Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(865,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.865");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.s (of order \(3\), 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: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.9391935744.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 5x^{6} + 12x^{5} - 76x^{4} + 84x^{3} + 245x^{2} - 1372x + 2401 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 865.2 | ||
Root | \(-2.47635 + 0.931486i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1512.865 |
Dual form | 1512.2.s.m.1297.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | ||||||||
\(5\) | −1.36603 | − | 2.36603i | −0.610905 | − | 1.05812i | −0.991088 | − | 0.133207i | \(-0.957472\pi\) |
0.380183 | − | 0.924911i | \(-0.375861\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.431486 | − | 2.61033i | 0.163087 | − | 0.986612i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.54487 | + | 4.40784i | −0.767307 | + | 1.32901i | 0.171712 | + | 0.985147i | \(0.445070\pi\) |
−0.939018 | + | 0.343867i | \(0.888263\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.48861 | −0.967566 | −0.483783 | − | 0.875188i | \(-0.660738\pi\) | ||||
−0.483783 | + | 0.875188i | \(0.660738\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.09808 | + | 3.63397i | −0.508858 | + | 0.881368i | 0.491089 | + | 0.871109i | \(0.336599\pi\) |
−0.999947 | + | 0.0102590i | \(0.996734\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.16354 | − | 5.47941i | −0.725765 | − | 1.25706i | −0.958658 | − | 0.284560i | \(-0.908153\pi\) |
0.232893 | − | 0.972502i | \(-0.425181\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.04182 | + | 5.26858i | 0.634262 | + | 1.09857i | 0.986671 | + | 0.162728i | \(0.0520295\pi\) |
−0.352408 | + | 0.935846i | \(0.614637\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.23205 | + | 2.13397i | −0.246410 | + | 0.426795i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.45800 | 1.19922 | 0.599610 | − | 0.800292i | \(-0.295322\pi\) | ||||
0.599610 | + | 0.800292i | \(0.295322\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.77692 | + | 8.27387i | −0.857960 | + | 1.48603i | 0.0159115 | + | 0.999873i | \(0.494935\pi\) |
−0.873872 | + | 0.486157i | \(0.838398\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.76553 | + | 2.54487i | −1.14358 | + | 0.430161i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.118669 | + | 0.205541i | 0.0195091 | + | 0.0337907i | 0.875615 | − | 0.483010i | \(-0.160456\pi\) |
−0.856106 | + | 0.516800i | \(0.827123\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.98332 | −0.934438 | −0.467219 | − | 0.884142i | \(-0.654744\pi\) | ||||
−0.467219 | + | 0.884142i | \(0.654744\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.6436 | 1.92813 | 0.964064 | − | 0.265672i | \(-0.0855937\pi\) | ||||
0.964064 | + | 0.265672i | \(0.0855937\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.31873 | + | 7.48027i | 0.629952 | + | 1.09111i | 0.987561 | + | 0.157238i | \(0.0502589\pi\) |
−0.357609 | + | 0.933872i | \(0.616408\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.62764 | − | 2.25264i | −0.946806 | − | 0.321806i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.30977 | + | 4.00063i | −0.317271 | + | 0.549529i | −0.979918 | − | 0.199403i | \(-0.936100\pi\) |
0.662647 | + | 0.748932i | \(0.269433\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 13.9054 | 1.87501 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.18718 | − | 3.78831i | 0.284747 | − | 0.493196i | −0.687801 | − | 0.725899i | \(-0.741424\pi\) |
0.972548 | + | 0.232703i | \(0.0747571\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.443740 | + | 0.768580i | 0.0568150 | + | 0.0984065i | 0.893034 | − | 0.449989i | \(-0.148572\pi\) |
−0.836219 | + | 0.548396i | \(0.815239\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.76553 | + | 8.25414i | 0.591091 | + | 1.02380i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.39559 | − | 7.61338i | 0.537007 | − | 0.930123i | −0.462057 | − | 0.886850i | \(-0.652888\pi\) |
0.999063 | − | 0.0432723i | \(-0.0137783\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.55384 | −0.303085 | −0.151542 | − | 0.988451i | \(-0.548424\pi\) | ||||
−0.151542 | + | 0.988451i | \(0.548424\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.52122 | + | 11.2951i | −0.763251 | + | 1.32199i | 0.177915 | + | 0.984046i | \(0.443065\pi\) |
−0.941166 | + | 0.337944i | \(0.890268\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.4078 | + | 8.54487i | 1.18608 | + | 0.973778i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.61338 | + | 4.52651i | 0.294028 | + | 0.509272i | 0.974758 | − | 0.223262i | \(-0.0716706\pi\) |
−0.680730 | + | 0.732534i | \(0.738337\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.73816 | −0.629844 | −0.314922 | − | 0.949117i | \(-0.601978\pi\) | ||||
−0.314922 | + | 0.949117i | \(0.601978\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.4641 | 1.24346 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.50305 | − | 2.60336i | −0.159323 | − | 0.275956i | 0.775302 | − | 0.631591i | \(-0.217598\pi\) |
−0.934625 | + | 0.355635i | \(0.884265\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.50529 | + | 9.10642i | −0.157797 | + | 0.954612i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.64294 | + | 14.9700i | −0.886747 | + | 1.53589i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.6436 | −1.28376 | −0.641880 | − | 0.766805i | \(-0.721845\pi\) | ||||
−0.641880 | + | 0.766805i | \(0.721845\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.63460 | + | 13.2235i | −0.759672 | + | 1.31579i | 0.183347 | + | 0.983048i | \(0.441307\pi\) |
−0.943018 | + | 0.332741i | \(0.892026\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.20841 | + | 3.82507i | 0.217601 | + | 0.376895i | 0.954074 | − | 0.299571i | \(-0.0968436\pi\) |
