Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(57,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1148.57");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.n (of order \(5\), 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: | \(9.16682615204\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{5})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 57.1 | ||
Character | \(\chi\) | \(=\) | 1148.57 |
Dual form | 1148.2.n.e.141.1 |
$q$-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 \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).
\(n\) | \(493\) | \(575\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) |
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 | ||||||||
\(3\) | −2.87361 | −1.65908 | −0.829539 | − | 0.558448i | \(-0.811397\pi\) | ||||
−0.829539 | + | 0.558448i | \(0.811397\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.43977 | + | 1.77260i | 1.09110 | + | 0.792729i | 0.979584 | − | 0.201034i | \(-0.0644302\pi\) |
0.111513 | + | 0.993763i | \(0.464430\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.309017 | − | 0.951057i | −0.116797 | − | 0.359466i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.25763 | 1.75254 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.220999 | + | 0.160565i | −0.0666338 | + | 0.0484123i | −0.620604 | − | 0.784125i | \(-0.713112\pi\) |
0.553970 | + | 0.832537i | \(0.313112\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.746236 | − | 2.29668i | 0.206969 | − | 0.636984i | −0.792658 | − | 0.609666i | \(-0.791303\pi\) |
0.999627 | − | 0.0273175i | \(-0.00869652\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −7.01094 | − | 5.09375i | −1.81022 | − | 1.31520i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.08179 | − | 1.51251i | 0.504909 | − | 0.366838i | −0.305980 | − | 0.952038i | \(-0.598984\pi\) |
0.810889 | + | 0.585200i | \(0.198984\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.484683 | − | 1.49170i | −0.111194 | − | 0.342219i | 0.879940 | − | 0.475084i | \(-0.157582\pi\) |
−0.991134 | + | 0.132865i | \(0.957582\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.887994 | + | 2.73296i | 0.193776 | + | 0.596382i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.540140 | + | 1.66238i | −0.112627 | + | 0.346630i | −0.991445 | − | 0.130527i | \(-0.958333\pi\) |
0.878818 | + | 0.477158i | \(0.158333\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.26529 | + | 3.89416i | 0.253058 | + | 0.778832i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −6.48754 | −1.24853 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.86762 | − | 3.53653i | −0.903893 | − | 0.656717i | 0.0355696 | − | 0.999367i | \(-0.488675\pi\) |
−0.939463 | + | 0.342650i | \(0.888675\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.36436 | + | 0.991266i | −0.245046 | + | 0.178037i | −0.703529 | − | 0.710667i | \(-0.748393\pi\) |
0.458482 | + | 0.888704i | \(0.348393\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.635066 | − | 0.461402i | 0.110551 | − | 0.0803198i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.931909 | − | 2.86812i | 0.157521 | − | 0.484801i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.90205 | + | 5.01463i | 1.13469 | + | 0.824400i | 0.986371 | − | 0.164539i | \(-0.0526138\pi\) |
0.148319 | + | 0.988940i | \(0.452614\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.14439 | + | 6.59975i | −0.343377 | + | 1.05681i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.41386 | − | 5.93071i | 0.376982 | − | 0.926221i | ||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.500213 | + | 1.53950i | −0.0762818 | + | 0.234771i | −0.981925 | − | 0.189269i | \(-0.939388\pi\) |
0.905644 | + | 0.424040i | \(0.139388\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 12.8274 | + | 9.31964i | 1.91219 | + | 1.38929i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.47917 | − | 4.55243i | 0.215760 | − | 0.664040i | −0.783339 | − | 0.621595i | \(-0.786485\pi\) |
0.999099 | − | 0.0424454i | \(-0.0135149\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.809017 | + | 0.587785i | −0.115574 | + | 0.0839693i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.98226 | + | 4.34636i | −0.837684 | + | 0.608613i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.63405 | + | 5.54646i | 1.04862 | + | 0.761865i | 0.971949 | − | 0.235191i | \(-0.0755717\pi\) |
0.0766685 | + | 0.997057i | \(0.475572\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.823805 | −0.111082 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.39279 | + | 4.28656i | 0.184479 | + | 0.567769i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.15789 | − | 6.64131i | 0.280934 | − | 0.864625i | −0.706655 | − | 0.707559i | \(-0.749797\pi\) |
0.987588 | − | 0.157066i | \(-0.0502035\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.03142 | − | 3.17438i | −0.132060 | − | 0.406438i | 0.863061 | − | 0.505099i | \(-0.168544\pi\) |
−0.995121 | + | 0.0986610i | \(0.968544\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.62470 | − | 5.00030i | −0.204692 | − | 0.629979i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.89172 | − | 4.28059i | 0.730778 | − | 0.530941i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.99833 | + | 5.08458i | 0.854982 | + | 0.621181i | 0.926515 | − | 0.376257i | \(-0.122789\pi\) |
−0.0715332 | + | 0.997438i | \(0.522789\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.55215 | − | 4.77703i | 0.186857 | − | 0.575087i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.3783 | − | 7.54028i | 1.23168 | − | 0.894867i | 0.234663 | − | 0.972077i | \(-0.424601\pi\) |
0.997015 | + | 0.0772100i | \(0.0246012\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.6539 | 1.48102 | 0.740511 | − | 0.672044i | \(-0.234583\pi\) | ||||
0.740511 | + | 0.672044i | \(0.234583\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.63595 | − | 11.1903i | −0.419843 | − | 1.29214i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.220999 | + | 0.160565i | 0.0251852 | + | 0.0182981i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.64773 | 1.08545 | 0.542727 | − | 0.839909i | \(-0.317392\pi\) | ||||
0.542727 | + | 0.839909i | \(0.317392\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.86976 | 0.318862 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.26220 | 0.577601 | 0.288801 | − | 0.957389i | \(-0.406744\pi\) | ||||
0.288801 | + | 0.957389i | \(0.406744\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.76016 | 0.841708 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 13.9876 | + | 10.1626i | 1.49963 | + | 1.08955i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.72574 | − | 11.4667i | −0.394928 | − | 1.21546i | −0.929018 | − | 0.370035i | \(-0.879346\pi\) |
0.534090 | − | 0.845428i | \(-0.320654\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.41487 | −0.253147 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.92064 | − | 2.84851i | 0.406551 | − | 0.295377i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.46167 | − | 4.49855i | 0.149964 | − | 0.461541i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.44801 | − | 3.23167i | −0.451627 | − | 0.328127i | 0.338611 | − | 0.940927i | \(-0.390043\pi\) |
−0.790238 | + | 0.612800i | \(0.790043\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.16193 | + | 0.844193i | −0.116779 | + | 0.0848446i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.04634 | + | 18.6087i | 0.601633 | + | 1.85164i | 0.518462 | + | 0.855101i | \(0.326505\pi\) |
0.0831711 | + | 0.996535i | \(0.473495\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.512876 | − | 1.57847i | −0.0505352 | − | 0.155531i | 0.922604 | − | 0.385748i | \(-0.126057\pi\) |
−0.973139 | + | 0.230217i | \(0.926057\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.67794 | + | 8.24185i | −0.261340 | + | 0.804323i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.39974 | + | 10.4633i | 0.328665 | + | 1.01153i | 0.969759 | + | 0.244065i | \(0.0784811\pi\) |
