Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [99,2,Mod(32,99)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(99, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("99.32");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 99 = 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 99.g (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.790518980011\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{6}]$ |
Embedding invariants
Embedding label | 32.2 | ||
Root | \(-1.18614 - 1.26217i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 99.32 |
Dual form | 99.2.g.a.65.2 |
$q$-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 \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).
\(n\) | \(46\) | \(56\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(3\) | 1.18614 | + | 1.26217i | 0.684819 | + | 0.728714i | ||||
\(4\) | 1.00000 | − | 1.73205i | 0.500000 | − | 0.866025i | ||||
\(5\) | −0.813859 | − | 0.469882i | −0.363969 | − | 0.210138i | 0.306851 | − | 0.951757i | \(-0.400725\pi\) |
−0.670820 | + | 0.741620i | \(0.734058\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.186141 | + | 2.99422i | −0.0620469 | + | 0.998073i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.87228 | + | 1.65831i | −0.866025 | + | 0.500000i | ||||
\(12\) | 3.37228 | − | 0.792287i | 0.973494 | − | 0.228714i | ||||
\(13\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.372281 | − | 1.58457i | −0.0961226 | − | 0.409135i | ||||
\(16\) | −2.00000 | − | 3.46410i | −0.500000 | − | 0.866025i | ||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(20\) | −1.62772 | + | 0.939764i | −0.363969 | + | 0.210138i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.87228 | − | 1.65831i | −0.598912 | − | 0.345782i | 0.169701 | − | 0.985496i | \(-0.445720\pi\) |
−0.768613 | + | 0.639713i | \(0.779053\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.05842 | − | 3.56529i | −0.411684 | − | 0.713058i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.00000 | + | 3.31662i | −0.769800 | + | 0.638285i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.05842 | + | 5.29734i | −0.549309 | + | 0.951431i | 0.449013 | + | 0.893525i | \(0.351776\pi\) |
−0.998322 | + | 0.0579057i | \(0.981558\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.50000 | − | 1.65831i | −0.957427 | − | 0.288675i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.00000 | + | 3.31662i | 0.833333 | + | 0.552771i | ||||
\(37\) | 12.1168 | 1.99200 | 0.995998 | − | 0.0893706i | \(-0.0284856\pi\) | ||||
0.995998 | + | 0.0893706i | \(0.0284856\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(44\) | 6.63325i | 1.00000i | ||||||||
\(45\) | 1.55842 | − | 2.34941i | 0.232316 | − | 0.350229i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.8723 | − | 6.85446i | 1.73175 | − | 0.999826i | 0.856560 | − | 0.516047i | \(-0.172597\pi\) |
0.875190 | − | 0.483779i | \(-0.160736\pi\) | |||||||
\(48\) | 2.00000 | − | 6.63325i | 0.288675 | − | 0.957427i | ||||
\(49\) | −3.50000 | + | 6.06218i | −0.500000 | + | 0.866025i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 11.8294i | − | 1.62489i | −0.583036 | − | 0.812447i | \(-0.698135\pi\) | ||
0.583036 | − | 0.812447i | \(-0.301865\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.11684 | 0.420275 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.6861 | + | 7.32435i | 1.65159 | + | 0.953549i | 0.976417 | + | 0.215894i | \(0.0692665\pi\) |
0.675178 | + | 0.737655i | \(0.264067\pi\) | |||||||
\(60\) | −3.11684 | − | 0.939764i | −0.402383 | − | 0.121323i | ||||
\(61\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.55842 | + | 13.0916i | −0.923408 | + | 1.59939i | −0.129307 | + | 0.991605i | \(0.541275\pi\) |
−0.794101 | + | 0.607785i | \(0.792058\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.31386 | − | 5.59230i | −0.158170 | − | 0.673233i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.8896i | 1.29236i | 0.763184 | + | 0.646181i | \(0.223635\pi\) | ||||
−0.763184 | + | 0.646181i | \(0.776365\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.05842 | − | 6.82701i | 0.237686 | − | 0.788316i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(80\) | 3.75906i | 0.420275i | ||||||||
\(81\) | −8.93070 | − | 1.11469i | −0.992300 | − | 0.123855i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 16.5831i | − | 1.75781i | −0.476999 | − | 0.878904i | \(-0.658275\pi\) | ||
