Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [672,2,Mod(223,672)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(672, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("672.223");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 672 = 2^{5} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 672.b (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: | \(5.36594701583\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.836829184.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 14x^{6} + 61x^{4} + 84x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 223.2 | ||
Root | \(2.63640i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 672.223 |
Dual form | 672.2.b.b.223.7 |
$q$-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 \(\left(\mathbb{Z}/672\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(421\) | \(449\) | \(577\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 2.31423i | − | 1.03495i | −0.855697 | − | 0.517477i | \(-0.826871\pi\) | ||
0.855697 | − | 0.517477i | \(-0.173129\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.222191 | + | 2.63640i | −0.0839804 | + | 0.996467i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 3.58704i | − | 1.08153i | −0.841173 | − | 0.540766i | \(-0.818134\pi\) | ||
0.841173 | − | 0.540766i | \(-0.181866\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.82843i | − | 0.784465i | −0.919866 | − | 0.392232i | \(-0.871703\pi\) | ||
0.919866 | − | 0.392232i | \(-0.128297\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 2.31423i | − | 0.597531i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 2.31423i | − | 0.561282i | −0.959813 | − | 0.280641i | \(-0.909453\pi\) | ||
0.959813 | − | 0.280641i | \(-0.0905471\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.90126 | 1.81267 | 0.906337 | − | 0.422556i | \(-0.138867\pi\) | ||||
0.906337 | + | 0.422556i | \(0.138867\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.222191 | + | 2.63640i | −0.0484861 | + | 0.575311i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.130157i | 0.0271395i | 0.999908 | + | 0.0135698i | \(0.00431953\pi\) | ||||
−0.999908 | + | 0.0135698i | \(0.995680\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.355642 | −0.0711284 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.199975 | 0.0371344 | 0.0185672 | − | 0.999828i | \(-0.494090\pi\) | ||||
0.0185672 | + | 0.999828i | \(0.494090\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.45688 | 0.620874 | 0.310437 | − | 0.950594i | \(-0.399525\pi\) | ||||
0.310437 | + | 0.950594i | \(0.399525\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 3.58704i | − | 0.624423i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.10124 | + | 0.514201i | 1.03130 | + | 0.0869158i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.5581 | −1.90014 | −0.950071 | − | 0.312033i | \(-0.898990\pi\) | ||||
−0.950071 | + | 0.312033i | \(0.898990\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 2.82843i | − | 0.452911i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 7.97108i | − | 1.24487i | −0.782670 | − | 0.622437i | \(-0.786143\pi\) | ||
0.782670 | − | 0.622437i | \(-0.213857\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.38404i | 0.668560i | 0.942474 | + | 0.334280i | \(0.108493\pi\) | ||||
−0.942474 | + | 0.334280i | \(0.891507\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 2.31423i | − | 0.344984i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.54562 | −0.954777 | −0.477388 | − | 0.878692i | \(-0.658417\pi\) | ||||
−0.477388 | + | 0.878692i | \(0.658417\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.90126 | − | 1.17157i | −0.985895 | − | 0.167368i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 2.31423i | − | 0.324056i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.3456 | 1.42108 | 0.710542 | − | 0.703655i | \(-0.248450\pi\) | ||||
0.710542 | + | 0.703655i | \(0.248450\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.30121 | −1.11934 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.90126 | 1.04655 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.65685 | 1.25722 | 0.628608 | − | 0.777723i | \(-0.283625\pi\) | ||||
0.628608 | + | 0.777723i | \(0.283625\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 6.19998i | − | 0.793825i | −0.917856 | − | 0.396913i | \(-0.870082\pi\) | ||
0.917856 | − | 0.396913i | \(-0.129918\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.222191 | + | 2.63640i | −0.0279935 | + | 0.332156i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.54562 | −0.811884 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.01250i | 1.10105i | 0.834818 | + | 0.550526i | \(0.185573\pi\) | ||||
−0.834818 | + | 0.550526i | \(0.814427\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.130157i | 0.0156690i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.75861i | 0.564743i | 0.959305 | + | 0.282371i | \(0.0911211\pi\) | ||||
−0.959305 | + | 0.282371i | \(0.908879\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.2853i | 1.20380i | 0.798570 | + | 0.601902i | \(0.205590\pi\) | ||||
−0.798570 | + | 0.601902i | \(0.794410\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.355642 | −0.0410660 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.45688 | + | 0.797008i | 1.07771 | + | 0.0908275i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.24441i | 0.477533i | 0.971077 | + | 0.238767i | \(0.0767431\pi\) | ||||
−0.971077 | + | 0.238767i | \(0.923257\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.768089 | −0.0843087 | −0.0421543 | − | 0.999111i | \(-0.513422\pi\) | ||||
−0.0421543 | + | 0.999111i | \(0.513422\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.35564 | −0.580901 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.199975 | 0.0214396 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 17.7486i | 1.88135i | 0.339310 | + | 0.940675i | \(0.389806\pi\) | ||||
−0.339310 | + | 0.940675i | \(0.610194\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.45688 | + | 0.628452i | 0.781693 | + | 0.0658797i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.45688 | 0.358462 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 18.2853i | − | 1.87603i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 9.02840i | − | 0.916695i | −0.888773 | − | 0.458348i | \(-0.848441\pi\) | ||
0.888773 | − | 0.458348i | \(-0.151559\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 3.58704i | − | 0.360511i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.6279i | 1.35603i | 0.735048 | + | 0.678015i | \(0.237160\pi\) | ||||
−0.735048 | + | 0.678015i | \(0.762840\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.4569 | −1.12888 | −0.564440 | − | 0.825474i | \(-0.690908\pi\) | ||||
−0.564440 | + | 0.825474i | \(0.690908\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.10124 | + | 0.514201i | 0.595420 | + | 0.0501809i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 6.95858i | − | 0.672712i | −0.941735 | − | 0.336356i | \(-0.890806\pi\) | ||
