Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [616,2,Mod(13,616)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(616, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 5, 5, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("616.13");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 616 = 2^{3} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 616.bi (of order \(10\), degree \(4\), 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: | \(4.91878476451\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{10})\) |
Coefficient field: | 8.0.37515625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - x^{6} + 3x^{5} - x^{4} + 6x^{3} - 4x^{2} - 8x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{10}]$ |
Embedding invariants
Embedding label | 293.2 | ||
Root | \(1.10362 - 0.884319i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 616.293 |
Dual form | 616.2.bi.b.349.2 |
$q$-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 \(\left(\mathbb{Z}/616\mathbb{Z}\right)^\times\).
\(n\) | \(57\) | \(309\) | \(353\) | \(463\) |
\(\chi(n)\) | \(e\left(\frac{7}{10}\right)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.10362 | + | 0.884319i | 0.780378 | + | 0.625308i | ||||
\(3\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(4\) | 0.435959 | + | 1.95191i | 0.217979 | + | 0.975953i | ||||
\(5\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.51626 | + | 0.817582i | −0.951057 | + | 0.309017i | ||||
\(8\) | −1.24498 | + | 2.53969i | −0.440165 | + | 0.897917i | ||||
\(9\) | 2.42705 | + | 1.76336i | 0.809017 | + | 0.587785i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.17317 | + | 0.964887i | 0.956746 | + | 0.290924i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(14\) | −3.50000 | − | 1.32288i | −0.935414 | − | 0.353553i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.61988 | + | 1.70190i | −0.904970 | + | 0.425475i | ||||
\(17\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(18\) | 1.11917 | + | 4.09236i | 0.263792 | + | 0.964580i | ||||
\(19\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.64871 | + | 3.87096i | 0.564706 | + | 0.825292i | ||||
\(23\) | −7.50465 | −1.56483 | −0.782414 | − | 0.622758i | \(-0.786012\pi\) | ||||
−0.782414 | + | 0.622758i | \(0.786012\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.54508 | + | 4.75528i | −0.309017 | + | 0.951057i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.69283 | − | 4.55507i | −0.508897 | − | 0.860828i | ||||
\(29\) | 1.42225 | + | 4.37724i | 0.264105 | + | 0.812833i | 0.991898 | + | 0.127036i | \(0.0405463\pi\) |
−0.727793 | + | 0.685797i | \(0.759454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(32\) | −5.50000 | − | 1.32288i | −0.972272 | − | 0.233854i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.38381 | + | 5.50613i | −0.397302 | + | 0.917688i | ||||
\(37\) | 8.53732 | − | 2.77394i | 1.40353 | − | 0.456033i | 0.493197 | − | 0.869918i | \(-0.335828\pi\) |
0.910330 | + | 0.413884i | \(0.135828\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.59794 | 1.00618 | 0.503088 | − | 0.864235i | \(-0.332197\pi\) | ||||
0.503088 | + | 0.864235i | \(0.332197\pi\) | |||||||
\(44\) | −0.500000 | + | 6.61438i | −0.0753778 | + | 0.997155i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.28229 | − | 6.63651i | −1.22116 | − | 0.978500i | ||||
\(47\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.66312 | − | 4.11450i | 0.809017 | − | 0.587785i | ||||
\(50\) | −5.91038 | + | 3.88168i | −0.835853 | + | 0.548953i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.48743 | − | 11.6819i | 1.16584 | − | 1.60464i | 0.479036 | − | 0.877795i | \(-0.340986\pi\) |
0.686803 | − | 0.726844i | \(-0.259014\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.05627 | − | 7.40839i | 0.141151 | − | 0.989988i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.30125 | + | 6.08854i | −0.302169 | + | 0.799464i | ||||
\(59\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.54878 | − | 2.45275i | −0.951057 | − | 0.309017i | ||||
\(64\) | −4.90007 | − | 6.32371i | −0.612509 | − | 0.790464i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 15.1939i | − | 1.85623i | −0.372295 | − | 0.928114i | \(-0.621429\pi\) | ||
0.372295 | − | 0.928114i | \(-0.378571\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.95588 | − | 5.78028i | 0.944189 | − | 0.685993i | −0.00523645 | − | 0.999986i | \(-0.501667\pi\) |
0.949425 | + | 0.313993i | \(0.101667\pi\) | |||||||
\(72\) | −7.50000 | + | 3.96863i | −0.883883 | + | 0.467707i | ||||
\(73\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(74\) | 11.8750 | + | 4.48833i | 1.38044 | + | 0.521758i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.77339 | + | 0.166419i | −0.999820 | + | 0.0189652i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.78485 | + | 6.58577i | −0.538337 | + | 0.740957i | −0.988372 | − | 0.152053i | \(-0.951411\pi\) |