0.476999 | − | 0.878904i | \(-0.341725\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −5.74456 | + | 3.31662i | −0.598912 | + | 0.345782i | ||||
\(93\) | −10.3139 | + | 2.42315i | −1.06950 | + | 0.251269i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.0584220 | − | 0.101190i | −0.00593185 | − | 0.0102743i | 0.863044 | − | 0.505128i | \(-0.168555\pi\) |
−0.868976 | + | 0.494854i | \(0.835222\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.43070 | − | 8.90892i | −0.445302 | − | 0.895380i | ||||
\(100\) | −8.23369 | −0.823369 | ||||||||
\(101\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.61684 | − | 13.1928i | 0.750510 | − | 1.29992i | −0.197066 | − | 0.980390i | \(-0.563141\pi\) |
0.947576 | − | 0.319531i | \(-0.103525\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 1.74456 | + | 10.2448i | 0.167871 | + | 0.985809i | ||||
\(109\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.3723 | + | 15.2935i | 1.36416 | + | 1.45160i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.3139 | − | 8.26411i | −1.34653 | − | 0.777422i | −0.358778 | − | 0.933423i | \(-0.616806\pi\) |
−0.987757 | + | 0.156001i | \(0.950140\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.55842 | + | 2.69927i | 0.145324 | + | 0.251708i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.50000 | − | 9.52628i | 0.500000 | − | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.11684 | + | 10.5947i | 0.549309 | + | 0.951431i | ||||
\(125\) | 8.56768i | 0.766317i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(132\) | −8.37228 | + | 7.86797i | −0.728714 | + | 0.684819i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.81386 | − | 0.819738i | 0.414311 | − | 0.0705519i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.80298 | + | 4.50506i | −0.666654 | + | 0.384893i | −0.794808 | − | 0.606861i | \(-0.792428\pi\) |
0.128154 | + | 0.991754i | \(0.459095\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 22.7337 | + | 6.85446i | 1.91452 | + | 0.577250i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 10.7446 | − | 5.34363i | 0.895380 | − | 0.445302i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −11.8030 | + | 2.77300i | −0.973494 | + | 0.228714i | ||||
\(148\) | 12.1168 | − | 20.9870i | 0.995998 | − | 1.72512i | ||||
\(149\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.97825 | − | 2.87419i | 0.399863 | − | 0.230861i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.44158 | − | 2.49689i | 0.115050 | − | 0.199273i | −0.802749 | − | 0.596316i | \(-0.796630\pi\) |
0.917800 | + | 0.397043i | \(0.129964\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 14.9307 | − | 14.0313i | 1.18408 | − | 1.11276i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.23369 | −0.723238 | −0.361619 | − | 0.932326i | \(-0.617776\pi\) | ||||
−0.361619 | + | 0.932326i | \(0.617776\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.69702 | + | 3.93398i | 0.287812 | + | 0.306260i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.50000 | − | 11.2583i | −0.500000 | − | 0.866025i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 11.4891 | + | 6.63325i | 0.866025 | + | 0.500000i | ||||
\(177\) | 5.80298 | + | 24.6998i | 0.436179 | + | 1.85655i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 26.4781i | 1.97907i | 0.144308 | + | 0.989533i | \(0.453905\pi\) | ||||
−0.144308 | + | 0.989533i | \(0.546095\pi\) | |||||||
\(180\) | −2.51087 | − | 5.04868i | −0.187150 | − | 0.376306i | ||||
\(181\) | 21.1168 | 1.56960 | 0.784801 | − | 0.619747i | \(-0.212765\pi\) | ||||
0.784801 | + | 0.619747i | \(0.212765\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.86141 | − | 5.69349i | −0.725025 | − | 0.418593i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − | 27.4179i | − | 1.99965i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.3030 | + | 12.2993i | −1.54143 | + | 0.889945i | −0.542681 | + | 0.839939i | \(0.682591\pi\) |
−0.998749 | + | 0.0500060i | \(0.984076\pi\) | |||||||
\(192\) | −9.48913 | − | 10.0974i | −0.684819 | − | 0.728714i | ||||
\(193\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.00000 | + | 12.1244i | 0.500000 | + | 0.866025i | ||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −27.2337 | −1.93054 | −0.965272 | − | 0.261245i | \(-0.915867\pi\) | ||||
−0.965272 | + | 0.261245i | \(0.915867\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −25.4891 | + | 5.98844i | −1.79786 | + | 0.422392i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.50000 | − | 8.29156i | 0.382276 | − | 0.576303i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(212\) | −20.4891 | − | 11.8294i | −1.40720 | − | 0.812447i | ||||
