Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(589,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.589");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.g (of order \(2\), degree \(1\), 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: | \(11.7380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.1698758656.6 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 589.7 | ||
Root | \(3.16053i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.589 |
Dual form | 1470.2.g.k.589.3 |
$q$-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 \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.63280 | − | 1.52773i | 0.730213 | − | 0.683220i | ||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 1.52773 | + | 1.63280i | 0.483109 | + | 0.516338i | ||||
\(11\) | 4.46967 | 1.34766 | 0.673828 | − | 0.738889i | \(-0.264649\pi\) | ||||
0.673828 | + | 0.738889i | \(0.264649\pi\) | |||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | 5.88388i | 1.63189i | 0.578126 | + | 0.815947i | \(0.303784\pi\) | ||||
−0.578126 | + | 0.815947i | \(0.696216\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.52773 | − | 1.63280i | −0.394457 | − | 0.421588i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.73528i | 1.87608i | 0.346527 | + | 0.938040i | \(0.387361\pi\) | ||||
−0.346527 | + | 0.938040i | \(0.612639\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | −6.61827 | −1.51834 | −0.759168 | − | 0.650895i | \(-0.774394\pi\) | ||||
−0.759168 | + | 0.650895i | \(0.774394\pi\) | |||||||
\(20\) | −1.63280 | + | 1.52773i | −0.365106 | + | 0.341610i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.46967i | 0.952936i | ||||||||
\(23\) | 2.61827i | 0.545947i | 0.962022 | + | 0.272974i | \(0.0880071\pi\) | ||||
−0.962022 | + | 0.272974i | \(0.911993\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 0.332104 | − | 4.98896i | 0.0664208 | − | 0.997792i | ||||
\(26\) | −5.88388 | −1.15392 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.17246 | 1.51759 | 0.758794 | − | 0.651331i | \(-0.225789\pi\) | ||||
0.758794 | + | 0.651331i | \(0.225789\pi\) | |||||||
\(30\) | 1.63280 | − | 1.52773i | 0.298108 | − | 0.278923i | ||||
\(31\) | 8.46967 | 1.52120 | 0.760598 | − | 0.649223i | \(-0.224906\pi\) | ||||
0.760598 | + | 0.649223i | \(0.224906\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | − | 4.46967i | − | 0.778069i | ||||||
\(34\) | −7.73528 | −1.32659 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | − | 3.18719i | − | 0.523970i | −0.965072 | − | 0.261985i | \(-0.915623\pi\) | ||
0.965072 | − | 0.261985i | \(-0.0843772\pi\) | |||||||
\(38\) | − | 6.61827i | − | 1.07363i | ||||||
\(39\) | 5.88388 | 0.942175 | ||||||||
\(40\) | −1.52773 | − | 1.63280i | −0.241555 | − | 0.258169i | ||||
\(41\) | 3.56282 | 0.556419 | 0.278209 | − | 0.960520i | \(-0.410259\pi\) | ||||
0.278209 | + | 0.960520i | \(0.410259\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.43108i | 0.218238i | 0.994029 | + | 0.109119i | \(0.0348029\pi\) | ||||
−0.994029 | + | 0.109119i | \(0.965197\pi\) | |||||||
\(44\) | −4.46967 | −0.673828 | ||||||||
\(45\) | −1.63280 | + | 1.52773i | −0.243404 | + | 0.227740i | ||||
\(46\) | −2.61827 | −0.386043 | ||||||||
\(47\) | − | 6.79073i | − | 0.990530i | −0.868742 | − | 0.495265i | \(-0.835071\pi\) | ||
0.868742 | − | 0.495265i | \(-0.164929\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.98896 | + | 0.332104i | 0.705545 | + | 0.0469666i | ||||
\(51\) | 7.73528 | 1.08316 | ||||||||
\(52\) | − | 5.88388i | − | 0.815947i | ||||||
\(53\) | − | 1.38173i | − | 0.189795i | −0.995487 | − | 0.0948976i | \(-0.969748\pi\) | ||
0.995487 | − | 0.0948976i | \(-0.0302524\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 7.29809 | − | 6.82843i | 0.984075 | − | 0.920745i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.61827i | 0.876611i | ||||||||
\(58\) | 8.17246i | 1.07310i | ||||||||
\(59\) | −4.66421 | −0.607228 | −0.303614 | − | 0.952795i | \(-0.598193\pi\) | ||||
−0.303614 | + | 0.952795i | \(0.598193\pi\) | |||||||
\(60\) | 1.52773 | + | 1.63280i | 0.197229 | + | 0.210794i | ||||
\(61\) | 9.79683 | 1.25436 | 0.627178 | − | 0.778876i | \(-0.284210\pi\) | ||||
0.627178 | + | 0.778876i | \(0.284210\pi\) | |||||||
\(62\) | 8.46967i | 1.07565i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 8.98896 | + | 9.60723i | 1.11494 | + | 1.19163i | ||||
\(66\) | 4.46967 | 0.550178 | ||||||||
\(67\) | − | 1.85140i | − | 0.226184i | −0.993585 | − | 0.113092i | \(-0.963925\pi\) | ||
0.993585 | − | 0.113092i | \(-0.0360755\pi\) | |||||||
\(68\) | − | 7.73528i | − | 0.938040i | ||||||
\(69\) | 2.61827 | 0.315203 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.02386 | 0.240187 | 0.120094 | − | 0.992763i | \(-0.461680\pi\) | ||||
0.120094 | + | 0.992763i | \(0.461680\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | 4.01687i | 0.470139i | 0.971979 | + | 0.235069i | \(0.0755318\pi\) | ||||
−0.971979 | + | 0.235069i | \(0.924468\pi\) | |||||||
\(74\) | 3.18719 | 0.370503 | ||||||||
\(75\) | −4.98896 | − | 0.332104i | −0.576075 | − | 0.0383481i | ||||
\(76\) | 6.61827 | 0.759168 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 5.88388i | 0.666218i | ||||||||
\(79\) | 6.98527 | 0.785904 | 0.392952 | − | 0.919559i | \(-0.371454\pi\) | ||||
0.392952 | + | 0.919559i | \(0.371454\pi\) | |||||||
\(80\) | 1.63280 | − | 1.52773i | 0.182553 | − | 0.170805i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.56282i | 0.393447i | ||||||||
\(83\) | 5.35965i | 0.588298i | 0.955760 | + | 0.294149i | \(0.0950361\pi\) | ||||
−0.955760 | + | 0.294149i | \(0.904964\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.8174 | + | 12.6302i | 1.28178 | + | 1.36994i | ||||
\(86\) | −1.43108 | −0.154318 | ||||||||
\(87\) | − | 8.17246i | − | 0.876180i | ||||||
\(88\) | − | 4.46967i | − | 0.476468i | ||||||
\(89\) | −14.3912 | −1.52547 | −0.762734 | − | 0.646712i | \(-0.776144\pi\) | ||||
−0.762734 | + | 0.646712i | \(0.776144\pi\) | |||||||
\(90\) | −1.52773 | − | 1.63280i | −0.161036 | − | 0.172113i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 2.61827i | − | 0.272974i | ||||||
\(93\) | − | 8.46967i | − | 0.878263i | ||||||
\(94\) | 6.79073 | 0.700410 | ||||||||
\(95\) | −10.8063 | + | 10.1109i | −1.10871 | + | 1.03736i | ||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 7.71966i | 0.783813i | 0.920005 | + | 0.391906i | \(0.128184\pi\) | ||||
−0.920005 | + | 0.391906i | \(0.871816\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.46967 | −0.449218 | ||||||||
\(100\) | −0.332104 | + | 4.98896i | −0.0332104 | + | 0.498896i | ||||
\(101\) | −13.3544 | −1.32882 | −0.664408 | − | 0.747370i | \(-0.731316\pi\) | ||||
−0.664408 | + | 0.747370i | \(0.731316\pi\) | |||||||
\(102\) | 7.73528i | 0.765906i | ||||||||
\(103\) | − | 9.35965i | − | 0.922233i | −0.887339 | − | 0.461117i | \(-0.847449\pi\) | ||
0.887339 | − | 0.461117i | \(-0.152551\pi\) | |||||||
\(104\) | 5.88388 | 0.576962 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.38173 | 0.134205 | ||||||||
\(107\) | − | 11.0165i | − | 1.06501i | −0.846428 | − | 0.532503i | \(-0.821252\pi\) | ||
0.846428 | − | 0.532503i | \(-0.178748\pi\) | |||||||
\(108\) | − | 1.00000i | − | 0.0962250i | ||||||
\(109\) | 4.69544 | 0.449741 | 0.224871 | − | 0.974389i | \(-0.427804\pi\) | ||||
0.224871 | + | 0.974389i | \(0.427804\pi\) | |||||||
\(110\) | 6.82843 | + | 7.29809i | 0.651065 | + | 0.695846i | ||||
\(111\) | −3.18719 | −0.302514 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 12.5723i | − | 1.18271i | −0.806413 | − | 0.591353i | \(-0.798594\pi\) | ||
0.806413 | − | 0.591353i | \(-0.201406\pi\) | |||||||
\(114\) | −6.61827 | −0.619858 | ||||||||
\(115\) | 4.00000 | + | 4.27512i | 0.373002 | + | 0.398657i | ||||
\(116\) | −8.17246 | −0.758794 | ||||||||
\(117\) | − | 5.88388i | − | 0.543965i | ||||||
