Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [363,2,Mod(161,363)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(363, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("363.161");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.f (of order \(10\), degree \(4\), not 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: | \(2.89856959337\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | 16.0.6879707136000000000000.7 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4x^{14} + 15x^{12} - 56x^{10} + 209x^{8} - 56x^{6} + 15x^{4} - 4x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 11^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{10}]$ |
Embedding invariants
Embedding label | 215.3 | ||
Root | \(0.492303 - 0.159959i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 363.215 |
Dual form | 363.2.f.g.233.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(244\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{9}{10}\right)\) |
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 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(3\) | 1.40126 | + | 1.01807i | 0.809017 | + | 0.587785i | ||||
\(4\) | 1.61803 | − | 1.17557i | 0.809017 | − | 0.587785i | ||||
\(5\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.35825 | − | 1.86947i | −0.513369 | − | 0.706592i | 0.471114 | − | 0.882073i | \(-0.343852\pi\) |
−0.984483 | + | 0.175480i | \(0.943852\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.927051 | + | 2.85317i | 0.309017 | + | 0.951057i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 3.46410 | 1.00000 | ||||||||
\(13\) | 6.00420 | − | 1.95088i | 1.66527 | − | 0.541078i | 0.683301 | − | 0.730137i | \(-0.260544\pi\) |
0.981966 | + | 0.189059i | \(0.0605438\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.23607 | − | 3.80423i | 0.309017 | − | 0.951057i | ||||
\(17\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.06905 | + | 6.97695i | −1.16292 | + | 1.60062i | −0.463091 | + | 0.886310i | \(0.653260\pi\) |
−0.699828 | + | 0.714311i | \(0.746740\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 4.00240i | − | 0.873396i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.04508 | − | 2.93893i | −0.809017 | − | 0.587785i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.60570 | + | 4.94183i | −0.309017 | + | 0.951057i | ||||
\(28\) | −4.39538 | − | 1.42815i | −0.830649 | − | 0.269894i | ||||
\(29\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.535233 | + | 1.64728i | 0.0961307 | + | 0.295860i | 0.987547 | − | 0.157326i | \(-0.0502874\pi\) |
−0.891416 | + | 0.453186i | \(0.850287\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.85410 | + | 3.52671i | 0.809017 | + | 0.587785i | ||||
\(37\) | −4.20378 | + | 3.05422i | −0.691096 | + | 0.502111i | −0.877020 | − | 0.480453i | \(-0.840472\pi\) |
0.185924 | + | 0.982564i | \(0.440472\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 10.3996 | + | 3.37903i | 1.66527 | + | 0.541078i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.69161i | 0.257969i | 0.991647 | + | 0.128984i | \(0.0411717\pi\) | ||||
−0.991647 | + | 0.128984i | \(0.958828\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(48\) | 5.60503 | − | 4.07230i | 0.809017 | − | 0.587785i | ||||
\(49\) | 0.513047 | − | 1.57900i | 0.0732924 | − | 0.225571i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 7.42160 | − | 10.2150i | 1.02919 | − | 1.41656i | ||||
\(53\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −14.2061 | + | 4.61584i | −1.88164 | + | 0.611383i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.81072 | − | 3.18769i | −1.25613 | − | 0.408142i | −0.396018 | − | 0.918243i | \(-0.629608\pi\) |
−0.860115 | + | 0.510100i | \(0.829608\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.07474 | − | 5.60840i | 0.513369 | − | 0.706592i | ||||
\(64\) | −2.47214 | − | 7.60845i | −0.309017 | − | 0.951057i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.1244 | −1.48123 | −0.740613 | − | 0.671932i | \(-0.765465\pi\) | ||||
−0.740613 | + | 0.671932i | \(0.765465\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.78554 | + | 10.7159i | 0.911229 | + | 1.25420i | 0.966745 | + | 0.255741i | \(0.0823196\pi\) |
−0.0555161 | + | 0.998458i | \(0.517680\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.67617 | − | 8.23639i | −0.309017 | − | 0.951057i | ||||
\(76\) | 17.2480i | 1.97848i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.588870 | − | 0.191335i | 0.0662530 | − | 0.0215269i | −0.275703 | − | 0.961243i | \(-0.588911\pi\) |