\(213\) | −13.7446 | + | 12.9166i | −0.941762 | + | 0.885034i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.11684 | − | 5.39853i | 0.210138 | − | 0.363969i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.500000 | + | 0.866025i | 0.0334825 | + | 0.0579934i | 0.882281 | − | 0.470723i | \(-0.156007\pi\) |
−0.848799 | + | 0.528716i | \(0.822674\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.0584 | − | 5.49972i | 0.737228 | − | 0.366648i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.50000 | + | 4.33013i | −0.165205 | + | 0.286143i | −0.936728 | − | 0.350058i | \(-0.886162\pi\) |
0.771523 | + | 0.636201i | \(0.219495\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.8832 | −0.840404 | ||||||||
\(236\) | 25.3723 | − | 14.6487i | 1.65159 | − | 0.953549i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(240\) | −4.74456 | + | 4.45877i | −0.306260 | + | 0.287812i | ||||
\(241\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −9.18614 | − | 12.5942i | −0.589291 | − | 0.807921i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.69702 | − | 3.28917i | 0.363969 | − | 0.210138i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 16.5831i | − | 1.04672i | −0.852112 | − | 0.523359i | \(-0.824679\pi\) | ||
0.852112 | − | 0.523359i | \(-0.175321\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.0000 | 0.691564 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | 22.9783 | + | 13.2665i | 1.43334 | + | 0.827541i | 0.997374 | − | 0.0724199i | \(-0.0230722\pi\) |
0.435970 | + | 0.899961i | \(0.356405\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.55842 | + | 9.62747i | −0.341451 | + | 0.591411i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 20.9307 | − | 19.6699i | 1.28094 | − | 1.20378i | ||||
\(268\) | 15.1168 | + | 26.1831i | 0.923408 | + | 1.59939i | ||||
\(269\) | 19.3475i | 1.17964i | 0.807535 | + | 0.589819i | \(0.200801\pi\) | ||||
−0.807535 | + | 0.589819i | \(0.799199\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.8247 | + | 6.82701i | 0.713058 | + | 0.411684i | ||||
\(276\) | −11.0000 | − | 3.31662i | −0.662122 | − | 0.199637i | ||||
\(277\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −15.2921 | − | 10.1436i | −0.915515 | − | 0.607284i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(284\) | 18.8614 | + | 10.8896i | 1.11922 | + | 0.646181i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.0584220 | − | 0.193764i | 0.00342476 | − | 0.0113586i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.88316 | − | 11.9220i | −0.400753 | − | 0.694124i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.98913 | − | 16.1595i | 0.347524 | − | 0.937671i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −9.76631 | − | 10.3923i | −0.563858 | − | 0.600000i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 25.6861 | − | 6.03473i | 1.46123 | − | 0.343304i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.36141 | + | 3.09541i | 0.304017 | + | 0.175525i | 0.644246 | − | 0.764818i | \(-0.277171\pi\) |
−0.340229 | + | 0.940343i | \(0.610505\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.50000 | + | 16.4545i | 0.536972 | + | 0.930062i | 0.999065 | + | 0.0432311i | \(0.0137652\pi\) |
−0.462093 | + | 0.886831i | \(0.652902\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.1060 | − | 11.6082i | 1.12926 | − | 0.651981i | 0.185514 | − | 0.982642i | \(-0.440605\pi\) |
0.943750 | + | 0.330661i | \(0.107272\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 6.51087 | + | 3.75906i | 0.363969 | + | 0.210138i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −10.8614 | + | 14.3537i | −0.603411 | + | 0.797430i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.44158 | + | 7.69304i | 0.244131 | + | 0.422848i | 0.961887 | − | 0.273447i | \(-0.0881639\pi\) |
−0.717756 | + | 0.696295i | \(0.754831\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.25544 | + | 36.2805i | −0.123597 | + | 1.98816i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.3030 | − | 7.10313i | 0.672184 | − | 0.388086i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.54755 | − | 27.8689i | −0.355614 | − | 1.51363i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 20.2873i | − | 1.09862i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.55842 | + | 5.16870i | −0.0839026 | + | 0.278274i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −31.5951 | + | 18.2414i | −1.68164 | + | 0.970894i | −0.721063 | + | 0.692869i | \(0.756346\pi\) |
