Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,2,Mod(449,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.449");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.bk (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.46176749826\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 10x^{14} + 46x^{12} + 126x^{10} + 315x^{8} + 1134x^{6} + 3726x^{4} + 7290x^{2} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{7} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 521.7 | ||
Root | \(-0.750719 - 1.56090i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 684.521 |
Dual form | 684.2.bk.a.449.7 |
$q$-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 \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.47786 | + | 1.43059i | 1.10813 | + | 0.639781i | 0.938345 | − | 0.345700i | \(-0.112358\pi\) |
0.169788 | + | 0.985481i | \(0.445692\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.93208 | 1.48619 | 0.743093 | − | 0.669188i | \(-0.233358\pi\) | ||||
0.743093 | + | 0.669188i | \(0.233358\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.80663i | 0.544721i | 0.962195 | + | 0.272360i | \(0.0878043\pi\) | ||||
−0.962195 | + | 0.272360i | \(0.912196\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.947142 | + | 0.546833i | −0.262690 | + | 0.151664i | −0.625561 | − | 0.780175i | \(-0.715130\pi\) |
0.362871 | + | 0.931839i | \(0.381797\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.36468 | + | 0.787896i | 0.330983 | + | 0.191093i | 0.656277 | − | 0.754520i | \(-0.272130\pi\) |
−0.325295 | + | 0.945613i | \(0.605464\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.09320 | − | 3.82342i | −0.480213 | − | 0.877152i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.33601 | + | 2.50340i | −0.904121 | + | 0.521995i | −0.878535 | − | 0.477678i | \(-0.841479\pi\) |
−0.0255863 | + | 0.999673i | \(0.508145\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.59320 | + | 2.75950i | 0.318640 | + | 0.551900i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.451406 | + | 0.781859i | 0.0838240 | + | 0.145188i | 0.904890 | − | 0.425647i | \(-0.139953\pi\) |
−0.821065 | + | 0.570834i | \(0.806620\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.02361i | − | 0.543056i | −0.962431 | − | 0.271528i | \(-0.912471\pi\) | ||
0.962431 | − | 0.271528i | \(-0.0875290\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 9.74314 | + | 5.62521i | 1.64689 | + | 0.950833i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 5.27640i | − | 0.867435i | −0.901049 | − | 0.433717i | \(-0.857202\pi\) | ||
0.901049 | − | 0.433717i | \(-0.142798\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.04245 | + | 7.00173i | −0.631325 | + | 1.09349i | 0.355956 | + | 0.934503i | \(0.384155\pi\) |
−0.987281 | + | 0.158984i | \(0.949178\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.05924 | − | 5.29875i | 0.466529 | − | 0.808052i | −0.532740 | − | 0.846279i | \(-0.678838\pi\) |
0.999269 | + | 0.0382267i | \(0.0121709\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.22283 | + | 1.86070i | −0.470098 | + | 0.271411i | −0.716281 | − | 0.697812i | \(-0.754157\pi\) |
0.246183 | + | 0.969223i | \(0.420824\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.46123 | 1.20875 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.06891 | + | 10.5117i | 0.833629 | + | 1.44389i | 0.895142 | + | 0.445781i | \(0.147074\pi\) |
−0.0615134 | + | 0.998106i | \(0.519593\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.58456 | + | 4.47659i | −0.348502 | + | 0.603623i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.06891 | − | 10.5117i | 0.790105 | − | 1.36850i | −0.135797 | − | 0.990737i | \(-0.543360\pi\) |
0.925902 | − | 0.377765i | \(-0.123307\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.27096 | + | 12.5937i | 0.930951 | + | 1.61245i | 0.781700 | + | 0.623654i | \(0.214353\pi\) |
0.149250 | + | 0.988799i | \(0.452314\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.12918 | −0.388127 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.17138 | − | 1.83100i | 0.387446 | − | 0.223692i | −0.293607 | − | 0.955926i | \(-0.594856\pi\) |
0.681053 | + | 0.732234i | \(0.261522\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.67423 | − | 6.36396i | 0.436051 | − | 0.755263i | −0.561329 | − | 0.827592i | \(-0.689710\pi\) |
0.997381 | + | 0.0723293i | \(0.0230432\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.10826 | − | 1.91957i | 0.129712 | − | 0.224668i | −0.793853 | − | 0.608110i | \(-0.791928\pi\) |
0.923565 | + | 0.383442i | \(0.125261\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.10383i | 0.809556i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.5205 | − | 7.22870i | −1.40866 | − | 0.813292i | −0.413404 | − | 0.910548i | \(-0.635660\pi\) |
−0.995259 | + | 0.0972560i | \(0.968993\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 10.9114i | − | 1.19769i | −0.800866 | − | 0.598843i | \(-0.795627\pi\) | ||
0.800866 | − | 0.598843i | \(-0.204373\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.25432 | + | 3.90459i | 0.244515 | + | 0.423513i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.37847 | − | 14.5119i | −0.888116 | − | 1.53826i | −0.842100 | − | 0.539321i | \(-0.818681\pi\) |
−0.0460153 | − | 0.998941i | \(-0.514652\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.72424 | + | 2.15019i | −0.390406 | + | 0.225401i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.283104 | − | 12.4684i | 0.0290458 | − | 1.27923i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.78990 | + | 1.61075i | 0.283272 | + | 0.163547i | 0.634904 | − | 0.772591i | \(-0.281040\pi\) |
−0.351632 | + | 0.936138i | \(0.614373\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.7696 | + | 6.79518i | −1.17112 | + | 0.676146i | −0.953943 | − | 0.299987i | \(-0.903018\pi\) |