−0.736473 | + | 0.676467i | \(0.763510\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.57834 | − | 14.8581i | −0.829300 | − | 1.43639i | −0.898588 | − | 0.438793i | \(-0.855406\pi\) |
0.0692884 | − | 0.997597i | \(-0.477927\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.55626 | − | 2.69552i | 0.149063 | − | 0.258184i | −0.781819 | − | 0.623506i | \(-0.785708\pi\) |
0.930881 | + | 0.365322i | \(0.119041\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.7439 | −1.48106 | −0.740530 | − | 0.672023i | \(-0.765426\pi\) | ||||
−0.740530 | + | 0.672023i | \(0.765426\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.31040 | − | 14.3940i | 0.774948 | − | 1.34225i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.58058 | + | 7.04468i | 0.786580 | + | 0.645785i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.45271 | − | 12.9085i | −0.677519 | − | 1.17350i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.92820 | −0.619677 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.0897 | −1.07279 | −0.536395 | − | 0.843967i | \(-0.680214\pi\) | ||||
−0.536395 | + | 0.843967i | \(0.680214\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.446792 | − | 0.773867i | −0.0390364 | − | 0.0676130i | 0.845847 | − | 0.533425i | \(-0.179095\pi\) |
−0.884884 | + | 0.465812i | \(0.845762\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −15.6681 | + | 5.89358i | −1.35859 | + | 0.511039i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.77997 | + | 11.7433i | −0.579252 | + | 1.00329i | 0.416313 | + | 0.909221i | \(0.363322\pi\) |
−0.995565 | + | 0.0940728i | \(0.970011\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.11424 | 0.433784 | 0.216892 | − | 0.976196i | \(-0.430408\pi\) | ||||
0.216892 | + | 0.976196i | \(0.430408\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.87805 | − | 15.3772i | 0.742420 | − | 1.28591i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.82179 | − | 15.2798i | −0.732610 | − | 1.26892i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.36603 | − | 5.83013i | −0.275756 | − | 0.477623i | 0.694570 | − | 0.719425i | \(-0.255595\pi\) |
−0.970325 | + | 0.241803i | \(0.922261\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.31282 | + | 2.27387i | −0.106836 | + | 0.185045i | −0.914487 | − | 0.404616i | \(-0.867405\pi\) |
0.807651 | + | 0.589661i | \(0.200739\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 26.1016 | 2.09653 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.10642 | + | 5.38047i | −0.247919 | + | 0.429408i | −0.962948 | − | 0.269686i | \(-0.913080\pi\) |
0.715029 | + | 0.699095i | \(0.246413\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.0652 | − | 5.66682i | 1.18731 | − | 0.446608i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.63703 | + | 6.29952i | 0.284874 | + | 0.493416i | 0.972579 | − | 0.232574i | \(-0.0747149\pi\) |
−0.687705 | + | 0.725991i | \(0.741382\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.01057 | −0.232965 | −0.116483 | − | 0.993193i | \(-0.537162\pi\) | ||||
−0.116483 | + | 0.993193i | \(0.537162\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.829615 | −0.0638165 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.08911 | − | 10.5466i | −0.462946 | − | 0.801846i | 0.536160 | − | 0.844116i | \(-0.319874\pi\) |
−0.999106 | + | 0.0422700i | \(0.986541\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.03876 | + | 4.13684i | 0.380895 | + | 0.312716i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.22900 | + | 15.9851i | −0.689808 | + | 1.19478i | 0.282092 | + | 0.959387i | \(0.408972\pi\) |
−0.971900 | + | 0.235395i | \(0.924362\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.30429 | −0.542924 | −0.271462 | − | 0.962449i | \(-0.587507\pi\) | ||||
−0.271462 | + | 0.962449i | \(0.587507\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.324210 | − | 0.561547i | 0.0238364 | − | 0.0412858i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.6787 | − | 18.4960i | −0.780901 | − | 1.35256i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.91986 | + | 17.1817i | 0.717776 | + | 1.24322i | 0.961879 | + | 0.273475i | \(0.0881732\pi\) |
−0.244103 | + | 0.969749i | \(0.578493\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.15825 | − | 2.00615i | 0.0833727 | − | 0.144406i | −0.821324 | − | 0.570462i | \(-0.806764\pi\) |
0.904697 | + | 0.426056i | \(0.140097\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.29684 | 0.0923959 | 0.0461980 | − | 0.998932i | \(-0.485289\pi\) | ||||
0.0461980 | + | 0.998932i | \(0.485289\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.7463 | − | 22.0773i | 0.903562 | − | 1.56501i | 0.0807256 | − | 0.996736i | \(-0.474276\pi\) |
0.822836 | − | 0.568279i | \(-0.192390\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.78654 | − | 16.8575i | 0.195577 | − | 1.18316i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.17337 | + | 14.1567i | 0.570853 | + | 0.988746i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 32.2031 | 2.22754 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.11825 | 0.490041 | 0.245020 | − | 0.969518i | \(-0.421205\pi\) | ||||
0.245020 | + | 0.969518i | \(0.421205\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −17.2714 | − | 29.9150i | −1.17790 | − | 2.04019i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.5363 | + | 16.0394i | 1.32621 | + | 1.08882i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.31937 | − | 12.6775i | 0.492354 | − | 0.852782i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.261844 | −0.0175344 | −0.00876719 | − | 0.999962i | \(-0.502791\pi\) | ||||
−0.00876719 | + | 0.999962i | \(0.502791\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.04792 | + | 3.54710i | −0.135925 | + | 0.235429i | −0.925951 | − | 0.377645i | \(-0.876734\pi\) |