0.341956 | + | 0.939716i | \(0.388911\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.28115 | + | 5.29007i | −0.809017 | + | 0.587785i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(84\) | −4.70511 | − | 6.47603i | −0.513369 | − | 0.706592i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.8023 | − | 8.57488i | −1.23722 | − | 0.898892i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.927051 | + | 2.85317i | −0.0961307 | + | 0.295860i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.54508 | − | 4.75528i | −0.156880 | − | 0.482826i | 0.841467 | − | 0.540309i | \(-0.181693\pi\) |
−0.998346 | + | 0.0574829i | \(0.981693\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −10.0000 | −1.00000 | ||||||||
\(101\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.66312 | + | 4.11450i | −0.558004 | + | 0.405413i | −0.830728 | − | 0.556679i | \(-0.812075\pi\) |
0.272724 | + | 0.962092i | \(0.412075\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(108\) | 3.21140 | + | 9.88367i | 0.309017 | + | 0.951057i | ||||
\(109\) | − | 19.5588i | − | 1.87339i | −0.350148 | − | 0.936694i | \(-0.613869\pi\) | ||
0.350148 | − | 0.936694i | \(-0.386131\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.00000 | −0.854242 | ||||||||
\(112\) | −8.79076 | + | 2.85629i | −0.830649 | + | 0.269894i | ||||
\(113\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 11.1324 | + | 15.3224i | 1.02919 | + | 1.41656i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.80252 | + | 2.03615i | 0.251673 | + | 0.182851i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.8149 | + | 5.13858i | 1.40335 | + | 0.455975i | 0.910272 | − | 0.414011i | \(-0.135873\pi\) |
0.493075 | + | 0.869987i | \(0.335873\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.72219 | + | 2.37039i | −0.151630 | + | 0.208701i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 19.9282 | 1.72799 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.8489 | − | 19.0614i | −1.17465 | − | 1.61676i | −0.619361 | − | 0.785106i | \(-0.712608\pi\) |
−0.555288 | − | 0.831658i | \(-0.687392\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 12.0000 | 1.00000 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.32645 | − | 1.69026i | 0.191882 | − | 0.139410i | ||||
\(148\) | −3.21140 | + | 9.88367i | −0.263975 | + | 0.812433i | ||||
\(149\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.41591 | + | 11.5835i | −0.684877 | + | 0.942652i | −0.999979 | − | 0.00640530i | \(-0.997961\pi\) |
0.315102 | + | 0.949058i | \(0.397961\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 20.7992 | − | 6.75806i | 1.66527 | − | 0.541078i | ||||
\(157\) | 18.2164 | + | 13.2350i | 1.45382 | + | 1.05626i | 0.984919 | + | 0.173016i | \(0.0553513\pi\) |
0.468905 | + | 0.883249i | \(0.344649\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.25329 | + | 16.1680i | 0.411469 | + | 1.26637i | 0.915371 | + | 0.402611i | \(0.131897\pi\) |
−0.503902 | + | 0.863761i | \(0.668103\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 21.7273 | − | 15.7858i | 1.67133 | − | 1.21429i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −24.6057 | − | 7.99487i | −1.88164 | − | 0.611383i | ||||
\(172\) | 1.98861 | + | 2.73709i | 0.151630 | + | 0.208701i | ||||
\(173\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.5539i | 0.873396i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.87132 | − | 18.0701i | 0.436412 | − | 1.34314i | −0.455221 | − | 0.890379i | \(-0.650440\pi\) |
0.891633 | − | 0.452759i | \(-0.149560\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.5020 | − | 14.4548i | −0.776333 | − | 1.06853i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 11.4195 | − | 3.71043i | 0.830649 | − | 0.269894i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(192\) | 4.28187 | − | 13.1782i | 0.309017 | − | 0.951057i | ||||
\(193\) | 4.98425 | + | 1.61948i | 0.358774 | + | 0.116573i | 0.482857 | − | 0.875699i | \(-0.339599\pi\) |
−0.124083 | + | 0.992272i | \(0.539599\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.02609 | − | 3.15799i | −0.0732924 | − | 0.225571i | ||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.9808 | 1.84173 | 0.920864 | − | 0.389885i | \(-0.127485\pi\) | ||||