\(118\) | − | 4.66421i | − | 0.429375i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.63280 | + | 1.52773i | −0.149054 | + | 0.139462i | ||||
\(121\) | 8.97792 | 0.816174 | ||||||||
\(122\) | 9.79683i | 0.886963i | ||||||||
\(123\) | − | 3.56282i | − | 0.321248i | ||||||
\(124\) | −8.46967 | −0.760598 | ||||||||
\(125\) | −7.07950 | − | 8.65336i | −0.633210 | − | 0.773980i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.59619i | 0.585317i | 0.956217 | + | 0.292658i | \(0.0945399\pi\) | ||||
−0.956217 | + | 0.292658i | \(0.905460\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 1.43108 | 0.126000 | ||||||||
\(130\) | −9.60723 | + | 8.98896i | −0.842610 | + | 0.788384i | ||||
\(131\) | −2.32106 | −0.202792 | −0.101396 | − | 0.994846i | \(-0.532331\pi\) | ||||
−0.101396 | + | 0.994846i | \(0.532331\pi\) | |||||||
\(132\) | 4.46967i | 0.389035i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.85140 | 0.159936 | ||||||||
\(135\) | 1.52773 | + | 1.63280i | 0.131486 | + | 0.140529i | ||||
\(136\) | 7.73528 | 0.663294 | ||||||||
\(137\) | 14.2751i | 1.21961i | 0.792553 | + | 0.609803i | \(0.208751\pi\) | ||||
−0.792553 | + | 0.609803i | \(0.791249\pi\) | |||||||
\(138\) | 2.61827i | 0.222882i | ||||||||
\(139\) | 14.9632 | 1.26916 | 0.634581 | − | 0.772857i | \(-0.281173\pi\) | ||||
0.634581 | + | 0.772857i | \(0.281173\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.79073 | −0.571883 | ||||||||
\(142\) | 2.02386i | 0.169838i | ||||||||
\(143\) | 26.2990i | 2.19923i | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 13.3440 | − | 12.4853i | 1.10816 | − | 1.03685i | ||||
\(146\) | −4.01687 | −0.332438 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.18719i | 0.261985i | ||||||||
\(149\) | −11.1651 | −0.914681 | −0.457341 | − | 0.889292i | \(-0.651198\pi\) | ||||
−0.457341 | + | 0.889292i | \(0.651198\pi\) | |||||||
\(150\) | 0.332104 | − | 4.98896i | 0.0271162 | − | 0.407347i | ||||
\(151\) | 0.664208 | 0.0540525 | 0.0270263 | − | 0.999635i | \(-0.491396\pi\) | ||||
0.0270263 | + | 0.999635i | \(0.491396\pi\) | |||||||
\(152\) | 6.61827i | 0.536813i | ||||||||
\(153\) | − | 7.73528i | − | 0.625360i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.8293 | − | 12.9393i | 1.11080 | − | 1.03931i | ||||
\(156\) | −5.88388 | −0.471087 | ||||||||
\(157\) | 8.08184i | 0.645001i | 0.946569 | + | 0.322500i | \(0.104523\pi\) | ||||
−0.946569 | + | 0.322500i | \(0.895477\pi\) | |||||||
\(158\) | 6.98527i | 0.555718i | ||||||||
\(159\) | −1.38173 | −0.109578 | ||||||||
\(160\) | 1.52773 | + | 1.63280i | 0.120777 | + | 0.129085i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | − | 0.836668i | − | 0.0655329i | −0.999463 | − | 0.0327664i | \(-0.989568\pi\) | ||
0.999463 | − | 0.0327664i | \(-0.0104317\pi\) | |||||||
\(164\) | −3.56282 | −0.278209 | ||||||||
\(165\) | −6.82843 | − | 7.29809i | −0.531592 | − | 0.568156i | ||||
\(166\) | −5.35965 | −0.415989 | ||||||||
\(167\) | − | 2.66762i | − | 0.206427i | −0.994659 | − | 0.103213i | \(-0.967088\pi\) | ||
0.994659 | − | 0.103213i | \(-0.0329125\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −21.6200 | −1.66308 | ||||||||
\(170\) | −12.6302 | + | 11.8174i | −0.968692 | + | 0.906352i | ||||
\(171\) | 6.61827 | 0.506112 | ||||||||
\(172\) | − | 1.43108i | − | 0.109119i | ||||||
\(173\) | 0.647340i | 0.0492164i | 0.999697 | + | 0.0246082i | \(0.00783382\pi\) | ||||
−0.999697 | + | 0.0246082i | \(0.992166\pi\) | |||||||
\(174\) | 8.17246 | 0.619553 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.46967 | 0.336914 | ||||||||
\(177\) | 4.66421i | 0.350583i | ||||||||
\(178\) | − | 14.3912i | − | 1.07867i | ||||||
\(179\) | 25.7374 | 1.92371 | 0.961853 | − | 0.273566i | \(-0.0882033\pi\) | ||||
0.961853 | + | 0.273566i | \(0.0882033\pi\) | |||||||
\(180\) | 1.63280 | − | 1.52773i | 0.121702 | − | 0.113870i | ||||
\(181\) | 7.42245 | 0.551707 | 0.275853 | − | 0.961200i | \(-0.411040\pi\) | ||||
0.275853 | + | 0.961200i | \(0.411040\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 9.79683i | − | 0.724203i | ||||||
\(184\) | 2.61827 | 0.193021 | ||||||||
\(185\) | −4.86915 | − | 5.20406i | −0.357987 | − | 0.382610i | ||||
\(186\) | 8.46967 | 0.621026 | ||||||||
\(187\) | 34.5741i | 2.52831i | ||||||||
\(188\) | 6.79073i | 0.495265i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −10.1109 | − | 10.8063i | −0.733522 | − | 0.783975i | ||||
\(191\) | −1.08452 | −0.0784733 | −0.0392367 | − | 0.999230i | \(-0.512493\pi\) | ||||
−0.0392367 | + | 0.999230i | \(0.512493\pi\) | |||||||
\(192\) | 1.00000i | 0.0721688i | ||||||||
\(193\) | − | 8.93933i | − | 0.643467i | −0.946830 | − | 0.321734i | \(-0.895734\pi\) | ||
0.946830 | − | 0.321734i | \(-0.104266\pi\) | |||||||
\(194\) | −7.71966 | −0.554239 | ||||||||
\(195\) | 9.60723 | − | 8.98896i | 0.687988 | − | 0.643713i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.45890i | 0.531425i | 0.964052 | + | 0.265712i | \(0.0856071\pi\) | ||||
−0.964052 | + | 0.265712i | \(0.914393\pi\) | |||||||
\(198\) | − | 4.46967i | − | 0.317645i | ||||||
\(199\) | −25.8293 | −1.83099 | −0.915496 | − | 0.402328i | \(-0.868201\pi\) | ||||
−0.915496 | + | 0.402328i | \(0.868201\pi\) | |||||||
\(200\) | −4.98896 | − | 0.332104i | −0.352773 | − | 0.0234833i | ||||
\(201\) | −1.85140 | −0.130587 | ||||||||
\(202\) | − | 13.3544i | − | 0.939615i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −7.73528 | −0.541578 | ||||||||
\(205\) | 5.81739 | − | 5.44301i | 0.406304 | − | 0.380156i | ||||
\(206\) | 9.35965 | 0.652118 | ||||||||
\(207\) | − | 2.61827i | − | 0.181982i | ||||||
\(208\) | 5.88388i | 0.407974i | ||||||||
\(209\) | −29.5815 | −2.04619 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.53375 | 0.380959 | 0.190479 | − | 0.981691i | \(-0.438996\pi\) | ||||
0.190479 | + | 0.981691i | \(0.438996\pi\) | |||||||
\(212\) | 1.38173i | 0.0948976i | ||||||||
\(213\) | − | 2.02386i | − | 0.138672i | ||||||
\(214\) | 11.0165 | 0.753073 | ||||||||
\(215\) | 2.18630 | + | 2.33668i | 0.149105 | + | 0.159360i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4.69544i | 0.318015i | ||||||||
\(219\) | 4.01687 | 0.271435 | ||||||||
\(220\) | −7.29809 | + | 6.82843i | −0.492037 | + | 0.460372i | ||||
\(221\) | −45.5134 | −3.06157 | ||||||||
\(222\) | − | 3.18719i | − | 0.213910i | ||||||
\(223\) | − | 3.28248i | − | 0.219811i | −0.993942 | − | 0.109906i | \(-0.964945\pi\) | ||
0.993942 | − | 0.109906i | \(-0.0350548\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.332104 | + | 4.98896i | −0.0221403 | + | 0.332597i | ||||
\(226\) | 12.5723 | 0.836299 | ||||||||
\(227\) | 4.42031i | 0.293387i | 0.989182 | + | 0.146693i | \(0.0468630\pi\) | ||||
−0.989182 | + | 0.146693i | \(0.953137\pi\) | |||||||
\(228\) | − | 6.61827i | − | 0.438306i | ||||||
\(229\) | 7.97270 | 0.526851 | 0.263426 | − | 0.964680i | \(-0.415148\pi\) | ||||
0.263426 | + | 0.964680i | \(0.415148\pi\) | |||||||
\(230\) | −4.27512 | + | 4.00000i | −0.281893 | + | 0.263752i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 8.17246i | − | 0.536548i | ||||||
\(233\) | 17.9558i | 1.17633i | 0.808742 | + | 0.588163i | \(0.200149\pi\) | ||||
−0.808742 | + | 0.588163i | \(0.799851\pi\) | |||||||
\(234\) | 5.88388 | 0.384641 | ||||||||
\(235\) | −10.3744 | − | 11.0879i | −0.676750 | − | 0.723297i | ||||
\(236\) | 4.66421 | 0.303614 | ||||||||
\(237\) | − | 6.98527i | − | 0.453742i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.41296 | −0.350135 | −0.175068 | − | 0.984556i | \(-0.556014\pi\) | ||||
−0.175068 | + | 0.984556i | \(0.556014\pi\) | |||||||
\(240\) | −1.52773 | − | 1.63280i | −0.0986143 | − | 0.105397i | ||||
\(241\) | −4.69669 | −0.302541 | −0.151270 | − | 0.988492i | \(-0.548336\pi\) | ||||
−0.151270 | + | 0.988492i | \(0.548336\pi\) | |||||||