−0.641093 | + | 0.767463i | \(0.721519\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.620648 | −0.0594473 | −0.0297236 | − | 0.999558i | \(-0.509463\pi\) | ||||
−0.0297236 | + | 0.999558i | \(0.509463\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −19.8338 | − | 14.4101i | −1.88254 | − | 1.36774i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.20554 | − | 0.875874i | 0.113407 | − | 0.0823953i | −0.529636 | − | 0.848225i | \(-0.677671\pi\) |
0.643043 | + | 0.765830i | \(0.277671\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.26455 | + | 3.09837i | −0.397671 | + | 0.288925i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.92343 | − | 12.0751i | 0.362721 | − | 1.11634i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.08179 | − | 1.51251i | −0.190838 | − | 0.138652i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.37613 | + | 10.3907i | −0.306921 | + | 0.944605i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.93649 | + | 17.0425i | −0.625442 | + | 1.53667i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.843784 | − | 2.59690i | 0.0754704 | − | 0.232274i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.41477 | + | 3.20752i | 0.391748 | + | 0.284622i | 0.766171 | − | 0.642636i | \(-0.222159\pi\) |
−0.374423 | + | 0.927258i | \(0.622159\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.43742 | − | 4.42391i | 0.126558 | − | 0.389504i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.531398 | − | 0.386083i | 0.0464285 | − | 0.0337323i | −0.564329 | − | 0.825550i | \(-0.690865\pi\) |
0.610757 | + | 0.791818i | \(0.290865\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.26892 | + | 0.921921i | −0.110029 | + | 0.0799407i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −15.8281 | − | 11.4998i | −1.36226 | − | 0.989743i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.28568 | 0.707893 | 0.353947 | − | 0.935266i | \(-0.384839\pi\) | ||||
0.353947 | + | 0.935266i | \(0.384839\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.04200 | − | 6.28462i | −0.173200 | − | 0.533055i | 0.826347 | − | 0.563162i | \(-0.190415\pi\) |
−0.999547 | + | 0.0301071i | \(0.990415\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.25057 | + | 13.0819i | −0.357962 | + | 1.10169i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.203849 | + | 0.627384i | 0.0170467 | + | 0.0524645i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.60702 | − | 17.2566i | −0.465637 | − | 1.43308i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.32480 | − | 1.68906i | 0.191746 | − | 0.139312i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.71915 | − | 5.60829i | −0.632377 | − | 0.459449i | 0.224846 | − | 0.974394i | \(-0.427812\pi\) |
−0.857223 | + | 0.514945i | \(0.827812\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.81315 | − | 5.58031i | 0.147552 | − | 0.454119i | −0.849778 | − | 0.527141i | \(-0.823264\pi\) |
0.997330 | + | 0.0730213i | \(0.0232641\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 10.9453 | − | 7.95222i | 0.884874 | − | 0.642899i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.08583 | −0.408504 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.93884 | + | 9.04482i | 0.234545 | + | 0.721855i | 0.997181 | + | 0.0750278i | \(0.0239046\pi\) |
−0.762636 | + | 0.646827i | \(0.776095\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −21.9373 | − | 15.9384i | −1.73974 | − | 1.26399i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.74793 | 0.137756 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.5406 | 1.68719 | 0.843594 | − | 0.536981i | \(-0.180435\pi\) | ||||
0.843594 | + | 0.536981i | \(0.180435\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.36729 | 0.184293 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.754749 | −0.0584042 | −0.0292021 | − | 0.999574i | \(-0.509297\pi\) | ||||
−0.0292021 | + | 0.999574i | \(0.509297\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.79936 | + | 4.21348i | 0.446105 | + | 0.324114i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.54828 | − | 7.84280i | −0.194872 | − | 0.599754i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −25.7360 | −1.95668 | −0.978338 | − | 0.207016i | \(-0.933625\pi\) | ||||
−0.978338 | + | 0.207016i | \(0.933625\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.31257 | − | 2.40672i | 0.250407 | − | 0.181931i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.20094 | + | 19.0845i | −0.466091 | + | 1.43448i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.96668 | − | 6.51468i | −0.670201 | − | 0.486930i | 0.199891 | − | 0.979818i | \(-0.435941\pi\) |
−0.870093 | + | 0.492888i | \(0.835941\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.00771 | − | 2.18523i | 0.223561 | − | 0.162427i | −0.470367 | − | 0.882471i | \(-0.655878\pi\) |
0.693928 | + | 0.720044i | \(0.255878\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.96390 | + | 9.12193i | 0.219097 | + | 0.674313i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.95048 | + | 24.4691i | 0.584531 | + | 1.79900i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.217218 | + | 0.668528i | −0.0158845 | + | 0.0488876i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.00476 | + | 6.17001i | 0.145825 | + | 0.448802i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.84706 | −0.278363 | −0.139182 | − | 0.990267i | \(-0.544447\pi\) | ||||
−0.139182 | + | 0.990267i | \(0.544447\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.8139 | − | 11.4894i | −1.13831 | − | 0.827028i | −0.151424 | − | 0.988469i | \(-0.548386\pi\) |
−0.986882 | + | 0.161441i | \(0.948386\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −16.9305 | + | 12.3007i | −1.21242 | + | 0.880874i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.0770 | + | 10.2276i | −1.00295 | + | 0.728684i | −0.962718 | − | 0.270506i | \(-0.912809\pi\) |
−0.0402295 | + | 0.999190i | \(0.512809\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.94118 | − | 9.05201i | 0.208495 | − | 0.641680i | −0.791057 | − | 0.611742i | \(-0.790469\pi\) |
0.999552 | − | 0.0299381i | \(-0.00953101\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −20.1105 | − | 14.6111i | −1.41848 | − | 1.03059i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.85926 | + | 5.72222i | −0.130495 | + | 0.401621i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 16.4020 | − | 10.1908i | 1.14557 | − | 0.711753i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.83986 | + | 8.74018i | −0.197384 | + | 0.607484i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.346630 | + | 0.251841i | 0.0239769 | + | 0.0174202i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.12707 | + | 15.7795i | −0.352962 | + | 1.08631i | 0.604219 | + | 0.796818i | \(0.293485\pi\) |
−0.957182 | + | 0.289488i | \(0.906515\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −29.8232 | + | 21.6678i | −2.04345 | + | 1.48465i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.94931 | + | 2.86934i | −0.269341 | + | 0.195688i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.36436 | + | 0.991266i | 0.0926188 | + | 0.0672915i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −36.3623 | −2.45713 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.92024 | − | 5.90990i | −0.129169 | − | 0.397543i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.09907 | + | 3.38260i | −0.0735994 | + | 0.226516i | −0.981088 | − | 0.193560i | \(-0.937997\pi\) |
0.907489 | + | 0.420076i | \(0.137997\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.65242 | + | 20.4740i | 0.443495 | + | 1.36494i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.271170 | + | 0.834575i | 0.0179982 | + | 0.0553927i | 0.959652 | − | 0.281190i | \(-0.0907290\pi\) |
−0.941654 | + | 0.336582i | \(0.890729\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.54286 | + | 5.48021i | −0.498446 | + | 0.362143i | −0.808423 | − | 0.588602i | \(-0.799679\pi\) |
