Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [420,2,Mod(53,420)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(420, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 6, 9, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("420.53");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 420.bv (of order \(12\), 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: | \(3.35371688489\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 317.11 | ||
Character | \(\chi\) | \(=\) | 420.317 |
Dual form | 420.2.bv.c.53.11 |
$q$-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 \(\left(\mathbb{Z}/420\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(241\) | \(281\) | \(337\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||||
\(3\) | 1.44552 | − | 0.954190i | 0.834570 | − | 0.550902i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.17211 | + | 0.530994i | −0.971395 | + | 0.237468i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.78762 | + | 1.95049i | 0.675657 | + | 0.737216i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.17904 | − | 2.75860i | 0.393014 | − | 0.919532i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.07693 | − | 1.19911i | 0.626217 | − | 0.361546i | −0.153069 | − | 0.988216i | \(-0.548916\pi\) |
0.779285 | + | 0.626669i | \(0.215582\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.37848 | − | 3.37848i | 0.937023 | − | 0.937023i | −0.0611083 | − | 0.998131i | \(-0.519464\pi\) |
0.998131 | + | 0.0611083i | \(0.0194635\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.63315 | + | 2.84016i | −0.679876 | + | 0.733327i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.74353 | + | 1.27103i | 1.15048 | + | 0.308269i | 0.783156 | − | 0.621826i | \(-0.213609\pi\) |
0.367320 | + | 0.930095i | \(0.380275\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.151250 | + | 0.0873244i | 0.0346992 | + | 0.0200336i | 0.517249 | − | 0.855835i | \(-0.326956\pi\) |
−0.482550 | + | 0.875868i | \(0.660289\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.44518 | + | 1.11374i | 0.970017 | + | 0.243038i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.21053 | + | 0.324361i | −0.252413 | + | 0.0676339i | −0.382807 | − | 0.923828i | \(-0.625043\pi\) |
0.130394 | + | 0.991462i | \(0.458376\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.43609 | − | 2.30675i | 0.887218 | − | 0.461350i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.927900 | − | 5.11263i | −0.178574 | − | 0.983926i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.65176 | −0.863811 | −0.431905 | − | 0.901919i | \(-0.642159\pi\) | ||||
−0.431905 | + | 0.901919i | \(0.642159\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.26323 | + | 2.18799i | 0.226884 | + | 0.392974i | 0.956883 | − | 0.290474i | \(-0.0938130\pi\) |
−0.729999 | + | 0.683448i | \(0.760480\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.85805 | − | 3.71512i | 0.323445 | − | 0.646720i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.91860 | − | 3.28746i | −0.831395 | − | 0.555682i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.9974 | + | 2.94674i | −1.80796 | + | 0.484441i | −0.995174 | − | 0.0981254i | \(-0.968715\pi\) |
−0.812783 | + | 0.582566i | \(0.802049\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.65994 | − | 8.10737i | 0.265803 | − | 1.29822i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.78650i | 0.279005i | 0.990222 | + | 0.139503i | \(0.0445504\pi\) | ||||
−0.990222 | + | 0.139503i | \(0.955450\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.46081 | + | 2.46081i | −0.375271 | + | 0.375271i | −0.869393 | − | 0.494122i | \(-0.835490\pi\) |
0.494122 | + | 0.869393i | \(0.335490\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.09621 | + | 6.61803i | −0.163413 | + | 0.986558i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.07195 | − | 7.73263i | −0.302225 | − | 1.12792i | −0.935308 | − | 0.353835i | \(-0.884877\pi\) |
0.633082 | − | 0.774084i | \(-0.281789\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.608831 | + | 6.97347i | −0.0869758 | + | 0.996210i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.06966 | − | 2.68894i | 1.12998 | − | 0.376527i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.92005 | + | 10.8978i | −0.401100 | + | 1.49692i | 0.410037 | + | 0.912069i | \(0.365516\pi\) |
−0.811137 | + | 0.584856i | \(0.801151\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.87458 | + | 3.70744i | −0.522448 | + | 0.499911i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.301959 | − | 0.0180926i | 0.0399954 | − | 0.00239642i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.06606 | + | 3.57852i | 0.268978 | + | 0.465884i | 0.968598 | − | 0.248631i | \(-0.0799807\pi\) |
−0.699620 | + | 0.714515i | \(0.746647\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.47828 | − | 6.02455i | 0.445348 | − | 0.771365i | −0.552729 | − | 0.833361i | \(-0.686413\pi\) |
0.998076 | + | 0.0619964i | \(0.0197467\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.48830 | − | 2.63161i | 0.943437 | − | 0.331552i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.54447 | + | 9.13238i | −0.687707 | + | 1.13273i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.12231 | − | 11.6526i | 0.381451 | − | 1.42359i | −0.462235 | − | 0.886757i | \(-0.652953\pi\) |
0.843686 | − | 0.536837i | \(-0.180381\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.44034 | + | 1.62395i | −0.173397 | + | 0.195500i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.9938i | 1.89811i | 0.315111 | + | 0.949055i | \(0.397958\pi\) | ||||
−0.315111 | + | 0.949055i | \(0.602042\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.23288 | − | 1.40215i | −0.612462 | − | 0.164109i | −0.0607633 | − | 0.998152i | \(-0.519353\pi\) |
−0.551699 | + | 0.834043i | \(0.686020\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.21137 | − | 7.56732i | 0.486287 | − | 0.873799i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.05161 | + | 1.90747i | 0.689645 | + | 0.217376i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.52266 | + | 3.18851i | 0.621348 | + | 0.358735i | 0.777394 | − | 0.629014i | \(-0.216541\pi\) |
−0.156046 | + | 0.987750i | \(0.549875\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.21972 | − | 6.50501i | −0.691080 | − | 0.722778i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.05025 | − | 3.05025i | −0.334808 | − | 0.334808i | 0.519601 | − | 0.854409i | \(-0.326081\pi\) |
−0.854409 | + | 0.519601i | \(0.826081\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.9784 | − | 0.242015i | −1.19077 | − | 0.0262502i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.72421 | + | 4.43867i | −0.720910 | + | 0.475875i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.58127 | + | 4.47089i | −0.273614 | + | 0.473914i | −0.969785 | − | 0.243963i | \(-0.921553\pi\) |
0.696170 | + | 0.717877i | \(0.254886\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.6291 | + | 0.550258i | 1.32389 | + | 0.0576827i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.91378 | + | 1.95741i | 0.405840 | + | 0.202974i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.374900 | − | 0.109365i | −0.0384640 | − | 0.0112206i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.70738 | − | 2.70738i | −0.274893 | − | 0.274893i | 0.556173 | − | 0.831066i | \(-0.312269\pi\) |
