | \(-0.0906364\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 20241.5 | − | 35059.3i | 0.869973 | − | 1.50684i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2938.07 | − | 1696.29i | 0.125814 | − | 0.0726387i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12870.4 | − | 7430.74i | 0.547114 | − | 0.315876i | −0.200843 | − | 0.979623i | \(-0.564368\pi\) |
0.747957 | + | 0.663747i | \(0.231035\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11450.4 | − | 19832.6i | 0.484975 | − | 0.840002i | −0.514876 | − | 0.857265i | \(-0.672162\pi\) |
0.999851 | + | 0.0172628i | \(0.00549519\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22216.5i | 0.934151i | 0.884217 | + | 0.467076i | \(0.154692\pi\) | ||||
−0.884217 | + | 0.467076i | \(0.845308\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14146.5 | + | 8167.47i | 0.592674 | + | 0.342181i | 0.766154 | − | 0.642657i | \(-0.222168\pi\) |
−0.173480 | + | 0.984837i | \(0.555501\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 15828.5 | − | 44351.7i | 0.658375 | − | 1.84477i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9911.28 | + | 17166.8i | 0.410771 | + | 0.711476i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3186.11 | −0.131104 | −0.0655522 | − | 0.997849i | \(-0.520881\pi\) | ||||
−0.0655522 | + | 0.997849i | \(0.520881\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13324.5 | 0.546334 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −18741.9 | − | 32461.9i | −0.763007 | − | 1.32157i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10954.5 | + | 15540.7i | 0.444393 | + | 0.630444i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12762.5 | − | 7368.45i | −0.514094 | − | 0.296812i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 15850.7i | − | 0.636245i | −0.948050 | − | 0.318123i | \(-0.896948\pi\) | ||
0.948050 | − | 0.318123i | \(-0.103052\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10826.0 | − | 18751.2i | 0.431517 | − | 0.747410i | −0.565487 | − | 0.824757i | \(-0.691312\pi\) |
0.997004 | + | 0.0773473i | \(0.0246450\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11070.4 | + | 6391.50i | −0.439717 | + | 0.253871i | −0.703478 | − | 0.710717i | \(-0.748370\pi\) |
0.263760 | + | 0.964588i | \(0.415037\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −21740.9 | + | 12552.1i | −0.857555 | + | 0.495110i | −0.863193 | − | 0.504874i | \(-0.831539\pi\) |
0.00563770 | + | 0.999984i | \(0.498205\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −29196.0 | + | 50568.9i | −1.14762 | + | 1.98774i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 16570.8i | − | 0.646866i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1860.75 | + | 1074.30i | 0.0723869 | + | 0.0417926i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −46583.4 | + | 4222.70i | −1.79978 | + | 0.163147i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25579.4 | − | 44304.9i | −0.984898 | − | 1.70589i | −0.642388 | − | 0.766379i | \(-0.722056\pi\) |
−0.342510 | − | 0.939514i | \(-0.611277\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21063.7 | −0.805510 | −0.402755 | − | 0.915308i | \(-0.631947\pi\) | ||||
−0.402755 | + | 0.915308i | \(0.631947\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 51.5775 | 0.00196571 | 0.000982855 | − | 1.00000i | \(-0.499687\pi\) | ||||
0.000982855 | 1.00000i | \(0.499687\pi\) | ||||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4460.79 | − | 7726.31i | −0.168860 | − | 0.292474i | 0.769159 | − | 0.639057i | \(-0.220675\pi\) |
−0.938019 | + | 0.346583i | \(0.887342\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −27821.4 | + | 2521.96i | −1.04961 | + | 0.0951449i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7154.32 | − | 4130.55i | −0.268097 | − | 0.154786i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 78147.4i | 2.91864i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5774.53 | − | 10001.8i | 0.214228 | − | 0.371054i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20496.8 | − | 11833.8i | 0.757876 | − | 0.437560i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 48695.2 | − | 28114.2i | 1.78860 | − | 1.03265i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2808.30 | + | 4864.13i | −0.102810 | + | 0.178071i | −0.912841 | − | 0.408315i | \(-0.866117\pi\) |
0.810032 | + | 0.586386i | \(0.199450\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19604.1i | 0.712967i | 0.934302 | + | 0.356484i | \(0.116024\pi\) | ||||