0.790025 | + | 0.613074i | \(0.210067\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.26553 | − | 2.19196i | −0.0836284 | − | 0.144849i | 0.821178 | − | 0.570673i | \(-0.193318\pi\) |
−0.904806 | + | 0.425824i | \(0.859984\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.0843 | − | 22.6626i | −0.857179 | − | 1.48468i | −0.874609 | − | 0.484829i | \(-0.838882\pi\) |
0.0174307 | − | 0.999848i | \(-0.494451\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.7990 | − | 20.4365i | 0.769682 | − | 1.33313i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.40898 | 0.414563 | 0.207281 | − | 0.978281i | \(-0.433538\pi\) | ||||
0.207281 | + | 0.978281i | \(0.433538\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.44660 | + | 16.3620i | −0.608509 | + | 1.05397i | 0.382977 | + | 0.923758i | \(0.374899\pi\) |
−0.991486 | + | 0.130211i | \(0.958434\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.72371 | + | 18.7583i | 0.237899 | + | 1.19843i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.0363 | + | 19.1155i | 0.702226 | + | 1.21629i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.5477 | −0.728886 | −0.364443 | − | 0.931226i | \(-0.618741\pi\) | ||||
−0.364443 | + | 0.931226i | \(0.618741\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −30.9641 | −1.94670 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.86908 | + | 4.96939i | 0.178968 | + | 0.309982i | 0.941527 | − | 0.336936i | \(-0.109391\pi\) |
−0.762559 | + | 0.646918i | \(0.776057\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.587733 | − | 0.221077i | 0.0365199 | − | 0.0137371i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.96168 | − | 12.0580i | 0.429276 | − | 0.743527i | −0.567533 | − | 0.823350i | \(-0.692102\pi\) |
0.996809 | + | 0.0798233i | \(0.0254356\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.6208 | 0.775289 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.98332 | − | 3.43521i | 0.120925 | − | 0.209449i | −0.799208 | − | 0.601055i | \(-0.794747\pi\) |
0.920133 | + | 0.391607i | \(0.128081\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.25942 | + | 12.5737i | 0.440978 | + | 0.763797i | 0.997762 | − | 0.0668603i | \(-0.0212982\pi\) |
−0.556784 | + | 0.830657i | \(0.687965\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.27081 | − | 10.8614i | −0.378144 | − | 0.654965i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.13460 | + | 8.89340i | −0.308509 | + | 0.534352i | −0.978036 | − | 0.208435i | \(-0.933163\pi\) |
0.669528 | + | 0.742787i | \(0.266496\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.1387 | 1.02241 | 0.511206 | − | 0.859458i | \(-0.329199\pi\) | ||||
0.511206 | + | 0.859458i | \(0.329199\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.23205 | + | 2.13397i | −0.0732378 | + | 0.126852i | −0.900319 | − | 0.435231i | \(-0.856667\pi\) |
0.827081 | + | 0.562083i | \(0.190000\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.58172 | + | 15.6184i | −0.152394 | + | 0.921927i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.303848 | − | 0.526279i | −0.0178734 | − | 0.0309576i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.2798 | −1.06792 | −0.533958 | − | 0.845511i | \(-0.679296\pi\) | ||||
−0.533958 | + | 0.845511i | \(0.679296\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.9510 | −0.695813 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.6117 | − | 18.3800i | −0.613691 | − | 1.06294i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.45553 | − | 33.0039i | 0.314452 | − | 1.90231i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.21232 | − | 2.09980i | 0.0694172 | − | 0.120234i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.40451 | 0.422598 | 0.211299 | − | 0.977421i | \(-0.432231\pi\) | ||||
0.211299 | + | 0.977421i | \(0.432231\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.1705 | − | 17.6158i | 0.576716 | − | 0.998902i | −0.419136 | − | 0.907923i | \(-0.637667\pi\) |
0.995853 | − | 0.0909788i | \(-0.0289995\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.5803 | + | 23.5219i | 0.767607 | + | 1.32953i | 0.938857 | + | 0.344306i | \(0.111886\pi\) |
−0.171251 | + | 0.985227i | \(0.554781\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.3360 | − | 19.6346i | −0.636696 | − | 1.10279i | −0.986153 | − | 0.165837i | \(-0.946967\pi\) |
0.349457 | − | 0.936952i | \(-0.386366\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.4348 | + | 28.4658i | −0.920169 | + | 1.59378i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 26.5494 | 1.47725 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.29814 | − | 7.44460i | 0.238418 | − | 0.412952i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 21.3894 | − | 8.04569i | 1.17924 | − | 0.443573i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.87280 | − | 8.43994i | −0.267834 | − | 0.463901i | 0.700469 | − | 0.713683i | \(-0.252974\pi\) |
−0.968302 | + | 0.249782i | \(0.919641\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −24.0179 | −1.31224 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.1492 | 0.607338 | 0.303669 | − | 0.952778i | \(-0.401788\pi\) | ||||
0.303669 | + | 0.952778i | \(0.401788\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −24.3133 | − | 42.1118i | −1.31664 | − | 2.28048i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.73988 | + | 16.3283i | −0.471909 | + | 0.881647i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.53590 | + | 14.7846i | −0.458231 | + | 0.793679i | −0.998868 | − | 0.0475768i | \(-0.984850\pi\) |
0.540637 | + | 0.841256i | \(0.318183\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.7317 | 0.681511 | 0.340755 | − | 0.940152i | \(-0.389317\pi\) | ||||
0.340755 | + | 0.940152i | \(0.389317\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.7272 | − | 30.7044i | 0.943524 | − | 1.63423i | 0.184844 | − | 0.982768i | \(-0.440822\pi\) |