−0.960574 | + | 0.278024i | \(0.910320\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.11684 | − | 8.86263i | 0.271574 | − | 0.470380i | ||||
\(356\) | −28.7228 | − | 16.5831i | −1.52231 | − | 0.878904i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.0000 | 1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 18.5475 | − | 4.35758i | 0.973494 | − | 0.228714i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.5584 | − | 23.4839i | −0.707744 | − | 1.22585i | −0.965692 | − | 0.259690i | \(-0.916380\pi\) |
0.257948 | − | 0.966159i | \(-0.416954\pi\) | |||||||
\(368\) | 13.2665i | 0.691564i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −6.11684 | + | 20.2873i | −0.317144 | + | 1.05185i | ||||
\(373\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.8139 | + | 10.1625i | −0.558425 | + | 0.524788i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.0000 | −1.28416 | −0.642082 | − | 0.766636i | \(-0.721929\pi\) | ||||
−0.642082 | + | 0.766636i | \(0.721929\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −27.8139 | − | 16.0583i | −1.42122 | − | 0.820543i | −0.424818 | − | 0.905279i | \(-0.639662\pi\) |
−0.996403 | + | 0.0847358i | \(0.972995\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.233688 | −0.0118637 | ||||||||
\(389\) | 4.54755 | − | 2.62553i | 0.230570 | − | 0.133120i | −0.380265 | − | 0.924878i | \(-0.624167\pi\) |
0.610835 | + | 0.791758i | \(0.290834\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −19.8614 | − | 1.23472i | −0.998073 | − | 0.0620469i | ||||
\(397\) | 33.4674 | 1.67968 | 0.839840 | − | 0.542834i | \(-0.182649\pi\) | ||||
0.839840 | + | 0.542834i | \(0.182649\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −8.23369 | + | 14.2612i | −0.411684 | + | 0.713058i | ||||
\(401\) | −33.9891 | − | 19.6236i | −1.69734 | − | 0.979957i | −0.948272 | − | 0.317460i | \(-0.897170\pi\) |
−0.749064 | − | 0.662497i | \(-0.769497\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.74456 | + | 5.10358i | 0.335140 | + | 0.253599i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −34.8030 | + | 20.0935i | −1.72512 | + | 0.995998i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.9416 | − | 4.50506i | −0.737014 | − | 0.222218i | ||||
\(412\) | −15.2337 | − | 26.3855i | −0.750510 | − | 1.29992i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 32.3614 | + | 18.6839i | 1.58096 | + | 0.912767i | 0.994720 | + | 0.102628i | \(0.0327251\pi\) |
0.586238 | + | 0.810139i | \(0.300608\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.7337 | − | 34.1798i | −0.961761 | − | 1.66582i | −0.718076 | − | 0.695965i | \(-0.754977\pi\) |
−0.243685 | − | 0.969854i | \(-0.578356\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 18.3139 | + | 36.8241i | 0.890450 | + | 1.79045i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | 19.4891 | + | 7.22316i | 0.937671 | + | 0.347524i | ||||
\(433\) | 29.0000 | 1.39365 | 0.696826 | − | 0.717241i | \(-0.254595\pi\) | ||||
0.696826 | + | 0.717241i | \(0.254595\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −17.5000 | − | 11.6082i | −0.833333 | − | 0.552771i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 31.5475 | − | 18.2140i | 1.49887 | − | 0.865373i | 0.498870 | − | 0.866677i | \(-0.333748\pi\) |
0.999999 | + | 0.00130426i | \(0.000415158\pi\) | |||||||
\(444\) | 40.8614 | − | 9.60002i | 1.93920 | − | 0.455597i | ||||
\(445\) | −7.79211 | + | 13.4963i | −0.369381 | + | 0.639787i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 42.0666i | 1.98524i | 0.121253 | + | 0.992622i | \(0.461309\pi\) | ||||
−0.121253 | + | 0.992622i | \(0.538691\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −28.6277 | + | 16.5282i | −1.34653 | + | 0.777422i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.23369 | 0.290647 | ||||||||
\(461\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.5000 | − | 26.8468i | 0.720346 | − | 1.24768i | −0.240515 | − | 0.970645i | \(-0.577316\pi\) |
0.960861 | − | 0.277031i | \(-0.0893503\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9.53262 | + | 2.87419i | 0.442065 | + | 0.133288i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 18.9600i | − | 0.877363i | −0.898642 | − | 0.438682i | \(-0.855446\pi\) | ||