0.920864 | + | 0.389885i | \(0.127485\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.9894 | − | 12.3435i | −1.19834 | − | 0.870643i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 25.2528i | − | 1.75096i | ||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.2145 | − | 8.51761i | 1.80468 | − | 0.586376i | 0.804708 | − | 0.593671i | \(-0.202322\pi\) |
0.999973 | + | 0.00729508i | \(0.00232212\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.35255 | − | 3.23801i | 0.159702 | − | 0.219811i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 22.9420i | 1.55028i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.6074 | + | 13.5191i | 1.24604 | + | 0.905303i | 0.997986 | − | 0.0634420i | \(-0.0202078\pi\) |
0.248058 | + | 0.968745i | \(0.420208\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.63525 | − | 14.2658i | 0.309017 | − | 0.951057i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(228\) | −17.5597 | + | 24.1689i | −1.16292 | + | 1.60062i | ||||
\(229\) | 6.42280 | + | 19.7673i | 0.424430 | + | 1.30626i | 0.903539 | + | 0.428507i | \(0.140960\pi\) |
−0.479108 | + | 0.877756i | \(0.659040\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.01995 | + | 0.331402i | 0.0662530 | + | 0.0215269i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 9.69642i | − | 0.624602i | −0.949983 | − | 0.312301i | \(-0.898900\pi\) | ||
0.949983 | − | 0.312301i | \(-0.101100\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.5885 | −1.00000 | ||||||||
\(244\) | −19.6214 | + | 6.37539i | −1.25613 | + | 0.408142i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −16.8244 | + | 51.7801i | −1.07051 | + | 3.29469i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(252\) | − | 13.8647i | − | 0.873396i | ||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −12.9443 | − | 9.40456i | −0.809017 | − | 0.587785i | ||||
\(257\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.4195 | + | 3.71043i | 0.709576 | + | 0.230555i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −19.6176 | + | 14.2530i | −1.19834 | + | 0.870643i | ||||
\(269\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.43868 | + | 6.10933i | 0.269631 | + | 0.371115i | 0.922265 | − | 0.386558i | \(-0.126336\pi\) |
−0.652634 | + | 0.757673i | \(0.726336\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.80823 | − | 24.0312i | −0.472575 | − | 1.45444i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −29.0011 | + | 9.42302i | −1.74251 | + | 0.566174i | −0.995161 | − | 0.0982624i | \(-0.968672\pi\) |
−0.747345 | + | 0.664437i | \(0.768672\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.20378 | + | 3.05422i | −0.251673 | + | 0.182851i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.7685 | − | 14.8215i | 0.640119 | − | 0.881048i | −0.358503 | − | 0.933528i | \(-0.616713\pi\) |
0.998622 | + | 0.0524806i | \(0.0167128\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.7533 | + | 9.99235i | 0.809017 | + | 0.587785i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.67617 | − | 8.23639i | 0.156880 | − | 0.482826i | ||||
\(292\) | 25.1946 | + | 8.18621i | 1.47440 | + | 0.479061i | ||||
\(293\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −14.0126 | − | 10.1807i | −0.809017 | − | 0.587785i | ||||
\(301\) | 3.16242 | − | 2.29763i | 0.182279 | − | 0.132433i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 20.2762 | + | 27.9078i | 1.16292 | + | 1.60062i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.38563i | 0.421520i | 0.977538 | + | 0.210760i | \(0.0675939\pi\) | ||||
−0.977538 | + | 0.210760i | \(0.932406\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.1244 | −0.689730 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.56373 | − | 26.3565i | 0.484051 | − | 1.48975i | −0.349300 | − | 0.937011i | \(-0.613581\pi\) |
0.833351 | − | 0.552744i | \(-0.186419\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.727883 | − | 1.00184i | 0.0409466 | − | 0.0563582i | ||||
\(317\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −5.56231 | + | 17.1190i | −0.309017 | + | 0.951057i | ||||
\(325\) | −30.0210 | − | 9.75442i | −1.66527 | − | 0.541078i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 19.9123 | − | 27.4069i | 1.10115 | − | 1.51560i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −31.0000 | −1.70391 | −0.851957 | − | 0.523612i | \(-0.824584\pi\) | ||||
−0.851957 | + | 0.523612i | \(0.824584\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −12.6113 | − | 9.16267i | −0.691096 | − | 0.502111i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −15.2260 | − | 4.94724i | −0.830649 | − | 0.269894i | ||||