0.758680 | − | 0.651464i | \(-0.225845\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.48861 | + | 6.04245i | 0.185156 | + | 0.320700i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.57834 | + | 14.8581i | 0.452748 | + | 0.784182i | 0.998556 | − | 0.0537283i | \(-0.0171105\pi\) |
−0.545808 | + | 0.837910i | \(0.683777\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.5159 | + | 18.2141i | −0.553470 | + | 0.958639i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 35.6326 | 1.86510 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.96738 | − | 6.87171i | 0.207096 | − | 0.358700i | −0.743703 | − | 0.668511i | \(-0.766932\pi\) |
0.950798 | + | 0.309810i | \(0.100265\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.44633 | + | 7.75547i | 0.490429 | + | 0.402644i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.4188 | − | 24.9741i | −0.746578 | − | 1.29311i | −0.949454 | − | 0.313906i | \(-0.898362\pi\) |
0.202876 | − | 0.979204i | \(-0.434971\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −22.5294 | −1.16032 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.2659 | −1.09235 | −0.546177 | − | 0.837670i | \(-0.683917\pi\) | ||||
−0.546177 | + | 0.837670i | \(0.683917\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.50655 | − | 16.4658i | −0.485762 | − | 0.841364i | 0.514104 | − | 0.857728i | \(-0.328124\pi\) |
−0.999866 | + | 0.0163634i | \(0.994791\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.00000 | − | 36.2977i | 0.305788 | − | 1.84990i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13.8942 | + | 24.0655i | −0.704465 | + | 1.22017i | 0.262420 | + | 0.964954i | \(0.415479\pi\) |
−0.966884 | + | 0.255215i | \(0.917854\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −25.5278 | −1.29100 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.13989 | − | 12.3667i | 0.359247 | − | 0.622234i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.64600 | + | 16.7074i | 0.484119 | + | 0.838518i | 0.999834 | − | 0.0182421i | \(-0.00580695\pi\) |
−0.515715 | + | 0.856760i | \(0.672474\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.6346 | − | 23.6158i | −0.680880 | − | 1.17932i | −0.974713 | − | 0.223461i | \(-0.928264\pi\) |
0.293833 | − | 0.955857i | \(-0.405069\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.6648 | − | 28.8643i | 0.830133 | − | 1.43783i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.20799 | −0.0598777 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.72266 | − | 11.6440i | 0.332414 | − | 0.575758i | −0.650570 | − | 0.759446i | \(-0.725470\pi\) |
0.982985 | + | 0.183688i | \(0.0588035\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.94500 | − | 7.34387i | −0.440155 | − | 0.361368i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.83847 | + | 13.5766i | 0.384775 | + | 0.666450i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.38620 | 0.0677203 | 0.0338601 | − | 0.999427i | \(-0.489220\pi\) | ||||
0.0338601 | + | 0.999427i | \(0.489220\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.0197 | 0.975699 | 0.487849 | − | 0.872928i | \(-0.337782\pi\) | ||||
0.487849 | + | 0.872928i | \(0.337782\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.16987 | − | 8.95448i | −0.250776 | − | 0.434356i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.19771 | − | 0.826675i | 0.106355 | − | 0.0400056i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.85526 | − | 6.67751i | 0.185702 | − | 0.321644i | −0.758111 | − | 0.652125i | \(-0.773878\pi\) |
0.943813 | + | 0.330481i | \(0.107211\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.16726 | 0.440551 | 0.220275 | − | 0.975438i | \(-0.429304\pi\) | ||||
0.220275 | + | 0.975438i | \(0.429304\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 19.2458 | − | 33.3347i | 0.920651 | − | 1.59461i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.43349 | + | 9.41108i | 0.259326 | + | 0.449166i | 0.966062 | − | 0.258312i | \(-0.0831661\pi\) |
−0.706735 | + | 0.707478i | \(0.749833\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.8330 | + | 30.8876i | 0.847271 | + | 1.46752i | 0.883634 | + | 0.468178i | \(0.155089\pi\) |
−0.0363633 | + | 0.999339i | \(0.511577\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.10642 | + | 7.11252i | −0.194663 | + | 0.337166i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.39841 | −0.160381 | −0.0801904 | − | 0.996780i | \(-0.525553\pi\) | ||||
−0.0801904 | + | 0.996780i | \(0.525553\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.2268 | − | 26.3735i | 0.717000 | − | 1.24188i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 23.6023 | − | 8.87805i | 1.10649 | − | 0.416209i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.4115 | − | 31.8897i | −0.861255 | − | 1.49174i | −0.870718 | − | 0.491782i | \(-0.836346\pi\) |
0.00946370 | − | 0.999955i | \(-0.496988\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.9356 | 1.30109 | 0.650545 | − | 0.759468i | \(-0.274541\pi\) | ||||
0.650545 | + | 0.759468i | \(0.274541\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.5678 | −1.14176 | −0.570881 | − | 0.821033i | \(-0.693398\pi\) | ||||
−0.570881 | + | 0.821033i | \(0.693398\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.6876 | + | 18.5115i | 0.494564 | + | 0.856611i | 0.999980 | − | 0.00626525i | \(-0.00199431\pi\) |
−0.505416 | + | 0.862876i | \(0.668661\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −17.9768 | − | 14.7590i | −0.830091 | − | 0.681507i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −32.1762 | + | 55.7309i | −1.47946 | + | 2.56251i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.5906 | 0.715344 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.44966 | − | 9.43908i | 0.249001 | − | 0.431283i | −0.714248 | − | 0.699893i | \(-0.753231\pi\) |