\(242\) | 8.97792i | 0.577122i | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | −9.79683 | −0.627178 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.56282 | 0.227157 | ||||||||
\(247\) | − | 38.9411i | − | 2.47776i | ||||||
\(248\) | − | 8.46967i | − | 0.537824i | ||||||
\(249\) | 5.35965 | 0.339654 | ||||||||
\(250\) | 8.65336 | − | 7.07950i | 0.547287 | − | 0.447747i | ||||
\(251\) | 7.73402 | 0.488167 | 0.244084 | − | 0.969754i | \(-0.421513\pi\) | ||||
0.244084 | + | 0.969754i | \(0.421513\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.7028i | 0.735748i | ||||||||
\(254\) | −6.59619 | −0.413882 | ||||||||
\(255\) | 12.6302 | − | 11.8174i | 0.790934 | − | 0.740033i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 1.34442i | − | 0.0838626i | −0.999120 | − | 0.0419313i | \(-0.986649\pi\) | ||
0.999120 | − | 0.0419313i | \(-0.0133511\pi\) | |||||||
\(258\) | 1.43108i | 0.0890953i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −8.98896 | − | 9.60723i | −0.557472 | − | 0.595815i | ||||
\(261\) | −8.17246 | −0.505863 | ||||||||
\(262\) | − | 2.32106i | − | 0.143396i | ||||||
\(263\) | − | 4.36700i | − | 0.269281i | −0.990895 | − | 0.134640i | \(-0.957012\pi\) | ||
0.990895 | − | 0.134640i | \(-0.0429879\pi\) | |||||||
\(264\) | −4.46967 | −0.275089 | ||||||||
\(265\) | −2.11091 | − | 2.25610i | −0.129672 | − | 0.138591i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.3912i | 0.880730i | ||||||||
\(268\) | 1.85140i | 0.113092i | ||||||||
\(269\) | −23.0671 | −1.40643 | −0.703213 | − | 0.710979i | \(-0.748252\pi\) | ||||
−0.703213 | + | 0.710979i | \(0.748252\pi\) | |||||||
\(270\) | −1.63280 | + | 1.52773i | −0.0993693 | + | 0.0929745i | ||||
\(271\) | 14.7209 | 0.894233 | 0.447117 | − | 0.894476i | \(-0.352451\pi\) | ||||
0.447117 | + | 0.894476i | \(0.352451\pi\) | |||||||
\(272\) | 7.73528i | 0.469020i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −14.2751 | −0.862392 | ||||||||
\(275\) | 1.48440 | − | 22.2990i | 0.0895124 | − | 1.34468i | ||||
\(276\) | −2.61827 | −0.157601 | ||||||||
\(277\) | 3.21104i | 0.192933i | 0.995336 | + | 0.0964665i | \(0.0307541\pi\) | ||||
−0.995336 | + | 0.0964665i | \(0.969246\pi\) | |||||||
\(278\) | 14.9632i | 0.897432i | ||||||||
\(279\) | −8.46967 | −0.507066 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.72488 | −0.460827 | −0.230414 | − | 0.973093i | \(-0.574008\pi\) | ||||
−0.230414 | + | 0.973093i | \(0.574008\pi\) | |||||||
\(282\) | − | 6.79073i | − | 0.404382i | ||||||
\(283\) | − | 29.5594i | − | 1.75712i | −0.477630 | − | 0.878561i | \(-0.658504\pi\) | ||
0.477630 | − | 0.878561i | \(-0.341496\pi\) | |||||||
\(284\) | −2.02386 | −0.120094 | ||||||||
\(285\) | 10.1109 | + | 10.8063i | 0.598918 | + | 0.640113i | ||||
\(286\) | −26.2990 | −1.55509 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | −42.8345 | −2.51968 | ||||||||
\(290\) | 12.4853 | + | 13.3440i | 0.733161 | + | 0.783589i | ||||
\(291\) | 7.71966 | 0.452535 | ||||||||
\(292\) | − | 4.01687i | − | 0.235069i | ||||||
\(293\) | 1.17679i | 0.0687487i | 0.999409 | + | 0.0343743i | \(0.0109438\pi\) | ||||
−0.999409 | + | 0.0343743i | \(0.989056\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.61574 | + | 7.12563i | −0.443406 | + | 0.414870i | ||||
\(296\) | −3.18719 | −0.185252 | ||||||||
\(297\) | 4.46967i | 0.259356i | ||||||||
\(298\) | − | 11.1651i | − | 0.646777i | ||||||
\(299\) | −15.4056 | −0.890928 | ||||||||
\(300\) | 4.98896 | + | 0.332104i | 0.288038 | + | 0.0191740i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0.664208i | 0.0382209i | ||||||||
\(303\) | 13.3544i | 0.767192i | ||||||||
\(304\) | −6.61827 | −0.379584 | ||||||||
\(305\) | 15.9963 | − | 14.9669i | 0.915946 | − | 0.857001i | ||||
\(306\) | 7.73528 | 0.442196 | ||||||||
\(307\) | − | 20.3761i | − | 1.16293i | −0.813572 | − | 0.581464i | \(-0.802480\pi\) | ||
0.813572 | − | 0.581464i | \(-0.197520\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.35965 | −0.532452 | ||||||||
\(310\) | 12.9393 | + | 13.8293i | 0.734905 | + | 0.785452i | ||||
\(311\) | −18.8934 | −1.07135 | −0.535673 | − | 0.844425i | \(-0.679942\pi\) | ||||
−0.535673 | + | 0.844425i | \(0.679942\pi\) | |||||||
\(312\) | − | 5.88388i | − | 0.333109i | ||||||
\(313\) | 16.4849i | 0.931781i | 0.884842 | + | 0.465891i | \(0.154266\pi\) | ||||
−0.884842 | + | 0.465891i | \(0.845734\pi\) | |||||||
\(314\) | −8.08184 | −0.456084 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.98527 | −0.392952 | ||||||||
\(317\) | 10.3211i | 0.579689i | 0.957074 | + | 0.289844i | \(0.0936035\pi\) | ||||
−0.957074 | + | 0.289844i | \(0.906396\pi\) | |||||||
\(318\) | − | 1.38173i | − | 0.0774836i | ||||||
\(319\) | 36.5282 | 2.04518 | ||||||||
\(320\) | −1.63280 | + | 1.52773i | −0.0912766 | + | 0.0854025i | ||||
\(321\) | −11.0165 | −0.614881 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 51.1941i | − | 2.84852i | ||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 29.3544 | + | 1.95406i | 1.62829 | + | 0.108392i | ||||
\(326\) | 0.836668 | 0.0463387 | ||||||||
\(327\) | − | 4.69544i | − | 0.259658i | ||||||
\(328\) | − | 3.56282i | − | 0.196724i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 7.29809 | − | 6.82843i | 0.401747 | − | 0.375893i | ||||
\(331\) | −19.1906 | −1.05481 | −0.527405 | − | 0.849614i | \(-0.676835\pi\) | ||||
−0.527405 | + | 0.849614i | \(0.676835\pi\) | |||||||
\(332\) | − | 5.35965i | − | 0.294149i | ||||||
\(333\) | 3.18719i | 0.174657i | ||||||||
\(334\) | 2.66762 | 0.145966 | ||||||||
\(335\) | −2.82843 | − | 3.02297i | −0.154533 | − | 0.165162i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 27.6035i | − | 1.50366i | −0.659357 | − | 0.751830i | \(-0.729171\pi\) | ||
0.659357 | − | 0.751830i | \(-0.270829\pi\) | |||||||
\(338\) | − | 21.6200i | − | 1.17598i | ||||||
\(339\) | −12.5723 | −0.682835 | ||||||||
\(340\) | −11.8174 | − | 12.6302i | −0.640888 | − | 0.684969i | ||||
\(341\) | 37.8566 | 2.05005 | ||||||||
\(342\) | 6.61827i | 0.357875i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1.43108 | 0.0771588 | ||||||||
\(345\) | 4.27512 | − | 4.00000i | 0.230165 | − | 0.215353i | ||||
\(346\) | −0.647340 | −0.0348012 | ||||||||
\(347\) | − | 20.3761i | − | 1.09385i | −0.837182 | − | 0.546924i | \(-0.815798\pi\) | ||
0.837182 | − | 0.546924i | \(-0.184202\pi\) | |||||||
\(348\) | 8.17246i | 0.438090i | ||||||||
\(349\) | 17.8281 | 0.954314 | 0.477157 | − | 0.878818i | \(-0.341667\pi\) | ||||
0.477157 | + | 0.878818i | \(0.341667\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.88388 | −0.314058 | ||||||||
\(352\) | 4.46967i | 0.238234i | ||||||||
\(353\) | 3.51347i | 0.187003i | 0.995619 | + | 0.0935014i | \(0.0298060\pi\) | ||||
−0.995619 | + | 0.0935014i | \(0.970194\pi\) | |||||||
\(354\) | −4.66421 | −0.247900 | ||||||||
\(355\) | 3.30456 | − | 3.09190i | 0.175388 | − | 0.164101i | ||||
\(356\) | 14.3912 | 0.762734 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 25.7374i | 1.36027i | ||||||||
\(359\) | 2.19796 | 0.116004 | 0.0580018 | − | 0.998316i | \(-0.481527\pi\) | ||||
0.0580018 | + | 0.998316i | \(0.481527\pi\) | |||||||
\(360\) | 1.52773 | + | 1.63280i | 0.0805182 | + | 0.0860564i | ||||
\(361\) | 24.8015 | 1.30534 | ||||||||
\(362\) | 7.42245i | 0.390116i | ||||||||
\(363\) | − | 8.97792i | − | 0.471218i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.13668 | + | 6.55876i | 0.321208 | + | 0.343301i | ||||
\(366\) | 9.79683 | 0.512089 | ||||||||
\(367\) | − | 28.7721i | − | 1.50189i | −0.660365 | − | 0.750945i | \(-0.729598\pi\) | ||
0.660365 | − | 0.750945i | \(-0.270402\pi\) | |||||||
\(368\) | 2.61827i | 0.136487i | ||||||||
\(369\) | −3.56282 | −0.185473 | ||||||||
\(370\) | 5.20406 | − | 4.86915i | 0.270546 | − | 0.253135i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 8.46967i | 0.439132i | ||||||||