−0.831066 | + | 0.556173i | \(0.812269\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.859088 | − | 7.14321i | −0.0863416 | − | 0.717919i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.03830 | − | 0.599462i | 0.103315 | − | 0.0596487i | −0.447452 | − | 0.894308i | \(-0.647669\pi\) |
0.550767 | + | 0.834659i | \(0.314335\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.39827 | − | 5.21841i | −0.137775 | − | 0.514185i | −0.999971 | − | 0.00760935i | \(-0.997578\pi\) |
0.862196 | − | 0.506575i | \(-0.169089\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −10.2468 | − | 0.0587995i | −0.999984 | − | 0.00573824i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.56642 | − | 9.57801i | −0.248105 | − | 0.925941i | −0.971797 | − | 0.235818i | \(-0.924223\pi\) |
0.723692 | − | 0.690123i | \(-0.242444\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.1440 | + | 7.58867i | −1.25896 | + | 0.726863i | −0.972873 | − | 0.231340i | \(-0.925689\pi\) |
−0.286090 | + | 0.958203i | \(0.592356\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −13.0852 | + | 14.7531i | −1.24199 | + | 1.40031i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.3407 | + | 11.3407i | 1.06685 | + | 1.06685i | 0.997600 | + | 0.0692464i | \(0.0220595\pi\) |
0.0692464 | + | 0.997600i | \(0.477941\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.45717 | − | 1.34733i | 0.229132 | − | 0.125639i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.33650 | − | 13.3033i | −0.493360 | − | 1.22989i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.00051 | + | 11.5243i | 0.550066 | + | 1.05643i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.62425 | + | 4.54534i | −0.238569 | + | 0.413213i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.70467 | + | 2.58242i | 0.153705 | + | 0.232849i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.41079 | + | 7.36605i | −0.752284 | + | 0.658839i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.7150 | − | 14.7150i | −1.30574 | − | 1.30574i | −0.924457 | − | 0.381287i | \(-0.875481\pi\) |
−0.381287 | − | 0.924457i | \(-0.624519\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.20907 | + | 5.90523i | −0.106452 | + | 0.519927i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.6665 | − | 6.73566i | −1.01931 | − | 0.588497i | −0.105404 | − | 0.994429i | \(-0.533614\pi\) |
−0.913903 | + | 0.405932i | \(0.866947\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.100053 | + | 0.451115i | 0.00867565 | + | 0.0391166i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.73027 | + | 10.6125i | 0.407117 | + | 0.913376i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.8468 | − | 3.44229i | −1.09758 | − | 0.294095i | −0.335799 | − | 0.941934i | \(-0.609006\pi\) |
−0.761777 | + | 0.647839i | \(0.775673\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.58221i | 0.388658i | 0.980936 | + | 0.194329i | \(0.0622530\pi\) | ||||
−0.980936 | + | 0.194329i | \(0.937747\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.3734 | − | 9.20061i | −0.873601 | − | 0.774832i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.96567 | − | 11.0680i | 0.248002 | − | 0.925556i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.1041 | − | 2.47006i | 0.839102 | − | 0.205127i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.77394 | + | 10.6612i | 0.476227 | + | 0.879322i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.58754 | + | 6.21379i | −0.293902 | + | 0.509054i | −0.974729 | − | 0.223391i | \(-0.928287\pi\) |
0.680827 | + | 0.732445i | \(0.261621\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.15084 | + | 3.72536i | 0.175033 | + | 0.303166i | 0.940173 | − | 0.340698i | \(-0.110663\pi\) |
−0.765140 | + | 0.643864i | \(0.777330\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 9.09907 | − | 11.5869i | 0.735616 | − | 0.936745i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.90569 | − | 4.08177i | −0.313712 | − | 0.327855i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.30081 | + | 8.58676i | −0.183625 | + | 0.685298i | 0.811296 | + | 0.584636i | \(0.198763\pi\) |
−0.994921 | + | 0.100662i | \(0.967904\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.17757 | + | 18.5392i | 0.489913 | + | 1.47026i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.79663 | − | 1.78130i | −0.220406 | − | 0.140386i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.53272 | − | 5.72018i | −0.120052 | − | 0.448039i | 0.879563 | − | 0.475782i | \(-0.157835\pi\) |
−0.999615 | + | 0.0277426i | \(0.991168\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.06317 | + | 9.05625i | −0.160618 | + | 0.705028i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.1499 | − | 16.1499i | 1.24972 | − | 1.24972i | 0.293876 | − | 0.955844i | \(-0.405055\pi\) |
0.955844 | − | 0.293876i | \(-0.0949452\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 9.82831i | − | 0.756024i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.419223 | − | 0.314279i | 0.0320588 | − | 0.0240335i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 24.8433 | − | 6.65674i | 1.88880 | − | 0.506102i | 0.890064 | − | 0.455836i | \(-0.150660\pi\) |
0.998736 | − | 0.0502667i | \(-0.0160071\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.4293 | + | 4.52896i | 0.939570 | + | 0.342357i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.40112 | + | 3.20140i | 0.481137 | + | 0.240632i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.95927 | − | 17.2500i | −0.744391 | − | 1.28932i | −0.950479 | − | 0.310789i | \(-0.899407\pi\) |
0.206088 | − | 0.978533i | \(-0.433927\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.4609 | 1.22353 | 0.611765 | − | 0.791040i | \(-0.290460\pi\) | ||||
0.611765 | + | 0.791040i | \(0.290460\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.720658 | − | 12.0275i | −0.0532726 | − | 0.889101i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 22.3228 | − | 12.2402i | 1.64120 | − | 0.899915i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.3761 | − | 3.04821i | 0.831900 | − | 0.222907i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.31341 | − | 10.9493i | 0.604712 | − | 0.796445i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.56368 | + | 0.902790i | 0.113144 | + | 0.0653236i | 0.555504 | − | 0.831514i | \(-0.312525\pi\) |
−0.442360 | + | 0.896837i | \(0.645859\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.16003 | − | 1.38263i | −0.371427 | − | 0.0995236i | 0.0682768 | − | 0.997666i | \(-0.478250\pi\) |
−0.439704 | + | 0.898143i | \(0.644917\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.699398 | + | 18.4915i | 0.0500849 | + | 1.32420i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.1248 | + | 15.1248i | −1.07760 | + | 1.07760i | −0.0808739 | + | 0.996724i | \(0.525771\pi\) |
−0.996724 | + | 0.0808739i | \(0.974229\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.10884 | − | 1.21754i | 0.149491 | − | 0.0863090i | −0.423388 | − | 0.905948i | \(-0.639159\pi\) |