0.450035 | + | 0.893011i | \(0.351411\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.78115 | + | 8.55951i | 0.309017 | + | 0.951057i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 7.28162 | + | 5.83468i | 0.785197 | + | 0.629170i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6.40103 | + | 6.85761i | −0.682352 | + | 0.731023i | ||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.27172 | − | 14.6484i | −0.341100 | − | 1.52720i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(98\) | 9.88847 | + | 0.467160i | 0.998886 | + | 0.0471903i | ||||
\(99\) | 6.00000 | + | 7.93725i | 0.603023 | + | 0.797724i | ||||
\(100\) | −9.95546 | − | 0.942755i | −0.995546 | − | 0.0942755i | ||||
\(101\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 19.6975 | − | 5.38684i | 1.91319 | − | 0.523217i | ||||
\(107\) | −0.354696 | + | 1.09164i | −0.0342898 | + | 0.105533i | −0.966736 | − | 0.255774i | \(-0.917670\pi\) |
0.932447 | + | 0.361308i | \(0.117670\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.50273 | 0.431283 | 0.215642 | − | 0.976473i | \(-0.430816\pi\) | ||||
0.215642 | + | 0.976473i | \(0.430816\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 7.71711 | − | 7.24197i | 0.729199 | − | 0.684302i | ||||
\(113\) | 4.34450 | − | 13.3710i | 0.408696 | − | 1.25784i | −0.509073 | − | 0.860724i | \(-0.670012\pi\) |
0.917769 | − | 0.397114i | \(-0.129988\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −7.92392 | + | 4.68440i | −0.735717 | + | 0.434935i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.13799 | + | 6.12350i | 0.830726 | + | 0.556682i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −6.16198 | − | 9.38243i | −0.548953 | − | 0.835853i | ||||
\(127\) | −11.8276 | − | 16.2794i | −1.04953 | − | 1.44456i | −0.889212 | − | 0.457495i | \(-0.848747\pi\) |
−0.160322 | − | 0.987065i | \(-0.551253\pi\) | |||||||
\(128\) | 0.184357 | − | 11.3122i | 0.0162950 | − | 0.999867i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 13.4362 | − | 16.7683i | 1.16072 | − | 1.44856i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.7856 | − | 13.6485i | 1.60496 | − | 1.16607i | 0.727909 | − | 0.685674i | \(-0.240493\pi\) |
0.877051 | − | 0.480397i | \(-0.159507\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 13.8919 | + | 0.656294i | 1.16578 | + | 0.0550750i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −11.7867 | − | 2.25253i | −0.982224 | − | 0.187711i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.13640 | + | 15.4547i | 0.751007 | + | 1.27037i | ||||
\(149\) | −17.7984 | + | 12.9313i | −1.45810 | + | 1.05937i | −0.474247 | + | 0.880392i | \(0.657280\pi\) |
−0.983853 | + | 0.178979i | \(0.942720\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.1531 | − | 6.54813i | −1.64003 | − | 0.532879i | −0.663487 | − | 0.748187i | \(-0.730924\pi\) |
−0.976546 | + | 0.215308i | \(0.930924\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −9.82966 | − | 7.57481i | −0.792097 | − | 0.610396i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(158\) | −11.1046 | + | 3.03687i | −0.883433 | + | 0.241600i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 18.8837 | − | 6.13567i | 1.48824 | − | 0.483559i | ||||
\(162\) | −4.50000 | + | 11.9059i | −0.353553 | + | 0.935414i | ||||
\(163\) | −14.0637 | + | 19.3570i | −1.10156 | + | 1.51616i | −0.268249 | + | 0.963350i | \(0.586445\pi\) |
−0.833307 | + | 0.552811i | \(0.813555\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.01722 | + | 12.3637i | 0.309017 | + | 0.951057i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.87643 | + | 12.8786i | 0.219326 | + | 0.981981i | ||||
\(173\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 13.2288i | − | 1.00000i | ||||||
\(176\) | −13.1286 | + | 1.90764i | −0.989608 | + | 0.143794i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.3937 | + | 3.70204i | 0.851605 | + | 0.276703i | 0.702118 | − | 0.712060i | \(-0.252238\pi\) |
0.149487 | + | 0.988764i | \(0.452238\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 9.34311 | − | 19.0595i | 0.688783 | − | 1.40509i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.80563 | + | 20.9456i | 0.492438 | + | 1.51557i | 0.820912 | + | 0.571055i | \(0.193466\pi\) |
−0.328474 | + | 0.944513i | \(0.606534\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.84619 | + | 5.29383i | 0.276855 | + | 0.381058i | 0.924689 | − | 0.380724i | \(-0.124325\pi\) |
−0.647834 | + | 0.761781i | \(0.724325\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 10.5000 | + | 9.26013i | 0.750000 | + | 0.661438i | ||||
\(197\) | 18.0995 | 1.28953 | 0.644767 | − | 0.764379i | \(-0.276954\pi\) | ||||
0.644767 | + | 0.764379i | \(0.276954\pi\) | |||||||