0.309977 | + | 0.950744i | \(0.399679\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.635066 | − | 0.461402i | −0.0417843 | − | 0.0303580i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.59966 | + | 8.00094i | −0.170310 | + | 0.524159i | −0.999388 | − | 0.0349728i | \(-0.988866\pi\) |
0.829079 | + | 0.559132i | \(0.188866\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.6785 | − | 8.48489i | 0.761818 | − | 0.553494i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −27.7238 | −1.80086 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.60865 | − | 23.4170i | −0.492163 | − | 1.51472i | −0.821332 | − | 0.570450i | \(-0.806769\pi\) |
0.329170 | − | 0.944271i | \(-0.393231\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.22375 | − | 3.79528i | −0.336491 | − | 0.244475i | 0.406689 | − | 0.913567i | \(-0.366683\pi\) |
−0.743180 | + | 0.669092i | \(0.766683\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.2160 | 0.719510 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.01572 | −0.192667 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.78764 | −0.241002 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −15.1215 | −0.958286 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.3634 | + | 16.9745i | 1.47468 | + | 1.07142i | 0.979222 | + | 0.202792i | \(0.0650016\pi\) |
0.495463 | + | 0.868629i | \(0.334998\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.147550 | − | 0.454113i | −0.00927640 | − | 0.0285498i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −22.2997 | −1.39646 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.3323 | − | 8.23339i | 0.706889 | − | 0.513585i | −0.175279 | − | 0.984519i | \(-0.556083\pi\) |
0.882169 | + | 0.470934i | \(0.156083\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.63635 | − | 8.11384i | 0.163815 | − | 0.504170i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −25.5921 | − | 18.5938i | −1.58411 | − | 1.15092i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.0995 | + | 13.1500i | −1.11606 | + | 0.810866i | −0.983607 | − | 0.180323i | \(-0.942286\pi\) |
−0.132454 | + | 0.991189i | \(0.542286\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.79368 | + | 27.0642i | 0.540192 | + | 1.66254i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.7063 | + | 32.9507i | 0.655216 | + | 2.01655i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.383077 | − | 1.17899i | 0.0233566 | − | 0.0718842i | −0.938699 | − | 0.344738i | \(-0.887968\pi\) |
0.962055 | + | 0.272854i | \(0.0879676\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.47488 | − | 10.6946i | −0.211084 | − | 0.649650i | −0.999408 | − | 0.0343904i | \(-0.989051\pi\) |
0.788324 | − | 0.615260i | \(-0.210949\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.93939 | 0.419991 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.904896 | − | 0.657445i | −0.0545673 | − | 0.0396454i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.91945 | + | 1.39456i | −0.115329 | + | 0.0837912i | −0.643955 | − | 0.765064i | \(-0.722707\pi\) |
0.528626 | + | 0.848855i | \(0.322707\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.17330 | + | 5.21170i | −0.429454 | + | 0.312017i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.00576 | − | 9.25078i | 0.179309 | − | 0.551855i | −0.820495 | − | 0.571653i | \(-0.806302\pi\) |
0.999804 | + | 0.0197979i | \(0.00630229\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.90299 | − | 5.74186i | −0.469784 | − | 0.341318i | 0.327573 | − | 0.944826i | \(-0.393769\pi\) |
−0.797357 | + | 0.603508i | \(0.793769\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.20026 | + | 12.9271i | −0.248802 | + | 0.765733i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.38636 | − | 0.463028i | −0.376975 | − | 0.0273317i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.20712 | + | 9.87049i | −0.188654 | + | 0.580617i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.7819 | + | 9.28656i | 0.749285 | + | 0.544388i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.47886 | − | 29.1729i | 0.553761 | − | 1.70430i | −0.145432 | − | 0.989368i | \(-0.546457\pi\) |
0.699193 | − | 0.714933i | \(-0.253543\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.0371 | − | 12.3782i | 0.991939 | − | 0.720686i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.43374 | − | 1.04167i | 0.0831941 | − | 0.0604441i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.41488 | + | 2.48106i | 0.197488 | + | 0.143483i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.61872 | 0.0933017 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −17.3748 | − | 53.4742i | −0.998157 | − | 3.07201i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.11047 | − | 9.57305i | 0.178105 | − | 0.548151i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.93497 | + | 15.1883i | 0.281653 | + | 0.866840i | 0.987382 | + | 0.158358i | \(0.0506199\pi\) |
−0.705728 | + | 0.708483i | \(0.749380\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.47380 | + | 4.53591i | 0.0838418 | + | 0.258039i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.7763 | + | 9.28254i | −0.724479 | + | 0.526365i | −0.887812 | − | 0.460206i | \(-0.847775\pi\) |
0.163333 | + | 0.986571i | \(0.447775\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.05452 | + | 4.39887i | 0.342222 | + | 0.248639i | 0.745599 | − | 0.666395i | \(-0.232164\pi\) |
−0.403377 | + | 0.915034i | \(0.632164\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.89963 | − | 15.0795i | 0.276063 | − | 0.849634i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.12076 | − | 5.90008i | 0.456107 | − | 0.331381i | −0.335895 | − | 0.941899i | \(-0.609039\pi\) |
0.792002 | + | 0.610518i | \(0.209039\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.64358 | 0.0920230 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.76953 | − | 30.0675i | −0.545282 | − | 1.67821i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.26522 | − | 2.37232i | −0.181682 | − | 0.132000i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.88784 | 0.548479 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.78350 | 0.0986277 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.78671 | −0.263900 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.9160 | 1.36951 | 0.684754 | − | 0.728774i | \(-0.259910\pi\) | ||||
0.684754 | + | 0.728774i | \(0.259910\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 36.2884 | + | 26.3651i | 1.98859 | + | 1.44480i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.06139 | + | 24.8104i | 0.440441 | + | 1.35554i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.73747 | −0.530434 | −0.265217 | − | 0.964189i | \(-0.585444\pi\) | ||||
−0.265217 | + | 0.964189i | \(0.585444\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.46424 | + | 2.51692i | −0.188152 | + | 0.136700i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.142360 | − | 0.438138i | 0.00770921 | − | 0.0237265i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.809017 | + | 0.587785i | 0.0436828 | + | 0.0317374i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 12.2546 | − | 8.90351i | 0.659767 | − | 0.479349i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.35809 | + | 16.4905i | 0.287637 | + | 0.885256i | 0.985596 | + | 0.169118i | \(0.0540919\pi\) |
−0.697959 | + | 0.716138i | \(0.745908\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.3138 | − | 31.7426i | −0.552084 | − | 1.69914i | −0.703522 | − | 0.710674i | \(-0.748390\pi\) |
0.151437 | − | 0.988467i | \(-0.451610\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.84123 | + | 14.8998i | −0.258406 | + | 0.795291i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.05991 | − | 24.8059i | −0.428986 | − | 1.32028i | −0.899126 | − | 0.437691i | \(-0.855797\pi\) |
0.470140 | − | 0.882592i | \(-0.344203\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 38.6865 | 2.05327 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.98226 | + | 4.34636i | 0.316615 | + | 0.230034i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.59440 | − | 6.24419i | 0.453595 | − | 0.329556i | −0.337419 | − | 0.941355i | \(-0.609554\pi\) |