0.572880 | + | 0.819639i | \(0.305826\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.60546 | − | 19.8233i | −0.465913 | − | 1.39823i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.31558 | − | 9.07322i | −0.583640 | − | 0.636815i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.948624 | − | 3.88048i | −0.0662547 | − | 0.271024i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.532487 | + | 3.72180i | −0.0370104 | + | 0.258683i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.418847 | 0.0289723 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.8080 | 0.950581 | 0.475291 | − | 0.879829i | \(-0.342343\pi\) | ||||
0.475291 | + | 0.879829i | \(0.342343\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 15.2611 | + | 23.1193i | 1.04567 | + | 1.58411i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.03847 | − | 6.65183i | 0.275421 | − | 0.453651i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.00946 | + | 6.37521i | −0.136411 | + | 0.432778i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.90213 | + | 2.96633i | −0.601550 | + | 0.200446i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 20.3201 | − | 11.7318i | 1.36688 | − | 0.789167i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.6103 | + | 17.6103i | −1.17928 | + | 1.17928i | −0.199347 | + | 0.979929i | \(0.563882\pi\) |
−0.979929 | + | 0.199347i | \(0.936118\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.13306 | − | 14.9571i | −0.0755373 | − | 0.997143i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.32132 | + | 1.69379i | 0.419561 | + | 0.112421i | 0.462422 | − | 0.886660i | \(-0.346981\pi\) |
−0.0428611 | + | 0.999081i | \(0.513647\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.8421 | + | 12.0332i | 1.37729 | + | 0.795177i | 0.991832 | − | 0.127550i | \(-0.0407115\pi\) |
0.385454 | + | 0.922727i | \(0.374045\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 10.5678 | − | 3.01711i | 0.695310 | − | 0.198512i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.94292 | + | 0.520604i | −0.127285 | + | 0.0341059i | −0.321899 | − | 0.946774i | \(-0.604321\pi\) |
0.194614 | + | 0.980880i | \(0.437655\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.60648 | + | 15.6959i | 0.561425 | + | 1.02389i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.0256 | − | 0.660622i | 0.716187 | − | 0.0429120i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.1453 | 0.656245 | 0.328123 | − | 0.944635i | \(-0.393584\pi\) | ||||
0.328123 | + | 0.944635i | \(0.393584\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.1599 | + | 19.3295i | 0.718871 | + | 1.24512i | 0.961448 | + | 0.274988i | \(0.0886740\pi\) |
−0.242577 | + | 0.970132i | \(0.577993\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.1977 | − | 3.46831i | −0.974935 | − | 0.222492i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.38043 | − | 15.4704i | −0.152080 | − | 0.988368i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.806020 | − | 0.215973i | 0.0512858 | − | 0.0137420i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.31971 | − | 1.49867i | −0.463868 | − | 0.0949744i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 4.37814i | − | 0.276346i | −0.990408 | − | 0.138173i | \(-0.955877\pi\) | ||
0.990408 | − | 0.138173i | \(-0.0441230\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.12524 | + | 2.12524i | −0.133613 | + | 0.133613i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −16.1003 | + | 10.1256i | −1.00824 | + | 0.634090i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.639388 | + | 2.38623i | 0.0398839 | + | 0.148849i | 0.982996 | − | 0.183625i | \(-0.0587833\pi\) |
−0.943112 | + | 0.332474i | \(0.892117\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −25.4067 | − | 16.1826i | −1.57870 | − | 1.00554i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.48463 | + | 12.8323i | −0.339490 | + | 0.794302i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.0785232 | + | 0.293053i | −0.00484195 | + | 0.0180704i | −0.968305 | − | 0.249773i | \(-0.919644\pi\) |
0.963463 | + | 0.267843i | \(0.0863108\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.556004 | − | 25.2217i | 0.0341551 | − | 1.54935i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.534809 | + | 8.92578i | 0.0327298 | + | 0.546249i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.59823 | − | 14.8926i | −0.524244 | − | 0.908017i | −0.999602 | − | 0.0282241i | \(-0.991015\pi\) |
0.475358 | − | 0.879792i | \(-0.342319\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.92042 | + | 8.52242i | −0.298894 | + | 0.517700i | −0.975883 | − | 0.218293i | \(-0.929951\pi\) |
0.676989 | + | 0.735993i | \(0.263284\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 18.7807 | − | 11.2552i | 1.13666 | − | 0.681196i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.44737 | − | 10.1103i | 0.388791 | − | 0.609676i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.48534 | − | 13.0075i | 0.209414 | − | 0.781543i | −0.778645 | − | 0.627465i | \(-0.784093\pi\) |
0.988059 | − | 0.154078i | \(-0.0492407\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.52518 | − | 0.905026i | 0.450521 | − | 0.0541825i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.4744i | 1.46002i | 0.683436 | + | 0.730011i | \(0.260485\pi\) | ||||
−0.683436 | + | 0.730011i | \(0.739515\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.55682 | − | 1.75689i | −0.389763 | − | 0.104437i | 0.0586154 | − | 0.998281i | \(-0.481331\pi\) |
−0.448378 | + | 0.893844i | \(0.647998\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.646280 | + | 0.199637i | −0.0382823 | + | 0.0118255i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.48456 | + | 3.19359i | −0.205687 | + | 0.188512i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.16315 | + | 3.55830i | 0.362538 | + | 0.209312i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.49693 | − | 1.33021i | −0.380857 | − | 0.0779784i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.9960 | − | 19.9960i | −1.16818 | − | 1.16818i | −0.982637 | − | 0.185541i | \(-0.940596\pi\) |
−0.185541 | − | 0.982637i | \(-0.559404\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.38787 | − | 6.67586i | −0.371916 | − | 0.388684i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −8.05780 | − | 9.50590i | −0.467561 | − | 0.551588i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.99391 | + | 5.18561i | −0.173142 | + | 0.299892i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.19879 | − | 0.400796i | −0.530210 | − | 0.0231015i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.928878 | − | 1.85727i | 0.0533626 | − | 0.106697i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.35618 | + | 14.9329i | −0.249434 | + | 0.855056i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.61961 | − | 5.61961i | −0.320728 | − | 0.320728i | 0.528318 | − | 0.849046i | \(-0.322823\pi\) |
−0.849046 | + | 0.528318i | \(0.822823\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.00057 | − | 6.20908i | −0.398249 | − | 0.353222i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.1827 | − | 15.1166i | 1.48468 | − | 0.857183i | 0.484836 | − | 0.874605i | \(-0.338879\pi\) |
0.999848 | + | 0.0174217i | \(0.00554578\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.77697 | + | 10.3638i | 0.156964 | + | 0.585796i | 0.998929 | + | 0.0462649i | \(0.0147318\pi\) |