0.963249 | + | 0.268610i | \(0.0865644\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.413989 | − | 0.717051i | −0.0188763 | − | 0.0326947i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 17.2714 | + | 29.9150i | 0.784256 | + | 1.35837i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.3675 | + | 17.9571i | −0.469797 | + | 0.813712i | −0.999404 | − | 0.0345311i | \(-0.989006\pi\) |
0.529607 | + | 0.848243i | \(0.322340\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.8670 | −0.761196 | −0.380598 | − | 0.924741i | \(-0.624282\pi\) | ||||
−0.380598 | + | 0.924741i | \(0.624282\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13.5494 | + | 23.4682i | −0.610233 | + | 1.05695i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.10195 | + | 6.66636i | −0.0494291 | + | 0.299027i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.4054 | − | 30.1471i | −0.779174 | − | 1.34957i | −0.932419 | − | 0.361380i | \(-0.882306\pi\) |
0.153245 | − | 0.988188i | \(-0.451028\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.98561 | 0.266885 | 0.133442 | − | 0.991057i | \(-0.457397\pi\) | ||||
0.133442 | + | 0.991057i | \(0.457397\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 41.7163 | 1.85635 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.9299 | + | 24.1273i | 0.617433 | + | 1.06943i | 0.989952 | + | 0.141401i | \(0.0451607\pi\) |
−0.372519 | + | 0.928024i | \(0.621506\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 26.6701 | + | 21.8962i | 1.17982 | + | 0.968632i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.03348 | − | 10.4503i | 0.265867 | − | 0.460495i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −43.9624 | −1.93347 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.20398 | + | 7.28151i | −0.184180 | + | 0.319009i | −0.943300 | − | 0.331942i | \(-0.892296\pi\) |
0.759120 | + | 0.650951i | \(0.225630\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.50373 | − | 16.4609i | −0.415569 | − | 0.719786i | 0.579919 | − | 0.814674i | \(-0.303084\pi\) |
−0.995488 | + | 0.0948876i | \(0.969751\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −20.0447 | − | 34.7184i | −0.873160 | − | 1.51236i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00529 | + | 12.1335i | −0.304578 | + | 0.527544i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 20.8735 | 0.904130 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −23.4365 | + | 40.5932i | −1.01325 | + | 1.75500i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 26.7958 | − | 23.4809i | 1.15418 | − | 1.01139i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.80585 | − | 10.0560i | −0.249613 | − | 0.432342i | 0.713805 | − | 0.700344i | \(-0.246970\pi\) |
−0.963418 | + | 0.268002i | \(0.913637\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.50356 | −0.364253 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −39.2855 | −1.67973 | −0.839864 | − | 0.542797i | \(-0.817365\pi\) | ||||
−0.839864 | + | 0.542797i | \(0.817365\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −20.4301 | − | 35.3860i | −0.870352 | − | 1.50749i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.9433 | − | 4.86866i | 0.550406 | − | 0.207036i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.93654 | − | 3.35419i | 0.0820540 | − | 0.142122i | −0.822078 | − | 0.569375i | \(-0.807185\pi\) |
0.904132 | + | 0.427253i | \(0.140519\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −44.1085 | −1.86559 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.863603 | + | 1.49580i | −0.0363965 | + | 0.0630407i | −0.883650 | − | 0.468148i | \(-0.844921\pi\) |
0.847253 | + | 0.531189i | \(0.178255\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 21.5065 | + | 37.2504i | 0.904787 | + | 1.56714i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.05016 | − | 7.01507i | −0.169791 | − | 0.294087i | 0.768555 | − | 0.639784i | \(-0.220976\pi\) |
−0.938346 | + | 0.345696i | \(0.887643\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.47393 | + | 16.4093i | −0.396472 | + | 0.686709i | −0.993288 | − | 0.115669i | \(-0.963099\pi\) |
0.596816 | + | 0.802378i | \(0.296432\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −14.9907 | −0.625155 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.32379 | − | 4.02492i | 0.0967407 | − | 0.167560i | −0.813593 | − | 0.581435i | \(-0.802492\pi\) |
0.910334 | + | 0.413875i | \(0.135825\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.47594 | + | 14.9785i | −0.102719 | + | 0.621412i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.7561 | − | 20.3622i | −0.486888 | − | 0.843314i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −30.4939 | −1.25862 | −0.629308 | − | 0.777156i | \(-0.716662\pi\) | ||||
−0.629308 | + | 0.777156i | \(0.716662\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 60.4478 | 2.49071 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.85400 | − | 3.21123i | −0.0761348 | − | 0.131869i | 0.825444 | − | 0.564483i | \(-0.190925\pi\) |
−0.901579 | + | 0.432614i | \(0.857591\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.94660 | − | 29.9251i | 0.202791 | − | 1.22681i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.1070 | + | 34.8264i | −0.821552 | + | 1.42297i | 0.0829748 | + | 0.996552i | \(0.473558\pi\) |
−0.904526 | + | 0.426418i | \(0.859775\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.4852 | −0.590866 | −0.295433 | − | 0.955364i | \(-0.595464\pi\) | ||||
−0.295433 | + | 0.955364i | \(0.595464\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −20.3612 | + | 35.2666i | −0.827800 | + | 1.43379i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.93193 | + | 15.4706i | 0.362536 | + | 0.627930i | 0.988377 | − | 0.152020i | \(-0.0485777\pi\) |
−0.625842 | + | 0.779950i | \(0.715244\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.0664 | − | 26.0957i | −0.609520 | − | 1.05572i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.2243 | − | 31.5655i | 0.736074 | − | 1.27492i | −0.218176 | − | 0.975909i | \(-0.570011\pi\) |