\(198\) | −0.397341 | + | 14.0656i | −0.0282378 | + | 0.999601i | ||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | −10.1534 | − | 9.84425i | −0.717951 | − | 0.696094i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.15750 | − | 9.85146i | −0.502358 | − | 0.691437i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −18.2142 | − | 13.2334i | −1.26597 | − | 0.919783i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.3570 | − | 12.6106i | −1.19490 | − | 0.868148i | −0.201129 | − | 0.979565i | \(-0.564461\pi\) |
−0.993774 | + | 0.111417i | \(0.964461\pi\) | |||||||
\(212\) | 26.5022 | + | 11.4738i | 1.82018 | + | 0.788026i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.35681 | + | 0.891096i | −0.0927497 | + | 0.0609140i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4.96931 | + | 3.98185i | 0.336564 | + | 0.269685i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(224\) | 14.9210 | − | 1.16800i | 0.996950 | − | 0.0780405i | ||||
\(225\) | −12.1353 | + | 8.81678i | −0.809017 | + | 0.587785i | ||||
\(226\) | 16.6189 | − | 10.9146i | 1.10547 | − | 0.726028i | ||||
\(227\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −12.8875 | − | 1.83748i | −0.846106 | − | 0.120636i | ||||
\(233\) | −12.4411 | + | 17.1237i | −0.815042 | + | 1.12181i | 0.175484 | + | 0.984482i | \(0.443851\pi\) |
−0.990526 | + | 0.137326i | \(0.956149\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 29.3012 | + | 9.52055i | 1.89534 | + | 0.615833i | 0.973726 | + | 0.227725i | \(0.0731287\pi\) |
0.921614 | + | 0.388108i | \(0.126871\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(242\) | 4.66974 | + | 14.8389i | 0.300183 | + | 0.953882i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(252\) | 1.49658 | − | 15.8038i | 0.0942755 | − | 0.995546i | ||||
\(253\) | −23.8135 | − | 7.24115i | −1.49714 | − | 0.455247i | ||||
\(254\) | 1.34291 | − | 28.4257i | 0.0842618 | − | 1.78358i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 10.2071 | − | 12.3214i | 0.637941 | − | 0.770085i | ||||
\(257\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −19.2142 | + | 13.9599i | −1.19391 | + | 0.867427i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.26675 | + | 13.1317i | −0.264105 | + | 0.812833i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.5282i | 0.895848i | 0.894072 | + | 0.447924i | \(0.147836\pi\) | ||||
−0.894072 | + | 0.447924i | \(0.852164\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 29.6571 | − | 6.62391i | 1.81159 | − | 0.404620i | ||||
\(269\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 32.8018 | + | 1.54965i | 1.98163 | + | 0.0936180i | ||||
\(275\) | −9.49113 | + | 13.5985i | −0.572336 | + | 0.820019i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −21.9284 | − | 15.9319i | −1.31755 | − | 0.957254i | −0.999959 | − | 0.00902525i | \(-0.997127\pi\) |
−0.317588 | − | 0.948229i | \(-0.602873\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.0478 | − | 26.2171i | −1.13630 | − | 1.56398i | −0.775515 | − | 0.631329i | \(-0.782510\pi\) |
−0.360782 | − | 0.932650i | \(-0.617490\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(284\) | 14.7510 | + | 13.0092i | 0.875311 | + | 0.771952i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −11.0161 | − | 12.9091i | −0.649129 | − | 0.760679i | ||||
\(289\) | −5.25329 | + | 16.1680i | −0.309017 | + | 0.951057i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.58379 | + | 25.1357i | −0.208304 | + | 1.46098i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −31.0780 | − | 1.46822i | −1.80030 | − | 0.0850516i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.6021 | + | 5.39436i | −0.956930 | + | 0.310925i | ||||
\(302\) | −16.4507 | − | 25.0484i | −0.946632 | − | 1.44137i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(308\) | −4.14967 | − | 17.0523i | −0.236449 | − | 0.971644i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14.9408 | − | 6.46845i | −0.840486 | − | 0.363879i | ||||
\(317\) | −6.71419 | + | 9.24129i | −0.377107 | + | 0.519043i | −0.954815 | − | 0.297200i | \(-0.903947\pi\) |
0.577708 | + | 0.816243i | \(0.303947\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.289499 | + | 15.2620i | 0.0162088 | + | 0.854509i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 26.2663 | + | 9.92772i | 1.46376 | + | 0.553250i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −15.4949 | + | 9.16014i | −0.860828 | + | 0.508897i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −32.6388 | + | 8.92603i | −1.80770 | + | 0.494367i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 35.8732i | − | 1.97177i | −0.167426 | − | 0.985885i | \(-0.553545\pi\) | ||
0.167426 | − | 0.985885i | \(-0.446455\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 25.6120 | + | 8.32183i | 1.40353 | + | 0.456033i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.9147 | + | 6.79560i | −1.13930 | + | 0.370180i | −0.817102 | − | 0.576493i | \(-0.804421\pi\) |