−0.841966 | + | 0.539531i | \(0.818602\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −14.8680 | + | 9.69238i | −0.837717 | + | 0.546104i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.75178 | − | 10.2698i | −0.154555 | − | 0.576808i | −0.999143 | − | 0.0413908i | \(-0.986821\pi\) |
0.844588 | − | 0.535417i | \(-0.179846\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.66136 | + | 5.57799i | −0.540933 | + | 0.312308i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.8490 | − | 11.3963i | −0.717164 | − | 0.636081i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.606469 | + | 0.606469i | 0.0337448 | + | 0.0337448i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.19394 | − | 22.7806i | 0.399048 | − | 1.26364i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −11.7588 | + | 23.5114i | −0.650263 | + | 1.30018i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.3786 | − | 17.8643i | 0.627320 | − | 0.984892i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.207490 | + | 0.359384i | −0.0114047 | + | 0.0197535i | −0.871671 | − | 0.490091i | \(-0.836964\pi\) |
0.860267 | + | 0.509844i | \(0.170297\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.83751 | + | 33.8117i | −0.265094 | + | 1.85287i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.594516 | + | 26.9686i | −0.0324819 | + | 1.47345i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.7807 | + | 12.7807i | 0.696210 | + | 0.696210i | 0.963591 | − | 0.267381i | \(-0.0861582\pi\) |
−0.267381 | + | 0.963591i | \(0.586158\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 27.2144 | + | 5.57201i | 1.47809 | + | 0.302630i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.24729 | + | 3.02952i | 0.284156 | + | 0.164058i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.6901 | + | 11.2784i | −0.793188 | + | 0.608976i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.26627 | − | 4.29220i | 0.122012 | − | 0.231084i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 31.3558 | + | 8.40176i | 1.68327 | + | 0.451030i | 0.968639 | − | 0.248473i | \(-0.0799289\pi\) |
0.714629 | + | 0.699504i | \(0.246596\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.1679i | 0.704860i | 0.935838 | + | 0.352430i | \(0.114645\pi\) | ||||
−0.935838 | + | 0.352430i | \(0.885355\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −20.4078 | − | 14.1380i | −1.08929 | − | 0.754633i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.55758 | + | 9.54503i | −0.136126 | + | 0.508031i | 0.863864 | + | 0.503725i | \(0.168037\pi\) |
−0.999991 | + | 0.00430620i | \(0.998629\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.49259 | − | 34.7401i | −0.450740 | − | 1.84381i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 19.6702 | + | 10.9330i | 1.04106 | + | 0.578635i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.54047 | − | 9.59637i | 0.292415 | − | 0.506477i | −0.681966 | − | 0.731384i | \(-0.738875\pi\) |
0.974380 | + | 0.224907i | \(0.0722079\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.48475 | − | 16.4281i | −0.499197 | − | 0.864635i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.543715 | + | 9.07441i | 0.0285376 | + | 0.476283i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.1109 | + | 0.266981i | 0.633913 | + | 0.0139744i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.03172 | + | 7.58247i | −0.106055 | + | 0.395802i | −0.998463 | − | 0.0554277i | \(-0.982348\pi\) |
0.892408 | + | 0.451230i | \(0.149014\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.92825 | + | 2.10636i | 0.256554 | + | 0.109653i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −26.4760 | + | 13.7855i | −1.37456 | + | 0.715710i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.82512 | − | 10.5435i | −0.146279 | − | 0.545921i | −0.999695 | − | 0.0246907i | \(-0.992140\pi\) |
0.853416 | − | 0.521230i | \(-0.174527\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.12933 | + | 18.6732i | −0.264878 | + | 0.964282i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −15.7159 | + | 15.7159i | −0.809410 | + | 0.809410i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.7144i | 0.858560i | 0.903172 | + | 0.429280i | \(0.141233\pi\) | ||||
−0.903172 | + | 0.429280i | \(0.858767\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −35.3117 | − | 7.22988i | −1.80907 | − | 0.370398i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.3453 | − | 3.30792i | 0.630817 | − | 0.169027i | 0.0707764 | − | 0.997492i | \(-0.477452\pi\) |
0.560040 | + | 0.828465i | \(0.310786\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −14.1576 | − | 0.929847i | −0.721538 | − | 0.0473894i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.88699 | + | 9.68980i | 0.197587 | + | 0.492560i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.5206 | − | 30.3465i | −0.888327 | − | 1.53863i | −0.841852 | − | 0.539709i | \(-0.818534\pi\) |
−0.0464754 | − | 0.998919i | \(-0.514799\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.15447 | −0.311245 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −23.2912 | + | 1.39555i | −1.17489 | + | 0.0703962i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.6889 | − | 3.99328i | −0.688763 | − | 0.200924i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.97792 | − | 0.529982i | 0.0992690 | − | 0.0265990i | −0.208843 | − | 0.977949i | \(-0.566970\pi\) |
0.308112 | + | 0.951350i | \(0.400303\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.575077 | + | 0.556625i | 0.0287899 | + | 0.0278661i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.0417 | − | 7.52965i | −0.651273 | − | 0.376013i | 0.137671 | − | 0.990478i | \(-0.456038\pi\) |
−0.788944 | + | 0.614465i | \(0.789372\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.6599 | + | 3.12426i | 0.580820 | + | 0.155630i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 16.9640 | + | 10.8269i | 0.842948 | + | 0.537994i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −19.3073 | + | 19.3073i | −0.957025 | + | 0.957025i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.10578 | + | 4.67987i | −0.400805 | + | 0.231405i | −0.686831 | − | 0.726817i | \(-0.740999\pi\) |
0.286026 | + | 0.958222i | \(0.407666\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −21.8549 | + | 7.28240i | −1.07802 | + | 0.359214i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.28654 | + | 10.4269i | −0.161720 | + | 0.513073i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.24513 | + | 5.00580i | 0.404738 | + | 0.245725i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.37230 | + | 6.62367i | 0.214113 | + | 0.324362i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.7118 | 1.01184 | 0.505919 | − | 0.862581i | \(-0.331153\pi\) | ||||
0.505919 | + | 0.862581i | \(0.331153\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.3198 | 0.892851 | 0.446426 | − | 0.894821i | \(-0.352697\pi\) | ||||