−0.217175 | + | 0.976133i | \(0.569684\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.8190i | 1.36163i | 0.732457 | + | 0.680814i | \(0.238374\pi\) | ||||
−0.732457 | + | 0.680814i | \(0.761626\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.61912 | 0.446547 | 0.223273 | − | 0.974756i | \(-0.428326\pi\) | ||||
0.223273 | + | 0.974756i | \(0.428326\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.5166 | − | 8.38119i | −1.39044 | − | 0.802772i | −0.397078 | − | 0.917785i | \(-0.629976\pi\) |
−0.993364 | + | 0.115013i | \(0.963309\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.0335 | −1.41424 | −0.707118 | − | 0.707095i | \(-0.750005\pi\) | ||||
−0.707118 | + | 0.707095i | \(0.750005\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −14.3254 | −1.33585 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.36601 | + | 3.09807i | 0.491901 | + | 0.283999i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.73607 | 0.703279 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 5.18906i | − | 0.464124i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.17521 | + | 4.14261i | −0.636697 | + | 0.367597i | −0.783341 | − | 0.621592i | \(-0.786486\pi\) |
0.146644 | + | 0.989189i | \(0.453153\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.22283 | + | 1.86070i | 0.281580 | + | 0.162570i | 0.634138 | − | 0.773220i | \(-0.281355\pi\) |
−0.352559 | + | 0.935790i | \(0.614688\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.23062 | − | 15.0340i | −0.713685 | − | 1.30361i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.57705 | + | 2.64256i | −0.391044 | + | 0.225769i | −0.682612 | − | 0.730781i | \(-0.739156\pi\) |
0.291569 | + | 0.956550i | \(0.405823\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.26458 | + | 3.92236i | 0.192079 | + | 0.332691i | 0.945939 | − | 0.324344i | \(-0.105144\pi\) |
−0.753860 | + | 0.657035i | \(0.771810\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.987927 | − | 1.71114i | −0.0826146 | − | 0.143093i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.58312i | 0.214516i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.45811 | + | 5.46064i | 0.774839 | + | 0.447353i | 0.834598 | − | 0.550859i | \(-0.185700\pi\) |
−0.0597593 | + | 0.998213i | \(0.519033\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 17.1655i | − | 1.39691i | −0.715656 | − | 0.698453i | \(-0.753872\pi\) | ||
0.715656 | − | 0.698453i | \(-0.246128\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.32556 | − | 7.49208i | 0.347437 | − | 0.601779i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.68640 | + | 9.84913i | −0.453824 | + | 0.786046i | −0.998620 | − | 0.0525228i | \(-0.983274\pi\) |
0.544796 | + | 0.838569i | \(0.316607\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −17.0495 | + | 9.84356i | −1.34369 | + | 0.775781i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.63487 | −0.441357 | −0.220679 | − | 0.975347i | \(-0.570827\pi\) | ||||
−0.220679 | + | 0.975347i | \(0.570827\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.82633 | − | 17.0197i | −0.760384 | − | 1.31702i | −0.942653 | − | 0.333775i | \(-0.891677\pi\) |
0.182268 | − | 0.983249i | \(-0.441656\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.90195 | + | 10.2225i | −0.453996 | + | 0.786344i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.95572 | − | 8.58356i | 0.376777 | − | 0.652596i | −0.613815 | − | 0.789450i | \(-0.710366\pi\) |
0.990591 | + | 0.136854i | \(0.0436991\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.26458 | + | 10.8506i | 0.473558 | + | 0.820226i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.4986 | −0.784700 | −0.392350 | − | 0.919816i | \(-0.628338\pi\) | ||||
−0.392350 | + | 0.919816i | \(0.628338\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.44714 | − | 4.87696i | 0.627871 | − | 0.362502i | −0.152056 | − | 0.988372i | \(-0.548589\pi\) |
0.779927 | + | 0.625870i | \(0.215256\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.54839 | − | 13.0742i | 0.554968 | − | 0.961233i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.42344 | + | 2.46547i | −0.104092 | + | 0.180293i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 5.85716i | − | 0.423809i | −0.977290 | − | 0.211905i | \(-0.932033\pi\) | ||
0.977290 | − | 0.211905i | \(-0.0679666\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.8491 | + | 6.26372i | 0.780935 | + | 0.450873i | 0.836761 | − | 0.547568i | \(-0.184446\pi\) |
−0.0558268 | + | 0.998440i | \(0.517779\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 16.6557i | − | 1.18667i | −0.804955 | − | 0.593336i | \(-0.797811\pi\) | ||
0.804955 | − | 0.593336i | \(-0.202189\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.22679 | + | 3.85691i | 0.157853 | + | 0.273409i | 0.934094 | − | 0.357027i | \(-0.116210\pi\) |
−0.776241 | + | 0.630436i | \(0.782876\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.77496 | + | 3.07433i | 0.124578 | + | 0.215776i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −20.0333 | + | 11.5662i | −1.39918 | + | 0.807820i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.90752 | − | 3.78164i | 0.477803 | − | 0.261582i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.6262 | + | 7.86708i | 0.938065 | + | 0.541592i | 0.889353 | − | 0.457221i | \(-0.151155\pi\) |
0.0487120 | + | 0.998813i | \(0.484488\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 15.1607 | − | 8.75305i | 1.03395 | − | 0.596953i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 11.8891i | − | 0.807082i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.72339 | −0.115928 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.5567 | − | 9.55901i | −1.10872 | − | 0.640119i | −0.170221 | − | 0.985406i | \(-0.554448\pi\) |
−0.938497 | + | 0.345287i | \(0.887781\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −19.4863 | −1.29335 | −0.646675 | − | 0.762766i | \(-0.723841\pi\) | ||||