−0.322195 | + | 0.946673i | \(0.604421\pi\) | |||||||
\(338\) | −6.50000 | + | 17.1974i | −0.353553 | + | 0.935414i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.8859 | + | 14.9832i | −0.587785 | + | 0.809017i | ||||
\(344\) | −8.21427 | + | 16.7567i | −0.442884 | + | 0.903462i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.2318 | − | 14.6993i | 1.08610 | − | 0.789100i | 0.107366 | − | 0.994220i | \(-0.465758\pi\) |
0.978737 | + | 0.205120i | \(0.0657585\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(350\) | 11.6984 | − | 14.5995i | 0.625308 | − | 0.780378i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −16.1760 | − | 9.50459i | −0.862183 | − | 0.506596i | ||||
\(353\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.30055 | + | 14.1613i | 0.491549 | + | 0.748449i | ||||
\(359\) | 18.1220 | − | 5.88820i | 0.956443 | − | 0.310767i | 0.211112 | − | 0.977462i | \(-0.432292\pi\) |
0.745331 | + | 0.666695i | \(0.232292\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.3713 | − | 11.1679i | −0.809017 | − | 0.587785i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(368\) | 27.1659 | − | 12.7722i | 1.41612 | − | 0.665796i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.8056 | + | 36.3340i | −0.612918 | + | 1.88637i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.0000 | −1.13912 | −0.569558 | − | 0.821951i | \(-0.692886\pi\) | ||||
−0.569558 | + | 0.821951i | \(0.692886\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.0196740 | + | 0.0270790i | 0.00101059 | + | 0.00139095i | 0.809522 | − | 0.587090i | \(-0.199726\pi\) |
−0.808511 | + | 0.588481i | \(0.799726\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −11.0117 | + | 29.1343i | −0.563409 | + | 1.49064i | ||||
\(383\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.436697 | + | 9.24364i | −0.0222273 | + | 0.470489i | ||||
\(387\) | 16.0135 | + | 11.6345i | 0.814013 | + | 0.591415i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 31.2611 | − | 10.1573i | 1.58500 | − | 0.514997i | 0.621660 | − | 0.783287i | \(-0.286458\pi\) |
0.963338 | + | 0.268290i | \(0.0864585\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 3.39911 | + | 19.5050i | 0.171681 | + | 0.985153i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 19.9750 | + | 16.0057i | 1.00632 | + | 0.806356i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −12.8770 | + | 15.1718i | −0.647095 | + | 0.762409i | ||||
\(397\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.50000 | − | 19.8431i | −0.125000 | − | 0.992157i | ||||
\(401\) | −7.78557 | + | 5.65655i | −0.388793 | + | 0.282475i | −0.764961 | − | 0.644077i | \(-0.777242\pi\) |
0.376168 | + | 0.926552i | \(0.377242\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.812664 | − | 17.2018i | 0.0403318 | − | 0.853711i | ||||
\(407\) | 29.7669 | − | 0.564636i | 1.47549 | − | 0.0279880i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −8.39902 | − | 30.7118i | −0.412789 | − | 1.50940i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.1864 | − | 4.60945i | −0.691404 | − | 0.224651i | −0.0578225 | − | 0.998327i | \(-0.518416\pi\) |
−0.633581 | + | 0.773676i | \(0.718416\pi\) | |||||||
\(422\) | −8.00374 | − | 29.2664i | −0.389616 | − | 1.42467i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 19.1019 | + | 36.0992i | 0.927671 | + | 1.75313i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −2.28542 | − | 0.216423i | −0.110470 | − | 0.0104612i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.0829 | + | 18.0071i | −0.630182 | + | 0.867371i | −0.998044 | − | 0.0625092i | \(-0.980090\pi\) |
0.367862 | + | 0.929880i | \(0.380090\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.96300 | + | 8.78891i | 0.0940109 | + | 0.420912i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 21.0000 | 1.00000 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.3194 | + | 5.62742i | 0.822870 | + | 0.267367i | 0.690039 | − | 0.723772i | \(-0.257593\pi\) |
0.132831 | + | 0.991139i | \(0.457593\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 17.5000 | + | 11.9059i | 0.826797 | + | 0.562500i | ||||
\(449\) | −32.0711 | − | 23.3010i | −1.51353 | − | 1.09964i | −0.964580 | − | 0.263790i | \(-0.915028\pi\) |
−0.548950 | − | 0.835855i | \(-0.684972\pi\) | |||||||
\(450\) | −21.1896 | − | 1.00106i | −0.998886 | − | 0.0471903i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 27.9930 | + | 2.65086i | 1.31668 | + | 0.124686i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.0431 | − | 15.1995i | −0.516575 | − | 0.711004i | 0.468436 | − | 0.883497i | \(-0.344818\pi\) |
−0.985011 | + | 0.172493i | \(0.944818\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 41.6915 | 1.93757 | 0.968784 | − | 0.247907i | \(-0.0797429\pi\) | ||||