0.898642 | − | 0.438682i | \(-0.144554\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.86141 | − | 1.14214i | 0.224002 | − | 0.0526272i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 35.4198 | + | 2.20193i | 1.62176 | + | 0.100820i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −11.0000 | − | 19.0526i | −0.500000 | − | 0.866025i | ||||
\(485\) | 0.109806i | 0.00498602i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 30.1168 | 1.36472 | 0.682362 | − | 0.731014i | \(-0.260953\pi\) | ||||
0.682362 | + | 0.731014i | \(0.260953\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.9525 | − | 11.6545i | −0.495287 | − | 0.527034i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.580171 | + | 9.33252i | −0.0260768 | + | 0.419465i | ||||
\(496\) | 24.4674 | 1.09862 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.38316 | + | 2.39570i | −0.0619186 | + | 0.107246i | −0.895323 | − | 0.445418i | \(-0.853055\pi\) |
0.833404 | + | 0.552664i | \(0.186389\pi\) | |||||||
\(500\) | 14.8397 | + | 8.56768i | 0.663650 | + | 0.383158i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.50000 | − | 21.5581i | 0.288675 | − | 0.957427i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.87228 | − | 1.65831i | −0.127312 | − | 0.0735034i | 0.434992 | − | 0.900434i | \(-0.356751\pi\) |
−0.562303 | + | 0.826931i | \(0.690085\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.3981 | + | 7.15803i | −0.546325 | + | 0.315421i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −22.7337 | + | 39.3759i | −0.999826 | + | 1.73175i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 34.5484i | − | 1.51359i | −0.653650 | − | 0.756797i | \(-0.726763\pi\) | ||
0.653650 | − | 0.756797i | \(-0.273237\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 5.25544 | + | 22.3692i | 0.228714 | + | 0.973494i | ||||
\(529\) | −6.00000 | − | 10.3923i | −0.260870 | − | 0.451839i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −24.2921 | + | 36.6217i | −1.05419 | + | 1.58925i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −33.4198 | + | 31.4067i | −1.44217 | + | 1.35530i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 23.2164i | − | 1.00000i | ||||||
\(540\) | 3.39403 | − | 9.15759i | 0.146056 | − | 0.394080i | ||||
\(541\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 25.0475 | + | 26.6530i | 1.07489 | + | 1.14379i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(548\) | 18.0202i | 0.769786i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.51087 | − | 19.2000i | −0.191476 | − | 0.814996i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(564\) | 34.6060 | − | 32.5214i | 1.45717 | − | 1.36940i | ||||
\(565\) | 7.76631 | + | 13.4516i | 0.326731 | + | 0.565915i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −40.7921 | − | 12.2993i | −1.70411 | − | 0.513810i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13.6540i | 0.569412i | ||||||||
\(576\) | 1.48913 | − | 23.9538i | 0.0620469 | − | 0.998073i | ||||
\(577\) | −14.8832 | −0.619594 | −0.309797 | − | 0.950803i | \(-0.600261\pi\) | ||||
−0.309797 | + | 0.950803i | \(0.600261\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19.6168 | + | 33.9774i | 0.812447 | + | 1.40720i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 38.8723 | − | 22.4429i | 1.60443 | − | 0.926319i | 0.613845 | − | 0.789427i | \(-0.289622\pi\) |
0.990586 | − | 0.136892i | \(-0.0437113\pi\) | |||||||
\(588\) | −7.00000 | + | 23.2164i | −0.288675 | + | 0.957427i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −24.2337 | − | 41.9740i | −0.995998 | − | 1.72512i | ||||
\(593\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −32.3030 | − | 34.3735i | −1.32207 | − | 1.40681i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −28.7228 | − | 16.5831i | −1.17358 | − | 0.677568i | −0.219061 | − | 0.975711i | \(-0.570299\pi\) |
−0.954521 | + | 0.298143i | \(0.903633\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −37.7921 | − | 25.0684i | −1.53901 | − | 1.02087i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.95245 | + | 5.16870i | −0.363969 | + | 0.210138i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.0109 | + | 11.5533i | 0.805607 | + | 0.465118i | 0.845428 | − | 0.534089i | \(-0.179345\pi\) |
−0.0398207 | + | 0.999207i | \(0.512679\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.2921 | + | 36.8790i | 0.855802 | + | 1.48229i | 0.875899 | + | 0.482495i | \(0.160269\pi\) |
−0.0200967 | + | 0.999798i | \(0.506397\pi\) | |||||||