\(373\) | 14.5689i | 0.754350i | 0.926142 | + | 0.377175i | \(0.123104\pi\) | ||||
−0.926142 | + | 0.377175i | \(0.876896\pi\) | |||||||
\(374\) | −34.5741 | −1.78778 | ||||||||
\(375\) | −8.65336 | + | 7.07950i | −0.446858 | + | 0.365584i | ||||
\(376\) | −6.79073 | −0.350205 | ||||||||
\(377\) | 48.0858i | 2.47654i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.7868 | 1.58141 | 0.790705 | − | 0.612197i | \(-0.209714\pi\) | ||||
0.790705 | + | 0.612197i | \(0.209714\pi\) | |||||||
\(380\) | 10.8063 | − | 10.1109i | 0.554354 | − | 0.518679i | ||||
\(381\) | 6.59619 | 0.337933 | ||||||||
\(382\) | − | 1.08452i | − | 0.0554890i | ||||||
\(383\) | 23.3410i | 1.19267i | 0.802736 | + | 0.596334i | \(0.203377\pi\) | ||||
−0.802736 | + | 0.596334i | \(0.796623\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.93933 | 0.455000 | ||||||||
\(387\) | − | 1.43108i | − | 0.0727460i | ||||||
\(388\) | − | 7.71966i | − | 0.391906i | ||||||
\(389\) | 1.21842 | 0.0617762 | 0.0308881 | − | 0.999523i | \(-0.490166\pi\) | ||||
0.0308881 | + | 0.999523i | \(0.490166\pi\) | |||||||
\(390\) | 8.98896 | + | 9.60723i | 0.455174 | + | 0.486481i | ||||
\(391\) | −20.2530 | −1.02424 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.32106i | 0.117082i | ||||||||
\(394\) | −7.45890 | −0.375774 | ||||||||
\(395\) | 11.4056 | − | 10.6716i | 0.573877 | − | 0.536946i | ||||
\(396\) | 4.46967 | 0.224609 | ||||||||
\(397\) | − | 8.40595i | − | 0.421883i | −0.977499 | − | 0.210941i | \(-0.932347\pi\) | ||
0.977499 | − | 0.210941i | \(-0.0676529\pi\) | |||||||
\(398\) | − | 25.8293i | − | 1.29471i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.332104 | − | 4.98896i | 0.0166052 | − | 0.249448i | ||||
\(401\) | −0.664208 | −0.0331690 | −0.0165845 | − | 0.999862i | \(-0.505279\pi\) | ||||
−0.0165845 | + | 0.999862i | \(0.505279\pi\) | |||||||
\(402\) | − | 1.85140i | − | 0.0923393i | ||||||
\(403\) | 49.8345i | 2.48243i | ||||||||
\(404\) | 13.3544 | 0.664408 | ||||||||
\(405\) | 1.63280 | − | 1.52773i | 0.0811347 | − | 0.0759133i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 14.2457i | − | 0.706131i | ||||||
\(408\) | − | 7.73528i | − | 0.382953i | ||||||
\(409\) | 7.38476 | 0.365153 | 0.182576 | − | 0.983192i | \(-0.441556\pi\) | ||||
0.182576 | + | 0.983192i | \(0.441556\pi\) | |||||||
\(410\) | 5.44301 | + | 5.81739i | 0.268811 | + | 0.287300i | ||||
\(411\) | 14.2751 | 0.704140 | ||||||||
\(412\) | 9.35965i | 0.461117i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 2.61827 | 0.128681 | ||||||||
\(415\) | 8.18807 | + | 8.75126i | 0.401937 | + | 0.429582i | ||||
\(416\) | −5.88388 | −0.288481 | ||||||||
\(417\) | − | 14.9632i | − | 0.732750i | ||||||
\(418\) | − | 29.5815i | − | 1.44688i | ||||||
\(419\) | −18.6274 | −0.910009 | −0.455004 | − | 0.890489i | \(-0.650362\pi\) | ||||
−0.455004 | + | 0.890489i | \(0.650362\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.5043 | −0.658159 | −0.329079 | − | 0.944302i | \(-0.606738\pi\) | ||||
−0.329079 | + | 0.944302i | \(0.606738\pi\) | |||||||
\(422\) | 5.53375i | 0.269379i | ||||||||
\(423\) | 6.79073i | 0.330177i | ||||||||
\(424\) | −1.38173 | −0.0671027 | ||||||||
\(425\) | 38.5910 | + | 2.56892i | 1.87194 | + | 0.124611i | ||||
\(426\) | 2.02386 | 0.0980561 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 11.0165i | 0.532503i | ||||||||
\(429\) | 26.2990 | 1.26973 | ||||||||
\(430\) | −2.33668 | + | 2.18630i | −0.112685 | + | 0.105433i | ||||
\(431\) | −31.6807 | −1.52601 | −0.763003 | − | 0.646395i | \(-0.776276\pi\) | ||||
−0.763003 | + | 0.646395i | \(0.776276\pi\) | |||||||
\(432\) | 1.00000i | 0.0481125i | ||||||||
\(433\) | 25.3184i | 1.21672i | 0.793660 | + | 0.608362i | \(0.208173\pi\) | ||||
−0.793660 | + | 0.608362i | \(0.791827\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.4853 | − | 13.3440i | −0.598623 | − | 0.639797i | ||||
\(436\) | −4.69544 | −0.224871 | ||||||||
\(437\) | − | 17.3284i | − | 0.828931i | ||||||
\(438\) | 4.01687i | 0.191933i | ||||||||
\(439\) | −32.8146 | −1.56615 | −0.783077 | − | 0.621924i | \(-0.786351\pi\) | ||||
−0.783077 | + | 0.621924i | \(0.786351\pi\) | |||||||
\(440\) | −6.82843 | − | 7.29809i | −0.325532 | − | 0.347923i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 45.5134i | − | 2.16485i | ||||||
\(443\) | − | 16.6421i | − | 0.790691i | −0.918532 | − | 0.395346i | \(-0.870625\pi\) | ||
0.918532 | − | 0.395346i | \(-0.129375\pi\) | |||||||
\(444\) | 3.18719 | 0.151257 | ||||||||
\(445\) | −23.4981 | + | 21.9859i | −1.11392 | + | 1.04223i | ||||
\(446\) | 3.28248 | 0.155430 | ||||||||
\(447\) | 11.1651i | 0.528091i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.1759 | −0.952158 | −0.476079 | − | 0.879402i | \(-0.657942\pi\) | ||||
−0.476079 | + | 0.879402i | \(0.657942\pi\) | |||||||
\(450\) | −4.98896 | − | 0.332104i | −0.235182 | − | 0.0156555i | ||||
\(451\) | 15.9246 | 0.749860 | ||||||||
\(452\) | 12.5723i | 0.591353i | ||||||||
\(453\) | − | 0.664208i | − | 0.0312072i | ||||||
\(454\) | −4.42031 | −0.207456 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.61827 | 0.309929 | ||||||||
\(457\) | − | 35.4124i | − | 1.65652i | −0.560342 | − | 0.828261i | \(-0.689330\pi\) | ||
0.560342 | − | 0.828261i | \(-0.310670\pi\) | |||||||
\(458\) | 7.97270i | 0.372540i | ||||||||
\(459\) | −7.73528 | −0.361052 | ||||||||
\(460\) | −4.00000 | − | 4.27512i | −0.186501 | − | 0.199329i | ||||
\(461\) | −12.5940 | −0.586562 | −0.293281 | − | 0.956026i | \(-0.594747\pi\) | ||||
−0.293281 | + | 0.956026i | \(0.594747\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 32.5061i | − | 1.51069i | −0.655330 | − | 0.755343i | \(-0.727470\pi\) | ||
0.655330 | − | 0.755343i | \(-0.272530\pi\) | |||||||
\(464\) | 8.17246 | 0.379397 | ||||||||
\(465\) | −12.9393 | − | 13.8293i | −0.600047 | − | 0.641319i | ||||
\(466\) | −17.9558 | −0.831788 | ||||||||
\(467\) | 9.20531i | 0.425971i | 0.977055 | + | 0.212985i | \(0.0683187\pi\) | ||||
−0.977055 | + | 0.212985i | \(0.931681\pi\) | |||||||
\(468\) | 5.88388i | 0.271982i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 11.0879 | − | 10.3744i | 0.511448 | − | 0.478534i | ||||
\(471\) | 8.08184 | 0.372391 | ||||||||
\(472\) | 4.66421i | 0.214688i | ||||||||
\(473\) | 6.39646i | 0.294109i | ||||||||
\(474\) | 6.98527 | 0.320844 | ||||||||
\(475\) | −2.19796 | + | 33.0183i | −0.100849 | + | 1.51498i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.38173i | 0.0632651i | ||||||||
\(478\) | − | 5.41296i | − | 0.247583i | ||||||
\(479\) | 39.4914 | 1.80441 | 0.902203 | − | 0.431312i | \(-0.141949\pi\) | ||||
0.902203 | + | 0.431312i | \(0.141949\pi\) | |||||||
\(480\) | 1.63280 | − | 1.52773i | 0.0745270 | − | 0.0697308i | ||||
\(481\) | 18.7530 | 0.855065 | ||||||||
\(482\) | − | 4.69669i | − | 0.213928i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.97792 | −0.408087 | ||||||||
\(485\) | 11.7935 | + | 12.6047i | 0.535517 | + | 0.572350i | ||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | − | 29.2678i | − | 1.32625i | −0.748509 | − | 0.663125i | \(-0.769230\pi\) | ||
0.748509 | − | 0.663125i | \(-0.230770\pi\) | |||||||
\(488\) | − | 9.79683i | − | 0.443482i | ||||||
\(489\) | −0.836668 | −0.0378354 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.3631 | 0.693325 | 0.346663 | − | 0.937990i | \(-0.387315\pi\) | ||||
0.346663 | + | 0.937990i | \(0.387315\pi\) | |||||||
\(492\) | 3.56282i | 0.160624i | ||||||||
\(493\) | 63.2162i | 2.84712i | ||||||||
\(494\) | 38.9411 | 1.75204 | ||||||||
\(495\) | −7.29809 | + | 6.82843i | −0.328025 | + | 0.306915i | ||||
\(496\) | 8.46967 | 0.380299 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 5.35965i | 0.240172i | ||||||||
\(499\) | −20.5502 | −0.919955 | −0.459978 | − | 0.887930i | \(-0.652143\pi\) | ||||
−0.459978 | + | 0.887930i | \(0.652143\pi\) | |||||||