\(337\) | −17.1958 | − | 23.6679i | −0.936713 | − | 1.28927i | −0.957183 | − | 0.289484i | \(-0.906516\pi\) |
0.0204700 | − | 0.999790i | \(-0.493484\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.0326 | + | 6.18405i | −1.02766 | + | 0.333908i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.2185 | − | 18.1938i | 0.707572 | − | 0.973889i | −0.292274 | − | 0.956335i | \(-0.594412\pi\) |
0.999846 | − | 0.0175547i | \(-0.00558811\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 32.8043i | 1.75096i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.1112 | − | 52.6629i | −0.900590 | − | 2.77173i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −29.1769 | −1.52929 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.23607 | − | 2.35114i | 0.168921 | − | 0.122729i | −0.500113 | − | 0.865960i | \(-0.666708\pi\) |
0.669034 | + | 0.743232i | \(0.266708\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.85410 | + | 5.70634i | 0.0961307 | + | 0.295860i | ||||
\(373\) | 38.4983i | 1.99337i | 0.0813690 | + | 0.996684i | \(0.474071\pi\) | ||||
−0.0813690 | + | 0.996684i | \(0.525929\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.47214 | − | 7.60845i | 0.126985 | − | 0.390820i | −0.867272 | − | 0.497834i | \(-0.834129\pi\) |
0.994258 | + | 0.107014i | \(0.0341289\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 16.9293 | + | 23.3012i | 0.867316 | + | 1.19376i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.82646 | + | 1.56821i | −0.245343 | + | 0.0797168i | ||||
\(388\) | −8.09017 | − | 5.87785i | −0.410716 | − | 0.298403i | ||||
\(389\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 35.0000 | 1.75660 | 0.878300 | − | 0.478110i | \(-0.158678\pi\) | ||||
0.878300 | + | 0.478110i | \(0.158678\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 27.9246 | + | 20.2884i | 1.39798 | + | 1.01569i | ||||
\(400\) | −16.1803 | + | 11.7557i | −0.809017 | + | 0.587785i | ||||
\(401\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.42730 | + | 8.84642i | 0.320166 | + | 0.440671i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.37543 | + | 1.09674i | −0.166904 | + | 0.0542305i | −0.391277 | − | 0.920273i | \(-0.627967\pi\) |
0.224373 | + | 0.974503i | \(0.427967\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.32624 | + | 13.3148i | −0.213138 | + | 0.655973i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 40.8091i | − | 1.99843i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.0252 | − | 20.3615i | −1.36586 | − | 0.992358i | −0.998048 | − | 0.0624590i | \(-0.980106\pi\) |
−0.367816 | − | 0.929899i | \(-0.619894\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.36609 | + | 22.6705i | 0.356470 | + | 1.09710i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(432\) | 16.8151 | + | 12.2169i | 0.809017 | + | 0.587785i | ||||
\(433\) | 29.9336 | − | 21.7481i | 1.43852 | − | 1.04514i | 0.450169 | − | 0.892943i | \(-0.351364\pi\) |
0.988350 | − | 0.152201i | \(-0.0486362\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −22.9927 | − | 31.6467i | −1.10115 | − | 1.51560i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 35.1151i | − | 1.67595i | −0.545707 | − | 0.837976i | \(-0.683739\pi\) | ||
0.545707 | − | 0.837976i | \(-0.316261\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.98076 | 0.237179 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(444\) | −14.5623 | + | 10.5801i | −0.691096 | + | 0.502111i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −10.8660 | + | 14.9557i | −0.513369 | + | 0.706592i | ||||
\(449\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −23.5857 | + | 7.66347i | −1.10815 | + | 0.360061i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.2303 | + | 6.89813i | 0.993109 | + | 0.322681i | 0.760109 | − | 0.649796i | \(-0.225146\pi\) |
0.233001 | + | 0.972477i | \(0.425146\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.0000 | −0.929479 | −0.464739 | − | 0.885448i | \(-0.653852\pi\) | ||||
−0.464739 | + | 0.885448i | \(0.653852\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(468\) | 36.0252 | + | 11.7053i | 1.66527 | + | 0.541078i | ||||
\(469\) | 16.4679 | + | 22.6661i | 0.760416 | + | 1.04662i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.0517 | + | 37.0912i | 0.555311 | + | 1.70907i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 41.0095 | − | 13.3248i | 1.88164 | − | 0.611383i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −19.2819 | + | 26.5392i | −0.879179 | + | 1.21009i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.80252 | + | 2.03615i | 0.126994 | + | 0.0922667i | 0.649469 | − | 0.760388i | \(-0.274991\pi\) |