0.954250 | − | 0.299009i | \(-0.0966559\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.8769 | −0.920990 | −0.460495 | − | 0.887662i | \(-0.652328\pi\) | ||||
−0.460495 | + | 0.887662i | \(0.652328\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.46082 | − | 16.3866i | 0.380262 | − | 0.658634i | −0.610837 | − | 0.791756i | \(-0.709167\pi\) |
0.991100 | + | 0.133122i | \(0.0425003\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.44418 | + | 2.80015i | −0.298245 | + | 0.112185i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.6244 | + | 27.0622i | 0.624974 | + | 1.08249i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.995906 | −0.0397094 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.38657 | −0.0551987 | −0.0275993 | − | 0.999619i | \(-0.508786\pi\) | ||||
−0.0275993 | + | 0.999619i | \(0.508786\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16.5149 | + | 28.6046i | 0.655373 | + | 1.13514i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 23.1212 | + | 7.85859i | 0.916097 | + | 0.311369i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.6625 | + | 23.6641i | −0.539636 | + | 0.934677i | 0.459288 | + | 0.888288i | \(0.348105\pi\) |
−0.998923 | + | 0.0463891i | \(0.985229\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.1795 | 1.15073 | 0.575363 | − | 0.817898i | \(-0.304861\pi\) | ||||
0.575363 | + | 0.817898i | \(0.304861\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.55384 | + | 14.8157i | −0.336286 | + | 0.582465i | −0.983731 | − | 0.179648i | \(-0.942504\pi\) |
0.647445 | + | 0.762112i | \(0.275838\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.1322 | + | 19.2815i | 0.436976 | + | 0.756865i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.26075 | + | 7.37984i | 0.166736 | + | 0.288795i | 0.937270 | − | 0.348603i | \(-0.113344\pi\) |
−0.770534 | + | 0.637398i | \(0.780011\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.22066 | + | 2.11424i | −0.0476951 | + | 0.0826103i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 38.6253 | 1.50463 | 0.752313 | − | 0.658806i | \(-0.228938\pi\) | ||||
0.752313 | + | 0.658806i | \(0.228938\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.0584 | − | 24.3498i | 0.546808 | − | 0.947099i | −0.451683 | − | 0.892178i | \(-0.649176\pi\) |
0.998491 | − | 0.0549202i | \(-0.0174905\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 35.3474 | + | 29.0203i | 1.37071 | + | 1.12536i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 19.6440 | + | 34.0245i | 0.760620 | + | 1.31743i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.51704 | −0.174378 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.10115 | 0.196635 | 0.0983174 | − | 0.995155i | \(-0.468654\pi\) | ||||
0.0983174 | + | 0.995155i | \(0.468654\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −23.7561 | − | 41.1468i | −0.913021 | − | 1.58140i | −0.809773 | − | 0.586743i | \(-0.800410\pi\) |
−0.103248 | − | 0.994656i | \(-0.532923\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.45553 | + | 33.0039i | −0.209364 | + | 1.26657i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.1639 | + | 27.9968i | −0.618496 | + | 1.07127i | 0.371264 | + | 0.928527i | \(0.378924\pi\) |
−0.989760 | + | 0.142739i | \(0.954409\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 37.0465 | 1.41547 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.05786 | − | 13.9566i | 0.306980 | − | 0.531705i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.99471 | − | 6.91905i | −0.151966 | − | 0.263213i | 0.779984 | − | 0.625799i | \(-0.215227\pi\) |
−0.931950 | + | 0.362586i | \(0.881894\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.98619 | − | 12.1004i | −0.265001 | − | 0.458995i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.5535 | − | 21.7432i | 0.475496 | − | 0.823584i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.9891 | 1.20821 | 0.604105 | − | 0.796905i | \(-0.293531\pi\) | ||||
0.604105 | + | 0.796905i | \(0.293531\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.750827 | − | 1.30047i | 0.0283180 | − | 0.0490482i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 31.2235 | + | 25.6346i | 1.17428 | + | 0.964089i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.9258 | + | 22.3881i | 0.485438 | + | 0.840803i | 0.999860 | − | 0.0167340i | \(-0.00532685\pi\) |
−0.514422 | + | 0.857537i | \(0.671994\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −58.1220 | −2.17669 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −48.5106 | −1.81419 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.7362 | + | 20.3277i | 0.437686 | + | 0.758094i | 0.997511 | − | 0.0705173i | \(-0.0224650\pi\) |
−0.559825 | + | 0.828611i | \(0.689132\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.9376 | − | 4.11420i | 0.407337 | − | 0.153221i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.95658 | + | 13.7812i | −0.295500 | + | 0.511821i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.63621 | 0.357387 | 0.178694 | − | 0.983905i | \(-0.442813\pi\) | ||||
0.178694 | + | 0.983905i | \(0.442813\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −26.5272 | + | 45.9464i | −0.981143 | + | 1.69939i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.5335 | + | 25.1727i | 0.536806 | + | 0.929776i | 0.999074 | + | 0.0430350i | \(0.0137027\pi\) |
−0.462267 | + | 0.886741i | \(0.652964\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 22.3724 | + | 38.7501i | 0.824097 | + | 1.42738i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.4527 | + | 18.1046i | −0.384509 | + | 0.665989i | −0.991701 | − | 0.128566i | \(-0.958963\pi\) |
0.607192 | + | 0.794555i | \(0.292296\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22.6497 | −0.830936 | −0.415468 | − | 0.909608i | \(-0.636382\pi\) | ||||