\(500\) | 7.07950 | + | 8.65336i | 0.316605 | + | 0.386990i | ||||
\(501\) | −2.66762 | −0.119181 | ||||||||
\(502\) | 7.73402i | 0.345186i | ||||||||
\(503\) | − | 20.4788i | − | 0.913105i | −0.889696 | − | 0.456553i | \(-0.849084\pi\) | ||
0.889696 | − | 0.456553i | \(-0.150916\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21.8052 | + | 20.4019i | −0.970318 | + | 0.907873i | ||||
\(506\) | −11.7028 | −0.520253 | ||||||||
\(507\) | 21.6200i | 0.960180i | ||||||||
\(508\) | − | 6.59619i | − | 0.292658i | ||||||
\(509\) | −12.0702 | −0.535001 | −0.267501 | − | 0.963558i | \(-0.586198\pi\) | ||||
−0.267501 | + | 0.963558i | \(0.586198\pi\) | |||||||
\(510\) | 11.8174 | + | 12.6302i | 0.523283 | + | 0.559275i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | − | 6.61827i | − | 0.292204i | ||||||
\(514\) | 1.34442 | 0.0592998 | ||||||||
\(515\) | −14.2990 | − | 15.2825i | −0.630088 | − | 0.673426i | ||||
\(516\) | −1.43108 | −0.0629999 | ||||||||
\(517\) | − | 30.3523i | − | 1.33489i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.647340 | 0.0284151 | ||||||||
\(520\) | 9.60723 | − | 8.98896i | 0.421305 | − | 0.394192i | ||||
\(521\) | 14.7049 | 0.644235 | 0.322117 | − | 0.946700i | \(-0.395605\pi\) | ||||
0.322117 | + | 0.946700i | \(0.395605\pi\) | |||||||
\(522\) | − | 8.17246i | − | 0.357699i | ||||||
\(523\) | − | 6.44417i | − | 0.281784i | −0.990025 | − | 0.140892i | \(-0.955003\pi\) | ||
0.990025 | − | 0.140892i | \(-0.0449970\pi\) | |||||||
\(524\) | 2.32106 | 0.101396 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.36700 | 0.190410 | ||||||||
\(527\) | 65.5152i | 2.85389i | ||||||||
\(528\) | − | 4.46967i | − | 0.194517i | ||||||
\(529\) | 16.1447 | 0.701942 | ||||||||
\(530\) | 2.25610 | − | 2.11091i | 0.0979985 | − | 0.0916919i | ||||
\(531\) | 4.66421 | 0.202409 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 20.9632i | 0.908016i | ||||||||
\(534\) | −14.3912 | −0.622770 | ||||||||
\(535\) | −16.8302 | − | 17.9878i | −0.727633 | − | 0.777680i | ||||
\(536\) | −1.85140 | −0.0799681 | ||||||||
\(537\) | − | 25.7374i | − | 1.11065i | ||||||
\(538\) | − | 23.0671i | − | 0.994494i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.52773 | − | 1.63280i | −0.0657429 | − | 0.0702647i | ||||
\(541\) | −11.5815 | −0.497926 | −0.248963 | − | 0.968513i | \(-0.580090\pi\) | ||||
−0.248963 | + | 0.968513i | \(0.580090\pi\) | |||||||
\(542\) | 14.7209i | 0.632318i | ||||||||
\(543\) | − | 7.42245i | − | 0.318528i | ||||||
\(544\) | −7.73528 | −0.331647 | ||||||||
\(545\) | 7.66674 | − | 7.17335i | 0.328407 | − | 0.307272i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.2656i | 0.823737i | 0.911243 | + | 0.411868i | \(0.135124\pi\) | ||||
−0.911243 | + | 0.411868i | \(0.864876\pi\) | |||||||
\(548\) | − | 14.2751i | − | 0.609803i | ||||||
\(549\) | −9.79683 | −0.418119 | ||||||||
\(550\) | 22.2990 | + | 1.48440i | 0.950832 | + | 0.0632948i | ||||
\(551\) | −54.0875 | −2.30421 | ||||||||
\(552\) | − | 2.61827i | − | 0.111441i | ||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −3.21104 | −0.136424 | ||||||||
\(555\) | −5.20406 | + | 4.86915i | −0.220900 | + | 0.206684i | ||||
\(556\) | −14.9632 | −0.634581 | ||||||||
\(557\) | 21.0404i | 0.891509i | 0.895155 | + | 0.445754i | \(0.147064\pi\) | ||||
−0.895155 | + | 0.445754i | \(0.852936\pi\) | |||||||
\(558\) | − | 8.46967i | − | 0.358550i | ||||||
\(559\) | −8.42031 | −0.356141 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 34.5741 | 1.45972 | ||||||||
\(562\) | − | 7.72488i | − | 0.325854i | ||||||
\(563\) | − | 3.61092i | − | 0.152182i | −0.997101 | − | 0.0760910i | \(-0.975756\pi\) | ||
0.997101 | − | 0.0760910i | \(-0.0242439\pi\) | |||||||
\(564\) | 6.79073 | 0.285941 | ||||||||
\(565\) | −19.2071 | − | 20.5282i | −0.808048 | − | 0.863626i | ||||
\(566\) | 29.5594 | 1.24247 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 2.02386i | − | 0.0849191i | ||||||
\(569\) | −33.2145 | −1.39242 | −0.696211 | − | 0.717837i | \(-0.745132\pi\) | ||||
−0.696211 | + | 0.717837i | \(0.745132\pi\) | |||||||
\(570\) | −10.8063 | + | 10.1109i | −0.452628 | + | 0.423499i | ||||
\(571\) | −32.1776 | −1.34659 | −0.673296 | − | 0.739373i | \(-0.735122\pi\) | ||||
−0.673296 | + | 0.739373i | \(0.735122\pi\) | |||||||
\(572\) | − | 26.2990i | − | 1.09962i | ||||||
\(573\) | 1.08452i | 0.0453066i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13.0624 | + | 0.869539i | 0.544741 | + | 0.0362623i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | − | 34.1902i | − | 1.42336i | −0.702505 | − | 0.711679i | \(-0.747935\pi\) | ||
0.702505 | − | 0.711679i | \(-0.252065\pi\) | |||||||
\(578\) | − | 42.8345i | − | 1.78168i | ||||||
\(579\) | −8.93933 | −0.371506 | ||||||||
\(580\) | −13.3440 | + | 12.4853i | −0.554081 | + | 0.518423i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 7.71966i | 0.319990i | ||||||||
\(583\) | − | 6.17587i | − | 0.255779i | ||||||
\(584\) | 4.01687 | 0.166219 | ||||||||
\(585\) | −8.98896 | − | 9.60723i | −0.371648 | − | 0.397210i | ||||
\(586\) | −1.17679 | −0.0486126 | ||||||||
\(587\) | − | 34.5962i | − | 1.42794i | −0.700178 | − | 0.713969i | \(-0.746896\pi\) | ||
0.700178 | − | 0.713969i | \(-0.253104\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −56.0545 | −2.30969 | ||||||||
\(590\) | −7.12563 | − | 7.61574i | −0.293358 | − | 0.313535i | ||||
\(591\) | 7.45890 | 0.306818 | ||||||||
\(592\) | − | 3.18719i | − | 0.130993i | ||||||
\(593\) | − | 33.0845i | − | 1.35862i | −0.733853 | − | 0.679309i | \(-0.762280\pi\) | ||
0.733853 | − | 0.679309i | \(-0.237720\pi\) | |||||||
\(594\) | −4.46967 | −0.183393 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 11.1651 | 0.457341 | ||||||||
\(597\) | 25.8293i | 1.05712i | ||||||||
\(598\) | − | 15.4056i | − | 0.629981i | ||||||
\(599\) | −6.07485 | −0.248212 | −0.124106 | − | 0.992269i | \(-0.539606\pi\) | ||||
−0.124106 | + | 0.992269i | \(0.539606\pi\) | |||||||
\(600\) | −0.332104 | + | 4.98896i | −0.0135581 | + | 0.203673i | ||||
\(601\) | −11.7469 | −0.479167 | −0.239584 | − | 0.970876i | \(-0.577011\pi\) | ||||
−0.239584 | + | 0.970876i | \(0.577011\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.85140i | 0.0753947i | ||||||||
\(604\) | −0.664208 | −0.0270263 | ||||||||
\(605\) | 14.6592 | − | 13.7158i | 0.595981 | − | 0.557627i | ||||
\(606\) | −13.3544 | −0.542487 | ||||||||
\(607\) | 45.8180i | 1.85970i | 0.367944 | + | 0.929848i | \(0.380062\pi\) | ||||
−0.367944 | + | 0.929848i | \(0.619938\pi\) | |||||||
\(608\) | − | 6.61827i | − | 0.268406i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 14.9669 | + | 15.9963i | 0.605991 | + | 0.647672i | ||||
\(611\) | 39.9558 | 1.61644 | ||||||||
\(612\) | 7.73528i | 0.312680i | ||||||||
\(613\) | 34.2514i | 1.38340i | 0.722184 | + | 0.691701i | \(0.243138\pi\) | ||||
−0.722184 | + | 0.691701i | \(0.756862\pi\) | |||||||
\(614\) | 20.3761 | 0.822314 | ||||||||
\(615\) | −5.44301 | − | 5.81739i | −0.219483 | − | 0.234580i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 38.8106i | 1.56246i | 0.624245 | + | 0.781228i | \(0.285407\pi\) | ||||
−0.624245 | + | 0.781228i | \(0.714593\pi\) | |||||||
\(618\) | − | 9.35965i | − | 0.376500i | ||||||
\(619\) | 4.27512 | 0.171832 | 0.0859159 | − | 0.996302i | \(-0.472618\pi\) | ||||
0.0859159 | + | 0.996302i | \(0.472618\pi\) | |||||||
\(620\) | −13.8293 | + | 12.9393i | −0.555399 | + | 0.519656i | ||||
\(621\) | −2.61827 | −0.105068 | ||||||||
\(622\) | − | 18.8934i | − | 0.757556i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 5.88388 | 0.235544 | ||||||||
\(625\) | −24.7794 | − | 3.31371i | −0.991177 | − | 0.132548i | ||||
\(626\) | −16.4849 | −0.658869 | ||||||||
\(627\) | 29.5815i | 1.18137i | ||||||||
\(628\) | − | 8.08184i | − | 0.322500i | ||||||