0.446426 | + | 0.894821i | \(0.352697\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −23.7741 | − | 3.40142i | −1.15594 | − | 0.165383i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 23.9747 | − | 5.30376i | 1.16294 | − | 0.257270i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17.9687 | − | 3.98526i | 0.869565 | − | 0.192860i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.27408 | − | 18.8289i | −0.302916 | − | 0.909066i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.725507 | − | 0.418872i | 0.0349464 | − | 0.0201763i | −0.482425 | − | 0.875937i | \(-0.660244\pi\) |
0.517371 | + | 0.855761i | \(0.326911\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.5356 | − | 11.5356i | 0.554366 | − | 0.554366i | −0.373332 | − | 0.927698i | \(-0.621785\pi\) |
0.927698 | + | 0.373332i | \(0.121785\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 12.2488 | − | 13.2118i | 0.587284 | − | 0.633456i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.211418 | − | 0.0566492i | −0.0101135 | − | 0.00270990i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −27.5755 | − | 15.9207i | −1.31611 | − | 0.759855i | −0.333008 | − | 0.942924i | \(-0.608063\pi\) |
−0.983100 | + | 0.183069i | \(0.941397\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.5192 | + | 9.90154i | 0.881865 | + | 0.471502i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −32.0596 | + | 8.59035i | −1.52320 | + | 0.408140i | −0.920793 | − | 0.390051i | \(-0.872457\pi\) |
−0.602405 | + | 0.798191i | \(0.705791\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.23278 | − | 11.0819i | 0.153248 | − | 0.525332i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.743295 | + | 12.4053i | 0.0351566 | + | 0.586752i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 32.3879 | 1.52848 | 0.764239 | − | 0.644933i | \(-0.223115\pi\) | ||||
0.764239 | + | 0.644933i | \(0.223115\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.14222 | + | 3.71044i | 0.100873 | + | 0.174718i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.66378 | + | 3.33277i | 0.313092 | + | 0.156587i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −27.7240 | + | 5.51078i | −1.29972 | + | 0.258350i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.4000 | − | 4.93026i | 0.860716 | − | 0.230628i | 0.198647 | − | 0.980071i | \(-0.436345\pi\) |
0.662069 | + | 0.749443i | \(0.269679\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.09676 | − | 25.4313i | 0.0978685 | − | 1.18703i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 24.9156i | − | 1.16044i | −0.814461 | − | 0.580218i | \(-0.802967\pi\) | ||
0.814461 | − | 0.580218i | \(-0.197033\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.6420 | + | 12.6420i | −0.587524 | + | 0.587524i | −0.936960 | − | 0.349436i | \(-0.886373\pi\) |
0.349436 | + | 0.936960i | \(0.386373\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.54052 | − | 2.17350i | −0.442431 | − | 0.100794i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.14017 | + | 11.7193i | 0.145310 | + | 0.542303i | 0.999741 | + | 0.0227391i | \(0.00723871\pi\) |
−0.854432 | + | 0.519563i | \(0.826095\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 28.3098 | − | 14.7404i | 1.30723 | − | 0.680649i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.86753 | + | 14.6077i | 0.224284 | + | 0.673088i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.16013 | + | 8.06172i | −0.0993229 | + | 0.370678i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.872395 | + | 0.0384821i | 0.0400282 | + | 0.00176568i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 26.6197 | + | 20.9042i | 1.21883 | + | 0.957137i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.14571 | + | 5.44853i | 0.143731 | + | 0.248950i | 0.928899 | − | 0.370333i | \(-0.120757\pi\) |
−0.785168 | + | 0.619283i | \(0.787423\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −27.1989 | + | 47.1100i | −1.24017 | + | 2.14803i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.74228 | + | 0.0936239i | −0.261283 | + | 0.00426004i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.31833 | + | 4.44312i | 0.332308 | + | 0.201752i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.64485 | − | 21.0669i | 0.255793 | − | 0.954632i | −0.711855 | − | 0.702326i | \(-0.752145\pi\) |
0.967648 | − | 0.252305i | \(-0.0811887\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.67371 | − | 6.80612i | −0.347017 | − | 0.307783i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 18.6876i | − | 0.843358i | −0.906745 | − | 0.421679i | \(-0.861441\pi\) | ||
0.906745 | − | 0.421679i | \(-0.138559\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −22.0658 | − | 5.91251i | −0.993793 | − | 0.266286i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.65903 | + | 15.0596i | 0.254355 | + | 0.676880i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −31.1957 | + | 28.5908i | −1.39932 | + | 1.28247i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.45427 | − | 5.45843i | −0.423231 | − | 0.244353i | 0.273228 | − | 0.961949i | \(-0.411909\pi\) |
−0.696459 | + | 0.717597i | \(0.745242\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.93491 | − | 38.7551i | 0.354505 | − | 1.73145i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.52544 | + | 8.52544i | 0.380131 | + | 0.380131i | 0.871149 | − | 0.491018i | \(-0.163375\pi\) |
−0.491018 | + | 0.871149i | \(0.663375\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.93698 | + | 1.85342i | −0.0861946 | + | 0.0824763i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.37807 | − | 14.2070i | −0.416495 | − | 0.630955i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.6925 | + | 28.9123i | −0.739883 | + | 1.28151i | 0.212665 | + | 0.977125i | \(0.431786\pi\) |
−0.952548 | + | 0.304389i | \(0.901548\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.61952 | − | 12.7132i | −0.292831 | − | 0.562398i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.306112 | − | 0.854315i | 0.0135152 | − | 0.0377189i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.80813 | + | 10.5925i | 0.255937 | + | 0.466760i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.5756 | − | 13.5756i | −0.597054 | − | 0.597054i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 29.5596 | − | 33.3276i | 1.29752 | − | 1.46292i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.3052 | + | 8.25910i | −0.626722 | + | 0.361838i | −0.779481 | − | 0.626425i | \(-0.784517\pi\) |
0.152760 | + | 0.988263i | \(0.451184\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.449698 | + | 1.67830i | 0.0196639 | + | 0.0733868i | 0.975061 | − | 0.221939i | \(-0.0712385\pi\) |
−0.955397 | + | 0.295326i | \(0.904572\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 22.2883 | − | 5.31326i | 0.972742 | − | 0.231890i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.21120 | + | 11.9844i | 0.139882 | + | 0.522048i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.5584 | + | 10.7147i | −0.806887 | + | 0.465857i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.3077 | − | 1.48020i | 0.534107 | − | 0.0642352i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.03568 | + | 6.03568i | 0.261434 | + | 0.261434i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.6604 | + | 19.4417i | 0.460889 | + | 0.840538i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −30.8560 | − | 15.4321i | −1.33154 | − | 0.665944i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.09749 | + | 15.2134i | 0.305710 | + | 0.655289i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.62294 | + | 2.81101i | −0.0697756 | + | 0.120855i | −0.898802 | − | 0.438354i | \(-0.855562\pi\) |