−0.934302 | + | 0.356484i | \(0.883976\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −19675.6 | − | 11359.7i | −0.713217 | − | 0.411776i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −22781.4 | − | 32319.1i | −0.820401 | − | 1.16387i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23979.7 | − | 41534.1i | −0.860737 | − | 1.49084i | −0.871218 | − | 0.490896i | \(-0.836670\pi\) |
0.0104809 | − | 0.999945i | \(-0.496664\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −15018.4 | −0.535575 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −29837.8 | −1.06060 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6868.87 | + | 11897.2i | 0.242584 | + | 0.420168i | 0.961450 | − | 0.274981i | \(-0.0886717\pi\) |
−0.718866 | + | 0.695149i | \(0.755338\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6246.49 | + | 5308.52i | −0.219893 | + | 0.186874i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 40416.0 | + | 23334.2i | 1.41363 | + | 0.816160i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 13590.7i | − | 0.473842i | −0.971529 | − | 0.236921i | \(-0.923862\pi\) | ||
0.971529 | − | 0.236921i | \(-0.0761383\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12655.2 | + | 21919.4i | −0.438414 | + | 0.759355i | −0.997567 | − | 0.0697090i | \(-0.977793\pi\) |
0.559153 | + | 0.829064i | \(0.311126\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −37906.9 | + | 21885.6i | −1.30903 | + | 0.755771i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 43071.4 | − | 24867.3i | 1.47796 | − | 0.853303i | 0.478274 | − | 0.878211i | \(-0.341263\pi\) |
0.999690 | + | 0.0249082i | \(0.00792934\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −428.440 | + | 742.080i | −0.0146552 | + | 0.0253835i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26069.9i | 0.886135i | 0.896488 | + | 0.443068i | \(0.146110\pi\) | ||||
−0.896488 | + | 0.443068i | \(0.853890\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22794.1 | + | 13160.2i | 0.772354 | + | 0.445919i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9604.26 | + | 4441.94i | 0.323397 | + | 0.149570i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8868.07 | − | 15359.9i | −0.297676 | − | 0.515590i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12307.7 | 0.410569 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40037.9 | 1.33147 | 0.665736 | − | 0.746187i | \(-0.268118\pi\) | ||||
0.665736 | + | 0.746187i | \(0.268118\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17155.3 | + | 29713.8i | 0.566981 | + | 0.982041i | 0.996862 | + | 0.0791551i | \(0.0252222\pi\) |
−0.429881 | + | 0.902886i | \(0.641444\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5022.50 | + | 55406.5i | 0.165482 | + | 1.82554i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21799.6 | + | 12586.0i | 0.713849 | + | 0.412141i | 0.812485 | − | 0.582982i | \(-0.198114\pi\) |
−0.0986353 | + | 0.995124i | \(0.531448\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7347.24i | 0.239856i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7087.40 | + | 12275.7i | −0.229962 | + | 0.398306i | −0.957797 | − | 0.287447i | \(-0.907194\pi\) |
0.727834 | + | 0.685753i | \(0.240527\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −39668.3 | + | 22902.5i | −1.28319 | + | 0.740848i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 15460.1 | − | 8925.90i | 0.497071 | − | 0.286984i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27259.1 | − | 47214.1i | 0.873777 | − | 1.51343i | 0.0157175 | − | 0.999876i | \(-0.494997\pi\) |
0.858060 | − | 0.513550i | \(-0.171670\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 21827.0i | 0.695439i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −381.200 | − | 220.086i | −0.0121090 | − | 0.00699116i | 0.493933 | − | 0.869500i | \(-0.335559\pi\) |
−0.506042 | + | 0.862509i | \(0.668892\pi\) | |||||||
\(998\) | 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 | 504.4.bl.a.17.2 | ✓ | 48 | |
3.2 | odd | 2 | inner | 504.4.bl.a.17.23 | yes | 48 | |
4.3 | odd | 2 | 1008.4.bt.d.17.2 | 48 | |||
7.5 | odd | 6 | inner | 504.4.bl.a.89.23 | yes | 48 | |
12.11 | even | 2 | 1008.4.bt.d.17.23 | 48 | |||
21.5 | even | 6 | inner | 504.4.bl.a.89.2 | yes | 48 | |
28.19 | even | 6 | 1008.4.bt.d.593.23 | 48 | |||
84.47 | odd | 6 | 1008.4.bt.d.593.2 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.4.bl.a.17.2 | ✓ | 48 | 1.1 | even | 1 | trivial | |
504.4.bl.a.17.23 | yes | 48 | 3.2 | odd | 2 | inner | |
504.4.bl.a.89.2 | yes | 48 | 21.5 | even | 6 | inner | |
504.4.bl.a.89.23 | yes | 48 | 7.5 | odd | 6 | inner | |
1008.4.bt.d.17.2 | 48 | 4.3 | odd | 2 | |||
1008.4.bt.d.17.23 | 48 | 12.11 | even | 2 | |||
1008.4.bt.d.593.2 | 48 | 84.47 | odd | 6 | |||
1008.4.bt.d.593.23 | 48 | 28.19 | even | 6 |