0.791013 | + | 0.611799i | \(0.209554\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.3811 | − | 9.72192i | 0.704267 | − | 0.511680i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.70167 | − | 29.8587i | 0.509206 | − | 1.56717i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 30.8725 | + | 22.4302i | 1.61594 | + | 1.17405i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.44409 | − | 22.9105i | 0.388578 | − | 1.19592i | −0.545273 | − | 0.838259i | \(-0.683574\pi\) |
0.933851 | − | 0.357662i | \(-0.116426\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 12.6912 | − | 31.1814i | 0.660676 | − | 1.62324i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.91595 | − | 8.97437i | 0.151388 | − | 0.465926i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.0758 | + | 12.4063i | 0.884153 | + | 0.642375i | 0.934347 | − | 0.356365i | \(-0.115984\pi\) |
−0.0501940 | + | 0.998739i | \(0.515984\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.42471 | + | 7.46248i | −0.125211 | + | 0.385361i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −11.7547 | + | 8.54026i | −0.605396 | + | 0.439846i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.0017 | − | 9.44629i | 0.667852 | − | 0.485223i | −0.201453 | − | 0.979498i | \(-0.564566\pi\) |
0.869306 | + | 0.494275i | \(0.164566\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.6863 | − | 9.21716i | −0.649941 | − | 0.472209i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −20.5966 | −1.05244 | −0.526219 | − | 0.850349i | \(-0.676391\pi\) | ||||
−0.526219 | + | 0.850349i | \(0.676391\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.254570 | + | 0.783485i | 0.0129741 | + | 0.0399301i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.62993 | + | 8.09411i | −0.133687 | + | 0.411447i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.95981 | + | 9.10936i | 0.150068 | + | 0.461863i | 0.997628 | − | 0.0688374i | \(-0.0219290\pi\) |
−0.847560 | + | 0.530700i | \(0.821929\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.38991 | + | 4.27770i | 0.0702907 | + | 0.216333i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.52703 | + | 1.10945i | −0.0770285 | + | 0.0559645i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 23.5382 | + | 17.1015i | 1.18434 | + | 0.860471i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.50215 | + | 23.0892i | −0.376522 | + | 1.15882i | 0.565924 | + | 0.824458i | \(0.308520\pi\) |
−0.942446 | + | 0.334359i | \(0.891480\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.64637 | − | 2.64924i | 0.182547 | − | 0.132628i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −31.3650 | −1.56629 | −0.783147 | − | 0.621837i | \(-0.786387\pi\) | ||||
−0.783147 | + | 0.621837i | \(0.786387\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.25848 | + | 3.87321i | 0.0626895 | + | 0.192938i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.00154 | + | 5.08692i | 0.347910 | + | 0.252771i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.33052 | −0.115520 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.32846 | −0.411816 | −0.205908 | − | 0.978571i | \(-0.566015\pi\) | ||||
−0.205908 | + | 0.978571i | \(0.566015\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −23.8098 | −1.17445 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.98308 | −0.343615 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.8385 | + | 9.32775i | 0.630219 | + | 0.457881i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.86790 | + | 18.0595i | 0.287352 | + | 0.884379i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.0231 | −0.733927 | −0.366964 | − | 0.930235i | \(-0.619603\pi\) | ||||
−0.366964 | + | 0.930235i | \(0.619603\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.8508 | − | 20.9613i | 1.40610 | − | 1.02159i | 0.412228 | − | 0.911081i | \(-0.364751\pi\) |
0.993875 | − | 0.110513i | \(-0.0352494\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.77694 | − | 23.9350i | 0.378128 | − | 1.16376i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.52403 | + | 6.19307i | 0.413476 | + | 0.300408i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.70029 | + | 1.96188i | −0.130676 | + | 0.0949418i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.585783 | − | 1.80286i | −0.0282819 | − | 0.0870427i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.41376 | − | 16.6618i | −0.260772 | − | 0.802572i | −0.992637 | − | 0.121124i | \(-0.961350\pi\) |
0.731866 | − | 0.681449i | \(-0.238650\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.2768 | − | 37.7840i | 0.589983 | − | 1.81578i | 0.0117209 | − | 0.999931i | \(-0.496269\pi\) |
0.578263 | − | 0.815851i | \(-0.303731\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 16.1124 | + | 49.5888i | 0.772529 | + | 2.37760i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.74157 | 0.131147 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.32033 | + | 6.04507i | 0.397108 | + | 0.288516i | 0.768362 | − | 0.640016i | \(-0.221072\pi\) |
−0.371254 | + | 0.928531i | \(0.621072\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.25351 | + | 3.09036i | −0.202548 | + | 0.147160i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −24.0536 | + | 17.4759i | −1.14282 | + | 0.830306i | −0.987509 | − | 0.157559i | \(-0.949637\pi\) |
−0.155309 | + | 0.987866i | \(0.549637\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.2358 | − | 34.5802i | 0.532628 | − | 1.63926i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 22.1818 | + | 16.1160i | 1.04916 | + | 0.762262i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.55811 | + | 17.1061i | −0.262303 | + | 0.807286i | 0.729999 | + | 0.683448i | \(0.239520\pi\) |
−0.992302 | + | 0.123838i | \(0.960480\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.418805 | + | 1.69826i | 0.0197208 | + | 0.0799682i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.21029 | + | 16.0356i | −0.244801 | + | 0.753420i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.89172 | − | 4.28059i | −0.276208 | − | 0.200677i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.21915 | − | 6.82984i | 0.103807 | − | 0.319486i | −0.885641 | − | 0.464370i | \(-0.846281\pi\) |
0.989449 | + | 0.144884i | \(0.0462808\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −13.5057 | + | 9.81247i | −0.630392 | + | 0.458007i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.3715 | − | 10.4415i | 0.669349 | − | 0.486310i | −0.200458 | − | 0.979702i | \(-0.564243\pi\) |
0.869807 | + | 0.493392i | \(0.164243\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.63579 | − | 3.36810i | −0.215444 | − | 0.156529i | 0.474830 | − | 0.880078i | \(-0.342510\pi\) |
−0.690273 | + | 0.723549i | \(0.742510\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 14.6147 | 0.677740 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.0825781 | + | 0.254149i | 0.00382126 | + | 0.0117606i | 0.952949 | − | 0.303131i | \(-0.0980319\pi\) |
−0.949128 | + | 0.314891i | \(0.898032\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.67312 | − | 8.22703i | 0.123433 | − | 0.379889i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.44508 | − | 25.9913i | −0.389129 | − | 1.19761i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.136643 | − | 0.420545i | −0.00628287 | − | 0.0193367i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.19566 | − | 3.77486i | 0.238393 | − | 0.173203i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 40.1370 | + | 29.1612i | 1.83775 | + | 1.33520i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.47328 | + | 26.0781i | −0.387154 | + | 1.19154i | 0.547752 | + | 0.836641i | \(0.315484\pi\) |