−0.646675 | + | 0.762766i | \(0.723841\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.8340 | 1.70716 | 0.853580 | − | 0.520961i | \(-0.174426\pi\) | ||||
0.853580 | + | 0.520961i | \(0.174426\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.6667 | − | 10.7772i | −1.22289 | − | 0.706038i | −0.257360 | − | 0.966316i | \(-0.582853\pi\) |
−0.965534 | + | 0.260278i | \(0.916186\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.6476 | −0.694575 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.58259i | 0.425792i | 0.977075 | + | 0.212896i | \(0.0682896\pi\) | ||||
−0.977075 | + | 0.212896i | \(0.931710\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.2267 | + | 5.90441i | −0.658762 | + | 0.380336i | −0.791805 | − | 0.610774i | \(-0.790858\pi\) |
0.133043 | + | 0.991110i | \(0.457525\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 20.9658 | + | 12.1046i | 1.33945 | + | 0.773334i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.07333 | + | 2.47669i | 0.259180 | + | 0.157588i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.88306 | + | 4.55129i | −0.497575 | + | 0.287275i | −0.727711 | − | 0.685883i | \(-0.759416\pi\) |
0.230137 | + | 0.973158i | \(0.426083\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.52273 | − | 7.83359i | −0.284341 | − | 0.492494i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.7396 | + | 18.6015i | 0.669918 | + | 1.16033i | 0.977927 | + | 0.208948i | \(0.0670040\pi\) |
−0.308009 | + | 0.951383i | \(0.599663\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 20.7472i | − | 1.28917i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 20.0104 | + | 11.5530i | 1.23390 | + | 0.712390i | 0.967840 | − | 0.251568i | \(-0.0809461\pi\) |
0.266056 | + | 0.963958i | \(0.414279\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 34.7286i | 2.13336i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.33601 | + | 7.51020i | −0.264371 | + | 0.457905i | −0.967399 | − | 0.253258i | \(-0.918498\pi\) |
0.703027 | + | 0.711163i | \(0.251831\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.00000 | + | 1.73205i | −0.0607457 | + | 0.105215i | −0.894799 | − | 0.446469i | \(-0.852681\pi\) |
0.834053 | + | 0.551684i | \(0.186015\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.98541 | + | 2.87833i | −0.300631 | + | 0.173570i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.8340 | 0.650953 | 0.325477 | − | 0.945550i | \(-0.394475\pi\) | ||||
0.325477 | + | 0.945550i | \(0.394475\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.09698 | − | 12.2923i | −0.423370 | − | 0.733299i | 0.572896 | − | 0.819628i | \(-0.305820\pi\) |
−0.996267 | + | 0.0863290i | \(0.972486\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.35552 | − | 16.2042i | 0.556128 | − | 0.963242i | −0.441687 | − | 0.897169i | \(-0.645620\pi\) |
0.997815 | − | 0.0660724i | \(-0.0210468\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −15.8952 | + | 27.5314i | −0.938266 | + | 1.62512i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.25844 | − | 12.5720i | −0.426967 | − | 0.739529i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 27.9710 | 1.63408 | 0.817042 | − | 0.576578i | \(-0.195612\pi\) | ||||
0.817042 | + | 0.576578i | \(0.195612\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 30.0758 | − | 17.3643i | 1.75108 | − | 1.01099i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.73788 | − | 4.74215i | 0.158336 | − | 0.274246i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.0292 | − | 20.8351i | 0.693349 | − | 1.20092i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 41.6071i | 2.38242i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.7537 | − | 9.67274i | −0.956183 | − | 0.552053i | −0.0611870 | − | 0.998126i | \(-0.519489\pi\) |
−0.894996 | + | 0.446074i | \(0.852822\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.8697i | 0.899886i | 0.893057 | + | 0.449943i | \(0.148556\pi\) | ||||
−0.893057 | + | 0.449943i | \(0.851444\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.70303 | − | 6.41384i | −0.209308 | − | 0.362532i | 0.742189 | − | 0.670191i | \(-0.233788\pi\) |
−0.951497 | + | 0.307659i | \(0.900454\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.19809 | + | 15.9316i | 0.516616 | + | 0.894806i | 0.999814 | + | 0.0192943i | \(0.00614196\pi\) |
−0.483198 | + | 0.875511i | \(0.660525\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.41253 | + | 0.815526i | −0.0790867 | + | 0.0456607i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.155919 | − | 6.86695i | 0.00867554 | − | 0.382087i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.01797 | − | 1.74243i | −0.167407 | − | 0.0966524i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.6724 | + | 7.31642i | −0.698653 | + | 0.403367i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.2489i | 0.893123i | 0.894753 | + | 0.446561i | \(0.147352\pi\) | ||||
−0.894753 | + | 0.446561i | \(0.852648\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.4777 | 0.572455 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.9186 | + | 8.03590i | 0.758194 | + | 0.437743i | 0.828647 | − | 0.559772i | \(-0.189111\pi\) |
−0.0704531 | + | 0.997515i | \(0.522445\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.46256 | 0.295814 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.74568 | 0.310238 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.2240 | − | 8.78955i | −0.817265 | − | 0.471848i | 0.0322076 | − | 0.999481i | \(-0.489746\pi\) |
−0.849472 | + | 0.527633i | \(0.823080\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.13123 | 0.435255 | 0.217627 | − | 0.976032i | \(-0.430168\pi\) | ||||
0.217627 | + | 0.976032i | \(0.430168\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 26.4166i | − | 1.40601i | −0.711184 | − | 0.703006i | \(-0.751841\pi\) | ||
0.711184 | − | 0.703006i | \(-0.248159\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 18.2085 | − | 10.5127i | 0.966406 | − | 0.557955i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.2657 | + | 6.50423i | 0.594579 | + | 0.343280i | 0.766906 | − | 0.641759i | \(-0.221795\pi\) |