−0.415468 | + | 0.909608i | \(0.636382\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.19615 | + | 15.9282i | −0.336921 | + | 0.583564i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −42.4860 | + | 15.9812i | −1.55241 | + | 0.583941i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.80757 | + | 6.59491i | 0.138940 | + | 0.240652i | 0.927096 | − | 0.374825i | \(-0.122297\pi\) |
−0.788155 | + | 0.615476i | \(0.788964\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.17337 | 0.261066 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.38838 | −0.0868073 | −0.0434036 | − | 0.999058i | \(-0.513820\pi\) | ||||
−0.0434036 | + | 0.999058i | \(0.513820\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.02278 | + | 8.69972i | 0.182076 | + | 0.315365i | 0.942587 | − | 0.333960i | \(-0.108385\pi\) |
−0.760511 | + | 0.649325i | \(0.775052\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.36470 | − | 5.22543i | −0.230417 | − | 0.189173i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.63022 | + | 13.2159i | −0.275511 | + | 0.477200i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.9120 | −0.681984 | −0.340992 | − | 0.940066i | \(-0.610763\pi\) | ||||
−0.340992 | + | 0.940066i | \(0.610763\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.53042 | + | 11.3110i | −0.234883 | + | 0.406829i | −0.959239 | − | 0.282597i | \(-0.908804\pi\) |
0.724356 | + | 0.689426i | \(0.242137\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11.7708 | − | 20.3876i | −0.422820 | − | 0.732346i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 18.9285 | + | 32.7851i | 0.678182 | + | 1.17465i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.49918 | − | 11.2569i | 0.232559 | − | 0.402804i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.9738 | 0.605820 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.4299 | − | 28.4575i | 0.585664 | − | 1.01440i | −0.409129 | − | 0.912477i | \(-0.634167\pi\) |
0.994792 | − | 0.101922i | \(-0.0324994\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.79327 | + | 41.0967i | −0.241541 | + | 1.46123i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.54803 | − | 2.68127i | −0.0549723 | − | 0.0952148i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.43559 | −0.227960 | −0.113980 | − | 0.993483i | \(-0.536360\pi\) | ||||
−0.113980 | + | 0.993483i | \(0.536360\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −36.2441 | −1.28223 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −33.1913 | − | 57.4890i | −1.17130 | − | 2.02874i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −33.9873 | − | 27.9037i | −1.19790 | − | 0.983476i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −0.768767 | + | 1.33154i | −0.0270284 | + | 0.0468146i | −0.879223 | − | 0.476410i | \(-0.841938\pi\) |
0.852195 | + | 0.523225i | \(0.175271\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.3467 | −1.27631 | −0.638153 | − | 0.769909i | \(-0.720301\pi\) | ||||
−0.638153 | + | 0.769909i | \(0.720301\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.93654 | − | 17.2106i | 0.348062 | − | 0.602861i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −39.9984 | − | 69.2793i | −1.39937 | − | 2.42378i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.10367 | − | 14.0360i | −0.282820 | − | 0.489859i | 0.689258 | − | 0.724516i | \(-0.257937\pi\) |
−0.972078 | + | 0.234657i | \(0.924603\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.0628 | − | 41.6780i | 0.838777 | − | 1.45280i | −0.0521412 | − | 0.998640i | \(-0.516605\pi\) |
0.890918 | − | 0.454164i | \(-0.150062\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34.4493 | 1.19792 | 0.598960 | − | 0.800779i | \(-0.295581\pi\) | ||||
0.598960 | + | 0.800779i | \(0.295581\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.5379 | + | 37.3047i | −0.748042 | + | 1.29565i | 0.200718 | + | 0.979649i | \(0.435673\pi\) |
−0.948760 | + | 0.315998i | \(0.897661\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 22.0913 | − | 19.3585i | 0.765420 | − | 0.670731i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.11252 | + | 7.12309i | 0.142320 | + | 0.246505i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 40.4772 | 1.39743 | 0.698714 | − | 0.715401i | \(-0.253756\pi\) | ||||
0.698714 | + | 0.715401i | \(0.253756\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.7057 | 0.438128 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.13327 | + | 1.96289i | 0.0389858 | + | 0.0675254i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −36.9111 | + | 13.8842i | −1.26828 | + | 0.477067i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.721938 | + | 1.25043i | −0.0247477 | + | 0.0428643i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.7194 | 0.367025 | 0.183512 | − | 0.983017i | \(-0.441253\pi\) | ||||
0.183512 | + | 0.983017i | \(0.441253\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13.7059 | − | 23.7394i | 0.468186 | − | 0.810922i | −0.531153 | − | 0.847276i | \(-0.678241\pi\) |
0.999339 | + | 0.0363540i | \(0.0115744\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.9307 | − | 24.1288i | −0.475311 | − | 0.823263i | 0.524289 | − | 0.851540i | \(-0.324331\pi\) |
−0.999600 | + | 0.0282777i | \(0.990998\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −10.8881 | − | 18.8588i | −0.370636 | − | 0.641960i | 0.619028 | − | 0.785369i | \(-0.287527\pi\) |
−0.989663 | + | 0.143409i | \(0.954193\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.6357 | + | 28.8140i | −0.565632 | + | 0.979704i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −26.6029 | −0.902440 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.3345 | + | 26.5601i | −0.519589 | + | 0.899955i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.98943 | + | 18.0849i | −0.101061 | + | 0.611381i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.26380 | + | 7.38513i | 0.143978 | + | 0.249378i | 0.928991 | − | 0.370101i | \(-0.120677\pi\) |