−0.934906 | + | 0.354896i | \(0.884516\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.6675 | − | 12.1097i | 0.759975 | − | 0.552154i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.02287 | −0.228548 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.12368 | − | 15.7691i | −0.232654 | − | 0.716036i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.00681 | + | 2.18457i | 0.136251 | + | 0.0989925i | 0.653823 | − | 0.756647i | \(-0.273164\pi\) |
−0.517572 | + | 0.855640i | \(0.673164\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −61.8992 | −2.79918 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.0665 | −0.499423 | −0.249712 | − | 0.968320i | \(-0.580336\pi\) | ||||
−0.249712 | + | 0.968320i | \(0.580336\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.4824 | −0.697292 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.33126 | −0.194676 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10.3783 | − | 7.54028i | −0.465531 | − | 0.338228i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.58014 | − | 7.94085i | −0.115503 | − | 0.355481i | 0.876549 | − | 0.481313i | \(-0.159840\pi\) |
−0.992052 | + | 0.125832i | \(0.959840\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.16885 | 0.0968972 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17.3754 | + | 12.6240i | −0.774732 | + | 0.562876i | −0.903393 | − | 0.428813i | \(-0.858932\pi\) |
0.128661 | + | 0.991689i | \(0.458932\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.2341 | + | 56.1187i | −0.811405 | + | 2.49725i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −16.6651 | − | 12.1079i | −0.740123 | − | 0.537731i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14.0340 | + | 10.1963i | −0.622044 | + | 0.451941i | −0.853635 | − | 0.520872i | \(-0.825607\pi\) |
0.231591 | + | 0.972813i | \(0.425607\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.91026 | − | 12.0345i | −0.172980 | − | 0.532377i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.14440 | + | 9.67745i | 0.138828 | + | 0.427270i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.54669 | − | 4.76022i | 0.0681553 | − | 0.209760i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.404066 | + | 1.24359i | 0.0177708 | + | 0.0546929i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 73.9553 | 3.24628 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.2289 | − | 15.4237i | −0.930054 | − | 0.675724i | 0.0159521 | − | 0.999873i | \(-0.494922\pi\) |
−0.946006 | + | 0.324149i | \(0.894922\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.1366 | + | 16.0832i | −0.967964 | + | 0.703267i | −0.954987 | − | 0.296649i | \(-0.904131\pi\) |
−0.0129775 | + | 0.999916i | \(0.504131\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −9.51903 | + | 6.91598i | −0.415445 | + | 0.301838i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.34101 | + | 4.12722i | −0.0584155 | + | 0.179784i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.1356 | + | 11.7232i | 0.701549 | + | 0.509705i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.3454 | − | 34.9175i | 0.492348 | − | 1.51529i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −11.8196 | − | 9.96956i | −0.511964 | − | 0.431830i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.2527 | + | 31.5545i | −0.443261 | + | 1.36422i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 25.7667 | + | 18.7206i | 1.11192 | + | 0.807855i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.0844142 | − | 0.259800i | 0.00363598 | − | 0.0111904i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −30.5035 | + | 22.1621i | −1.31145 | + | 0.952823i | −0.311452 | + | 0.950262i | \(0.600815\pi\) |
−0.999997 | + | 0.00256100i | \(0.999185\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.64298 | + | 6.27949i | −0.370906 | + | 0.269479i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.51424 | − | 1.10016i | −0.0648628 | − | 0.0471256i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.106511 | −0.00455408 | −0.00227704 | − | 0.999997i | \(-0.500725\pi\) | ||||
−0.00227704 | + | 0.999997i | \(0.500725\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.42282 | − | 16.6897i | −0.231440 | − | 0.712300i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.91619 | + | 8.97511i | −0.124234 | + | 0.382353i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.98131 | − | 9.17554i | −0.126778 | − | 0.390184i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −22.8466 | − | 70.3145i | −0.969783 | − | 2.98469i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −21.4701 | + | 15.5990i | −0.909718 | + | 0.660949i | −0.940944 | − | 0.338563i | \(-0.890059\pi\) |
0.0312252 | + | 0.999512i | \(0.490059\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.16245 | + | 2.29766i | 0.133758 | + | 0.0971805i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.624199 | − | 1.92109i | 0.0263537 | − | 0.0811084i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.1223 | + | 13.8931i | −0.805907 | + | 0.585526i | −0.912641 | − | 0.408762i | \(-0.865961\pi\) |
0.106734 | + | 0.994288i | \(0.465961\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.49380 | 0.189056 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.886804 | − | 2.72930i | −0.0372423 | − | 0.114620i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.99185 | + | 1.44716i | 0.0835027 | + | 0.0606682i | 0.628753 | − | 0.777605i | \(-0.283566\pi\) |
−0.545251 | + | 0.838273i | \(0.683566\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −41.2970 | −1.72823 | −0.864113 | − | 0.503299i | \(-0.832120\pi\) | ||||
−0.864113 | + | 0.503299i | \(0.832120\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.0549 | 0.461827 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.15701 | −0.298468 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 30.0416 | 1.25065 | 0.625324 | − | 0.780365i | \(-0.284967\pi\) | ||||
0.625324 | + | 0.780365i | \(0.284967\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 45.4428 | + | 33.0162i | 1.88854 | + | 1.37210i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.62611 | − | 5.00465i | −0.0674624 | − | 0.207628i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.57769 | −0.106757 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 30.9765 | − | 22.5057i | 1.28072 | − | 0.930497i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.39272 | − | 4.28635i | 0.0574837 | − | 0.176917i | −0.918192 | − | 0.396136i | \(-0.870351\pi\) |
0.975676 | + | 0.219219i | \(0.0703510\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.13995 | + | 1.55477i | 0.0881752 | + | 0.0640630i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 40.4519 | − | 29.3900i | 1.66397 | − | 1.20894i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.14275 | − | 18.9055i | −0.252253 | − | 0.776354i | −0.994359 | − | 0.106071i | \(-0.966173\pi\) |
0.742106 | − | 0.670283i | \(-0.233827\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.39802 | − | 7.38035i | −0.0983093 | − | 0.302565i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.45179 | + | 26.0119i | −0.345909 | + | 1.06460i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.942036 | + | 2.89929i | 0.0384906 | + | 0.118462i | 0.968456 | − | 0.249186i | \(-0.0801631\pi\) |
−0.929965 | + | 0.367648i | \(0.880163\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.0139 | −1.02034 | −0.510169 | − | 0.860074i | \(-0.670417\pi\) | ||||
−0.510169 | + | 0.860074i | \(0.670417\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 36.7946 | + | 26.7328i | 1.49839 | + | 1.08865i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −26.6554 | + | 19.3663i | −1.08370 | + | 0.787351i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.1043 | + | 10.2474i | −0.572476 | + | 0.415928i | −0.836004 | − | 0.548724i | \(-0.815114\pi\) |
0.263528 | + | 0.964652i | \(0.415114\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.34280 | − | 16.4434i | 0.216501 | − | 0.666322i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.35165 | − | 6.79437i | −0.378327 | − | 0.274871i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.16706 | − | 22.0579i | 0.289475 | − | 0.890912i | −0.695547 | − | 0.718481i | \(-0.744838\pi\) |