0.941735 | − | 0.336356i | \(-0.109194\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.88877 | −0.276694 | −0.138347 | − | 0.990384i | \(-0.544179\pi\) | ||||
−0.138347 | + | 0.990384i | \(0.544179\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.5581 | −1.09705 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.36814 | 0.222776 | 0.111388 | − | 0.993777i | \(-0.464470\pi\) | ||||
0.111388 | + | 0.993777i | \(0.464470\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.301212 | 0.0280882 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 2.82843i | − | 0.261488i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.10124 | + | 0.514201i | 0.559299 | + | 0.0471367i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.86683 | −0.169712 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 7.97108i | − | 0.718728i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 10.7481i | − | 0.961339i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.55812i | 0.670674i | 0.942098 | + | 0.335337i | \(0.108850\pi\) | ||||
−0.942098 | + | 0.335337i | \(0.891150\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.38404i | 0.385994i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.4594 | −1.52543 | −0.762716 | − | 0.646733i | \(-0.776135\pi\) | ||||
−0.762716 | + | 0.646733i | \(0.776135\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.75559 | + | 20.8309i | −0.152229 | + | 1.80627i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 2.31423i | − | 0.199177i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −18.2025 | −1.55514 | −0.777571 | − | 0.628795i | \(-0.783548\pi\) | ||||
−0.777571 | + | 0.628795i | \(0.783548\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.3137 | −1.29889 | −0.649446 | − | 0.760408i | \(-0.724999\pi\) | ||||
−0.649446 | + | 0.760408i | \(0.724999\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.54562 | −0.551241 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.1457 | −0.848424 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 0.462787i | − | 0.0384324i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.90126 | − | 1.17157i | −0.569206 | − | 0.0966297i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 22.5481 | 1.84721 | 0.923607 | − | 0.383341i | \(-0.125227\pi\) | ||||
0.923607 | + | 0.383341i | \(0.125227\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.8434i | 1.45208i | 0.687654 | + | 0.726039i | \(0.258641\pi\) | ||||
−0.687654 | + | 0.726039i | \(0.741359\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 2.31423i | − | 0.187094i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 8.00000i | − | 0.642575i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.11373i | 0.408120i | 0.978958 | + | 0.204060i | \(0.0654138\pi\) | ||||
−0.978958 | + | 0.204060i | \(0.934586\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.3456 | 0.820463 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.343146 | − | 0.0289197i | −0.0270437 | − | 0.00227919i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 10.3012i | − | 0.806853i | −0.915012 | − | 0.403427i | \(-0.867819\pi\) | ||
0.915012 | − | 0.403427i | \(-0.132181\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.30121 | −0.646248 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.0250 | −1.08529 | −0.542643 | − | 0.839963i | \(-0.682576\pi\) | ||||
−0.542643 | + | 0.839963i | \(0.682576\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000 | 0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.90126 | 0.604225 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 8.02892i | − | 0.610427i | −0.952284 | − | 0.305214i | \(-0.901272\pi\) | ||
0.952284 | − | 0.305214i | \(-0.0987279\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.0790206 | − | 0.937617i | 0.00597340 | − | 0.0708772i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.65685 | 0.725854 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 21.1043i | 1.57741i | 0.614774 | + | 0.788703i | \(0.289247\pi\) | ||||
−0.614774 | + | 0.788703i | \(0.710753\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.2060i | 1.20458i | 0.798276 | + | 0.602292i | \(0.205746\pi\) | ||||
−0.798276 | + | 0.602292i | \(0.794254\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 6.19998i | − | 0.458315i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 26.7481i | 1.96656i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.30121 | −0.607045 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.222191 | + | 2.63640i | −0.0161620 | + | 0.191770i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.60953i | 0.550606i | 0.961357 | + | 0.275303i | \(0.0887782\pi\) | ||||
−0.961357 | + | 0.275303i | \(0.911222\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.6694 | 0.767997 | 0.383998 | − | 0.923334i | \(-0.374547\pi\) | ||||
0.383998 | + | 0.923334i | \(0.374547\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.54562 | −0.468742 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.68879 | 0.334062 | 0.167031 | − | 0.985952i | \(-0.446582\pi\) | ||||
0.167031 | + | 0.985952i | \(0.446582\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.4694 | 1.59281 | 0.796406 | − | 0.604762i | \(-0.206732\pi\) | ||||
0.796406 | + | 0.604762i | \(0.206732\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.01250i | 0.635692i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.0444327 | + | 0.527215i | −0.00311857 | + | 0.0370032i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −18.4469 | −1.28839 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.130157i | 0.00904652i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 28.3421i | − | 1.96046i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.4185i | 1.06145i | 0.847543 | + | 0.530726i | \(0.178081\pi\) | ||||
−0.847543 | + | 0.530726i | \(0.821919\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.75861i | 0.326055i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.1457 | 0.691929 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.768089 | + | 9.11373i | −0.0521413 | + | 0.618681i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.2853i | 0.695017i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.54562 | −0.440306 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.86933 | −0.192144 | −0.0960721 | − | 0.995374i | \(-0.530628\pi\) | ||||
−0.0960721 | + | 0.995374i | \(0.530628\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.355642 | −0.0237095 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.91376 | 0.193393 | 0.0966965 | − | 0.995314i | \(-0.469172\pi\) | ||||
0.0966965 | + | 0.995314i | \(0.469172\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 20.0853i | − | 1.32728i | −0.748054 | − | 0.663638i | \(-0.769012\pi\) | ||
0.748054 | − | 0.663638i | \(-0.230988\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.45688 | + | 0.797008i | 0.622217 | + | 0.0524393i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.343146 | −0.0224802 | −0.0112401 | − | 0.999937i | \(-0.503578\pi\) | ||||