−0.522475 | + | 0.852655i | \(0.674991\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.09896 | + | 28.0037i | −0.411469 | + | 1.26637i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.92820 | 0.311086 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −35.0315 | + | 25.4518i | −1.56822 | + | 1.13938i | −0.639391 | + | 0.768882i | \(0.720813\pi\) |
−0.928833 | + | 0.370499i | \(0.879187\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 46.5167 | 2.06588 | ||||||||
\(508\) | 31.6298 | − | 10.2772i | 1.40335 | − | 0.455975i | ||||
\(509\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.45830 | − | 29.1096i | 0.418410 | − | 1.28774i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −26.3396 | − | 36.2533i | −1.16292 | − | 1.60062i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 5.85993i | 0.257969i | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −39.4007 | − | 12.8020i | −1.72287 | − | 0.559794i | −0.730481 | − | 0.682933i | \(-0.760704\pi\) |
−0.992389 | + | 0.123139i | \(0.960704\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −11.7628 | + | 16.1901i | −0.513369 | + | 0.706592i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.0000 | 1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 32.2445 | − | 23.4270i | 1.39798 | − | 1.01569i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 35.5941 | − | 11.5652i | 1.53031 | − | 0.497228i | 0.581628 | − | 0.813455i | \(-0.302416\pi\) |
0.948684 | + | 0.316227i | \(0.102416\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 26.6239 | − | 19.3434i | 1.14254 | − | 0.830105i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.7035 | + | 36.7542i | −1.14176 | + | 1.57150i | −0.378245 | + | 0.925706i | \(0.623472\pi\) |
−0.763514 | + | 0.645791i | \(0.776528\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 30.9468i | − | 1.32078i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.15753 | − | 0.840992i | −0.0492230 | − | 0.0357626i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −44.8160 | − | 14.5616i | −1.90062 | − | 0.617549i | ||||
\(557\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.30014 | + | 10.1568i | 0.139581 | + | 0.429587i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 19.7792 | + | 6.42666i | 0.830649 | + | 0.269894i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.1103i | 1.13453i | 0.823535 | + | 0.567265i | \(0.191999\pi\) | ||||
−0.823535 | + | 0.567265i | \(0.808001\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 19.4164 | − | 14.1068i | 0.809017 | − | 0.587785i | ||||
\(577\) | 14.4513 | − | 44.4765i | 0.601615 | − | 1.85158i | 0.0830461 | − | 0.996546i | \(-0.473535\pi\) |
0.518569 | − | 0.855036i | \(-0.326465\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.33547 | + | 7.34365i | 0.221735 | + | 0.305192i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(588\) | 1.77725 | − | 5.46980i | 0.0732924 | − | 0.225571i | ||||
\(589\) | −14.2061 | − | 4.61584i | −0.585352 | − | 0.190192i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.42280 | + | 19.7673i | 0.263975 | + | 0.812433i | ||||
\(593\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 36.4058 | + | 26.4503i | 1.48999 | + | 1.08254i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.6458 | − | 27.0402i | −0.801370 | − | 1.10299i | −0.992598 | − | 0.121446i | \(-0.961247\pi\) |
0.191228 | − | 0.981546i | \(-0.438753\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.2399 | − | 34.5928i | −0.457724 | − | 1.40873i | ||||
\(604\) | 28.6360i | 1.16518i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.8349 | − | 5.46998i | 0.683306 | − | 0.222020i | 0.0532640 | − | 0.998580i | \(-0.483038\pi\) |
0.630042 | + | 0.776561i | \(0.283038\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29.0560 | − | 39.9922i | 1.17356 | − | 1.61527i | 0.539519 | − | 0.841973i | \(-0.318606\pi\) |
0.634044 | − | 0.773297i | \(-0.281394\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.8885 | − | 18.8091i | −1.04055 | − | 0.756003i | −0.0701559 | − | 0.997536i | \(-0.522350\pi\) |
−0.970393 | + | 0.241533i | \(0.922350\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 25.7092 | − | 35.3857i | 1.02919 | − | 1.41656i | ||||