0.968784 | + | 0.247907i | \(0.0797429\pi\) | |||||||
\(464\) | −12.5980 | − | 13.4245i | −0.584848 | − | 0.623219i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −28.8730 | + | 7.89616i | −1.33752 | + | 0.365782i | ||||
\(467\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.4223 | + | 38.2318i | 0.573606 | + | 1.76538i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 20.9364 | + | 6.36627i | 0.962655 | + | 0.292721i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 41.1989 | − | 13.3863i | 1.88637 | − | 0.612918i | ||||
\(478\) | 23.9183 | + | 36.4187i | 1.09400 | + | 1.66575i | ||||
\(479\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.96871 | + | 20.5061i | −0.362214 | + | 0.932095i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.727878 | − | 2.24018i | 0.0329833 | − | 0.101512i | −0.933210 | − | 0.359333i | \(-0.883004\pi\) |
0.966193 | + | 0.257821i | \(0.0830043\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.5967 | − | 41.8465i | −0.613613 | − | 1.88851i | −0.420363 | − | 0.907356i | \(-0.638097\pi\) |
−0.193249 | − | 0.981150i | \(-0.561903\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −15.2932 | + | 21.0493i | −0.685993 | + | 0.944189i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −40.4816 | + | 13.1533i | −1.81220 | + | 0.588821i | −0.812219 | + | 0.583352i | \(0.801741\pi\) |
−0.999985 | + | 0.00546838i | \(0.998259\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(504\) | 15.6273 | − | 16.1180i | 0.696094 | − | 0.717951i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −19.8776 | − | 29.0502i | −0.883668 | − | 1.29144i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 26.6194 | − | 30.1836i | 1.18105 | − | 1.33918i | ||||
\(509\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.1607 | − | 4.57181i | 0.979376 | − | 0.202047i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −33.5502 | − | 1.58501i | −1.47411 | − | 0.0696414i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(522\) | −16.3215 | + | 10.7193i | −0.714373 | + | 0.469169i | ||||
\(523\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.8476 | + | 16.0336i | −0.560181 | + | 0.699100i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 33.3198 | 1.44869 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 38.5878 | + | 18.9160i | 1.66674 | + | 0.817048i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 21.9401 | − | 7.59172i | 0.945025 | − | 0.326998i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.9284 | − | 23.9239i | −1.41570 | − | 1.02857i | −0.992463 | − | 0.122548i | \(-0.960893\pi\) |
−0.423238 | − | 0.906019i | \(-0.639107\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.5967 | + | 41.8465i | −0.581355 | + | 1.78923i | 0.0320849 | + | 0.999485i | \(0.489785\pi\) |
−0.613440 | + | 0.789741i | \(0.710215\pi\) | |||||||
\(548\) | 34.8304 | + | 30.7175i | 1.48788 | + | 1.31219i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −22.5000 | + | 6.61438i | −0.959403 | + | 0.282038i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.65550 | − | 20.4835i | 0.283021 | − | 0.871048i | ||||
\(554\) | −10.1117 | − | 36.9744i | −0.429606 | − | 1.57089i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.57775 | + | 29.4773i | 0.405822 | + | 1.24899i | 0.920207 | + | 0.391433i | \(0.128020\pi\) |
−0.514384 | + | 0.857560i | \(0.671980\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.16269 | − | 45.7781i | 0.0912276 | − | 1.93103i | ||||
\(563\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −13.9962 | − | 19.2641i | −0.587785 | − | 0.809017i | ||||
\(568\) | 4.77527 | + | 27.4018i | 0.200366 | + | 1.14975i | ||||
\(569\) | −40.2601 | − | 13.0813i | −1.68779 | − | 0.548397i | −0.701395 | − | 0.712773i | \(-0.747439\pi\) |
−0.986398 | + | 0.164375i | \(0.947439\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 44.0566 | 1.84371 | 0.921856 | − | 0.387534i | \(-0.126673\pi\) | ||||
0.921856 | + | 0.387534i | \(0.126673\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11.5953 | − | 35.6868i | 0.483559 | − | 1.48824i | ||||
\(576\) | −0.741773 | − | 23.9885i | −0.0309072 | − | 0.999522i | ||||
\(577\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(578\) | −20.0953 | + | 13.1977i | −0.835853 | + | 0.548953i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 38.2038 | − | 28.8794i | 1.58224 | − | 1.19606i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −26.1831 | + | 24.5710i | −1.07612 | + | 1.00986i | ||||
\(593\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −33.0000 | − | 29.1033i | −1.35173 | − | 1.19212i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20.4997 | − | 14.8939i | 0.837597 | − | 0.608550i | −0.0841014 | − | 0.996457i | \(-0.526802\pi\) |