−0.0112401 | + | 0.999937i | \(0.503578\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.1480i | 0.988149i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.24441i | 0.275704i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 8.56113i | − | 0.553774i | −0.960903 | − | 0.276887i | \(-0.910697\pi\) | ||
0.960903 | − | 0.276887i | \(-0.0893027\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 6.40598i | − | 0.412646i | −0.978484 | − | 0.206323i | \(-0.933850\pi\) | ||
0.978484 | − | 0.206323i | \(-0.0661497\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.71128 | + | 15.9711i | −0.173218 | + | 1.02035i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 22.3481i | − | 1.42198i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.768089 | −0.0486756 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.2025 | −1.52765 | −0.763823 | − | 0.645425i | \(-0.776680\pi\) | ||||
−0.763823 | + | 0.645425i | \(0.776680\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.466877 | 0.0293523 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.35564 | −0.335383 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 1.22798i | − | 0.0765996i | −0.999266 | − | 0.0382998i | \(-0.987806\pi\) | ||
0.999266 | − | 0.0382998i | \(-0.0121942\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.56811 | − | 30.4719i | 0.159575 | − | 1.89343i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.199975 | 0.0123781 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.01551i | 0.370932i | 0.982651 | + | 0.185466i | \(0.0593795\pi\) | ||||
−0.982651 | + | 0.185466i | \(0.940620\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 23.9422i | − | 1.47076i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 17.7486i | 1.08620i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 22.3771i | − | 1.36435i | −0.731187 | − | 0.682177i | \(-0.761033\pi\) | ||
0.731187 | − | 0.682177i | \(-0.238967\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.63436 | 0.585246 | 0.292623 | − | 0.956228i | \(-0.405472\pi\) | ||||
0.292623 | + | 0.956228i | \(0.405472\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.45688 | + | 0.628452i | 0.451311 | + | 0.0380357i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.27570i | 0.0769277i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.9581 | 0.718491 | 0.359245 | − | 0.933243i | \(-0.383034\pi\) | ||||
0.359245 | + | 0.933243i | \(0.383034\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.45688 | 0.206958 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.6818 | −1.05481 | −0.527405 | − | 0.849614i | \(-0.676835\pi\) | ||||
−0.527405 | + | 0.849614i | \(0.676835\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.50131 | −0.208131 | −0.104066 | − | 0.994570i | \(-0.533185\pi\) | ||||
−0.104066 | + | 0.994570i | \(0.533185\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 18.2853i | − | 1.08313i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 21.0150 | + | 1.77111i | 1.24048 | + | 0.104545i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.6444 | 0.684962 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 9.02840i | − | 0.529254i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.40047i | 0.198657i | 0.995055 | + | 0.0993287i | \(0.0316695\pi\) | ||||
−0.995055 | + | 0.0993287i | \(0.968330\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 22.3481i | − | 1.30116i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 3.58704i | − | 0.208141i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.368139 | 0.0212900 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.5581 | − | 0.974097i | −0.666199 | − | 0.0561460i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 13.6279i | 0.782904i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −14.3481 | −0.821572 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.1037 | −0.690797 | −0.345398 | − | 0.938456i | \(-0.612256\pi\) | ||||
−0.345398 | + | 0.938456i | \(0.612256\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.4569 | −0.651759 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.7481 | 1.51675 | 0.758373 | − | 0.651821i | \(-0.225995\pi\) | ||||
0.758373 | + | 0.651821i | \(0.225995\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.8343i | 1.57329i | 0.617406 | + | 0.786645i | \(0.288184\pi\) | ||||
−0.617406 | + | 0.786645i | \(0.711816\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.10124 | + | 0.514201i | 0.343766 | + | 0.0289719i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.85683 | 0.328952 | 0.164476 | − | 0.986381i | \(-0.447407\pi\) | ||||
0.164476 | + | 0.986381i | \(0.447407\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 0.717318i | − | 0.0401621i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 6.95858i | − | 0.388390i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 18.2853i | − | 1.01742i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00591i | 0.0557977i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.88877 | −0.159749 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.45438 | − | 17.2569i | 0.0801826 | − | 0.951404i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.84787i | 0.156533i | 0.996932 | + | 0.0782665i | \(0.0249385\pi\) | ||||
−0.996932 | + | 0.0782665i | \(0.975062\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −11.5581 | −0.633381 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 20.8570 | 1.13954 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.4888 | −0.571362 | −0.285681 | − | 0.958325i | \(-0.592220\pi\) | ||||
−0.285681 | + | 0.958325i | \(0.592220\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.36814 | 0.128620 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 12.4000i | − | 0.671495i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.62214 | − | 17.9342i | 0.249572 | − | 0.968356i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.301212 | 0.0162167 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 21.8145i | − | 1.17106i | −0.810649 | − | 0.585532i | \(-0.800886\pi\) | ||
0.810649 | − | 0.585532i | \(-0.199114\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 28.7188i | − | 1.53728i | −0.639681 | − | 0.768641i | \(-0.720934\pi\) | ||
0.639681 | − | 0.768641i | \(-0.279066\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 2.82843i | − | 0.150970i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.91428i | 0.314785i | 0.987536 | + | 0.157393i | \(0.0503088\pi\) | ||||
−0.987536 | + | 0.157393i | \(0.949691\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.0125 | 0.584483 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.10124 | + | 0.514201i | 0.322912 | + | 0.0272144i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.4723i | 1.08048i | 0.841509 | + | 0.540242i | \(0.181667\pi\) | ||||
−0.841509 | + | 0.540242i | \(0.818333\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 43.4299 | 2.28579 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.86683 | −0.0979830 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 23.8025 | 1.24588 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.4494 | 1.48505 | 0.742523 | − | 0.669821i | \(-0.233629\pi\) | ||||