\(629\) | 24.6538 | 0.983011 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.8419 | 1.46665 | 0.733326 | − | 0.679878i | \(-0.237967\pi\) | ||||
0.733326 | + | 0.679878i | \(0.237967\pi\) | |||||||
\(632\) | − | 6.98527i | − | 0.277859i | ||||||
\(633\) | − | 5.53375i | − | 0.219947i | ||||||
\(634\) | −10.3211 | −0.409902 | ||||||||
\(635\) | 10.0772 | + | 10.7703i | 0.399900 | + | 0.427406i | ||||
\(636\) | 1.38173 | 0.0547892 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 36.5282i | 1.44616i | ||||||||
\(639\) | −2.02386 | −0.0800625 | ||||||||
\(640\) | −1.52773 | − | 1.63280i | −0.0603887 | − | 0.0645423i | ||||
\(641\) | 49.9043 | 1.97110 | 0.985551 | − | 0.169382i | \(-0.0541770\pi\) | ||||
0.985551 | + | 0.169382i | \(0.0541770\pi\) | |||||||
\(642\) | − | 11.0165i | − | 0.434787i | ||||||
\(643\) | 29.0091i | 1.14401i | 0.820251 | + | 0.572004i | \(0.193834\pi\) | ||||
−0.820251 | + | 0.572004i | \(0.806166\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.33668 | − | 2.18630i | 0.0920066 | − | 0.0860855i | ||||
\(646\) | 51.1941 | 2.01421 | ||||||||
\(647\) | − | 4.94329i | − | 0.194341i | −0.995268 | − | 0.0971705i | \(-0.969021\pi\) | ||
0.995268 | − | 0.0971705i | \(-0.0309792\pi\) | |||||||
\(648\) | − | 1.00000i | − | 0.0392837i | ||||||
\(649\) | −20.8475 | −0.818334 | ||||||||
\(650\) | −1.95406 | + | 29.3544i | −0.0766446 | + | 1.15138i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.836668i | 0.0327664i | ||||||||
\(653\) | 9.40559i | 0.368069i | 0.982920 | + | 0.184035i | \(0.0589158\pi\) | ||||
−0.982920 | + | 0.184035i | \(0.941084\pi\) | |||||||
\(654\) | 4.69544 | 0.183606 | ||||||||
\(655\) | −3.78984 | + | 3.54595i | −0.148081 | + | 0.138552i | ||||
\(656\) | 3.56282 | 0.139105 | ||||||||
\(657\) | − | 4.01687i | − | 0.156713i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.4090 | −0.522340 | −0.261170 | − | 0.965293i | \(-0.584108\pi\) | ||||
−0.261170 | + | 0.965293i | \(0.584108\pi\) | |||||||
\(660\) | 6.82843 | + | 7.29809i | 0.265796 | + | 0.284078i | ||||
\(661\) | 13.2509 | 0.515400 | 0.257700 | − | 0.966225i | \(-0.417035\pi\) | ||||
0.257700 | + | 0.966225i | \(0.417035\pi\) | |||||||
\(662\) | − | 19.1906i | − | 0.745864i | ||||||
\(663\) | 45.5134i | 1.76760i | ||||||||
\(664\) | 5.35965 | 0.207995 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.18719 | −0.123501 | ||||||||
\(667\) | 21.3977i | 0.828522i | ||||||||
\(668\) | 2.66762i | 0.103213i | ||||||||
\(669\) | −3.28248 | −0.126908 | ||||||||
\(670\) | 3.02297 | − | 2.82843i | 0.116787 | − | 0.109272i | ||||
\(671\) | 43.7886 | 1.69044 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.8236i | 0.841237i | 0.907238 | + | 0.420619i | \(0.138187\pi\) | ||||
−0.907238 | + | 0.420619i | \(0.861813\pi\) | |||||||
\(674\) | 27.6035 | 1.06325 | ||||||||
\(675\) | 4.98896 | + | 0.332104i | 0.192025 | + | 0.0127827i | ||||
\(676\) | 21.6200 | 0.831540 | ||||||||
\(677\) | − | 41.0572i | − | 1.57796i | −0.614421 | − | 0.788979i | \(-0.710610\pi\) | ||
0.614421 | − | 0.788979i | \(-0.289390\pi\) | |||||||
\(678\) | − | 12.5723i | − | 0.482837i | ||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 12.6302 | − | 11.8174i | 0.484346 | − | 0.453176i | ||||
\(681\) | 4.42031 | 0.169387 | ||||||||
\(682\) | 37.8566i | 1.44960i | ||||||||
\(683\) | 31.0642i | 1.18864i | 0.804229 | + | 0.594320i | \(0.202579\pi\) | ||||
−0.804229 | + | 0.594320i | \(0.797421\pi\) | |||||||
\(684\) | −6.61827 | −0.253056 | ||||||||
\(685\) | 21.8085 | + | 23.3085i | 0.833259 | + | 0.890572i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 7.97270i | − | 0.304178i | ||||||
\(688\) | 1.43108i | 0.0545595i | ||||||||
\(689\) | 8.12993 | 0.309726 | ||||||||
\(690\) | 4.00000 | + | 4.27512i | 0.152277 | + | 0.162751i | ||||
\(691\) | −32.0012 | −1.21738 | −0.608692 | − | 0.793407i | \(-0.708305\pi\) | ||||
−0.608692 | + | 0.793407i | \(0.708305\pi\) | |||||||
\(692\) | − | 0.647340i | − | 0.0246082i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 20.3761 | 0.773468 | ||||||||
\(695\) | 24.4320 | − | 22.8597i | 0.926757 | − | 0.867116i | ||||
\(696\) | −8.17246 | −0.309776 | ||||||||
\(697\) | 27.5594i | 1.04389i | ||||||||
\(698\) | 17.8281i | 0.674802i | ||||||||
\(699\) | 17.9558 | 0.679152 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −45.4635 | −1.71713 | −0.858567 | − | 0.512701i | \(-0.828645\pi\) | ||||
−0.858567 | + | 0.512701i | \(0.828645\pi\) | |||||||
\(702\) | − | 5.88388i | − | 0.222073i | ||||||
\(703\) | 21.0937i | 0.795563i | ||||||||
\(704\) | −4.46967 | −0.168457 | ||||||||
\(705\) | −11.0879 | + | 10.3744i | −0.417596 | + | 0.390722i | ||||
\(706\) | −3.51347 | −0.132231 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | − | 4.66421i | − | 0.175292i | ||||||
\(709\) | 47.7597 | 1.79365 | 0.896826 | − | 0.442384i | \(-0.145867\pi\) | ||||
0.896826 | + | 0.442384i | \(0.145867\pi\) | |||||||
\(710\) | 3.09190 | + | 3.30456i | 0.116037 | + | 0.124018i | ||||
\(711\) | −6.98527 | −0.261968 | ||||||||
\(712\) | 14.3912i | 0.539335i | ||||||||
\(713\) | 22.1759i | 0.830493i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 40.1776 | + | 42.9411i | 1.50256 | + | 1.60591i | ||||
\(716\) | −25.7374 | −0.961853 | ||||||||
\(717\) | 5.41296i | 0.202151i | ||||||||
\(718\) | 2.19796i | 0.0820270i | ||||||||
\(719\) | −13.1611 | −0.490828 | −0.245414 | − | 0.969418i | \(-0.578924\pi\) | ||||
−0.245414 | + | 0.969418i | \(0.578924\pi\) | |||||||
\(720\) | −1.63280 | + | 1.52773i | −0.0608510 | + | 0.0569350i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 24.8015i | 0.923016i | ||||||||
\(723\) | 4.69669i | 0.174672i | ||||||||
\(724\) | −7.42245 | −0.275853 | ||||||||
\(725\) | 2.71411 | − | 40.7721i | 0.100799 | − | 1.51424i | ||||
\(726\) | 8.97792 | 0.333202 | ||||||||
\(727\) | 8.17082i | 0.303039i | 0.988454 | + | 0.151519i | \(0.0484166\pi\) | ||||
−0.988454 | + | 0.151519i | \(0.951583\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −6.55876 | + | 6.13668i | −0.242751 | + | 0.227129i | ||||
\(731\) | −11.0698 | −0.409432 | ||||||||
\(732\) | 9.79683i | 0.362101i | ||||||||
\(733\) | 2.01510i | 0.0744293i | 0.999307 | + | 0.0372146i | \(0.0118485\pi\) | ||||
−0.999307 | + | 0.0372146i | \(0.988151\pi\) | |||||||
\(734\) | 28.7721 | 1.06200 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.61827 | −0.0965107 | ||||||||
\(737\) | − | 8.27512i | − | 0.304818i | ||||||
\(738\) | − | 3.56282i | − | 0.131149i | ||||||
\(739\) | 3.82590 | 0.140738 | 0.0703690 | − | 0.997521i | \(-0.477582\pi\) | ||||
0.0703690 | + | 0.997521i | \(0.477582\pi\) | |||||||
\(740\) | 4.86915 | + | 5.20406i | 0.178994 | + | 0.191305i | ||||
\(741\) | −38.9411 | −1.43054 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 36.6654i | 1.34512i | 0.740041 | + | 0.672562i | \(0.234806\pi\) | ||||
−0.740041 | + | 0.672562i | \(0.765194\pi\) | |||||||
\(744\) | −8.46967 | −0.310513 | ||||||||
\(745\) | −18.2304 | + | 17.0572i | −0.667912 | + | 0.624928i | ||||
\(746\) | −14.5689 | −0.533406 | ||||||||
\(747\) | − | 5.35965i | − | 0.196099i | ||||||
\(748\) | − | 34.5741i | − | 1.26415i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −7.07950 | − | 8.65336i | −0.258507 | − | 0.315976i | ||||
\(751\) | −20.4657 | −0.746804 | −0.373402 | − | 0.927670i | \(-0.621809\pi\) | ||||
−0.373402 | + | 0.927670i | \(0.621809\pi\) | |||||||
\(752\) | − | 6.79073i | − | 0.247632i | ||||||
\(753\) | − | 7.73402i | − | 0.281843i | ||||||
\(754\) | −48.0858 | −1.75118 | ||||||||
\(755\) | 1.08452 | − | 1.01473i | 0.0394698 | − | 0.0369298i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 37.9575i | − | 1.37959i | −0.724006 | − | 0.689794i | \(-0.757701\pi\) | ||
0.724006 | − | 0.689794i | \(-0.242299\pi\) | |||||||
\(758\) | 30.7868i | 1.11823i | ||||||||
\(759\) | 11.7028 | 0.424784 | ||||||||