\(625\) | 7.72542 | + | 23.7764i | 0.309017 | + | 0.951057i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 45.0333 | 1.79703 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.6176 | + | 14.2530i | −0.780965 | + | 0.567404i | −0.905269 | − | 0.424840i | \(-0.860330\pi\) |
0.124303 | + | 0.992244i | \(0.460330\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 45.4049 | + | 14.7529i | 1.80468 | + | 0.586376i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 10.4815i | − | 0.415292i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.5238 | + | 44.6997i | −0.572763 | + | 1.76278i | 0.0709114 | + | 0.997483i | \(0.477409\pi\) |
−0.643674 | + | 0.765300i | \(0.722591\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.59307 | − | 2.14222i | 0.258403 | − | 0.0839602i | ||||
\(652\) | 27.5066 | + | 19.9847i | 1.07724 | + | 0.782661i | ||||
\(653\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −23.3566 | + | 32.1476i | −0.911229 | + | 1.25420i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −50.2295 | −1.95370 | −0.976850 | − | 0.213925i | \(-0.931375\pi\) | ||||
−0.976850 | + | 0.213925i | \(0.931375\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.3104 | + | 37.8874i | 0.475946 | + | 1.46481i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.0368 | + | 8.13494i | −0.965096 | + | 0.313579i | −0.748835 | − | 0.662757i | \(-0.769386\pi\) |
−0.216262 | + | 0.976335i | \(0.569386\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 21.0189 | − | 15.2711i | 0.809017 | − | 0.587785i | ||||
\(676\) | 16.5982 | − | 51.0839i | 0.638391 | − | 1.96477i | ||||
\(677\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.79124 | + | 9.34734i | −0.260624 | + | 0.358718i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(684\) | −49.2114 | + | 15.9897i | −1.88164 | + | 0.611383i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11.1246 | + | 34.2380i | −0.424430 | + | 1.30626i | ||||
\(688\) | 6.43529 | + | 2.09095i | 0.245343 | + | 0.0797168i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.1418 | − | 46.6018i | −0.576022 | − | 1.77281i | −0.632671 | − | 0.774421i | \(-0.718041\pi\) |
0.0566486 | − | 0.998394i | \(-0.481959\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 13.5825 | + | 18.6947i | 0.513369 | + | 0.706592i | ||||
\(701\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 44.8115i | − | 1.69010i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.9865 | + | 46.1238i | −0.562831 | + | 1.73222i | 0.111479 | + | 0.993767i | \(0.464441\pi\) |
−0.674310 | + | 0.738448i | \(0.735559\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.09182 | + | 1.50277i | 0.0409466 | + | 0.0563582i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.3838 | + | 4.99851i | 0.572924 | + | 0.186154i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.87168 | − | 13.5872i | 0.367132 | − | 0.505313i | ||||
\(724\) | −11.7426 | − | 36.1401i | −0.436412 | − | 1.34314i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −31.1769 | −1.15629 | −0.578144 | − | 0.815935i | \(-0.696223\pi\) | ||||
−0.578144 | + | 0.815935i | \(0.696223\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −21.8435 | − | 15.8702i | −0.809017 | − | 0.587785i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −33.9853 | − | 11.0425i | −1.25613 | − | 0.408142i | ||||
\(733\) | 29.4200 | + | 40.4931i | 1.08665 | + | 1.49565i | 0.851980 | + | 0.523574i | \(0.175402\pi\) |
0.234672 | + | 0.972075i | \(0.424598\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −43.7960 | + | 14.2302i | −1.61106 | + | 0.523466i | −0.969810 | − | 0.243863i | \(-0.921585\pi\) |
−0.641253 | + | 0.767329i | \(0.721585\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −76.2913 | + | 55.4289i | −2.80263 | + | 2.03623i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −43.4390 | − | 31.5603i | −1.58511 | − | 1.15165i | −0.910523 | − | 0.413458i | \(-0.864321\pi\) |
−0.674589 | − | 0.738194i | \(-0.735679\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 14.1153 | − | 19.4281i | 0.513369 | − | 0.706592i | ||||
\(757\) | 0.535233 | + | 1.64728i | 0.0194534 | + | 0.0598713i | 0.960312 | − | 0.278928i | \(-0.0899792\pi\) |
−0.940859 | + | 0.338800i | \(0.889979\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −36.5645 | + | 26.5656i | −1.32372 | + | 0.961740i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −8.56373 | − | 26.3565i | −0.309017 | − | 0.951057i | ||||
\(769\) | 54.0547i | 1.94926i | 0.223819 | + | 0.974631i | \(0.428148\pi\) | ||||