\(620\) | − | 11.4968i | − | 0.461722i | ||||||
\(621\) | 16.9891 | − | 2.89303i | 0.681750 | − | 0.116093i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.26631 | + | 10.8536i | −0.250652 | + | 0.434143i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.88316 | − | 4.99377i | −0.115050 | − | 0.199273i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −39.5842 | −1.57582 | −0.787911 | − | 0.615789i | \(-0.788838\pi\) | ||||
−0.787911 | + | 0.615789i | \(0.788838\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −9.37228 | − | 39.8921i | −0.371635 | − | 1.58182i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −32.6060 | − | 2.02700i | −1.28987 | − | 0.0801871i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.1060 | − | 11.6082i | 0.794138 | − | 0.458496i | −0.0472793 | − | 0.998882i | \(-0.515055\pi\) |
0.841417 | + | 0.540386i | \(0.181722\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.5000 | + | 35.5070i | −0.808441 | + | 1.40026i | 0.105502 | + | 0.994419i | \(0.466355\pi\) |
−0.913943 | + | 0.405842i | \(0.866978\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 43.1161i | 1.69507i | 0.530740 | + | 0.847535i | \(0.321914\pi\) | ||||
−0.530740 | + | 0.847535i | \(0.678086\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −48.5842 | −1.90710 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9.23369 | + | 15.9932i | −0.361619 | + | 0.626343i | ||||
\(653\) | 39.6861 | + | 22.9128i | 1.55304 | + | 0.896647i | 0.997892 | + | 0.0648948i | \(0.0206712\pi\) |
0.555147 | + | 0.831753i | \(0.312662\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(660\) | 10.5109 | − | 2.46943i | 0.409135 | − | 0.0961226i | ||||
\(661\) | 18.2921 | − | 31.6829i | 0.711481 | − | 1.23232i | −0.252821 | − | 0.967513i | \(-0.581358\pi\) |
0.964301 | − | 0.264807i | \(-0.0853084\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.500000 | + | 1.65831i | −0.0193311 | + | 0.0641141i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 20.0584 | + | 7.43415i | 0.772049 | + | 0.286141i | ||||
\(676\) | −26.0000 | −1.00000 | ||||||||
\(677\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.43176i | 0.0930489i | 0.998917 | + | 0.0465244i | \(0.0148145\pi\) | ||||
−0.998917 | + | 0.0465244i | \(0.985185\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.46738 | 0.323522 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.43070 | + | 1.98072i | −0.321651 | + | 0.0755691i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.7921 | + | 44.6732i | 0.981178 | + | 1.69945i | 0.657823 | + | 0.753173i | \(0.271478\pi\) |
0.323355 | + | 0.946278i | \(0.395189\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 22.9783 | − | 13.2665i | 0.866025 | − | 0.500000i | ||||
\(705\) | −15.2812 | − | 16.2607i | −0.575525 | − | 0.612414i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 48.5842 | + | 14.6487i | 1.82591 | + | 0.550532i | ||||
\(709\) | 16.7921 | + | 29.0848i | 0.630641 | + | 1.09230i | 0.987421 | + | 0.158114i | \(0.0505412\pi\) |
−0.356780 | + | 0.934188i | \(0.616125\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 17.5693 | − | 10.1436i | 0.657975 | − | 0.379882i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 45.8614 | + | 26.4781i | 1.71392 | + | 0.989533i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 35.8757i | − | 1.33794i | −0.743290 | − | 0.668970i | \(-0.766736\pi\) | ||
0.743290 | − | 0.668970i | \(-0.233264\pi\) | |||||||
\(720\) | −11.2554 | − | 0.699713i | −0.419465 | − | 0.0260768i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 21.1168 | − | 36.5754i | 0.784801 | − | 1.35932i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.94158 | + | 15.4873i | 0.331625 | + | 0.574391i | 0.982831 | − | 0.184510i | \(-0.0590699\pi\) |
−0.651206 | + | 0.758901i | \(0.725737\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.00000 | − | 26.5330i | 0.185185 | − | 0.982704i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 10.9090 | + | 3.28917i | 0.402383 | + | 0.121323i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 50.1369i | − | 1.84682i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(740\) | −19.7228 | + | 11.3870i | −0.725025 | + | 0.418593i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.2921 | − | 47.2713i | 0.995903 | − | 1.72496i | 0.419641 | − | 0.907690i | \(-0.362156\pi\) |
0.576262 | − | 0.817265i | \(-0.304511\pi\) | |||||||
\(752\) | −47.4891 | − | 27.4179i | −1.73175 | − | 0.999826i | ||||