\(760\) | 10.1109 | + | 10.8063i | 0.366761 | + | 0.391987i | ||||
\(761\) | −34.6131 | −1.25472 | −0.627361 | − | 0.778728i | \(-0.715865\pi\) | ||||
−0.627361 | + | 0.778728i | \(0.715865\pi\) | |||||||
\(762\) | 6.59619i | 0.238955i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1.08452 | 0.0392367 | ||||||||
\(765\) | −11.8174 | − | 12.6302i | −0.427258 | − | 0.456646i | ||||
\(766\) | −23.3410 | −0.843344 | ||||||||
\(767\) | − | 27.4436i | − | 0.990932i | ||||||
\(768\) | − | 1.00000i | − | 0.0360844i | ||||||
\(769\) | 1.48961 | 0.0537167 | 0.0268584 | − | 0.999639i | \(-0.491450\pi\) | ||||
0.0268584 | + | 0.999639i | \(0.491450\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.34442 | −0.0484181 | ||||||||
\(772\) | 8.93933i | 0.321734i | ||||||||
\(773\) | − | 0.992258i | − | 0.0356891i | −0.999841 | − | 0.0178445i | \(-0.994320\pi\) | ||
0.999841 | − | 0.0178445i | \(-0.00568039\pi\) | |||||||
\(774\) | 1.43108 | 0.0514392 | ||||||||
\(775\) | 2.81281 | − | 42.2548i | 0.101039 | − | 1.51784i | ||||
\(776\) | 7.71966 | 0.277120 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.21842i | 0.0436824i | ||||||||
\(779\) | −23.5797 | −0.844830 | ||||||||
\(780\) | −9.60723 | + | 8.98896i | −0.343994 | + | 0.321856i | ||||
\(781\) | 9.04596 | 0.323690 | ||||||||
\(782\) | − | 20.2530i | − | 0.724247i | ||||||
\(783\) | 8.17246i | 0.292060i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.3468 | + | 13.1961i | 0.440677 | + | 0.470988i | ||||
\(786\) | −2.32106 | −0.0827896 | ||||||||
\(787\) | − | 10.2513i | − | 0.365418i | −0.983167 | − | 0.182709i | \(-0.941513\pi\) | ||
0.983167 | − | 0.182709i | \(-0.0584867\pi\) | |||||||
\(788\) | − | 7.45890i | − | 0.265712i | ||||||
\(789\) | −4.36700 | −0.155469 | ||||||||
\(790\) | 10.6716 | + | 11.4056i | 0.379678 | + | 0.405793i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 4.46967i | 0.158823i | ||||||||
\(793\) | 57.6434i | 2.04698i | ||||||||
\(794\) | 8.40595 | 0.298316 | ||||||||
\(795\) | −2.25610 | + | 2.11091i | −0.0800155 | + | 0.0748661i | ||||
\(796\) | 25.8293 | 0.915496 | ||||||||
\(797\) | − | 32.6811i | − | 1.15762i | −0.815461 | − | 0.578812i | \(-0.803517\pi\) | ||
0.815461 | − | 0.578812i | \(-0.196483\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 52.5282 | 1.85831 | ||||||||
\(800\) | 4.98896 | + | 0.332104i | 0.176386 | + | 0.0117417i | ||||
\(801\) | 14.3912 | 0.508490 | ||||||||
\(802\) | − | 0.664208i | − | 0.0234540i | ||||||
\(803\) | 17.9541i | 0.633585i | ||||||||
\(804\) | 1.85140 | 0.0652937 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −49.8345 | −1.75535 | ||||||||
\(807\) | 23.0671i | 0.812001i | ||||||||
\(808\) | 13.3544i | 0.469807i | ||||||||
\(809\) | −22.4515 | −0.789354 | −0.394677 | − | 0.918820i | \(-0.629144\pi\) | ||||
−0.394677 | + | 0.918820i | \(0.629144\pi\) | |||||||
\(810\) | 1.52773 | + | 1.63280i | 0.0536788 | + | 0.0573709i | ||||
\(811\) | 37.6581 | 1.32235 | 0.661177 | − | 0.750230i | \(-0.270057\pi\) | ||||
0.661177 | + | 0.750230i | \(0.270057\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 14.7209i | − | 0.516286i | ||||||
\(814\) | 14.2457 | 0.499310 | ||||||||
\(815\) | −1.27820 | − | 1.36612i | −0.0447734 | − | 0.0478529i | ||||
\(816\) | 7.73528 | 0.270789 | ||||||||
\(817\) | − | 9.47129i | − | 0.331358i | ||||||
\(818\) | 7.38476i | 0.258202i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.81739 | + | 5.44301i | −0.203152 | + | 0.190078i | ||||
\(821\) | −21.4838 | −0.749791 | −0.374896 | − | 0.927067i | \(-0.622321\pi\) | ||||
−0.374896 | + | 0.927067i | \(0.622321\pi\) | |||||||
\(822\) | 14.2751i | 0.497902i | ||||||||
\(823\) | − | 18.6127i | − | 0.648797i | −0.945921 | − | 0.324398i | \(-0.894838\pi\) | ||
0.945921 | − | 0.324398i | \(-0.105162\pi\) | |||||||
\(824\) | −9.35965 | −0.326059 | ||||||||
\(825\) | −22.2990 | − | 1.48440i | −0.776351 | − | 0.0516800i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.4254i | 0.640713i | 0.947297 | + | 0.320356i | \(0.103803\pi\) | ||||
−0.947297 | + | 0.320356i | \(0.896197\pi\) | |||||||
\(828\) | 2.61827i | 0.0909912i | ||||||||
\(829\) | −32.0377 | −1.11271 | −0.556357 | − | 0.830943i | \(-0.687801\pi\) | ||||
−0.556357 | + | 0.830943i | \(0.687801\pi\) | |||||||
\(830\) | −8.75126 | + | 8.18807i | −0.303761 | + | 0.284212i | ||||
\(831\) | 3.21104 | 0.111390 | ||||||||
\(832\) | − | 5.88388i | − | 0.203987i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 14.9632 | 0.518133 | ||||||||
\(835\) | −4.07540 | − | 4.35571i | −0.141035 | − | 0.150735i | ||||
\(836\) | 29.5815 | 1.02310 | ||||||||
\(837\) | 8.46967i | 0.292754i | ||||||||
\(838\) | − | 18.6274i | − | 0.643473i | ||||||
\(839\) | −8.45154 | −0.291780 | −0.145890 | − | 0.989301i | \(-0.546605\pi\) | ||||
−0.145890 | + | 0.989301i | \(0.546605\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 37.7891 | 1.30307 | ||||||||
\(842\) | − | 13.5043i | − | 0.465389i | ||||||
\(843\) | 7.72488i | 0.266059i | ||||||||
\(844\) | −5.53375 | −0.190479 | ||||||||
\(845\) | −35.3013 | + | 33.0295i | −1.21440 | + | 1.13625i | ||||
\(846\) | −6.79073 | −0.233470 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 1.38173i | − | 0.0474488i | ||||||
\(849\) | −29.5594 | −1.01448 | ||||||||
\(850\) | −2.56892 | + | 38.5910i | −0.0881132 | + | 1.32366i | ||||
\(851\) | 8.34492 | 0.286060 | ||||||||
\(852\) | 2.02386i | 0.0693361i | ||||||||
\(853\) | 50.6270i | 1.73344i | 0.498798 | + | 0.866718i | \(0.333775\pi\) | ||||
−0.498798 | + | 0.866718i | \(0.666225\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.8063 | − | 10.1109i | 0.369569 | − | 0.345786i | ||||
\(856\) | −11.0165 | −0.376536 | ||||||||
\(857\) | − | 12.0013i | − | 0.409955i | −0.978767 | − | 0.204978i | \(-0.934288\pi\) | ||
0.978767 | − | 0.204978i | \(-0.0657121\pi\) | |||||||
\(858\) | 26.2990i | 0.897832i | ||||||||
\(859\) | 35.7119 | 1.21848 | 0.609238 | − | 0.792988i | \(-0.291475\pi\) | ||||
0.609238 | + | 0.792988i | \(0.291475\pi\) | |||||||
\(860\) | −2.18630 | − | 2.33668i | −0.0745523 | − | 0.0796801i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 31.6807i | − | 1.07905i | ||||||
\(863\) | 1.28425i | 0.0437164i | 0.999761 | + | 0.0218582i | \(0.00695824\pi\) | ||||
−0.999761 | + | 0.0218582i | \(0.993042\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 0.988958 | + | 1.05698i | 0.0336256 | + | 0.0359384i | ||||
\(866\) | −25.3184 | −0.860353 | ||||||||
\(867\) | 42.8345i | 1.45474i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 31.2218 | 1.05913 | ||||||||
\(870\) | 13.3440 | − | 12.4853i | 0.452405 | − | 0.423291i | ||||
\(871\) | 10.8934 | 0.369109 | ||||||||
\(872\) | − | 4.69544i | − | 0.159008i | ||||||
\(873\) | − | 7.71966i | − | 0.261271i | ||||||
\(874\) | 17.3284 | 0.586142 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.01687 | −0.135717 | ||||||||
\(877\) | 38.3501i | 1.29499i | 0.762069 | + | 0.647496i | \(0.224184\pi\) | ||||
−0.762069 | + | 0.647496i | \(0.775816\pi\) | |||||||
\(878\) | − | 32.8146i | − | 1.10744i | ||||||
\(879\) | 1.17679 | 0.0396921 | ||||||||
\(880\) | 7.29809 | − | 6.82843i | 0.246019 | − | 0.230186i | ||||
\(881\) | 0.389472 | 0.0131216 | 0.00656082 | − | 0.999978i | \(-0.497912\pi\) | ||||
0.00656082 | + | 0.999978i | \(0.497912\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.5412i | 0.623962i | 0.950088 | + | 0.311981i | \(0.100993\pi\) | ||||
−0.950088 | + | 0.311981i | \(0.899007\pi\) | |||||||
\(884\) | 45.5134 | 1.53078 | ||||||||
\(885\) | 7.12563 | + | 7.61574i | 0.239526 | + | 0.256000i | ||||
\(886\) | 16.6421 | 0.559103 | ||||||||
\(887\) | − | 42.4806i | − | 1.42636i | −0.700982 | − | 0.713179i | \(-0.747255\pi\) | ||
0.700982 | − | 0.713179i | \(-0.252745\pi\) | |||||||
\(888\) | 3.18719i | 0.106955i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −21.9859 | − | 23.4981i | −0.736968 | − | 0.787658i | ||||