−0.172327 | + | 0.985040i | \(0.555129\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.2370 | + | 16.0063i | −0.538792 | + | 0.842439i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.49224 | − | 3.17095i | 0.287477 | − | 0.165975i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.34526 | − | 10.9903i | −0.331220 | − | 0.573690i | 0.651532 | − | 0.758622i | \(-0.274127\pi\) |
−0.982751 | + | 0.184932i | \(0.940793\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 23.8634 | + | 41.3327i | 1.23893 | + | 2.14588i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 0.873676i | − | 0.0452372i | −0.999744 | − | 0.0226186i | \(-0.992800\pi\) | ||
0.999744 | − | 0.0226186i | \(-0.00720034\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.855092 | − | 0.493688i | −0.0440395 | − | 0.0254262i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.8405i | 1.32734i | 0.748027 | + | 0.663669i | \(0.231002\pi\) | ||||
−0.748027 | + | 0.663669i | \(0.768998\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.8792 | − | 24.0396i | 0.709196 | − | 1.22836i | −0.255960 | − | 0.966687i | \(-0.582391\pi\) |
0.965156 | − | 0.261676i | \(-0.0842752\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.1627 | + | 17.6023i | −0.517939 | + | 0.897096i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −20.8911 | + | 12.0615i | −1.05922 | + | 0.611542i | −0.925217 | − | 0.379439i | \(-0.876117\pi\) |
−0.134004 | + | 0.990981i | \(0.542784\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.88967 | −0.398998 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −20.6827 | − | 35.8234i | −1.04066 | − | 1.80247i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.9548 | − | 29.3666i | 0.850937 | − | 1.47387i | −0.0294262 | − | 0.999567i | \(-0.509368\pi\) |
0.880363 | − | 0.474300i | \(-0.157299\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.2899 | + | 31.6791i | −0.913355 | + | 1.58198i | −0.104062 | + | 0.994571i | \(0.533184\pi\) |
−0.809293 | + | 0.587406i | \(0.800149\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.65341 | + | 2.86379i | 0.0823622 | + | 0.142655i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.53253 | 0.472510 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.41092 | + | 2.54665i | −0.218106 | + | 0.125924i | −0.605073 | − | 0.796170i | \(-0.706856\pi\) |
0.386967 | + | 0.922094i | \(0.373523\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 23.8634 | − | 41.3327i | 1.17424 | − | 2.03385i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.6098 | − | 27.0370i | 0.766257 | − | 1.32720i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.55747i | 0.222647i | 0.993784 | + | 0.111323i | \(0.0355089\pi\) | ||||
−0.993784 | + | 0.111323i | \(0.964491\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.85940 | + | 5.11498i | 0.431781 | + | 0.249289i | 0.700105 | − | 0.714040i | \(-0.253137\pi\) |
−0.268324 | + | 0.963329i | \(0.586470\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.02110i | 0.243559i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 28.5900 | + | 49.5193i | 1.38357 | + | 2.39641i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.68862 | + | 11.5850i | 0.322179 | + | 0.558031i | 0.980937 | − | 0.194324i | \(-0.0622513\pi\) |
−0.658758 | + | 0.752355i | \(0.728918\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.33378 | + | 4.23416i | −0.352439 | + | 0.203481i | −0.665759 | − | 0.746167i | \(-0.731892\pi\) |
0.313320 | + | 0.949648i | \(0.398559\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 18.6477 | + | 11.3383i | 0.892039 | + | 0.542384i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.0783 | + | 18.5204i | 1.53101 | + | 0.883932i | 0.999315 | + | 0.0369989i | \(0.0117798\pi\) |
0.531700 | + | 0.846933i | \(0.321554\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.9891 | − | 7.49923i | 0.617129 | − | 0.356299i | −0.158622 | − | 0.987339i | \(-0.550705\pi\) |
0.775750 | + | 0.631040i | \(0.217372\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 47.9447i | − | 2.27280i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.3441 | 0.818517 | 0.409258 | − | 0.912419i | \(-0.365788\pi\) | ||||
0.409258 | + | 0.912419i | \(0.365788\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.6496 | − | 7.30324i | −0.595645 | − | 0.343896i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −12.3042 | −0.576829 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.0333 | 1.03067 | 0.515337 | − | 0.856988i | \(-0.327667\pi\) | ||||
0.515337 | + | 0.856988i | \(0.327667\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.7374 | − | 9.08599i | −0.732963 | − | 0.423177i | 0.0865419 | − | 0.996248i | \(-0.472418\pi\) |
−0.819505 | + | 0.573072i | \(0.805752\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −42.6463 | −1.98194 | −0.990970 | − | 0.134085i | \(-0.957191\pi\) | ||||
−0.990970 | + | 0.134085i | \(0.957191\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 34.3222i | 1.58824i | 0.607760 | + | 0.794121i | \(0.292068\pi\) | ||||
−0.607760 | + | 0.794121i | \(0.707932\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.4701 | − | 7.19962i | 0.575816 | − | 0.332448i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.57291 | + | 5.52692i | 0.440163 | + | 0.254128i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.21584 | − | 11.8676i | 0.331086 | − | 0.544525i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −30.5606 | + | 17.6441i | −1.39635 | + | 0.806182i | −0.994008 | − | 0.109309i | \(-0.965136\pi\) |
−0.402340 | + | 0.915490i | \(0.631803\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.88531 | + | 4.99750i | 0.131559 | + | 0.227866i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.60866 | + | 7.98243i | 0.209268 | + | 0.362464i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 9.59157i | − | 0.434635i | −0.976101 | − | 0.217318i | \(-0.930269\pi\) | ||