0.921698 | + | 0.387907i | \(0.126802\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(602\) | −23.0928 | − | 8.72825i | −0.941191 | − | 0.355737i | ||||
\(603\) | 26.7922 | − | 36.8763i | 1.09106 | − | 1.50172i | ||||
\(604\) | 3.99543 | − | 42.1916i | 0.162572 | − | 1.71675i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.2668 | − | 46.9862i | 0.616618 | − | 1.89776i | 0.243974 | − | 0.969782i | \(-0.421549\pi\) |
0.372644 | − | 0.927974i | \(-0.378451\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 10.5000 | − | 22.4889i | 0.423057 | − | 0.906103i | ||||
\(617\) | −45.9166 | −1.84853 | −0.924266 | − | 0.381749i | \(-0.875322\pi\) | ||||
−0.924266 | + | 0.381749i | \(0.875322\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.2254 | − | 14.6946i | −0.809017 | − | 0.587785i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.4683 | + | 38.3736i | 0.496357 | + | 1.52763i | 0.814832 | + | 0.579698i | \(0.196829\pi\) |
−0.318475 | + | 0.947931i | \(0.603171\pi\) | |||||||
\(632\) | −10.7688 | − | 20.3512i | −0.428361 | − | 0.809526i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −15.5822 | + | 4.26140i | −0.618847 | + | 0.169242i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −13.1770 | + | 17.0995i | −0.521683 | + | 0.676976i | ||||
\(639\) | 29.5020 | 1.16708 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.3445 | − | 47.2255i | 0.606071 | − | 1.86530i | 0.116820 | − | 0.993153i | \(-0.462730\pi\) |
0.489251 | − | 0.872143i | \(-0.337270\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(644\) | 20.2088 | + | 34.1842i | 0.796336 | + | 1.34705i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(648\) | −25.2010 | − | 3.59311i | −0.989988 | − | 0.141151i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −43.9143 | − | 19.0122i | −1.71982 | − | 0.744575i | ||||
\(653\) | 48.3357 | − | 15.7052i | 1.89152 | − | 0.614593i | 0.913196 | − | 0.407520i | \(-0.133606\pi\) |
0.978326 | − | 0.207072i | \(-0.0663936\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 44.0000 | 1.71400 | 0.856998 | − | 0.515319i | \(-0.172327\pi\) | ||||
0.856998 | + | 0.515319i | \(0.172327\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(662\) | 31.7234 | − | 39.5904i | 1.23296 | − | 1.53873i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 20.9067 | + | 31.8333i | 0.810120 | + | 1.23351i | ||||
\(667\) | −10.6735 | − | 32.8497i | −0.413280 | − | 1.27194i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.4948 | + | 41.9725i | −1.17549 | + | 1.61792i | −0.578208 | + | 0.815890i | \(0.696248\pi\) |
−0.597281 | + | 0.802032i | \(0.703752\pi\) | |||||||
\(674\) | −29.0914 | − | 10.9955i | −1.12056 | − | 0.423532i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −22.3815 | + | 13.2313i | −0.860828 | + | 0.508897i | ||||
\(677\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 47.8198i | − | 1.82977i | −0.403711 | − | 0.914886i | \(-0.632280\pi\) | ||
0.403711 | − | 0.914886i | \(-0.367720\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −25.2639 | + | 6.90914i | −0.964580 | + | 0.263792i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −23.8837 | + | 11.2290i | −0.910559 | + | 0.428103i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −21.5869 | − | 15.0667i | −0.820019 | − | 0.572336i | ||||
\(694\) | 35.3272 | + | 1.66896i | 1.34100 | + | 0.0633528i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 25.8213 | − | 5.76719i | 0.975953 | − | 0.217979i | ||||
\(701\) | 15.3604 | − | 47.2743i | 0.580153 | − | 1.78553i | −0.0377695 | − | 0.999286i | \(-0.512025\pi\) |
0.617922 | − | 0.786239i | \(-0.287975\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −9.44708 | − | 24.7942i | −0.356050 | − | 0.934467i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27.2355 | + | 37.4865i | 1.02285 | + | 1.40784i | 0.910185 | + | 0.414202i | \(0.135939\pi\) |
0.112667 | + | 0.993633i | \(0.464061\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −23.2261 | + | 7.54663i | −0.871048 | + | 0.283021i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.25885 | + | 23.8534i | −0.0844172 | + | 0.891443i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 25.2069 | + | 9.52730i | 0.940712 | + | 0.355556i | ||||
\(719\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −7.08811 | − | 25.9183i | −0.263792 | − | 0.964580i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −23.0125 | −0.854663 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.34346 | + | 25.6785i | −0.309017 | + | 0.951057i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 41.2756 | + | 9.92772i | 1.52144 | + | 0.365941i | ||||
\(737\) | 14.6604 | − | 48.2128i | 0.540022 | − | 1.77594i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 41.5832 | + | 30.2120i | 1.52966 | + | 1.11137i | 0.956425 | + | 0.291977i | \(0.0943129\pi\) |