−0.223819 | + | 0.974631i | \(0.571852\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 9.96850 | − | 3.23896i | 0.358774 | − | 0.116573i | ||||
\(773\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.67617 | − | 8.23639i | 0.0961307 | − | 0.295860i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 12.2242 | + | 16.8252i | 0.438542 | + | 0.603601i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.37269 | − | 3.90349i | −0.191882 | − | 0.139410i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 39.9895 | + | 12.9934i | 1.42547 | + | 0.463164i | 0.917336 | − | 0.398113i | \(-0.130335\pi\) |
0.508136 | + | 0.861277i | \(0.330335\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −65.1244 | −2.31263 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 42.0378 | − | 30.5422i | 1.48999 | − | 1.08254i | ||||
\(797\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −42.0000 | −1.48123 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.61898 | + | 3.60471i | −0.0919647 | + | 0.126579i | −0.852520 | − | 0.522695i | \(-0.824927\pi\) |
0.760555 | + | 0.649273i | \(0.224927\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.0797i | 0.458723i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11.8023 | − | 8.57488i | −0.412911 | − | 0.299997i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 13.5242 | − | 41.6233i | 0.472575 | − | 1.45444i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.54508 | − | 4.75528i | −0.0538583 | − | 0.165759i | 0.920509 | − | 0.390721i | \(-0.127774\pi\) |
−0.974368 | + | 0.224962i | \(0.927774\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.66312 | + | 4.11450i | −0.196688 | + | 0.142902i | −0.681770 | − | 0.731566i | \(-0.738790\pi\) |
0.485082 | + | 0.874469i | \(0.338790\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −50.2313 | − | 16.3211i | −1.74251 | − | 0.566174i | ||||
\(832\) | −29.6864 | − | 40.8598i | −1.02919 | − | 1.41656i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.00000 | −0.311086 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.96149 | + | 27.5806i | −0.309017 | + | 0.951057i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 32.4029 | − | 44.5988i | 1.11535 | − | 1.53515i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 30.1788 | − | 9.80569i | 1.03573 | − | 0.336530i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.6414 | − | 6.70679i | −0.706748 | − | 0.229636i | −0.0664795 | − | 0.997788i | \(-0.521177\pi\) |
−0.640268 | + | 0.768152i | \(0.721177\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.0000 | 0.443554 | 0.221777 | − | 0.975097i | \(-0.428814\pi\) | ||||
0.221777 | + | 0.975097i | \(0.428814\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.09896 | + | 28.0037i | 0.309017 | + | 0.951057i | ||||
\(868\) | − | 8.00481i | − | 0.271701i | ||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −72.7971 | + | 23.6532i | −2.46664 | + | 0.801458i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12.1353 | − | 8.81678i | 0.410716 | − | 0.298403i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 26.9699 | + | 37.1209i | 0.911229 | + | 1.25420i | ||||
\(877\) | 22.3623 | − | 30.7791i | 0.755122 | − | 1.03934i | −0.242482 | − | 0.970156i | \(-0.577962\pi\) |
0.997604 | − | 0.0691806i | \(-0.0220385\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.2164 | + | 13.2350i | 0.613029 | + | 0.445392i | 0.850480 | − | 0.526008i | \(-0.176312\pi\) |
−0.237450 | + | 0.971400i | \(0.576312\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.8742 | − | 36.5449i | −0.398247 | − | 1.22568i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 46.0000 | 1.54019 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −9.27051 | − | 28.5317i | −0.309017 | − | 0.951057i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.77053 | 0.225309 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.87132 | − | 18.0701i | 0.194954 | − | 0.600007i | −0.805023 | − | 0.593244i | \(-0.797847\pi\) |
0.999977 | − | 0.00676342i | \(-0.00215288\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(912\) | 59.7487i | 1.97848i | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 33.6302 | + | 24.4338i | 1.11117 | + | 0.807315i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 41.4406 | + | 13.4649i | 1.36700 | + | 0.444164i | 0.898373 | − | 0.439233i | \(-0.144750\pi\) |