\(753\) | 20.9307 | − | 19.6699i | 0.762757 | − | 0.716812i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.4674 | 0.562171 | 0.281086 | − | 0.959683i | \(-0.409305\pi\) | ||||
0.281086 | + | 0.959683i | \(0.409305\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 13.0475 | + | 13.8839i | 0.473596 | + | 0.503952i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 49.1971i | 1.77989i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −26.9783 | + | 6.33830i | −0.973494 | + | 0.228714i | ||||
\(769\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.5109 | + | 44.7384i | 0.378540 | + | 1.61121i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.2665i | 0.477163i | 0.971123 | + | 0.238581i | \(0.0766824\pi\) | ||||
−0.971123 | + | 0.238581i | \(0.923318\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 25.1821 | 0.904567 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.0584 | − | 31.2781i | −0.646181 | − | 1.11922i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 28.0000 | 1.00000 | ||||||||
\(785\) | −2.34648 | + | 1.35474i | −0.0837496 | + | 0.0483528i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −18.7446 | + | 4.40387i | −0.664801 | + | 0.156189i | ||||
\(796\) | −27.2337 | + | 47.1701i | −0.965272 | + | 1.67190i | ||||
\(797\) | −26.6644 | − | 15.3947i | −0.944501 | − | 0.545308i | −0.0531327 | − | 0.998587i | \(-0.516921\pi\) |
−0.891368 | + | 0.453279i | \(0.850254\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 49.6535 | + | 3.08679i | 1.75442 | + | 0.109066i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −15.1168 | + | 50.1369i | −0.533130 | + | 1.76819i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −24.4198 | + | 22.9489i | −0.859619 | + | 0.807839i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.51492 | + | 4.33874i | 0.263236 | + | 0.151980i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.5000 | − | 42.4352i | 0.854016 | − | 1.47920i | −0.0235383 | − | 0.999723i | \(-0.507493\pi\) |
0.877555 | − | 0.479477i | \(-0.159174\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.40895 | + | 23.0226i | 0.188316 | + | 0.801544i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(828\) | −8.86141 | − | 17.8178i | −0.307955 | − | 0.619213i | ||||
\(829\) | −57.5842 | −1.99998 | −0.999991 | − | 0.00416865i | \(-0.998673\pi\) | ||||
−0.999991 | + | 0.00416865i | \(0.998673\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.33561 | − | 31.3330i | −0.184426 | − | 1.08303i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −31.5951 | + | 18.2414i | −1.09078 | + | 0.629764i | −0.933785 | − | 0.357834i | \(-0.883515\pi\) |
−0.156999 | + | 0.987599i | \(0.550182\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.5000 | − | 25.1147i | 0.500000 | − | 0.866025i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.2169i | 0.420275i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −40.9783 | + | 23.6588i | −1.40720 | + | 0.812447i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −34.8030 | − | 20.0935i | −1.19303 | − | 0.688797i | ||||
\(852\) | 8.62772 | + | 36.7229i | 0.295581 | + | 1.25811i | ||||
\(853\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.7921 | − | 23.8886i | 0.470581 | − | 0.815070i | −0.528853 | − | 0.848713i | \(-0.677378\pi\) |
0.999434 | + | 0.0336436i | \(0.0107111\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 46.4327i | − | 1.58059i | −0.612727 | − | 0.790295i | \(-0.709928\pi\) | ||
0.612727 | − | 0.790295i | \(-0.290072\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −20.1644 | − | 21.4569i | −0.684819 | − | 0.728714i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.313859 | − | 0.156093i | 0.0106225 | − | 0.00528294i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.23369 | − | 10.7971i | −0.210138 | − | 0.363969i | ||||
\(881\) | 57.6550i | 1.94245i | 0.238171 | + | 0.971223i | \(0.423452\pi\) | ||||
−0.238171 | + | 0.971223i | \(0.576548\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −45.2337 | −1.52223 | −0.761117 | − | 0.648614i | \(-0.775349\pi\) | ||||
−0.761117 | + | 0.648614i | \(0.775349\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.88316 | − | 22.8288i | 0.231375 | − | 0.767383i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 27.5000 | − | 11.6082i | 0.921285 | − | 0.388889i | ||||