0.573238 | + | 0.819389i | \(0.305687\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −45.1598 | + | 29.6590i | −1.65787 | + | 1.08882i | ||||
\(743\) | 31.4335 | + | 43.2645i | 1.15318 | + | 1.58722i | 0.733729 | + | 0.679442i | \(0.237778\pi\) |
0.419453 | + | 0.907777i | \(0.362222\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −24.2797 | − | 19.4550i | −0.888942 | − | 0.712299i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 3.03685i | − | 0.110964i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.19208 | + | 9.82420i | −0.116481 | + | 0.358490i | −0.992253 | − | 0.124234i | \(-0.960353\pi\) |
0.875772 | + | 0.482724i | \(0.160353\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.6891 | + | 32.6052i | −0.860994 | + | 1.18506i | 0.120338 | + | 0.992733i | \(0.461602\pi\) |
−0.981332 | + | 0.192323i | \(0.938398\pi\) | |||||||
\(758\) | −0.00223379 | + | 0.0472831i | −8.11350e−5 | + | 0.00171740i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.3300 | + | 3.68135i | −0.410175 | + | 0.133274i | ||||
\(764\) | −37.9168 | + | 22.4154i | −1.37178 | + | 0.810959i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −8.65627 | + | 9.81529i | −0.311546 | + | 0.353260i | ||||
\(773\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(774\) | 7.38425 | + | 27.0012i | 0.265421 | + | 0.970537i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 43.4827 | + | 16.4349i | 1.55893 | + | 0.589220i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 30.8227 | − | 10.6653i | 1.10292 | − | 0.381634i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −13.4973 | + | 24.5321i | −0.482048 | + | 0.876145i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(788\) | 7.89062 | + | 35.3285i | 0.281092 | + | 1.25853i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 37.1969i | 1.32257i | ||||||||
\(792\) | −27.6280 | + | 5.35646i | −0.981719 | + | 0.190334i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 14.7886 | − | 24.1101i | 0.522856 | − | 0.852421i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −13.5945 | − | 0.642245i | −0.480039 | − | 0.0226785i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13.5536 | + | 18.6550i | 0.476521 | + | 0.655874i | 0.977832 | − | 0.209393i | \(-0.0671487\pi\) |
−0.501311 | + | 0.865267i | \(0.667149\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(812\) | 16.1088 | − | 18.2656i | 0.565306 | − | 0.640997i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 33.3507 | + | 25.7003i | 1.16894 | + | 0.900795i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.79837 | + | 20.9232i | 0.237265 | + | 0.730226i | 0.996813 | + | 0.0797750i | \(0.0254202\pi\) |
−0.759548 | + | 0.650451i | \(0.774580\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −43.5906 | − | 31.6704i | −1.51947 | − | 1.10396i | −0.961748 | − | 0.273936i | \(-0.911674\pi\) |
−0.557725 | − | 0.830026i | \(-0.688326\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35.5967 | + | 25.8626i | 1.23782 | + | 0.899329i | 0.997451 | − | 0.0713526i | \(-0.0227315\pi\) |
0.240369 | + | 0.970682i | \(0.422732\pi\) | |||||||
\(828\) | 17.8897 | − | 41.3216i | 0.621710 | − | 1.43602i | ||||
\(829\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.32408 | − | 4.59471i | 0.218072 | − | 0.158438i | ||||
\(842\) | −11.5802 | − | 17.6324i | −0.399080 | − | 0.607653i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 17.0477 | − | 39.3769i | 0.586807 | − | 1.35541i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −28.0000 | − | 7.93725i | −0.962091 | − | 0.272727i | ||||
\(848\) | −10.8420 | + | 56.7320i | −0.372315 | + | 1.94819i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −64.0696 | + | 20.8175i | −2.19628 | + | 0.713614i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.33085 | − | 2.25989i | −0.0796668 | − | 0.0772414i | ||||
\(857\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −30.3626 | + | 8.30353i | −1.03415 | + | 0.282819i | ||||
\(863\) | 6.47214 | − | 4.70228i | 0.220314 | − | 0.160068i | −0.472154 | − | 0.881516i | \(-0.656523\pi\) |
0.692468 | + | 0.721449i | \(0.256523\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −21.5376 | + | 16.2809i | −0.730615 | + | 0.552293i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −5.60579 | + | 11.4355i | −0.189836 | + | 0.387257i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.73325 | − | 20.7228i | 0.227366 | − | 0.699759i | −0.770677 | − | 0.637226i | \(-0.780082\pi\) |
0.998043 | − | 0.0625337i | \(-0.0199181\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 23.1760 | + | 18.5707i | 0.780378 | + | 0.625308i | ||||
\(883\) | −55.3577 | − | 17.9868i | −1.86293 | − | 0.605304i | −0.993863 | − | 0.110619i | \(-0.964717\pi\) |
−0.869072 | − | 0.494686i | \(-0.835283\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 14.1376 | + | 21.5264i | 0.474963 | + | 0.723194i | ||||