0.742523 | + | 0.669821i | \(0.233629\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 7.97108i | − | 0.414958i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.29871 | + | 27.2753i | −0.119343 | + | 1.41606i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.2913 | 1.36131 | 0.680657 | − | 0.732602i | \(-0.261694\pi\) | ||||
0.680657 | + | 0.732602i | \(0.261694\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 10.7481i | − | 0.555029i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 0.565615i | − | 0.0291306i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 9.44347i | − | 0.485079i | −0.970142 | − | 0.242539i | \(-0.922020\pi\) | ||
0.970142 | − | 0.242539i | \(-0.0779803\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.55812i | 0.387214i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.14567 | −0.109639 | −0.0548193 | − | 0.998496i | \(-0.517458\pi\) | ||||
−0.0548193 | + | 0.998496i | \(0.517458\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.84446 | − | 21.8854i | 0.0940023 | − | 1.11538i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.38404i | 0.222853i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −20.7388 | −1.05150 | −0.525749 | − | 0.850640i | \(-0.676215\pi\) | ||||
−0.525749 | + | 0.850640i | \(0.676215\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.301212 | 0.0152329 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −17.4594 | −0.880709 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.82252 | 0.494225 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 19.8568i | − | 0.996586i | −0.867009 | − | 0.498293i | \(-0.833960\pi\) | ||
0.867009 | − | 0.498293i | \(-0.166040\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.75559 | + | 20.8309i | −0.0878895 | + | 1.04285i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.4249 | 0.620472 | 0.310236 | − | 0.950660i | \(-0.399592\pi\) | ||||
0.310236 | + | 0.950660i | \(0.399592\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 9.77753i | − | 0.487054i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 2.31423i | − | 0.114995i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 41.4594i | 2.05507i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.54903i | 0.472169i | 0.971733 | + | 0.236085i | \(0.0758642\pi\) | ||||
−0.971733 | + | 0.236085i | \(0.924136\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.2025 | −0.897862 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.14567 | + | 25.4594i | −0.105582 | + | 1.25277i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.77753i | 0.0872556i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −15.3137 | −0.749916 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 21.2569 | 1.03847 | 0.519234 | − | 0.854632i | \(-0.326217\pi\) | ||||
0.519234 | + | 0.854632i | \(0.326217\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.1582 | 0.933712 | 0.466856 | − | 0.884333i | \(-0.345387\pi\) | ||||
0.466856 | + | 0.884333i | \(0.345387\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.54562 | −0.318259 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.823037i | 0.0399231i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 16.3456 | + | 1.37758i | 0.791021 | + | 0.0666658i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −10.1457 | −0.489838 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 23.3042i | − | 1.12253i | −0.827638 | − | 0.561263i | \(-0.810316\pi\) | ||
0.827638 | − | 0.561263i | \(-0.189684\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 33.9482i | − | 1.63145i | −0.578443 | − | 0.815723i | \(-0.696339\pi\) | ||
0.578443 | − | 0.815723i | \(-0.303661\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 0.462787i | − | 0.0221890i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.02840i | 0.0491951i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.13567 | −0.436022 | −0.218011 | − | 0.975946i | \(-0.569957\pi\) | ||||
−0.218011 | + | 0.975946i | \(0.569957\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.90126 | − | 1.17157i | −0.328632 | − | 0.0557892i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.5258i | 1.35530i | 0.735384 | + | 0.677651i | \(0.237002\pi\) | ||||
−0.735384 | + | 0.677651i | \(0.762998\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 41.0743 | 1.94711 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 22.5481 | 1.06649 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −34.3731 | −1.62217 | −0.811084 | − | 0.584929i | \(-0.801122\pi\) | ||||
−0.811084 | + | 0.584929i | \(0.801122\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −28.5926 | −1.34637 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 17.8434i | 0.838357i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.45438 | − | 17.2569i | 0.0681824 | − | 0.809016i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −34.8938 | −1.63226 | −0.816131 | − | 0.577867i | \(-0.803885\pi\) | ||||
−0.816131 | + | 0.577867i | \(0.803885\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 2.31423i | − | 0.108019i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.2908i | 0.991612i | 0.868433 | + | 0.495806i | \(0.165127\pi\) | ||||
−0.868433 | + | 0.495806i | \(0.834873\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.33565i | 0.0620728i | 0.999518 | + | 0.0310364i | \(0.00988078\pi\) | ||||
−0.999518 | + | 0.0310364i | \(0.990119\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 8.00000i | − | 0.370991i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.98000 | 0.461820 | 0.230910 | − | 0.972975i | \(-0.425830\pi\) | ||||
0.230910 | + | 0.972975i | \(0.425830\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −23.7606 | − | 2.00250i | −1.09716 | − | 0.0924668i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.11373i | 0.235628i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 15.7257 | 0.723070 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.81002 | −0.128933 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.3456 | 0.473695 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.42939 | −0.156693 | −0.0783464 | − | 0.996926i | \(-0.524964\pi\) | ||||
−0.0783464 | + | 0.996926i | \(0.524964\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 32.6913i | 1.49059i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.343146 | − | 0.0289197i | −0.0156137 | − | 0.00131589i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −20.8938 | −0.948737 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.7522i | 0.940371i | 0.882568 | + | 0.470186i | \(0.155813\pi\) | ||||
−0.882568 | + | 0.470186i | \(0.844187\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 10.3012i | − | 0.465837i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 36.6154i | − | 1.65243i | −0.563354 | − | 0.826216i | \(-0.690489\pi\) | ||