\(891\) | 4.46967 | 0.149739 | ||||||||
\(892\) | 3.28248i | 0.109906i | ||||||||
\(893\) | 44.9429i | 1.50396i | ||||||||
\(894\) | −11.1651 | −0.373417 | ||||||||
\(895\) | 42.0242 | − | 39.3198i | 1.40471 | − | 1.31431i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.4056i | 0.514378i | ||||||||
\(898\) | − | 20.1759i | − | 0.673278i | ||||||
\(899\) | 69.2180 | 2.30855 | ||||||||
\(900\) | 0.332104 | − | 4.98896i | 0.0110701 | − | 0.166299i | ||||
\(901\) | 10.6881 | 0.356071 | ||||||||
\(902\) | 15.9246i | 0.530231i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12.5723 | −0.418150 | ||||||||
\(905\) | 12.1194 | − | 11.3395i | 0.402863 | − | 0.376937i | ||||
\(906\) | 0.664208 | 0.0220668 | ||||||||
\(907\) | − | 41.1686i | − | 1.36698i | −0.729959 | − | 0.683491i | \(-0.760461\pi\) | ||
0.729959 | − | 0.683491i | \(-0.239539\pi\) | |||||||
\(908\) | − | 4.42031i | − | 0.146693i | ||||||
\(909\) | 13.3544 | 0.442939 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.1703 | −0.833929 | −0.416964 | − | 0.908923i | \(-0.636906\pi\) | ||||
−0.416964 | + | 0.908923i | \(0.636906\pi\) | |||||||
\(912\) | 6.61827i | 0.219153i | ||||||||
\(913\) | 23.9558i | 0.792822i | ||||||||
\(914\) | 35.4124 | 1.17134 | ||||||||
\(915\) | −14.9669 | − | 15.9963i | −0.494790 | − | 0.528822i | ||||
\(916\) | −7.97270 | −0.263426 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − | 7.73528i | − | 0.255302i | ||||||
\(919\) | 5.03681 | 0.166149 | 0.0830745 | − | 0.996543i | \(-0.473526\pi\) | ||||
0.0830745 | + | 0.996543i | \(0.473526\pi\) | |||||||
\(920\) | 4.27512 | − | 4.00000i | 0.140947 | − | 0.131876i | ||||
\(921\) | −20.3761 | −0.671417 | ||||||||
\(922\) | − | 12.5940i | − | 0.414762i | ||||||
\(923\) | 11.9081i | 0.391961i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.9007 | − | 1.05848i | −0.522813 | − | 0.0348026i | ||||
\(926\) | 32.5061 | 1.06822 | ||||||||
\(927\) | 9.35965i | 0.307411i | ||||||||
\(928\) | 8.17246i | 0.268274i | ||||||||
\(929\) | 14.2846 | 0.468663 | 0.234332 | − | 0.972157i | \(-0.424710\pi\) | ||||
0.234332 | + | 0.972157i | \(0.424710\pi\) | |||||||
\(930\) | 13.8293 | − | 12.9393i | 0.453481 | − | 0.424297i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 17.9558i | − | 0.588163i | ||||||
\(933\) | 18.8934i | 0.618542i | ||||||||
\(934\) | −9.20531 | −0.301207 | ||||||||
\(935\) | 52.8198 | + | 56.4528i | 1.72739 | + | 1.84620i | ||||
\(936\) | −5.88388 | −0.192321 | ||||||||
\(937\) | − | 19.8403i | − | 0.648153i | −0.946031 | − | 0.324077i | \(-0.894946\pi\) | ||
0.946031 | − | 0.324077i | \(-0.105054\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.4849 | 0.537964 | ||||||||
\(940\) | 10.3744 | + | 11.0879i | 0.338375 | + | 0.361649i | ||||
\(941\) | 15.9054 | 0.518502 | 0.259251 | − | 0.965810i | \(-0.416524\pi\) | ||||
0.259251 | + | 0.965810i | \(0.416524\pi\) | |||||||
\(942\) | 8.08184i | 0.263320i | ||||||||
\(943\) | 9.32842i | 0.303775i | ||||||||
\(944\) | −4.66421 | −0.151807 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.39646 | −0.207967 | ||||||||
\(947\) | 9.55815i | 0.310598i | 0.987867 | + | 0.155299i | \(0.0496341\pi\) | ||||
−0.987867 | + | 0.155299i | \(0.950366\pi\) | |||||||
\(948\) | 6.98527i | 0.226871i | ||||||||
\(949\) | −23.6348 | −0.767217 | ||||||||
\(950\) | −33.0183 | − | 2.19796i | −1.07125 | − | 0.0713111i | ||||
\(951\) | 10.3211 | 0.334683 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 23.7505i | − | 0.769354i | −0.923051 | − | 0.384677i | \(-0.874313\pi\) | ||
0.923051 | − | 0.384677i | \(-0.125687\pi\) | |||||||
\(954\) | −1.38173 | −0.0447352 | ||||||||
\(955\) | −1.77081 | + | 1.65685i | −0.0573022 | + | 0.0536145i | ||||
\(956\) | 5.41296 | 0.175068 | ||||||||
\(957\) | − | 36.5282i | − | 1.18079i | ||||||
\(958\) | 39.4914i | 1.27591i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.52773 | + | 1.63280i | 0.0493072 | + | 0.0526986i | ||||
\(961\) | 40.7352 | 1.31404 | ||||||||
\(962\) | 18.7530i | 0.604622i | ||||||||
\(963\) | 11.0165i | 0.355002i | ||||||||
\(964\) | 4.69669 | 0.151270 | ||||||||
\(965\) | −13.6569 | − | 14.5962i | −0.439630 | − | 0.469868i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 56.9706i | − | 1.83205i | −0.401121 | − | 0.916025i | \(-0.631379\pi\) | ||
0.401121 | − | 0.916025i | \(-0.368621\pi\) | |||||||
\(968\) | − | 8.97792i | − | 0.288561i | ||||||
\(969\) | −51.1941 | −1.64459 | ||||||||
\(970\) | −12.6047 | + | 11.7935i | −0.404713 | + | 0.378667i | ||||
\(971\) | 33.0857 | 1.06177 | 0.530886 | − | 0.847443i | \(-0.321859\pi\) | ||||
0.530886 | + | 0.847443i | \(0.321859\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 29.2678 | 0.937800 | ||||||||
\(975\) | 1.95406 | − | 29.3544i | 0.0625801 | − | 0.940094i | ||||
\(976\) | 9.79683 | 0.313589 | ||||||||
\(977\) | − | 24.6127i | − | 0.787429i | −0.919233 | − | 0.393715i | \(-0.871190\pi\) | ||
0.919233 | − | 0.393715i | \(-0.128810\pi\) | |||||||
\(978\) | − | 0.836668i | − | 0.0267537i | ||||||
\(979\) | −64.3241 | −2.05581 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.69544 | −0.149914 | ||||||||
\(982\) | 15.3631i | 0.490255i | ||||||||
\(983\) | − | 42.4806i | − | 1.35492i | −0.735559 | − | 0.677460i | \(-0.763081\pi\) | ||
0.735559 | − | 0.677460i | \(-0.236919\pi\) | |||||||
\(984\) | −3.56282 | −0.113578 | ||||||||
\(985\) | 11.3952 | + | 12.1789i | 0.363080 | + | 0.388053i | ||||
\(986\) | −63.2162 | −2.01321 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 38.9411i | 1.23888i | ||||||||
\(989\) | −3.74696 | −0.119146 | ||||||||
\(990\) | −6.82843 | − | 7.29809i | −0.217022 | − | 0.231949i | ||||
\(991\) | −0.838308 | −0.0266297 | −0.0133149 | − | 0.999911i | \(-0.504238\pi\) | ||||
−0.0133149 | + | 0.999911i | \(0.504238\pi\) | |||||||
\(992\) | 8.46967i | 0.268912i | ||||||||
\(993\) | 19.1906i | 0.608995i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −42.1742 | + | 39.4601i | −1.33701 | + | 1.25097i | ||||
\(996\) | −5.35965 | −0.169827 | ||||||||
\(997\) | − | 31.5940i | − | 1.00059i | −0.865854 | − | 0.500297i | \(-0.833224\pi\) | ||
0.865854 | − | 0.500297i | \(-0.166776\pi\) | |||||||
\(998\) | − | 20.5502i | − | 0.650507i | ||||||
\(999\) | 3.18719 | 0.100838 |
(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 | 1470.2.g.k.589.7 | yes | 8 | |
5.2 | odd | 4 | 7350.2.a.dr.1.4 | 4 | |||
5.3 | odd | 4 | 7350.2.a.du.1.4 | 4 | |||
5.4 | even | 2 | inner | 1470.2.g.k.589.3 | yes | 8 | |
7.2 | even | 3 | 1470.2.n.k.949.5 | 16 | |||
7.3 | odd | 6 | 1470.2.n.l.79.2 | 16 | |||
7.4 | even | 3 | 1470.2.n.k.79.3 | 16 | |||
7.5 | odd | 6 | 1470.2.n.l.949.8 | 16 | |||
7.6 | odd | 2 | 1470.2.g.j.589.6 | yes | 8 | ||
35.4 | even | 6 | 1470.2.n.k.79.5 | 16 | |||
35.9 | even | 6 | 1470.2.n.k.949.3 | 16 | |||
35.13 | even | 4 | 7350.2.a.dt.1.4 | 4 | |||
35.19 | odd | 6 | 1470.2.n.l.949.2 | 16 | |||
35.24 | odd | 6 | 1470.2.n.l.79.8 | 16 | |||
35.27 | even | 4 | 7350.2.a.ds.1.4 | 4 | |||
35.34 | odd | 2 | 1470.2.g.j.589.2 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1470.2.g.j.589.2 | ✓ | 8 | 35.34 | odd | 2 | ||
1470.2.g.j.589.6 | yes | 8 | 7.6 | odd | 2 | ||
1470.2.g.k.589.3 | yes | 8 | 5.4 | even | 2 | inner | |
1470.2.g.k.589.7 | yes | 8 | 1.1 | even | 1 | trivial | |
1470.2.n.k.79.3 | 16 | 7.4 | even | 3 | |||
1470.2.n.k.79.5 | 16 | 35.4 | even | 6 | |||
1470.2.n.k.949.3 | 16 | 35.9 | even | 6 | |||
1470.2.n.k.949.5 | 16 | 7.2 | even | 3 | |||
1470.2.n.l.79.2 | 16 | 7.3 | odd | 6 | |||
1470.2.n.l.79.8 | 16 | 35.24 | odd | 6 | |||
1470.2.n.l.949.2 | 16 | 35.19 | odd | 6 | |||
1470.2.n.l.949.8 | 16 | 7.5 | odd | 6 | |||
7350.2.a.dr.1.4 | 4 | 5.2 | odd | 4 | |||
7350.2.a.ds.1.4 | 4 | 35.27 | even | 4 | |||
7350.2.a.dt.1.4 | 4 | 35.13 | even | 4 | |||
7350.2.a.du.1.4 | 4 | 5.3 | odd | 4 |