\(887\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 43.0711 | + | 31.2930i | 1.44456 | + | 1.04953i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.566103 | + | 29.8443i | 0.0189652 | + | 0.999820i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 8.78477 | + | 28.6152i | 0.293478 | + | 0.955966i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −14.7888 | − | 54.0767i | −0.493509 | − | 1.80456i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −22.5000 | − | 19.8431i | −0.750000 | − | 0.661438i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 28.5494 | + | 27.6803i | 0.949540 | + | 0.920632i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23.2457 | − | 31.9950i | −0.771862 | − | 1.06238i | −0.996134 | − | 0.0878507i | \(-0.972000\pi\) |
0.224271 | − | 0.974527i | \(-0.428000\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.9443 | + | 9.40456i | 0.428863 | + | 0.311587i | 0.781194 | − | 0.624288i | \(-0.214611\pi\) |
−0.352331 | + | 0.935875i | \(0.614611\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 1.25384 | − | 26.5402i | 0.0414732 | − | 0.877870i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.03022 | − | 1.41798i | −0.0339839 | − | 0.0467748i | 0.791687 | − | 0.610927i | \(-0.209203\pi\) |
−0.825671 | + | 0.564152i | \(0.809203\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 44.8833i | 1.47576i | ||||||||
\(926\) | 46.0116 | + | 36.8686i | 1.51203 | + | 1.21158i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.03184 | − | 25.9563i | −0.0666984 | − | 0.852056i | ||||
\(929\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −38.8476 | − | 16.8186i | −1.27249 | − | 0.550911i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(938\) | −20.0996 | + | 53.1786i | −0.656276 | + | 1.73634i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 17.4760 | + | 25.5404i | 0.568194 | + | 0.830389i | ||||
\(947\) | 58.2065i | 1.89146i | 0.324956 | + | 0.945729i | \(0.394650\pi\) | ||||
−0.324956 | + | 0.945729i | \(0.605350\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −58.6820 | + | 19.0669i | −1.90090 | + | 0.617639i | −0.939402 | + | 0.342817i | \(0.888619\pi\) |
−0.961495 | + | 0.274822i | \(0.911381\pi\) | |||||||
\(954\) | 57.3057 | + | 21.6595i | 1.85534 | + | 0.701253i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −5.80909 | + | 61.3438i | −0.187880 | + | 1.98400i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −36.1106 | + | 49.7019i | −1.16607 | + | 1.60496i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.57953 | + | 29.4828i | 0.309017 | + | 0.951057i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.78582 | + | 2.02402i | −0.0897719 | + | 0.0652231i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 23.3258i | − | 0.750107i | −0.927003 | − | 0.375053i | \(-0.877624\pi\) | ||
0.927003 | − | 0.375053i | \(-0.122376\pi\) | |||||||
\(968\) | −26.9284 | + | 15.5841i | −0.865511 | + | 0.500891i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 2.78433 | − | 1.82863i | 0.0892158 | − | 0.0585931i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21.0711 | − | 15.3091i | −0.674126 | − | 0.489781i | 0.197278 | − | 0.980348i | \(-0.436790\pi\) |
−0.871404 | + | 0.490567i | \(0.836790\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.9284 | + | 7.93992i | 0.348916 | + | 0.253502i | ||||
\(982\) | 22.0000 | − | 58.2065i | 0.702048 | − | 1.85744i | ||||
\(983\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −49.5152 | −1.57449 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.0000 | −0.762385 | −0.381193 | − | 0.924496i | \(-0.624487\pi\) | ||||
−0.381193 | + | 0.924496i | \(0.624487\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −35.4922 | + | 9.70635i | −1.12574 | + | 0.307867i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(998\) | −56.3080 | − | 21.2824i | −1.78240 | − | 0.673683i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 616.2.bi.b.293.2 | yes | 8 | |
7.6 | odd | 2 | CM | 616.2.bi.b.293.2 | yes | 8 | |
8.5 | even | 2 | 616.2.bi.a.293.1 | ✓ | 8 | ||
11.8 | odd | 10 | 616.2.bi.a.349.1 | yes | 8 | ||
56.13 | odd | 2 | 616.2.bi.a.293.1 | ✓ | 8 | ||
77.41 | even | 10 | 616.2.bi.a.349.1 | yes | 8 | ||
88.85 | odd | 10 | inner | 616.2.bi.b.349.2 | yes | 8 | |
616.349 | even | 10 | inner | 616.2.bi.b.349.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
616.2.bi.a.293.1 | ✓ | 8 | 8.5 | even | 2 | ||
616.2.bi.a.293.1 | ✓ | 8 | 56.13 | odd | 2 | ||
616.2.bi.a.349.1 | yes | 8 | 11.8 | odd | 10 | ||
616.2.bi.a.349.1 | yes | 8 | 77.41 | even | 10 | ||
616.2.bi.b.293.2 | yes | 8 | 1.1 | even | 1 | trivial | |
616.2.bi.b.293.2 | yes | 8 | 7.6 | odd | 2 | CM | |
616.2.bi.b.349.2 | yes | 8 | 88.85 | odd | 10 | inner | |
616.2.bi.b.349.2 | yes | 8 | 616.349 | even | 10 | inner |