0.985022 | − | 0.172431i | \(-0.0551622\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −47.1329 | + | 29.2842i | −1.90058 | + | 1.18085i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.5806 | + | 35.6414i | −0.466217 | + | 1.43487i | 0.391230 | + | 0.920293i | \(0.372050\pi\) |
−0.857446 | + | 0.514574i | \(0.827950\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 35.7744 | + | 25.9916i | 1.43790 | + | 1.04469i | 0.988477 | + | 0.151371i | \(0.0483689\pi\) |
0.449419 | + | 0.893321i | \(0.351631\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.50418 | − | 10.7848i | 0.140618 | − | 0.432777i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.75412 | + | 7.08678i | −0.390790 | + | 0.283926i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.2247 | − | 16.8738i | 0.928990 | − | 0.674951i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.996079 | − | 0.723694i | −0.0397796 | − | 0.0289015i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 21.9533 | 0.875336 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.72904 | − | 26.8652i | −0.347498 | − | 1.06949i | −0.960233 | − | 0.279200i | \(-0.909931\pi\) |
0.612735 | − | 0.790288i | \(-0.290069\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.7332 | − | 45.3441i | 0.585592 | − | 1.80227i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.08539 | + | 15.6512i | 0.201808 | + | 0.621100i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.746236 | + | 2.29668i | 0.0295669 | + | 0.0909977i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 54.5653 | − | 39.6440i | 2.15857 | − | 1.56829i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.58143 | + | 4.78169i | 0.259951 | + | 0.188865i | 0.710125 | − | 0.704075i | \(-0.248638\pi\) |
−0.450175 | + | 0.892941i | \(0.648638\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.51145 | − | 20.0402i | 0.256787 | − | 0.790308i | −0.736686 | − | 0.676235i | \(-0.763610\pi\) |
0.993472 | − | 0.114073i | \(-0.0363897\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.3488 | − | 8.24537i | 0.446858 | − | 0.324661i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.0147 | 0.629604 | 0.314802 | − | 0.949157i | \(-0.398062\pi\) | ||||
0.314802 | + | 0.949157i | \(0.398062\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.589472 | + | 1.81421i | 0.0231388 | + | 0.0712139i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.92064 | − | 2.84851i | −0.153662 | − | 0.111642i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22.5776 | −0.883529 | −0.441765 | − | 0.897131i | \(-0.645647\pi\) | ||||
−0.441765 | + | 0.897131i | \(0.645647\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.98086 | 0.0773985 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 66.5293 | 2.59555 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20.7103 | −0.806760 | −0.403380 | − | 0.915033i | \(-0.632165\pi\) | ||||
−0.403380 | + | 0.915033i | \(0.632165\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.8505 | + | 14.4222i | 0.772095 | + | 0.560960i | 0.902596 | − | 0.430488i | \(-0.141659\pi\) |
−0.130501 | + | 0.991448i | \(0.541659\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.51802 | + | 16.9827i | 0.214302 | + | 0.659555i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.73005 | −0.183424 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.50825 | − | 6.18161i | 0.329441 | − | 0.239353i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.15831 | − | 9.72027i | 0.122107 | − | 0.375807i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.737639 | + | 0.535926i | 0.0284762 | + | 0.0206892i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.1606 | − | 11.0148i | 0.584397 | − | 0.424590i | −0.255909 | − | 0.966701i | \(-0.582375\pi\) |
0.840307 | + | 0.542111i | \(0.182375\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −8.20861 | − | 25.2635i | −0.315950 | − | 0.972393i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.89816 | − | 18.1527i | −0.226685 | − | 0.697664i | −0.998116 | − | 0.0613518i | \(-0.980459\pi\) |
0.771431 | − | 0.636313i | \(-0.219541\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.69899 | + | 5.22895i | −0.0652013 | + | 0.200669i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.779236 | − | 2.39824i | −0.0298604 | − | 0.0919008i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 40.6570 | 1.55570 | 0.777848 | − | 0.628453i | \(-0.216311\pi\) | ||||
0.777848 | + | 0.628453i | \(0.216311\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.2151 | + | 14.6872i | 0.772381 | + | 0.561168i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 21.6752 | − | 15.7480i | 0.826962 | − | 0.600823i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 18.4352 | − | 13.3940i | 0.702327 | − | 0.510270i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.0326 | − | 33.9549i | 0.419700 | − | 1.29170i | −0.488278 | − | 0.872688i | \(-0.662375\pi\) |
0.907979 | − | 0.419017i | \(-0.137625\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.16193 | + | 0.844193i | 0.0441382 | + | 0.0320682i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.15809 | − | 18.9527i | 0.233590 | − | 0.718915i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.94510 | − | 15.9975i | −0.149431 | − | 0.605948i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.47042 | − | 22.9916i | 0.282557 | − | 0.869621i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.7397 | − | 14.3417i | −0.745558 | − | 0.541679i | 0.148889 | − | 0.988854i | \(-0.452430\pi\) |
−0.894447 | + | 0.447175i | \(0.852430\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.13502 | − | 12.7263i | 0.155955 | − | 0.479981i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −33.5593 | + | 24.3823i | −1.26392 | + | 0.918289i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15.8295 | − | 11.5008i | 0.595330 | − | 0.432533i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.42178 | + | 1.03298i | 0.0533960 | + | 0.0387945i | 0.614163 | − | 0.789179i | \(-0.289494\pi\) |
−0.560767 | + | 0.827974i | \(0.689494\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 50.7242 | 1.90231 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.910915 | − | 2.80351i | −0.0341140 | − | 0.104992i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.614753 | + | 1.89201i | −0.0229904 | + | 0.0707573i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 21.8643 | + | 67.2913i | 0.816536 | + | 2.51304i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.17997 | + | 12.8646i | 0.155886 | + | 0.479769i | 0.998250 | − | 0.0591412i | \(-0.0188362\pi\) |
−0.842363 | + | 0.538910i | \(0.818836\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.34273 | + | 0.975548i | −0.0500058 | + | 0.0363313i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 15.0110 | + | 10.9061i | 0.558266 | + | 0.405604i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.61287 | − | 23.4300i | 0.282735 | − | 0.870169i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.0062 | + | 18.1680i | −0.927427 | + | 0.673815i | −0.945361 | − | 0.326024i | \(-0.894291\pi\) |
0.0179346 | + | 0.999839i | \(0.494291\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −40.8398 | −1.51259 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.28717 | + | 3.96149i | 0.0476076 | + | 0.146521i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 39.6390 | + | 28.7994i | 1.46410 | + | 1.06373i | 0.982271 | + | 0.187467i | \(0.0600277\pi\) |
0.481830 | + | 0.876265i | \(0.339972\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8.66600 | 0.319650 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.36303 | −0.0870435 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −44.3312 | −1.63075 | −0.815375 | − | 0.578933i | \(-0.803469\pi\) | ||||
−0.815375 | + | 0.578933i | \(0.803469\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.8842 | 0.399841 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23.1410 | − | 16.8129i | −0.848960 | − | 0.616806i | 0.0758989 | − | 0.997116i | \(-0.475817\pi\) |