0.976101 | − | 0.217318i | \(-0.0697308\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.99071 | + | 4.03609i | 0.315486 | + | 0.182146i | 0.649379 | − | 0.760465i | \(-0.275029\pi\) |
−0.333893 | + | 0.942611i | \(0.608362\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.42264i | 0.0640727i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 14.4474 | − | 25.0236i | 0.648053 | − | 1.12246i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.5743 | + | 20.0473i | −0.518137 | + | 0.897439i | 0.481641 | + | 0.876369i | \(0.340041\pi\) |
−0.999778 | + | 0.0210709i | \(0.993292\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.67069 | + | 2.69663i | −0.208256 | + | 0.120237i | −0.600501 | − | 0.799624i | \(-0.705032\pi\) |
0.392245 | + | 0.919861i | \(0.371699\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −38.8846 | −1.73034 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.95218 | − | 10.3095i | −0.263826 | − | 0.456960i | 0.703430 | − | 0.710765i | \(-0.251651\pi\) |
−0.967255 | + | 0.253805i | \(0.918318\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.35778 | − | 7.54789i | 0.192777 | − | 0.333899i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −19.7694 | + | 34.2416i | −0.871143 | + | 1.50886i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.36161 | − | 5.82247i | −0.147843 | − | 0.256072i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.9651 | −0.962309 | −0.481155 | − | 0.876636i | \(-0.659782\pi\) | ||||
−0.481155 | + | 0.876636i | \(0.659782\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.0371082 | + | 0.0214244i | −0.00162263 | + | 0.000936824i | −0.500811 | − | 0.865557i | \(-0.666965\pi\) |
0.499188 | + | 0.866493i | \(0.333632\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.38229 | − | 4.12625i | 0.103774 | − | 0.179742i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.03401 | − | 1.79096i | 0.0449570 | − | 0.0778677i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 8.84219i | − | 0.382998i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.4455 | + | 6.60808i | 0.494834 | + | 0.285692i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15.2864i | 0.658430i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.15724 | + | 5.46850i | 0.135740 | + | 0.235109i | 0.925880 | − | 0.377818i | \(-0.123325\pi\) |
−0.790140 | + | 0.612927i | \(0.789992\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −23.9801 | − | 41.5348i | −1.02720 | − | 1.77916i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.9330 | + | 8.04422i | −0.595732 | + | 0.343946i | −0.767361 | − | 0.641216i | \(-0.778430\pi\) |
0.171629 | + | 0.985162i | \(0.445097\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.04449 | − | 3.36250i | 0.0870982 | − | 0.143247i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −49.2315 | − | 28.4238i | −2.09353 | − | 1.20870i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 28.0014 | − | 16.1666i | 1.18646 | − | 0.685003i | 0.228959 | − | 0.973436i | \(-0.426468\pi\) |
0.957500 | + | 0.288433i | \(0.0931344\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.69157i | 0.283023i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 28.3247 | 1.19374 | 0.596872 | − | 0.802337i | \(-0.296410\pi\) | ||||
0.596872 | + | 0.802337i | \(0.296410\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −37.2510 | − | 21.5069i | −1.56716 | − | 0.904802i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −36.5760 | −1.53334 | −0.766672 | − | 0.642039i | \(-0.778089\pi\) | ||||
−0.766672 | + | 0.642039i | \(0.778089\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.4818 | 1.10823 | 0.554113 | − | 0.832441i | \(-0.313057\pi\) | ||||
0.554113 | + | 0.832441i | \(0.313057\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.8163 | − | 7.97682i | −0.576178 | − | 0.332656i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −33.1089 | −1.37834 | −0.689170 | − | 0.724600i | \(-0.742025\pi\) | ||||
−0.689170 | + | 0.724600i | \(0.742025\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 42.9046i | − | 1.77998i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.9907 | + | 10.9643i | −0.786516 | + | 0.454095i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −38.9220 | − | 22.4716i | −1.60648 | − | 0.927503i | −0.990149 | − | 0.140017i | \(-0.955284\pi\) |
−0.616333 | − | 0.787486i | \(-0.711382\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.5605 | + | 6.32901i | −0.476343 | + | 0.260782i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.8247 | − | 9.13638i | 0.649842 | − | 0.375186i | −0.138554 | − | 0.990355i | \(-0.544245\pi\) |
0.788396 | + | 0.615169i | \(0.210912\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.86415 | + | 15.3532i | 0.363395 | + | 0.629418i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.1805 | + | 19.3653i | 0.456825 | + | 0.791244i | 0.998791 | − | 0.0491564i | \(-0.0156533\pi\) |
−0.541966 | + | 0.840400i | \(0.682320\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.6726i | 1.00641i | 0.864166 | + | 0.503207i | \(0.167847\pi\) | ||||
−0.864166 | + | 0.503207i | \(0.832153\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 19.1689 | + | 11.0672i | 0.779327 | + | 0.449945i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 47.4017i | 1.92398i | 0.273090 | + | 0.961988i | \(0.411954\pi\) | ||||
−0.273090 | + | 0.961988i | \(0.588046\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.03498 | − | 3.52470i | 0.0823267 | − | 0.142594i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.807176 | − | 1.39807i | 0.0326015 | − | 0.0564675i | −0.849264 | − | 0.527968i | \(-0.822954\pi\) |
0.881866 | + | 0.471500i | \(0.156287\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19.0845 | + | 11.0185i | −0.768314 | + | 0.443586i | −0.832273 | − | 0.554366i | \(-0.812961\pi\) |