−0.785013 | + | 0.619479i | \(0.787344\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.394489 | 0.0132907 | 0.00664533 | − | 0.999978i | \(-0.497885\pi\) | ||||
0.00664533 | + | 0.999978i | \(0.497885\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.60457 | −0.289567 | −0.144783 | − | 0.989463i | \(-0.546249\pi\) | ||||
−0.144783 | + | 0.989463i | \(0.546249\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 23.1812 | + | 40.1510i | 0.778348 | + | 1.34814i | 0.932893 | + | 0.360153i | \(0.117276\pi\) |
−0.154545 | + | 0.987986i | \(0.549391\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.21656 | + | 31.5582i | −0.174958 | + | 1.05843i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 27.3250 | − | 47.3282i | 0.914395 | − | 1.58378i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 50.4282 | 1.68563 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −30.8493 | + | 53.4326i | −1.02888 | + | 1.78208i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.69213 | − | 16.7873i | −0.322892 | − | 0.559265i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.97785 | + | 17.2821i | 0.331675 | + | 0.574478i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.43021 | + | 5.94129i | −0.113898 | + | 0.197277i | −0.917339 | − | 0.398108i | \(-0.869667\pi\) |
0.803441 | + | 0.595385i | \(0.203000\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.4343 | 0.411968 | 0.205984 | − | 0.978555i | \(-0.433961\pi\) | ||||
0.205984 | + | 0.978555i | \(0.433961\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.6029 | − | 25.2929i | 0.483284 | − | 0.837072i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.21283 | + | 0.832362i | −0.0730741 | + | 0.0274870i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23.1447 | + | 40.0878i | 0.763474 | + | 1.32238i | 0.941050 | + | 0.338268i | \(0.109841\pi\) |
−0.177576 | + | 0.984107i | \(0.556826\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.90934 | 0.293255 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.584825 | −0.0192289 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11.8008 | + | 20.4395i | 0.387171 | + | 0.670600i | 0.992068 | − | 0.125704i | \(-0.0401190\pi\) |
−0.604897 | + | 0.796304i | \(0.706786\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.62363 | + | 43.4419i | 0.282628 | + | 1.42375i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −29.1746 | + | 50.5319i | −0.954112 | + | 1.65257i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.22028 | 0.170539 | 0.0852696 | − | 0.996358i | \(-0.472825\pi\) | ||||
0.0852696 | + | 0.996358i | \(0.472825\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.2966 | + | 24.7624i | −0.466055 | + | 0.807231i | −0.999248 | − | 0.0387621i | \(-0.987659\pi\) |
0.533193 | + | 0.845993i | \(0.320992\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18.2002 | − | 31.5236i | −0.592679 | − | 1.02655i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −19.8253 | − | 34.3384i | −0.644235 | − | 1.11585i | −0.984478 | − | 0.175510i | \(-0.943842\pi\) |
0.340242 | − | 0.940338i | \(-0.389491\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22.7500 | − | 39.4041i | 0.738496 | − | 1.27911i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.14322 | 0.296178 | 0.148089 | − | 0.988974i | \(-0.452688\pi\) | ||||
0.148089 | + | 0.988974i | \(0.452688\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 27.1016 | − | 46.9413i | 0.876986 | − | 1.51898i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 27.7283 | + | 22.7650i | 0.895393 | + | 0.735121i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.1379 | − | 52.2004i | −0.972191 | − | 1.68388i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.32880 | −0.203731 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.4184 | −0.495824 | −0.247912 | − | 0.968783i | \(-0.579744\pi\) | ||||
−0.247912 | + | 0.968783i | \(0.579744\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.8102 | − | 32.5802i | −0.603648 | − | 1.04555i | −0.992264 | − | 0.124149i | \(-0.960380\pi\) |
0.388615 | − | 0.921400i | \(-0.372954\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.20673 | − | 13.3499i | 0.0707444 | − | 0.427977i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12.3222 | − | 21.3427i | 0.394223 | − | 0.682814i | −0.598779 | − | 0.800915i | \(-0.704347\pi\) |
0.993002 | + | 0.118100i | \(0.0376804\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.3003 | 0.488999 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −29.2336 | + | 50.6341i | −0.932408 | + | 1.61498i | −0.153217 | + | 0.988193i | \(0.548963\pi\) |
−0.779192 | + | 0.626786i | \(0.784370\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.77151 | − | 3.06835i | −0.0564451 | − | 0.0977658i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 38.4594 | + | 66.6137i | 1.22294 | + | 2.11819i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.0731 | + | 19.1792i | −0.351749 | + | 0.609247i | −0.986556 | − | 0.163424i | \(-0.947746\pi\) |
0.634807 | + | 0.772671i | \(0.281079\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −69.6471 | −2.20796 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.752874 | + | 1.30402i | −0.0238438 | + | 0.0412986i | −0.877701 | − | 0.479209i | \(-0.840924\pi\) |
0.853857 | + | 0.520507i | \(0.174257\pi\) | |||||||
\(998\) | 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 | 1512.2.s.m.865.2 | ✓ | 8 | |
3.2 | odd | 2 | 1512.2.s.p.865.4 | yes | 8 | ||
7.2 | even | 3 | inner | 1512.2.s.m.1297.2 | yes | 8 | |
21.2 | odd | 6 | 1512.2.s.p.1297.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.s.m.865.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
1512.2.s.m.1297.2 | yes | 8 | 7.2 | even | 3 | inner | |
1512.2.s.p.865.4 | yes | 8 | 3.2 | odd | 2 | ||
1512.2.s.p.1297.4 | yes | 8 | 21.2 | odd | 6 |