0.829027 | + | 0.559209i | \(0.188895\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 23.7945 | − | 15.7068i | 1.02112 | − | 0.674045i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 24.5205 | − | 23.4628i | 1.05034 | − | 1.00503i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.2003 | + | 17.2003i | 0.735434 | + | 0.735434i | 0.971691 | − | 0.236257i | \(-0.0759207\pi\) |
−0.236257 | + | 0.971691i | \(0.575921\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.5183 | − | 16.6984i | −0.534267 | − | 0.712669i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.703580 | − | 0.406212i | −0.0299735 | − | 0.0173052i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.65326 | + | 16.4717i | 0.155352 | + | 0.700450i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 20.5885 | − | 38.9935i | 0.873933 | − | 1.65518i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19.2930 | + | 5.16955i | 0.817472 | + | 0.219041i | 0.643241 | − | 0.765664i | \(-0.277589\pi\) |
0.174231 | + | 0.984705i | \(0.444256\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.6276i | 0.703274i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.5357 | − | 15.2612i | 0.571479 | − | 0.644327i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.69046 | − | 36.1653i | 0.408404 | − | 1.52419i | −0.389285 | − | 0.921117i | \(-0.627278\pi\) |
0.797690 | − | 0.603068i | \(-0.206055\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −30.6551 | − | 18.6114i | −1.28967 | − | 0.782988i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.56946 | − | 23.7600i | 0.0659113 | − | 0.997825i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.83961 | + | 15.3107i | −0.370576 | + | 0.641856i | −0.989654 | − | 0.143473i | \(-0.954173\pi\) |
0.619078 | + | 0.785329i | \(0.287506\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.16309 | + | 15.8709i | 0.383463 | + | 0.664178i | 0.991555 | − | 0.129689i | \(-0.0413980\pi\) |
−0.608092 | + | 0.793867i | \(0.708065\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.12176 | − | 0.187047i | 0.130413 | − | 0.00781401i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.62181 | + | 4.23129i | −0.192743 | + | 0.176457i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.68675 | + | 10.0271i | −0.111851 | + | 0.417433i | −0.999032 | − | 0.0439883i | \(-0.985994\pi\) |
0.887181 | + | 0.461421i | \(0.152660\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.77820 | + | 2.92504i | −0.364810 | + | 0.121560i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.496798 | − | 11.4022i | 0.0206107 | − | 0.473042i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.00294 | + | 26.1353i | 0.290032 | + | 1.08242i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 18.6554 | + | 26.0624i | 0.771306 | + | 1.07755i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16.5786 | − | 16.5786i | 0.684270 | − | 0.684270i | −0.276689 | − | 0.960959i | \(-0.589237\pi\) |
0.960959 | + | 0.276689i | \(0.0892372\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.441244i | 0.0181812i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.43124 | + | 36.2951i | −0.305680 | + | 1.49298i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −13.4136 | + | 3.59418i | −0.550832 | + | 0.147595i | −0.523491 | − | 0.852031i | \(-0.675371\pi\) |
−0.0273412 | + | 0.999626i | \(0.508704\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −19.1531 | − | 21.8458i | −0.785200 | − | 0.895592i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.88660 | − | 3.77220i | 0.0772133 | − | 0.154386i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.15232 | + | 1.99588i | 0.0470827 | + | 0.0815496i | 0.888606 | − | 0.458671i | \(-0.151674\pi\) |
−0.841524 | + | 0.540220i | \(0.818341\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.55165 | −0.308038 | −0.154019 | − | 0.988068i | \(-0.549222\pi\) | ||||
−0.154019 | + | 0.988068i | \(0.549222\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −28.4635 | − | 22.3521i | −1.15913 | − | 0.910249i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.28661 | − | 11.2664i | 0.133620 | − | 0.458045i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −31.7660 | + | 8.51167i | −1.28934 | + | 0.345478i | −0.837411 | − | 0.546574i | \(-0.815932\pi\) |
−0.451932 | + | 0.892053i | \(0.649265\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −20.6779 | − | 5.18085i | −0.837911 | − | 0.209939i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −33.1246 | − | 19.1245i | −1.34008 | − | 0.773695i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.8867 | + | 5.32864i | 0.803218 | + | 0.215222i | 0.636996 | − | 0.770867i | \(-0.280177\pi\) |
0.166222 | + | 0.986088i | \(0.446843\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.07397 | − | 4.70413i | −0.204602 | − | 0.189689i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.0456 | − | 21.0456i | 0.847265 | − | 0.847265i | −0.142526 | − | 0.989791i | \(-0.545522\pi\) |
0.989791 | + | 0.142526i | \(0.0455224\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.1068 | − | 13.9181i | 0.968933 | − | 0.559414i | 0.0700222 | − | 0.997545i | \(-0.477693\pi\) |
0.898911 | + | 0.438132i | \(0.144360\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.78159 | + | 5.88803i | 0.111621 | + | 0.236278i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −13.3348 | + | 2.95751i | −0.534246 | + | 0.118490i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.3578 | − | 20.4659i | 0.574312 | − | 0.818637i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.605451 | − | 0.399660i | 0.0241794 | − | 0.0159609i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −55.9118 | −2.22935 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 43.7136 | 1.74021 | 0.870105 | − | 0.492867i | \(-0.164051\pi\) | ||||
0.870105 | + | 0.492867i | \(0.164051\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 19.9597 | − | 13.1754i | 0.793326 | − | 0.523677i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 39.7761 | + | 24.1489i | 1.57847 | + | 0.958321i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 21.5028 | + | 25.6167i | 0.851974 | + | 1.01497i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 44.1203 | + | 18.8573i | 1.74537 | + | 0.745984i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.97235 | − | 2.29344i | 0.156898 | − | 0.0905854i | −0.419495 | − | 0.907758i | \(-0.637793\pi\) |
0.576394 | + | 0.817172i | \(0.304460\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.3311 | − | 18.3311i | 0.722906 | − | 0.722906i | −0.246290 | − | 0.969196i | \(-0.579212\pi\) |
0.969196 | + | 0.246290i | \(0.0792115\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.509426 | − | 13.4688i | −0.0200586 | − | 0.530333i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −42.1467 | − | 11.2932i | −1.65696 | − | 0.443980i | −0.695408 | − | 0.718615i | \(-0.744776\pi\) |
−0.961549 | + | 0.274635i | \(0.911443\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.58210 | + | 4.95488i | 0.336877 | + | 0.194496i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.17845 | + | 11.1329i | 0.124573 | + | 0.436332i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.0659 | + | 3.76895i | −0.550442 | + | 0.147490i | −0.523312 | − | 0.852141i | \(-0.675304\pi\) |