0.0639588 | + | 0.997953i | \(0.479627\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.1090 | −0.647474 | −0.323737 | − | 0.946147i | \(-0.604939\pi\) | ||||
−0.323737 | + | 0.946147i | \(0.604939\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −32.9448 | − | 57.0620i | −1.31990 | − | 2.28614i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.3894 | − | 26.6553i | 0.615577 | − | 1.06621i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.15725 | − | 7.20058i | 0.165761 | − | 0.287106i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.35620 | + | 5.81311i | 0.133608 | + | 0.231416i | 0.925065 | − | 0.379809i | \(-0.124010\pi\) |
−0.791457 | + | 0.611225i | \(0.790677\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −23.7056 | −0.940727 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.01399 | + | 4.62688i | −0.317526 | + | 0.183324i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.20662 | − | 15.9463i | 0.363640 | − | 0.629842i | −0.624917 | − | 0.780691i | \(-0.714867\pi\) |
0.988557 | + | 0.150849i | \(0.0482006\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.40066 | − | 12.8183i | 0.291854 | − | 0.505505i | −0.682394 | − | 0.730984i | \(-0.739061\pi\) |
0.974248 | + | 0.225479i | \(0.0723946\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.5539i | 0.532857i | 0.963855 | + | 0.266429i | \(0.0858436\pi\) | ||||
−0.963855 | + | 0.266429i | \(0.914156\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.9907 | + | 10.9643i | 0.745451 | + | 0.430386i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 41.4603i | − | 1.62247i | −0.584723 | − | 0.811233i | \(-0.698797\pi\) | ||
0.584723 | − | 0.811233i | \(-0.301203\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.32381 | + | 9.22112i | 0.208019 | + | 0.360299i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.46165 | − | 14.6560i | −0.329619 | − | 0.570917i | 0.652817 | − | 0.757516i | \(-0.273587\pi\) |
−0.982436 | + | 0.186598i | \(0.940254\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.45347 | − | 3.14856i | 0.212116 | − | 0.122465i | −0.390179 | − | 0.920739i | \(-0.627587\pi\) |
0.602294 | + | 0.798274i | \(0.294253\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.11319 | − | 49.0268i | 0.0431675 | − | 1.90118i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.91461 | − | 2.26010i | −0.151574 | − | 0.0875114i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −22.7522 | + | 13.1360i | −0.878337 | + | 0.507108i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 3.33167i | − | 0.128426i | −0.997936 | − | 0.0642132i | \(-0.979546\pi\) | ||
0.997936 | − | 0.0642132i | \(-0.0204538\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23.5183 | 0.903881 | 0.451940 | − | 0.892048i | \(-0.350732\pi\) | ||||
0.451940 | + | 0.892048i | \(0.350732\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.9701 | + | 6.33360i | 0.420994 | + | 0.243061i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 39.3092 | 1.50412 | 0.752062 | − | 0.659092i | \(-0.229059\pi\) | ||||
0.752062 | + | 0.659092i | \(0.229059\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.1217 | −0.577771 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.4962 | − | 6.63736i | −0.437972 | − | 0.252863i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.5925 | 1.20183 | 0.600917 | − | 0.799311i | \(-0.294802\pi\) | ||||
0.600917 | + | 0.799311i | \(0.294802\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.9588i | 0.491554i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.0333 | + | 6.37007i | −0.417915 | + | 0.241283i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.4470 | + | 14.6918i | 0.961120 | + | 0.554903i | 0.896517 | − | 0.443008i | \(-0.146089\pi\) |
0.0646023 | + | 0.997911i | \(0.479422\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −20.1739 | + | 11.0445i | −0.760872 | + | 0.416553i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −46.2790 | + | 26.7192i | −1.74050 | + | 1.00488i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.67388 | − | 8.09540i | −0.175531 | − | 0.304029i | 0.764814 | − | 0.644251i | \(-0.222831\pi\) |
−0.940345 | + | 0.340222i | \(0.889498\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.56930 | + | 13.1104i | 0.283472 | + | 0.490989i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 5.65329i | − | 0.211421i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.86840 | + | 5.69752i | 0.368029 | + | 0.212482i | 0.672597 | − | 0.740009i | \(-0.265179\pi\) |
−0.304568 | + | 0.952491i | \(0.598512\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 54.3374i | 2.02363i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.43836 | + | 2.49131i | −0.0534193 | + | 0.0925250i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.61852 | − | 7.99952i | 0.171292 | − | 0.296686i | −0.767580 | − | 0.640953i | \(-0.778539\pi\) |
0.938872 | + | 0.344267i | \(0.111873\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.34973 | − | 4.82072i | 0.308826 | − | 0.178301i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.20877 | 0.229326 | 0.114663 | − | 0.993404i | \(-0.463421\pi\) | ||||
0.114663 | + | 0.993404i | \(0.463421\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.30794 | + | 5.72953i | 0.121850 | + | 0.211050i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.1240 | − | 24.4634i | 0.519559 | − | 0.899902i | −0.480183 | − | 0.877168i | \(-0.659430\pi\) |
0.999742 | − | 0.0227338i | \(-0.00723703\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.17002 | − | 14.1509i | 0.299729 | − | 0.519146i | −0.676345 | − | 0.736585i | \(-0.736437\pi\) |
0.976074 | + | 0.217439i | \(0.0697704\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.6239 | + | 27.0614i | 0.572416 | + | 0.991454i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.1627 | 0.663652 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.30271 | − | 2.48417i | 0.157008 | − | 0.0906487i | −0.419437 | − | 0.907784i | \(-0.637773\pi\) |