−0.924859 | + | 0.380310i | \(0.875817\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.89171 | − | 27.3659i | −0.325767 | − | 1.00261i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 27.6667 | 1.01227 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.90064 | − | 6.46669i | 0.325222 | − | 0.236288i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.1383 | + | 49.6686i | −0.588895 | + | 1.81243i | −0.00586589 | + | 0.999983i | \(0.501867\pi\) |
−0.583030 | + | 0.812451i | \(0.698133\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −67.1373 | − | 48.7781i | −2.44662 | − | 1.77757i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.3153 | − | 10.4007i | 0.520987 | − | 0.378519i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.37161 | + | 13.4544i | 0.158889 | + | 0.489009i | 0.998534 | − | 0.0541258i | \(-0.0172372\pi\) |
−0.839645 | + | 0.543135i | \(0.817237\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.424002 | + | 1.30494i | 0.0153903 | + | 0.0473664i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.19461 | + | 12.9097i | −0.152055 | + | 0.467976i | −0.997851 | − | 0.0655305i | \(-0.979126\pi\) |
0.845796 | + | 0.533507i | \(0.179126\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.191791 | + | 0.590271i | 0.00694329 | + | 0.0213693i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 40.8000 | 1.47513 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −13.6426 | − | 9.91196i | −0.492607 | − | 0.357900i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.6709 | + | 25.1899i | −1.25026 | + | 0.908370i | −0.998237 | − | 0.0593496i | \(-0.981097\pi\) |
−0.252027 | + | 0.967720i | \(0.581097\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −32.5646 | + | 23.6596i | −1.17278 | + | 0.852078i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.95241 | + | 24.4750i | −0.286028 | + | 0.880305i | 0.700060 | + | 0.714084i | \(0.253156\pi\) |
−0.986089 | + | 0.166221i | \(0.946844\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.58646 | − | 4.05880i | −0.200671 | − | 0.145796i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.57583 | + | 23.3160i | −0.271781 | + | 0.836457i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −10.0168 | − | 0.726244i | −0.358889 | − | 0.0260204i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.08289 | + | 3.33279i | −0.0387489 | + | 0.119257i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 31.5788 | + | 22.9434i | 1.12854 | + | 0.819929i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.86272 | + | 27.2766i | −0.316324 | + | 0.973545i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23.2716 | + | 16.9078i | −0.829544 | + | 0.602699i | −0.919430 | − | 0.393253i | \(-0.871350\pi\) |
0.0898862 | + | 0.995952i | \(0.471350\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 52.0108 | − | 37.7881i | 1.85163 | − | 1.34529i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.20554 | − | 0.875874i | −0.0428639 | − | 0.0311425i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.06022 | −0.286227 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −25.2696 | − | 77.7718i | −0.896220 | − | 2.75828i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.07312 | + | 24.8465i | −0.285965 | + | 0.880108i | 0.700143 | + | 0.714002i | \(0.253119\pi\) |
−0.986108 | + | 0.166106i | \(0.946881\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.80627 | − | 11.7145i | −0.134656 | − | 0.414429i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −19.5886 | − | 60.2874i | −0.692128 | − | 2.13015i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.79650 | + | 2.03177i | −0.0986862 | + | 0.0716997i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.26455 | + | 3.09837i | 0.150305 | + | 0.109203i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.10081 | + | 3.38795i | −0.0387504 | + | 0.119262i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.47988 | − | 5.43445i | 0.262978 | − | 0.191065i | −0.448481 | − | 0.893793i | \(-0.648035\pi\) |
0.711459 | + | 0.702728i | \(0.248035\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.59256 | −0.231496 | −0.115748 | − | 0.993279i | \(-0.536927\pi\) | ||||
−0.115748 | + | 0.993279i | \(0.536927\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.98546 | + | 30.7321i | 0.350205 | + | 1.07782i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 52.5540 | + | 38.1827i | 1.84089 | + | 1.33748i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.53891 | 0.0888253 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −12.6965 | −0.443651 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.4153 | −0.817199 | −0.408600 | − | 0.912714i | \(-0.633983\pi\) | ||||
−0.408600 | + | 0.912714i | \(0.633983\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −39.6248 | −1.38123 | −0.690616 | − | 0.723222i | \(-0.742661\pi\) | ||||
−0.690616 | + | 0.723222i | \(0.742661\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.60032 | + | 1.88924i | 0.0905314 | + | 0.0657749i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.2480 | − | 43.8508i | −0.495451 | − | 1.52484i | −0.816253 | − | 0.577694i | \(-0.803953\pi\) |
0.320803 | − | 0.947146i | \(-0.396047\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 43.9088 | 1.52502 | 0.762508 | − | 0.646979i | \(-0.223968\pi\) | ||||
0.762508 | + | 0.646979i | \(0.223968\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.51576 | − | 4.00743i | 0.191339 | − | 0.139016i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.795174 | + | 2.44729i | −0.0275511 | + | 0.0847937i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.84141 | − | 1.33786i | −0.0637247 | − | 0.0462987i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.85133 | − | 6.43087i | 0.305947 | − | 0.222283i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.3969 | + | 41.2315i | 0.462513 | + | 1.42347i | 0.862083 | + | 0.506766i | \(0.169159\pi\) |
−0.399570 | + | 0.916703i | \(0.630841\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.22514 | + | 6.84829i | 0.0767291 | + | 0.236148i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8.63738 | + | 26.5831i | −0.297487 | + | 0.915571i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.68030 | + | 20.5598i | 0.229809 | + | 0.707280i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.9254 | 0.375400 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 22.7101 | + | 16.4999i | 0.779409 | + | 0.566274i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.0643 | + | 8.76523i | −0.413559 | + | 0.300468i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32.8044 | − | 23.8338i | 1.12320 | − | 0.816054i | 0.138511 | − | 0.990361i | \(-0.455769\pi\) |
0.984691 | + | 0.174307i | \(0.0557685\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.68490 | − | 23.6517i | 0.262818 | − | 0.808871i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.0876652 | + | 0.0636925i | 0.00299459 | + | 0.00217569i | 0.589282 | − | 0.807928i | \(-0.299411\pi\) |
−0.586287 | + | 0.810103i | \(0.699411\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.23313 | + | 6.87287i | −0.0761934 | + | 0.234499i | −0.981898 | − | 0.189410i | \(-0.939342\pi\) |
0.905705 | + | 0.423909i | \(0.139342\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18.3519 | + | 1.33056i | 0.625431 | + | 0.0453454i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.7514 | − | 45.4002i | 0.502145 | − | 1.54544i | −0.303374 | − | 0.952872i | \(-0.598113\pi\) |
0.805518 | − | 0.592571i | \(-0.201887\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −62.7900 | − | 45.6196i | −2.13492 | − | 1.55111i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.21600 | − | 28.3639i | 0.312992 | − | 0.963290i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.13214 | + | 1.54909i | −0.0723280 | + | 0.0525494i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.9001 | − | 12.2786i | 0.572636 | − | 0.416045i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −23.3860 | − | 16.9909i | −0.791496 | − | 0.575056i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.73054 | −0.0923092 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.0297 | + | 43.1791i | 0.473750 | + | 1.45805i | 0.847636 | + | 0.530579i | \(0.178025\pi\) |