0.563354 | − | 0.826216i | \(-0.309511\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 0.462787i | − | 0.0208429i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.30121 | −0.373112 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.5456 | − | 1.05732i | −0.562748 | − | 0.0474274i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 34.7004i | − | 1.55340i | −0.629869 | − | 0.776701i | \(-0.716892\pi\) | ||
0.629869 | − | 0.776701i | \(-0.283108\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14.0250 | −0.626590 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −41.8593 | −1.86642 | −0.933208 | − | 0.359338i | \(-0.883003\pi\) | ||||
−0.933208 | + | 0.359338i | \(0.883003\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 31.5381 | 1.40343 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.00000 | 0.222058 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 37.2908i | − | 1.65289i | −0.563020 | − | 0.826443i | \(-0.690361\pi\) | ||
0.563020 | − | 0.826443i | \(-0.309639\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27.1162 | − | 2.28531i | −1.19955 | − | 0.101096i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.90126 | 0.348849 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 26.5138i | 1.16834i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 23.4794i | 1.03262i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 8.02892i | − | 0.352430i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 7.46330i | − | 0.326973i | −0.986546 | − | 0.163487i | \(-0.947726\pi\) | ||
0.986546 | − | 0.163487i | \(-0.0522741\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.17748 | 0.0952146 | 0.0476073 | − | 0.998866i | \(-0.484840\pi\) | ||||
0.0476073 | + | 0.998866i | \(0.484840\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.0790206 | − | 0.937617i | 0.00344874 | − | 0.0409210i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 8.00000i | − | 0.348485i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.9831 | 0.999263 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.65685 | 0.419072 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −22.5456 | −0.976559 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.1037 | −0.696225 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 21.1043i | 0.910716i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.20247 | + | 24.7551i | −0.181013 | + | 1.06628i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.1555 | −0.694581 | −0.347291 | − | 0.937758i | \(-0.612898\pi\) | ||||
−0.347291 | + | 0.937758i | \(0.612898\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 16.2060i | 0.695466i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.68526i | 0.286365i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.06930i | 0.131234i | 0.997845 | + | 0.0656169i | \(0.0209015\pi\) | ||||
−0.997845 | + | 0.0656169i | \(0.979098\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 6.19998i | − | 0.264608i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.58005 | 0.0673126 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.1900 | − | 0.943071i | −0.475846 | − | 0.0401034i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 26.7481i | 1.13539i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.7656 | −0.540895 | −0.270448 | − | 0.962735i | \(-0.587172\pi\) | ||||
−0.270448 | + | 0.962735i | \(0.587172\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.4000 | 0.524462 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.30121 | −0.350477 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −17.5044 | −0.737721 | −0.368861 | − | 0.929485i | \(-0.620252\pi\) | ||||
−0.368861 | + | 0.929485i | \(0.620252\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 5.48041i | − | 0.230563i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.222191 | + | 2.63640i | −0.00933116 | + | 0.110719i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.47937 | −0.229707 | −0.114854 | − | 0.993382i | \(-0.536640\pi\) | ||||
−0.114854 | + | 0.993382i | \(0.536640\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 3.67380i | − | 0.153744i | −0.997041 | − | 0.0768718i | \(-0.975507\pi\) | ||
0.997041 | − | 0.0768718i | \(-0.0244932\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.60953i | 0.317893i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 0.0462892i | − | 0.00193039i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 36.0050i | 1.49891i | 0.662057 | + | 0.749454i | \(0.269684\pi\) | ||||
−0.662057 | + | 0.749454i | \(0.730316\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.6694 | 0.443403 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.170663 | − | 2.02499i | 0.00708028 | − | 0.0840109i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 37.1102i | − | 1.53695i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.54562 | −0.270628 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.2663 | −0.753933 | −0.376966 | − | 0.926227i | \(-0.623033\pi\) | ||||
−0.376966 | + | 0.926227i | \(0.623033\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27.3137 | 1.12544 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.68879 | 0.192871 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 24.4789i | 1.00523i | 0.864511 | + | 0.502613i | \(0.167628\pi\) | ||||
−0.864511 | + | 0.502613i | \(0.832372\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.18998 | − | 14.1196i | 0.0487843 | − | 0.578849i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 22.4694 | 0.919610 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 27.1257i | − | 1.10833i | −0.832408 | − | 0.554163i | \(-0.813038\pi\) | ||
0.832408 | − | 0.554163i | \(-0.186962\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 46.5188i | 1.89754i | 0.315965 | + | 0.948771i | \(0.397672\pi\) | ||||
−0.315965 | + | 0.948771i | \(0.602328\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.01250i | 0.367017i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.32026i | 0.175644i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.9606 | −0.647819 | −0.323910 | − | 0.946088i | \(-0.604997\pi\) | ||||
−0.323910 | + | 0.946088i | \(0.604997\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.0444327 | + | 0.527215i | −0.00180050 | + | 0.0213638i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.5138i | 0.748989i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.33870 | 0.296407 | 0.148204 | − | 0.988957i | \(-0.452651\pi\) | ||||
0.148204 | + | 0.988957i | \(0.452651\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −18.4469 | −0.743850 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 38.6524 | 1.55609 | 0.778044 | − | 0.628210i | \(-0.216212\pi\) | ||||
0.778044 | + | 0.628210i | \(0.216212\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26.8688 | 1.07995 | 0.539974 | − | 0.841682i | \(-0.318434\pi\) | ||||
0.539974 | + | 0.841682i | \(0.318434\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.130157i | 0.00522301i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −46.7925 | − | 3.94359i | −1.87470 | − | 0.157997i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −26.6517 | −1.06607 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 28.3421i | − | 1.13187i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 26.7481i | 1.06652i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 22.7900i | − | 0.907257i | −0.891191 | − | 0.453628i | \(-0.850129\pi\) | ||