0.576446 | + | 0.817136i | \(0.304439\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24.5568 | − | 42.5336i | 0.893714 | − | 1.54796i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.4951 | − | 38.9627i | 0.817600 | − | 1.41612i | −0.0898459 | − | 0.995956i | \(-0.528637\pi\) |
0.907446 | − | 0.420169i | \(-0.138029\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.8971i | 0.395021i | 0.980301 | + | 0.197510i | \(0.0632856\pi\) | ||||
−0.980301 | + | 0.197510i | \(0.936714\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −57.0805 | − | 32.9555i | −2.06645 | − | 1.19307i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 13.2747i | 0.479322i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.53013 | + | 7.84642i | 0.163361 | + | 0.282949i | 0.936072 | − | 0.351809i | \(-0.114433\pi\) |
−0.772711 | + | 0.634758i | \(0.781100\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.45179 | − | 7.71073i | −0.160120 | − | 0.277336i | 0.774792 | − | 0.632217i | \(-0.217855\pi\) |
−0.934911 | + | 0.354881i | \(0.884521\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.34365 | − | 4.81721i | 0.299713 | − | 0.173039i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 35.2322 | + | 0.799971i | 1.26232 | + | 0.0286619i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.4974 | + | 6.63800i | 0.411408 | + | 0.237526i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −28.1802 | + | 16.2698i | −1.00579 | + | 0.580696i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.4374i | 0.906746i | 0.891321 | + | 0.453373i | \(0.149779\pi\) | ||||
−0.891321 | + | 0.453373i | \(0.850221\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −59.1131 | −2.10182 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.7733 | − | 7.95200i | −0.489103 | − | 0.282384i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9.50776 | −0.336782 | −0.168391 | − | 0.985720i | \(-0.553857\pi\) | ||||
−0.168391 | + | 0.985720i | \(0.553857\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.86415 | −0.207459 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.46796 | + | 2.00223i | 0.122382 | + | 0.0706570i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −56.3285 | −1.98532 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 41.8158i | 1.47016i | 0.677978 | + | 0.735082i | \(0.262857\pi\) | ||||
−0.677978 | + | 0.735082i | \(0.737143\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.3840 | + | 10.0366i | −0.610434 | + | 0.352434i | −0.773135 | − | 0.634241i | \(-0.781313\pi\) |
0.162701 | + | 0.986675i | \(0.447979\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13.9624 | − | 8.06121i | −0.489083 | − | 0.282372i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −26.6629 | − | 0.605400i | −0.932818 | − | 0.0211803i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −42.3352 | + | 24.4422i | −1.47751 | + | 0.853040i | −0.999677 | − | 0.0254110i | \(-0.991911\pi\) |
−0.477832 | + | 0.878451i | \(0.658577\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.434625 | + | 0.752793i | 0.0151501 | + | 0.0262407i | 0.873501 | − | 0.486822i | \(-0.161844\pi\) |
−0.858351 | + | 0.513063i | \(0.828511\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.29366 | − | 16.0971i | −0.323172 | − | 0.559751i | 0.657968 | − | 0.753046i | \(-0.271416\pi\) |
−0.981141 | + | 0.193295i | \(0.938083\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.7240i | 0.476653i | 0.971185 | + | 0.238327i | \(0.0765989\pi\) | ||||
−0.971185 | + | 0.238327i | \(0.923401\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 11.5468 | + | 6.66657i | 0.400074 | + | 0.230983i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 56.2300i | − | 1.94592i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.43320 | + | 5.94648i | −0.118527 | + | 0.205295i | −0.919184 | − | 0.393828i | \(-0.871151\pi\) |
0.800657 | + | 0.599123i | \(0.204484\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.0925 | − | 24.4089i | 0.485947 | − | 0.841685i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −29.2484 | + | 16.8866i | −1.00618 | + | 0.580916i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 30.4188 | 1.04520 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13.2089 | + | 22.8785i | 0.452796 | + | 0.784266i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.36573 | + | 14.4899i | −0.286437 | + | 0.496124i | −0.972957 | − | 0.230988i | \(-0.925804\pi\) |
0.686520 | + | 0.727111i | \(0.259138\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 26.3106 | − | 45.5713i | 0.898754 | − | 1.55669i | 0.0696644 | − | 0.997570i | \(-0.477807\pi\) |
0.829089 | − | 0.559116i | \(-0.188860\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.70563 | − | 6.41834i | −0.126435 | − | 0.218991i | 0.795858 | − | 0.605483i | \(-0.207020\pi\) |
−0.922293 | + | 0.386492i | \(0.873687\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.66016 | −0.0565126 | −0.0282563 | − | 0.999601i | \(-0.508995\pi\) | ||||
−0.0282563 | + | 0.999601i | \(0.508995\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24.5592 | − | 14.1793i | 0.835037 | − | 0.482109i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.0596 | − | 22.6199i | 0.443017 | − | 0.767328i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.00250 | + | 3.46843i | −0.0678521 | + | 0.117523i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 20.4038i | − | 0.689774i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.3451 | + | 10.0142i | 0.585703 | + | 0.338156i | 0.763397 | − | 0.645930i | \(-0.223530\pi\) |
−0.177694 | + | 0.984086i | \(0.556864\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.41033i | 0.0475153i | 0.999718 | + | 0.0237577i | \(0.00756301\pi\) | ||||
−0.999718 | + | 0.0237577i | \(0.992437\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.76203 | + | 4.78398i | 0.0929497 | + | 0.160994i | 0.908751 | − | 0.417339i | \(-0.137037\pi\) |