−0.373885 | + | 0.927475i | \(0.621975\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −27.2385 | + | 83.8316i | −0.918733 | + | 2.82757i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.03494 | + | 6.26292i | 0.0685590 | + | 0.211003i | 0.979466 | − | 0.201608i | \(-0.0646168\pi\) |
−0.910907 | + | 0.412611i | \(0.864617\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.52632 | + | 4.69754i | 0.0513649 | + | 0.158085i | 0.973449 | − | 0.228905i | \(-0.0735147\pi\) |
−0.922084 | + | 0.386990i | \(0.873515\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −48.9580 | + | 35.5700i | −1.64570 | + | 1.19567i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 29.7264 | + | 21.5975i | 0.998115 | + | 0.725173i | 0.961683 | − | 0.274163i | \(-0.0884009\pi\) |
0.0364316 | + | 0.999336i | \(0.488401\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.68629 | − | 5.18988i | 0.0565565 | − | 0.174063i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.634215 | + | 0.460784i | −0.0212470 | + | 0.0154368i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.50779 | −0.251239 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.3287 | − | 31.7886i | −0.345252 | − | 1.06258i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.81303 | − | 7.12958i | −0.327648 | − | 0.238050i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.1468 | 0.338415 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.2816 | 0.808937 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.65158 | −0.154795 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11.2116 | 0.372688 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23.3614 | + | 16.9730i | 0.775702 | + | 0.563581i | 0.903686 | − | 0.428196i | \(-0.140851\pi\) |
−0.127984 | + | 0.991776i | \(0.540851\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 31.7894 | + | 97.8377i | 1.05439 | + | 3.24507i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.2256 | −1.13395 | −0.566973 | − | 0.823736i | \(-0.691886\pi\) | ||||
−0.566973 | + | 0.823736i | \(0.691886\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.16294 | + | 0.844927i | −0.0384878 | + | 0.0279630i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.93828 | + | 27.5092i | −0.295490 | + | 0.909426i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.531398 | − | 0.386083i | −0.0175483 | − | 0.0127496i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.24912 | − | 3.81371i | 0.173152 | − | 0.125803i | −0.497834 | − | 0.867273i | \(-0.665871\pi\) |
0.670986 | + | 0.741470i | \(0.265871\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −14.1812 | − | 43.6451i | −0.467285 | − | 1.43816i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.57293 | − | 29.4625i | −0.315097 | − | 0.969768i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.7947 | + | 33.2226i | −0.354927 | + | 1.09235i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.69651 | − | 8.29901i | −0.0885650 | − | 0.272575i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 42.4963 | 1.39426 | 0.697129 | − | 0.716946i | \(-0.254461\pi\) | ||||
0.697129 | + | 0.716946i | \(0.254461\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.26892 | + | 0.921921i | 0.0415870 | + | 0.0302147i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 36.7142 | − | 26.6744i | 1.20197 | − | 0.873280i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.71499 | + | 1.24601i | −0.0560862 | + | 0.0407490i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.42291 | + | 10.5346i | −0.111822 | + | 0.344152i | −0.991271 | − | 0.131841i | \(-0.957911\pi\) |
0.879449 | + | 0.475993i | \(0.157911\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17.3983 | − | 12.6406i | −0.567773 | − | 0.412511i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.594556 | − | 1.82985i | 0.0193820 | − | 0.0596516i | −0.940898 | − | 0.338691i | \(-0.890016\pi\) |
0.960280 | + | 0.279039i | \(0.0900159\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.55527 | + | 7.21617i | 0.278598 | + | 0.234991i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.04579 | + | 18.6070i | −0.196670 | + | 0.605287i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.94810 | + | 5.04809i | 0.225783 | + | 0.164041i | 0.694926 | − | 0.719081i | \(-0.255437\pi\) |
−0.469143 | + | 0.883122i | \(0.655437\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.44277 | − | 29.0618i | 0.306525 | − | 0.943387i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23.3359 | + | 16.9545i | −0.756718 | + | 0.549788i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 37.8247 | − | 27.4813i | 1.22526 | − | 0.890206i | 0.228738 | − | 0.973488i | \(-0.426540\pi\) |
0.996526 | + | 0.0832818i | \(0.0265402\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.38593 | − | 6.81928i | −0.303722 | − | 0.220667i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.72302 | −0.152673 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.56042 | − | 7.88015i | −0.0826801 | − | 0.254463i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.70066 | + | 26.7779i | −0.280666 | + | 0.863802i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 17.8746 | + | 55.0123i | 0.576000 | + | 1.77275i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −18.2160 | − | 56.0632i | −0.586395 | − | 1.80474i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.5598 | − | 29.4684i | 1.30432 | − | 0.947640i | 0.304327 | − | 0.952568i | \(-0.401568\pi\) |
0.999988 | + | 0.00492704i | \(0.00156833\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.38297 | + | 6.81712i | 0.301424 | + | 0.218998i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.77004 | − | 20.8360i | 0.217261 | − | 0.668660i | −0.781724 | − | 0.623624i | \(-0.785660\pi\) |
0.998985 | − | 0.0450363i | \(-0.0143403\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.34602 | + | 3.88411i | −0.171385 | + | 0.124519i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −28.4138 | −0.909969 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −12.7349 | − | 39.1939i | −0.407424 | − | 1.25392i | −0.918854 | − | 0.394598i | \(-0.870884\pi\) |
0.511430 | − | 0.859325i | \(-0.329116\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.66453 | + | 1.93590i | 0.0851589 | + | 0.0618716i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.26313 | −0.104184 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 37.1120 | 1.18369 | 0.591845 | − | 0.806052i | \(-0.298400\pi\) | ||||
0.591845 | + | 0.806052i | \(0.298400\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −52.4741 | −1.67196 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 13.7551 | 0.437830 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.28905 | − | 1.66309i | −0.0727875 | − | 0.0528832i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.7727 | + | 39.3104i | 0.405739 | + | 1.24874i | 0.920276 | + | 0.391269i | \(0.127964\pi\) |
−0.514537 | + | 0.857468i | \(0.672036\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −71.5989 | −2.27212 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 23.2213 | − | 16.8713i | 0.736166 | − | 0.534856i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.4313 | + | 50.5702i | −0.520383 | + | 1.60158i | 0.252885 | + | 0.967496i | \(0.418621\pi\) |
−0.773268 | + | 0.634079i | \(0.781379\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −44.7773 | − | 32.5326i | −1.41669 | − | 1.02929i |
(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 | 1148.2.n.e.57.1 | ✓ | 24 | |
41.18 | even | 5 | inner | 1148.2.n.e.141.1 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.n.e.57.1 | ✓ | 24 | 1.1 | even | 1 | trivial | |
1148.2.n.e.141.1 | yes | 24 | 41.18 | even | 5 | inner |