0.891191 | − | 0.453628i | \(-0.149871\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 15.4185i | 0.612830i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 17.4912 | 0.694117 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.31371 | + | 19.5197i | −0.131294 | + | 0.773399i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.75861i | 0.188248i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.3776 | 0.607378 | 0.303689 | − | 0.952771i | \(-0.401782\pi\) | ||||
0.303689 | + | 0.952771i | \(0.401782\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.1900 | 1.15114 | 0.575570 | − | 0.817752i | \(-0.304780\pi\) | ||||
0.575570 | + | 0.817752i | \(0.304780\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.1457 | 0.399485 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.2275 | −0.402083 | −0.201042 | − | 0.979583i | \(-0.564433\pi\) | ||||
−0.201042 | + | 0.979583i | \(0.564433\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 34.6395i | − | 1.35972i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.768089 | + | 9.11373i | −0.0301038 | + | 0.357195i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.48187 | 0.292788 | 0.146394 | − | 0.989226i | \(-0.453233\pi\) | ||||
0.146394 | + | 0.989226i | \(0.453233\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 40.4049i | 1.57875i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.2853i | 0.401268i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27.9602i | 1.08917i | 0.838704 | + | 0.544587i | \(0.183314\pi\) | ||||
−0.838704 | + | 0.544587i | \(0.816686\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 9.23441i | − | 0.359177i | −0.983742 | − | 0.179588i | \(-0.942523\pi\) | ||
0.983742 | − | 0.179588i | \(-0.0574766\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.54562 | −0.254211 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 48.2075 | + | 4.06284i | 1.86941 | + | 0.157550i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.0260281i | 0.00100781i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.86933 | −0.110935 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −22.2395 | −0.858548 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.9607 | 0.576692 | 0.288346 | − | 0.957526i | \(-0.406895\pi\) | ||||
0.288346 | + | 0.957526i | \(0.406895\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.355642 | −0.0136887 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 5.45727i | − | 0.209740i | −0.994486 | − | 0.104870i | \(-0.966557\pi\) | ||
0.994486 | − | 0.104870i | \(-0.0334426\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 23.8025 | + | 2.00603i | 0.913457 | + | 0.0769845i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.91376 | 0.111655 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 25.4274i | − | 0.972953i | −0.873694 | − | 0.486476i | \(-0.838282\pi\) | ||
0.873694 | − | 0.486476i | \(-0.161718\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 42.1246i | 1.60950i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 20.0853i | − | 0.766303i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 29.2619i | − | 1.11479i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29.0962 | −1.10687 | −0.553437 | − | 0.832891i | \(-0.686684\pi\) | ||||
−0.553437 | + | 0.832891i | \(0.686684\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.45688 | + | 0.797008i | 0.359237 | + | 0.0302758i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 35.4394i | 1.34429i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.4469 | −0.698725 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.343146 | −0.0129790 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −45.8618 | −1.73218 | −0.866089 | − | 0.499890i | \(-0.833374\pi\) | ||||
−0.866089 | + | 0.499890i | \(0.833374\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −91.3237 | −3.44434 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 15.1480i | 0.570508i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −35.9288 | − | 3.02801i | −1.35124 | − | 0.113880i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.1775 | 0.457335 | 0.228667 | − | 0.973505i | \(-0.426563\pi\) | ||||
0.228667 | + | 0.973505i | \(0.426563\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.24441i | 0.159178i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.449936i | 0.0168502i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 23.4794i | 0.878079i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 8.56113i | − | 0.319721i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.5706 | 0.468805 | 0.234402 | − | 0.972140i | \(-0.424687\pi\) | ||||
0.234402 | + | 0.972140i | \(0.424687\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.54562 | − | 30.2050i | 0.0948038 | − | 1.12489i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 6.40598i | − | 0.238241i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.0711196 | −0.00264131 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.22941 | −0.342300 | −0.171150 | − | 0.985245i | \(-0.554748\pi\) | ||||
−0.171150 | + | 0.985245i | \(0.554748\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.1457 | 0.375251 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.2216i | 0.931580i | 0.884895 | + | 0.465790i | \(0.154230\pi\) | ||||
−0.884895 | + | 0.465790i | \(0.845770\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.71128 | + | 15.9711i | −0.100007 | + | 0.589102i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 32.3281 | 1.19082 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 4.93070i | − | 0.181379i | −0.995879 | − | 0.0906894i | \(-0.971093\pi\) | ||
0.995879 | − | 0.0906894i | \(-0.0289070\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 22.3481i | − | 0.820980i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 50.3126i | 1.84579i | 0.385050 | + | 0.922896i | \(0.374184\pi\) | ||||
−0.385050 | + | 0.922896i | \(0.625816\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 52.1814i | − | 1.91178i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.768089 | −0.0281029 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.3456 | + | 1.54614i | 0.670335 | + | 0.0564946i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 27.1321i | − | 0.990066i | −0.868874 | − | 0.495033i | \(-0.835156\pi\) | ||
0.868874 | − | 0.495033i | \(-0.164844\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −24.2025 | −0.881987 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 41.2937 | 1.50283 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.6913 | −1.26088 | −0.630438 | − | 0.776239i | \(-0.717125\pi\) | ||||
−0.630438 | + | 0.776239i | \(0.717125\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.466877 | 0.0169466 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.9082i | 0.721673i | 0.932629 | + | 0.360837i | \(0.117509\pi\) | ||||