−0.0271304 | + | 0.999632i | \(0.508637\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 28.9175 | + | 8.43572i | 1.12990 | + | 0.329611i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −10.0377 | + | 12.7822i | −0.391610 | + | 0.498682i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.4487 | 0.757615 | 0.378808 | − | 0.925475i | \(-0.376334\pi\) | ||||
0.378808 | + | 0.925475i | \(0.376334\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.9402 | − | 27.6092i | −0.620001 | − | 1.07387i | −0.989485 | − | 0.144637i | \(-0.953799\pi\) |
0.369483 | − | 0.929237i | \(-0.379535\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 18.1787 | − | 36.3478i | 0.706001 | − | 1.41163i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.456864 | − | 0.926742i | −0.0177164 | − | 0.0359375i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.63111 | − | 1.50885i | 0.218037 | − | 0.0584229i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.65245 | + | 42.2597i | −0.334523 | + | 1.63385i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 16.6834i | − | 0.644055i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.2491 | − | 13.2491i | 0.510715 | − | 0.510715i | −0.404031 | − | 0.914745i | \(-0.632391\pi\) |
0.914745 | + | 0.404031i | \(0.132391\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −15.9098 | − | 20.5397i | −0.612369 | − | 0.790572i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.45368 | + | 9.15724i | 0.0943024 | + | 0.351941i | 0.996913 | − | 0.0785172i | \(-0.0250185\pi\) |
−0.902610 | + | 0.430459i | \(0.858352\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.440955 | − | 10.1205i | 0.0169223 | − | 0.388389i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.7538 | − | 3.58333i | 0.412086 | − | 0.137314i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.869046 | + | 3.24333i | −0.0332531 | + | 0.124102i | −0.980557 | − | 0.196233i | \(-0.937129\pi\) |
0.947304 | + | 0.320336i | \(0.103796\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 29.7325 | + | 0.655444i | 1.13602 | + | 0.0250432i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 41.6096 | − | 2.49314i | 1.58751 | − | 0.0951192i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 26.9526 | + | 46.6833i | 1.02681 | + | 1.77849i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.681637 | − | 1.18063i | 0.0259307 | − | 0.0449133i | −0.852769 | − | 0.522289i | \(-0.825078\pi\) |
0.878700 | + | 0.477375i | \(0.158412\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 12.3970 | − | 14.4450i | 0.470924 | − | 0.548719i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.43313 | − | 9.95305i | −0.0922938 | − | 0.377541i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.27069 | + | 8.47434i | −0.0860086 | + | 0.320989i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.31177 | + | 2.60646i | −0.0874391 | + | 0.0985852i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.8670i | 0.637057i | 0.947913 | + | 0.318528i | \(0.103189\pi\) | ||||
−0.947913 | + | 0.318528i | \(0.896811\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.92068 | − | 0.514644i | −0.0724397 | − | 0.0194102i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 27.4177 | + | 14.4765i | 1.03261 | + | 0.545216i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.02533 | + | 0.953582i | 0.113779 | + | 0.0358631i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.24998 | − | 3.60843i | −0.234723 | − | 0.135517i | 0.378026 | − | 0.925795i | \(-0.376603\pi\) |
−0.612749 | + | 0.790278i | \(0.709936\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15.3073 | − | 11.4754i | 0.574067 | − | 0.430362i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.23888 | − | 2.23888i | −0.0838468 | − | 0.0838468i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.564691 | + | 25.6157i | −0.0211183 | + | 0.957974i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 14.6652 | − | 9.68055i | 0.547683 | − | 0.361527i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.0886 | + | 20.9381i | −0.450829 | + | 0.780858i | −0.998438 | − | 0.0558760i | \(-0.982205\pi\) |
0.547609 | + | 0.836734i | \(0.315538\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.67888 | − | 12.0558i | 0.285977 | − | 0.448983i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 34.5758 | + | 17.2924i | 1.28589 | + | 0.643113i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −20.6356 | + | 10.7305i | −0.766388 | + | 0.398519i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.9329 | + | 20.9329i | 0.776359 | + | 0.776359i | 0.979210 | − | 0.202850i | \(-0.0650205\pi\) |
−0.202850 | + | 0.979210i | \(0.565021\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.2780 | + | 9.48802i | −0.936222 | + | 0.351408i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −14.8007 | + | 8.54519i | −0.547424 | + | 0.316055i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.64570 | + | 17.3380i | 0.171593 | + | 0.640393i | 0.997107 | + | 0.0760117i | \(0.0242186\pi\) |
−0.825514 | + | 0.564381i | \(0.809115\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −18.2027 | − | 20.0914i | −0.671415 | − | 0.741081i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.48801 | − | 27.9456i | −0.275824 | − | 1.02939i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.9418 | + | 11.5134i | −0.733569 | + | 0.423526i | −0.819727 | − | 0.572755i | \(-0.805875\pi\) |
0.0861572 | + | 0.996282i | \(0.472541\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.959038 | − | 1.08129i | 0.0352311 | − | 0.0397221i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.5081 | − | 14.5081i | −0.532251 | − | 0.532251i | 0.388990 | − | 0.921242i | \(-0.372824\pi\) |
−0.921242 | + | 0.388990i | \(0.872824\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.49302 | − | 15.4020i | 0.164612 | − | 0.564285i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12.0108 | + | 4.81804i | −0.439452 | + | 0.176283i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.0940 | − | 22.1276i | 0.514985 | − | 0.808526i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.6139 | − | 27.0440i | 0.569758 | − | 0.986850i | −0.426831 | − | 0.904331i | \(-0.640370\pi\) |
0.996590 | − | 0.0825187i | \(-0.0262964\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.17758 | − | 6.32868i | −0.152239 | − | 0.230630i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.65000 | − | 6.94980i | −0.242018 | − | 0.252929i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.35485 | − | 8.35485i | −0.303662 | − | 0.303662i | 0.538783 | − | 0.842445i | \(-0.318884\pi\) |
−0.842445 | + | 0.538783i | \(0.818884\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.04419 | + | 5.09995i | −0.0379016 | + | 0.185116i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.1307 | + | 9.31307i | 0.584738 | + | 0.337598i | 0.763014 | − | 0.646382i | \(-0.223719\pi\) |