\(892\) | 2.00000 | 0.0669650 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.4416 | − | 21.5494i | 0.415876 | − | 0.720319i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 1.53262 | − | 24.6535i | 0.0510875 | − | 0.821782i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −17.1861 | − | 9.92242i | −0.571287 | − | 0.329832i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.00000 | − | 6.92820i | −0.132818 | − | 0.230047i | 0.791944 | − | 0.610594i | \(-0.209069\pi\) |
−0.924762 | + | 0.380547i | \(0.875736\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.1277 | + | 24.3224i | −1.39575 | + | 0.805839i | −0.993944 | − | 0.109885i | \(-0.964952\pi\) |
−0.401809 | + | 0.915723i | \(0.631619\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.00000 | + | 8.66025i | 0.165205 | + | 0.286143i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −24.9416 | − | 43.2001i | −0.820074 | − | 1.42041i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 38.0842 | + | 25.2622i | 1.25085 | + | 0.829720i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.478251 | + | 0.276118i | −0.0156909 | + | 0.00905914i | −0.507825 | − | 0.861460i | \(-0.669550\pi\) |
0.492134 | + | 0.870519i | \(0.336217\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.45245 | + | 10.4386i | 0.0802897 | + | 0.341744i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.50000 | + | 31.5079i | −0.310021 | + | 1.02822i | ||||
\(940\) | −12.8832 | + | 22.3143i | −0.420202 | + | 0.727812i | ||||
\(941\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | − | 58.5948i | − | 1.90710i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 32.6970 | − | 18.8776i | 1.06251 | − | 0.613441i | 0.136385 | − | 0.990656i | \(-0.456452\pi\) |
0.926126 | + | 0.377215i | \(0.123118\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 38.5000 | + | 11.6082i | 1.24845 | + | 0.376421i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 23.1168 | 0.748044 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.97825 | + | 12.6766i | 0.0961226 | + | 0.409135i | ||||
\(961\) | −3.20789 | − | 5.55623i | −0.103480 | − | 0.179233i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 43.1161i | 1.38366i | 0.722059 | + | 0.691831i | \(0.243196\pi\) | ||||
−0.722059 | + | 0.691831i | \(0.756804\pi\) | |||||||
\(972\) | −31.0000 | + | 3.31662i | −0.994325 | + | 0.106381i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 48.8288 | + | 28.1913i | 1.56217 | + | 0.901920i | 0.997037 | + | 0.0769208i | \(0.0245089\pi\) |
0.565134 | + | 0.824999i | \(0.308824\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 27.5000 | + | 47.6314i | 0.878904 | + | 1.52231i | ||||
\(980\) | − | 13.1567i | − | 0.420275i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −22.4525 | + | 12.9629i | −0.716122 | + | 0.413453i | −0.813324 | − | 0.581811i | \(-0.802344\pi\) |
0.0972017 | + | 0.995265i | \(0.469011\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.0000 | 0.635321 | 0.317660 | − | 0.948205i | \(-0.397103\pi\) | ||||
0.317660 | + | 0.948205i | \(0.397103\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.44158 | + | 14.7310i | −0.140949 | + | 0.467476i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22.1644 | + | 12.7966i | 0.702658 | + | 0.405680i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −48.4674 | + | 40.1870i | −1.53344 | + | 1.27146i |
(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 | 99.2.g.a.32.2 | ✓ | 4 | |
3.2 | odd | 2 | 297.2.g.a.98.1 | 4 | |||
9.2 | odd | 6 | inner | 99.2.g.a.65.2 | yes | 4 | |
9.4 | even | 3 | 891.2.d.a.890.3 | 4 | |||
9.5 | odd | 6 | 891.2.d.a.890.2 | 4 | |||
9.7 | even | 3 | 297.2.g.a.197.1 | 4 | |||
11.10 | odd | 2 | CM | 99.2.g.a.32.2 | ✓ | 4 | |
33.32 | even | 2 | 297.2.g.a.98.1 | 4 | |||
99.32 | even | 6 | 891.2.d.a.890.2 | 4 | |||
99.43 | odd | 6 | 297.2.g.a.197.1 | 4 | |||
99.65 | even | 6 | inner | 99.2.g.a.65.2 | yes | 4 | |
99.76 | odd | 6 | 891.2.d.a.890.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.2.g.a.32.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
99.2.g.a.32.2 | ✓ | 4 | 11.10 | odd | 2 | CM | |
99.2.g.a.65.2 | yes | 4 | 9.2 | odd | 6 | inner | |
99.2.g.a.65.2 | yes | 4 | 99.65 | even | 6 | inner | |
297.2.g.a.98.1 | 4 | 3.2 | odd | 2 | |||
297.2.g.a.98.1 | 4 | 33.32 | even | 2 | |||
297.2.g.a.197.1 | 4 | 9.7 | even | 3 | |||
297.2.g.a.197.1 | 4 | 99.43 | odd | 6 | |||
891.2.d.a.890.2 | 4 | 9.5 | odd | 6 | |||
891.2.d.a.890.2 | 4 | 99.32 | even | 6 | |||
891.2.d.a.890.3 | 4 | 9.4 | even | 3 | |||
891.2.d.a.890.3 | 4 | 99.76 | odd | 6 |