0.468625 | + | 0.883397i | \(0.344750\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.51912 | + | 10.3492i | −0.247763 | + | 0.341017i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 25.9808 | 0.854242 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −16.9894 | − | 12.3435i | −0.558004 | − | 0.405413i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.41591 | + | 11.5835i | 0.275820 | + | 0.379634i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.2418 | + | 3.32776i | −0.334585 | + | 0.108713i | −0.471491 | − | 0.881871i | \(-0.656284\pi\) |
0.136906 | + | 0.990584i | \(0.456284\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 38.8328 | − | 28.2137i | 1.26726 | − | 0.920719i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(948\) | 2.03990 | − | 0.662805i | 0.0662530 | − | 0.0215269i | ||||
\(949\) | 67.6514 | + | 49.1516i | 2.19606 | + | 1.59553i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.6525 | − | 16.4580i | 0.730725 | − | 0.530903i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −11.3988 | − | 15.6891i | −0.367132 | − | 0.505313i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 62.0595i | − | 1.99570i | −0.0655495 | − | 0.997849i | \(-0.520880\pi\) | ||
0.0655495 | − | 0.997849i | \(-0.479120\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(972\) | −25.2227 | + | 18.3253i | −0.809017 | + | 0.587785i | ||||
\(973\) | −16.8244 | + | 51.7801i | −0.539365 | + | 1.66000i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −32.1365 | − | 44.2321i | −1.02919 | − | 1.41656i | ||||
\(976\) | −24.2534 | + | 33.3820i | −0.776333 | + | 1.06853i | ||||
\(977\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 55.8044 | − | 18.1320i | 1.78170 | − | 0.578909i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 33.6488 | + | 103.560i | 1.07051 | + | 3.29469i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.0333 | 1.43053 | 0.715265 | − | 0.698853i | \(-0.246306\pi\) | ||||
0.715265 | + | 0.698853i | \(0.246306\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −43.4390 | − | 31.5603i | −1.37850 | − | 1.00154i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.80832 | − | 5.24170i | −0.120611 | − | 0.166006i | 0.744442 | − | 0.667687i | \(-0.232715\pi\) |
−0.865053 | + | 0.501680i | \(0.832715\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.34346 | − | 25.6785i | −0.263975 | − | 0.812433i |
(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 | 363.2.f.g.215.3 | 16 | ||
3.2 | odd | 2 | CM | 363.2.f.g.215.3 | 16 | ||
11.2 | odd | 10 | inner | 363.2.f.g.233.3 | 16 | ||
11.3 | even | 5 | 363.2.d.d.362.2 | yes | 4 | ||
11.4 | even | 5 | inner | 363.2.f.g.239.2 | 16 | ||
11.5 | even | 5 | inner | 363.2.f.g.161.1 | 16 | ||
11.6 | odd | 10 | inner | 363.2.f.g.161.2 | 16 | ||
11.7 | odd | 10 | inner | 363.2.f.g.239.1 | 16 | ||
11.8 | odd | 10 | 363.2.d.d.362.1 | ✓ | 4 | ||
11.9 | even | 5 | inner | 363.2.f.g.233.4 | 16 | ||
11.10 | odd | 2 | inner | 363.2.f.g.215.4 | 16 | ||
33.2 | even | 10 | inner | 363.2.f.g.233.3 | 16 | ||
33.5 | odd | 10 | inner | 363.2.f.g.161.1 | 16 | ||
33.8 | even | 10 | 363.2.d.d.362.1 | ✓ | 4 | ||
33.14 | odd | 10 | 363.2.d.d.362.2 | yes | 4 | ||
33.17 | even | 10 | inner | 363.2.f.g.161.2 | 16 | ||
33.20 | odd | 10 | inner | 363.2.f.g.233.4 | 16 | ||
33.26 | odd | 10 | inner | 363.2.f.g.239.2 | 16 | ||
33.29 | even | 10 | inner | 363.2.f.g.239.1 | 16 | ||
33.32 | even | 2 | inner | 363.2.f.g.215.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
363.2.d.d.362.1 | ✓ | 4 | 11.8 | odd | 10 | ||
363.2.d.d.362.1 | ✓ | 4 | 33.8 | even | 10 | ||
363.2.d.d.362.2 | yes | 4 | 11.3 | even | 5 | ||
363.2.d.d.362.2 | yes | 4 | 33.14 | odd | 10 | ||
363.2.f.g.161.1 | 16 | 11.5 | even | 5 | inner | ||
363.2.f.g.161.1 | 16 | 33.5 | odd | 10 | inner | ||
363.2.f.g.161.2 | 16 | 11.6 | odd | 10 | inner | ||
363.2.f.g.161.2 | 16 | 33.17 | even | 10 | inner | ||
363.2.f.g.215.3 | 16 | 1.1 | even | 1 | trivial | ||
363.2.f.g.215.3 | 16 | 3.2 | odd | 2 | CM | ||
363.2.f.g.215.4 | 16 | 11.10 | odd | 2 | inner | ||
363.2.f.g.215.4 | 16 | 33.32 | even | 2 | inner | ||
363.2.f.g.233.3 | 16 | 11.2 | odd | 10 | inner | ||
363.2.f.g.233.3 | 16 | 33.2 | even | 10 | inner | ||
363.2.f.g.233.4 | 16 | 11.9 | even | 5 | inner | ||
363.2.f.g.233.4 | 16 | 33.20 | odd | 10 | inner | ||
363.2.f.g.239.1 | 16 | 11.7 | odd | 10 | inner | ||
363.2.f.g.239.1 | 16 | 33.29 | even | 10 | inner | ||
363.2.f.g.239.2 | 16 | 11.4 | even | 5 | inner | ||
363.2.f.g.239.2 | 16 | 33.26 | odd | 10 | inner |