−0.932629 | + | 0.360837i | \(0.882491\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.641859 | − | 7.61596i | 0.0232368 | − | 0.275716i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.35564 | −0.193634 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 27.3137i | − | 0.986241i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.83434i | 0.138270i | 0.997607 | + | 0.0691348i | \(0.0220239\pi\) | ||||
−0.997607 | + | 0.0691348i | \(0.977976\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 1.22798i | − | 0.0442248i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 1.33660i | − | 0.0480740i | −0.999711 | − | 0.0240370i | \(-0.992348\pi\) | ||
0.999711 | − | 0.0240370i | \(-0.00765195\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.22941 | −0.0441618 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.56811 | − | 30.4719i | 0.0921306 | − | 1.09317i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 62.9816i | − | 2.25655i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.0693 | 0.610788 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.199975 | 0.00714652 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.8343 | 0.422386 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.11386 | 0.0753509 | 0.0376755 | − | 0.999290i | \(-0.488005\pi\) | ||||
0.0376755 | + | 0.999290i | \(0.488005\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.01551i | 0.214158i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.526180 | + | 6.24337i | −0.0187088 | + | 0.221989i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17.5362 | −0.622728 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 23.9422i | − | 0.849141i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 31.1770i | 1.10434i | 0.833730 | + | 0.552172i | \(0.186201\pi\) | ||||
−0.833730 | + | 0.552172i | \(0.813799\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.1480i | 0.535899i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 17.7486i | 0.627116i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 36.8938 | 1.30195 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.0669267 | + | 0.794117i | −0.00235886 | + | 0.0279889i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 22.3771i | − | 0.787710i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −40.6395 | −1.42881 | −0.714404 | − | 0.699733i | \(-0.753302\pi\) | ||||
−0.714404 | + | 0.699733i | \(0.753302\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.3187 | 0.397454 | 0.198727 | − | 0.980055i | \(-0.436319\pi\) | ||||
0.198727 | + | 0.980055i | \(0.436319\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.63436 | 0.337892 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −23.8393 | −0.835055 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 34.6395i | 1.21188i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.45688 | + | 0.628452i | 0.260564 | + | 0.0219599i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −37.2594 | −1.30036 | −0.650181 | − | 0.759779i | \(-0.725307\pi\) | ||||
−0.650181 | + | 0.759779i | \(0.725307\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 50.9975i | 1.77766i | 0.458236 | + | 0.888831i | \(0.348481\pi\) | ||||
−0.458236 | + | 0.888831i | \(0.651519\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.27570i | 0.0444142i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 41.2439i | − | 1.43419i | −0.696975 | − | 0.717095i | \(-0.745471\pi\) | ||
0.696975 | − | 0.717095i | \(-0.254529\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 10.8734i | − | 0.377649i | −0.982011 | − | 0.188825i | \(-0.939532\pi\) | ||
0.982011 | − | 0.188825i | \(-0.0604678\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.9581 | 0.414821 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.71128 | + | 15.9711i | −0.0939404 | + | 0.553365i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 32.4570i | 1.12322i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.45688 | 0.119487 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 36.5438 | 1.26163 | 0.630816 | − | 0.775932i | \(-0.282720\pi\) | ||||
0.630816 | + | 0.775932i | \(0.282720\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9600 | −0.998621 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −17.6818 | −0.608995 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 11.5711i | − | 0.398059i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.414793 | − | 4.92171i | 0.0142524 | − | 0.169112i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.50131 | −0.120165 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1.50437i | − | 0.0515690i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 4.09818i | − | 0.140319i | −0.997536 | − | 0.0701596i | \(-0.977649\pi\) | ||
0.997536 | − | 0.0701596i | \(-0.0223508\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 18.2853i | − | 0.625344i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 7.40547i | − | 0.252966i | −0.991969 | − | 0.126483i | \(-0.959631\pi\) | ||
0.991969 | − | 0.126483i | \(-0.0403689\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.5287 | 0.768669 | 0.384334 | − | 0.923194i | \(-0.374431\pi\) | ||||
0.384334 | + | 0.923194i | \(0.374431\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 21.0150 | + | 1.77111i | 0.716189 | + | 0.0603591i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 24.2748i | − | 0.826324i | −0.910658 | − | 0.413162i | \(-0.864424\pi\) | ||
0.910658 | − | 0.413162i | \(-0.135576\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.5807 | −0.631764 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11.6444 | 0.395463 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15.2248 | 0.516467 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 25.4912 | 0.863736 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 9.02840i | − | 0.305565i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 28.3363 | + | 2.38813i | 0.957943 | + | 0.0807337i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.46993 | −0.150939 | −0.0754694 | − | 0.997148i | \(-0.524046\pi\) | ||||
−0.0754694 | + | 0.997148i | \(0.524046\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.40047i | 0.114695i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.8504i | 0.668777i | 0.942435 | + | 0.334389i | \(0.108530\pi\) | ||||
−0.942435 | + | 0.334389i | \(0.891470\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42.2116i | 1.42053i | 0.703933 | + | 0.710266i | \(0.251425\pi\) | ||||
−0.703933 | + | 0.710266i | \(0.748575\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 22.3481i | − | 0.751225i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.22509 | −0.175441 | −0.0877207 | − | 0.996145i | \(-0.527958\pi\) | ||||