−0.815801 | + | 0.578332i | \(0.803704\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.02330 | + | 12.1647i | 0.235819 | + | 0.408451i | 0.959510 | − | 0.281673i | \(-0.0908894\pi\) |
−0.723691 | + | 0.690124i | \(0.757556\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −28.2135 | + | 16.2891i | −0.946250 | + | 0.546318i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13.8603 | + | 8.42740i | 0.463816 | + | 0.282012i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −26.0140 | − | 15.0192i | −0.869552 | − | 0.502036i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.36403 | − | 1.36488i | 0.0788450 | − | 0.0455212i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.1267i | 0.637202i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 27.9078 | 0.927687 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.33510 | − | 0.770819i | −0.0443312 | − | 0.0255946i | 0.477671 | − | 0.878539i | \(-0.341481\pi\) |
−0.522002 | + | 0.852944i | \(0.674815\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.652297 | −0.0216116 | −0.0108058 | − | 0.999942i | \(-0.503440\pi\) | ||||
−0.0108058 | + | 0.999942i | \(0.503440\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19.7130 | 0.652405 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12.6724 | + | 7.31642i | 0.418480 | + | 0.241609i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.9270 | 0.954213 | 0.477107 | − | 0.878845i | \(-0.341686\pi\) | ||||
0.477107 | + | 0.878845i | \(0.341686\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.03677i | 0.264534i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.5602 | − | 8.40635i | 0.478737 | − | 0.276399i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.0544542 | − | 0.0314391i | −0.00178658 | − | 0.00103149i | 0.499106 | − | 0.866541i | \(-0.333662\pi\) |
−0.500893 | + | 0.865509i | \(0.666995\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.7110 | − | 32.3508i | −0.580456 | − | 1.06026i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.05418 | + | 4.07273i | −0.230696 | + | 0.133193i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.8491 | + | 27.4514i | 0.517767 | + | 0.896799i | 0.999787 | + | 0.0206388i | \(0.00656999\pi\) |
−0.482020 | + | 0.876160i | \(0.660097\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.9057 | + | 27.5495i | 0.518511 | + | 0.898087i | 0.999769 | + | 0.0215081i | \(0.00684676\pi\) |
−0.481258 | + | 0.876579i | \(0.659820\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 40.4795i | − | 1.31819i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 30.7308 | + | 17.7424i | 0.998617 | + | 0.576552i | 0.907839 | − | 0.419320i | \(-0.137731\pi\) |
0.0907779 | + | 0.995871i | \(0.471065\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.42414i | 0.0786909i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.47432 | + | 6.01770i | −0.112544 | + | 0.194932i | −0.916795 | − | 0.399357i | \(-0.869233\pi\) |
0.804251 | + | 0.594290i | \(0.202567\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.37922 | − | 14.5132i | 0.271145 | − | 0.469637i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17.9973 | + | 10.3907i | −0.581163 | + | 0.335535i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.8578 | 0.705090 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 17.9217 | + | 31.0413i | 0.576920 | + | 0.999254i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27.9439 | + | 48.4003i | −0.898616 | + | 1.55645i | −0.0693505 | + | 0.997592i | \(0.522093\pi\) |
−0.829265 | + | 0.558855i | \(0.811241\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.8370 | + | 37.8227i | −0.700781 | + | 1.21379i | 0.267411 | + | 0.963583i | \(0.413832\pi\) |
−0.968192 | + | 0.250207i | \(0.919501\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.90450 | + | 15.4230i | 0.285465 | + | 0.494440i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −26.4159 | −0.845120 | −0.422560 | − | 0.906335i | \(-0.638868\pi\) | ||||
−0.422560 | + | 0.906335i | \(0.638868\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 26.2178 | − | 15.1368i | 0.837923 | − | 0.483775i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.13810 | − | 12.3635i | 0.227670 | − | 0.394336i | −0.729447 | − | 0.684037i | \(-0.760223\pi\) |
0.957117 | + | 0.289701i | \(0.0935560\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 23.8276 | − | 41.2706i | 0.759210 | − | 1.31499i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 30.6340i | 0.974103i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 53.1901 | + | 30.7093i | 1.68964 | + | 0.975514i | 0.954789 | + | 0.297284i | \(0.0960807\pi\) |
0.734850 | + | 0.678230i | \(0.237253\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12.7425i | 0.403964i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.31360 | + | 5.73933i | 0.104943 | + | 0.181766i | 0.913715 | − | 0.406356i | \(-0.133201\pi\) |
−0.808772 | + | 0.588122i | \(0.799867\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 684.2.bk.a.521.7 | yes | 16 | |
3.2 | odd | 2 | inner | 684.2.bk.a.521.2 | yes | 16 | |
4.3 | odd | 2 | 2736.2.dc.d.1889.7 | 16 | |||
12.11 | even | 2 | 2736.2.dc.d.1889.2 | 16 | |||
19.12 | odd | 6 | inner | 684.2.bk.a.449.2 | ✓ | 16 | |
57.50 | even | 6 | inner | 684.2.bk.a.449.7 | yes | 16 | |
76.31 | even | 6 | 2736.2.dc.d.449.2 | 16 | |||
228.107 | odd | 6 | 2736.2.dc.d.449.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.2.bk.a.449.2 | ✓ | 16 | 19.12 | odd | 6 | inner | |
684.2.bk.a.449.7 | yes | 16 | 57.50 | even | 6 | inner | |
684.2.bk.a.521.2 | yes | 16 | 3.2 | odd | 2 | inner | |
684.2.bk.a.521.7 | yes | 16 | 1.1 | even | 1 | trivial | |
2736.2.dc.d.449.2 | 16 | 76.31 | even | 6 | |||
2736.2.dc.d.449.7 | 16 | 228.107 | odd | 6 | |||
2736.2.dc.d.1889.2 | 16 | 12.11 | even | 2 | |||
2736.2.dc.d.1889.7 | 16 | 4.3 | odd | 2 |