−0.0877207 | + | 0.996145i | \(0.527958\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19.9263 | − | 1.67935i | −0.668305 | − | 0.0563235i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 3.58704i | − | 0.120170i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −51.7187 | −1.73070 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 48.8400 | 1.63254 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.368139 | 0.0122918 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.691289 | 0.0230558 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 23.9422i | − | 0.797629i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −11.5581 | − | 0.974097i | −0.384630 | − | 0.0324159i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 37.5044 | 1.24669 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 51.1371i | 1.69798i | 0.528408 | + | 0.848990i | \(0.322789\pi\) | ||||
−0.528408 | + | 0.848990i | \(0.677211\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13.6279i | 0.452010i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.9811i | 0.628871i | 0.949279 | + | 0.314436i | \(0.101815\pi\) | ||||
−0.949279 | + | 0.314436i | \(0.898185\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.75516i | 0.0911826i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −14.3481 | −0.474335 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.87932 | − | 46.0300i | 0.128107 | − | 1.52004i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 12.3890i | − | 0.408677i | −0.978900 | − | 0.204338i | \(-0.934496\pi\) | ||
0.978900 | − | 0.204338i | \(-0.0655043\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.1037 | −0.398832 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.4594 | 0.443021 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.11055 | 0.135154 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11.4569 | −0.376293 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 2.87984i | − | 0.0944845i | −0.998883 | − | 0.0472423i | \(-0.984957\pi\) | ||
0.998883 | − | 0.0472423i | \(-0.0150433\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −54.5287 | − | 9.25690i | −1.78711 | − | 0.303383i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 26.7481 | 0.875693 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 19.2109i | 0.628263i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 27.5551i | − | 0.900185i | −0.892982 | − | 0.450092i | \(-0.851391\pi\) | ||
0.892982 | − | 0.450092i | \(-0.148609\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 27.8343i | 0.908339i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 0.707358i | − | 0.0230592i | −0.999934 | − | 0.0115296i | \(-0.996330\pi\) | ||
0.999934 | − | 0.0115296i | \(-0.00367007\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.03749 | 0.0337853 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.10124 | + | 0.514201i | 0.198473 | + | 0.0167270i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.64725i | 0.151015i | 0.997145 | + | 0.0755077i | \(0.0240577\pi\) | ||||
−0.997145 | + | 0.0755077i | \(0.975942\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 29.0912 | 0.944342 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.85683 | 0.189921 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.77516 | 0.219469 | 0.109734 | − | 0.993961i | \(-0.465000\pi\) | ||||
0.109734 | + | 0.993961i | \(0.465000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.6102 | 0.569852 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 0.717318i | − | 0.0231876i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.04443 | − | 47.9891i | 0.130602 | − | 1.54965i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.0500 | −0.614516 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 6.95858i | − | 0.224237i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 24.6913i | − | 0.794841i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.0375i | 0.483573i | 0.970329 | + | 0.241787i | \(0.0777334\pi\) | ||||
−0.970329 | + | 0.241787i | \(0.922267\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 18.2853i | − | 0.587409i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −35.5601 | −1.14118 | −0.570588 | − | 0.821236i | \(-0.693285\pi\) | ||||
−0.570588 | + | 0.821236i | \(0.693285\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.40257 | − | 40.3731i | 0.109082 | − | 1.29430i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.00591i | 0.0322148i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 44.8370 | 1.43446 | 0.717231 | − | 0.696836i | \(-0.245409\pi\) | ||||
0.717231 | + | 0.696836i | \(0.245409\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 63.6649 | 2.03474 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.88877 | −0.0922312 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18.1386 | −0.578532 | −0.289266 | − | 0.957249i | \(-0.593411\pi\) | ||||
−0.289266 | + | 0.957249i | \(0.593411\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 10.8509i | − | 0.345739i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.45438 | − | 17.2569i | 0.0462934 | − | 0.549293i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.570613 | −0.0181444 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.0659i | 1.27273i | 0.771386 | + | 0.636367i | \(0.219564\pi\) | ||||
−0.771386 | + | 0.636367i | \(0.780436\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.84787i | 0.0903743i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 51.9992i | − | 1.64849i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 44.7824i | − | 1.41827i | −0.705071 | − | 0.709136i | \(-0.749085\pi\) | ||
0.705071 | − | 0.709136i | \(-0.250915\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −11.5581 | −0.365683 |
(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 | 672.2.b.b.223.2 | yes | 8 | |
3.2 | odd | 2 | 2016.2.b.c.1567.7 | 8 | |||
4.3 | odd | 2 | 672.2.b.a.223.2 | ✓ | 8 | ||
7.6 | odd | 2 | 672.2.b.a.223.7 | yes | 8 | ||
8.3 | odd | 2 | 1344.2.b.h.895.7 | 8 | |||
8.5 | even | 2 | 1344.2.b.g.895.7 | 8 | |||
12.11 | even | 2 | 2016.2.b.a.1567.7 | 8 | |||
21.20 | even | 2 | 2016.2.b.a.1567.2 | 8 | |||
24.5 | odd | 2 | 4032.2.b.q.3583.2 | 8 | |||
24.11 | even | 2 | 4032.2.b.o.3583.2 | 8 | |||
28.27 | even | 2 | inner | 672.2.b.b.223.7 | yes | 8 | |
56.13 | odd | 2 | 1344.2.b.h.895.2 | 8 | |||
56.27 | even | 2 | 1344.2.b.g.895.2 | 8 | |||
84.83 | odd | 2 | 2016.2.b.c.1567.2 | 8 | |||
168.83 | odd | 2 | 4032.2.b.q.3583.7 | 8 | |||
168.125 | even | 2 | 4032.2.b.o.3583.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.2.b.a.223.2 | ✓ | 8 | 4.3 | odd | 2 | ||
672.2.b.a.223.7 | yes | 8 | 7.6 | odd | 2 | ||
672.2.b.b.223.2 | yes | 8 | 1.1 | even | 1 | trivial | |
672.2.b.b.223.7 | yes | 8 | 28.27 | even | 2 | inner | |
1344.2.b.g.895.2 | 8 | 56.27 | even | 2 | |||
1344.2.b.g.895.7 | 8 | 8.5 | even | 2 | |||
1344.2.b.h.895.2 | 8 | 56.13 | odd | 2 | |||
1344.2.b.h.895.7 | 8 | 8.3 | odd | 2 | |||
2016.2.b.a.1567.2 | 8 | 21.20 | even | 2 | |||
2016.2.b.a.1567.7 | 8 | 12.11 | even | 2 | |||
2016.2.b.c.1567.2 | 8 | 84.83 | odd | 2 | |||
2016.2.b.c.1567.7 | 8 | 3.2 | odd | 2 | |||
4032.2.b.o.3583.2 | 8 | 24.11 | even | 2 | |||
4032.2.b.o.3583.7 | 8 | 168.125 | even | 2 | |||
4032.2.b.q.3583.2 | 8 | 24.5 | odd | 2 | |||
4032.2.b.q.3583.7 | 8 | 168.83 | odd | 2 |