−0.178276 | + | 0.983980i | \(0.557052\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −38.2980 | − | 12.0715i | −1.38648 | − | 0.437018i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −13.6116 | + | 29.9995i | −0.492127 | + | 1.08464i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 19.0701 | + | 5.10982i | 0.688582 | + | 0.184505i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.68431i | 0.241042i | 0.992711 | + | 0.120521i | \(0.0384566\pi\) | ||||
−0.992711 | + | 0.120521i | \(0.961543\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.20116 | + | 2.83924i | 0.115287 | + | 0.102253i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.503766 | − | 1.88008i | 0.0181192 | − | 0.0676217i | −0.956274 | − | 0.292471i | \(-0.905522\pi\) |
0.974393 | + | 0.224850i | \(0.0721891\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.6510 | + | 6.79213i | 0.382594 | + | 0.243981i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −52.1672 | + | 0.850550i | −1.87149 | + | 0.0305133i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.156005 | + | 0.270209i | −0.00558947 | + | 0.00968125i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19.1783 | + | 33.2178i | 0.686254 | + | 1.18863i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.31637 | + | 23.7828i | 0.154255 | + | 0.849926i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.438096 | − | 19.8731i | 0.0156363 | − | 0.709300i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.08117 | − | 33.8914i | 0.323709 | − | 1.20810i | −0.591895 | − | 0.806015i | \(-0.701620\pi\) |
0.915604 | − | 0.402082i | \(-0.131713\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.166121 | + | 0.498539i | 0.00591407 | + | 0.0177485i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.84708 | + | 42.3929i | −0.0656746 | + | 1.50732i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.60255 | − | 32.1052i | −0.305486 | − | 1.14009i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −23.2625 | − | 36.9889i | −0.825037 | − | 1.31186i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.84195 | − | 9.84195i | 0.348620 | − | 0.348620i | −0.510975 | − | 0.859595i | \(-0.670716\pi\) |
0.859595 | + | 0.510975i | \(0.170716\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 39.3135i | − | 1.39081i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.28997 | + | 12.3921i | 0.328245 | + | 0.437852i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.5496 | + | 3.36266i | −0.442867 | + | 0.118666i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.02044 | + | 2.38417i | 0.247438 | + | 0.0840310i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −26.6393 | − | 13.3231i | −0.937746 | − | 0.468997i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.50324 | + | 6.06779i | 0.123167 | + | 0.213332i | 0.921015 | − | 0.389527i | \(-0.127361\pi\) |
−0.797848 | + | 0.602859i | \(0.794028\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −49.1753 | −1.72678 | −0.863390 | − | 0.504538i | \(-0.831663\pi\) | ||||
−0.863390 | + | 0.504538i | \(0.831663\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.01945 | + | 17.0143i | 0.0357538 | + | 0.596718i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.36661 | + | 11.6110i | 0.223013 | + | 0.406715i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.587087 | + | 0.157310i | −0.0205396 | + | 0.00550357i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 16.4082 | − | 34.1900i | 0.573350 | − | 1.19469i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.37009 | − | 3.10042i | −0.187417 | − | 0.108206i | 0.403356 | − | 0.915043i | \(-0.367844\pi\) |
−0.590773 | + | 0.806838i | \(0.701177\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.2275 | − | 3.00839i | −0.391365 | − | 0.104866i | 0.0577701 | − | 0.998330i | \(-0.481601\pi\) |
−0.449135 | + | 0.893464i | \(0.648268\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.327383 | − | 20.7667i | −0.0113980 | − | 0.723003i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −30.1289 | + | 30.1289i | −1.04769 | + | 1.04769i | −0.0488806 | + | 0.998805i | \(0.515565\pi\) |
−0.998805 | + | 0.0488806i | \(0.984435\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.1605 | − | 6.44350i | 0.387619 | − | 0.223792i | −0.293509 | − | 0.955956i | \(-0.594823\pi\) |
0.681128 | + | 0.732164i | \(0.261490\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.37347 | − | 22.1282i | −0.255783 | − | 0.767619i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −11.7515 | + | 32.3050i | −0.407164 | + | 1.11930i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −26.5039 | + | 43.6549i | −0.917204 | + | 1.51074i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.0142 | − | 8.48868i | 0.346142 | − | 0.293412i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.48689 | −0.223952 | −0.111976 | − | 0.993711i | \(-0.535718\pi\) | ||||
−0.111976 | + | 0.993711i | \(0.535718\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.36110 | −0.253831 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 23.3533 | + | 35.3782i | 0.804329 | + | 1.21849i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.21877 | + | 21.3481i | 0.179531 | + | 0.734398i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13.5568 | + | 3.00676i | −0.465818 | + | 0.103313i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −11.1544 | + | 3.71683i | −0.382818 | + | 0.127561i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.3569 | − | 7.13424i | 0.423588 | − | 0.244559i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14.9986 | + | 14.9986i | −0.513542 | + | 0.513542i | −0.915610 | − | 0.402068i | \(-0.868292\pi\) |
0.402068 | + | 0.915610i | \(0.368292\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.743717 | + | 0.905253i | −0.0254346 | + | 0.0309590i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 20.5175 | + | 5.49764i | 0.700864 | + | 0.187796i | 0.591618 | − | 0.806219i | \(-0.298490\pi\) |
0.109246 | + | 0.994015i | \(0.465156\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29.8226 | + | 17.2181i | 1.01753 | + | 0.587474i | 0.913389 | − | 0.407088i | \(-0.133456\pi\) |
0.104146 | + | 0.994562i | \(0.466789\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.98970 | + | 7.94133i | −0.0678089 | + | 0.270640i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 34.2780 | − | 9.18477i | 1.16684 | − | 0.312653i | 0.377144 | − | 0.926155i | \(-0.376906\pi\) |
0.789694 | + | 0.613501i | \(0.210239\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −50.4276 | + | 27.6508i | −1.71459 | + | 0.940155i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 12.3042 | − | 0.737237i | 0.417874 | − | 0.0250379i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15.2935 | 0.518798 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −28.8195 | − | 49.9168i | −0.976512 | − | 1.69137i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −10.6607 | + | 4.27646i | −0.360810 | + | 0.144736i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −29.4027 | − | 3.23748i | −0.993993 | − | 0.109447i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −45.5843 | + | 12.2143i | −1.53927 | + | 0.412446i | −0.926030 | − | 0.377450i | \(-0.876801\pi\) |
−0.613241 | + | 0.789896i | \(0.710134\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −47.9845 | − | 9.82457i | −1.61848 | − | 0.331375i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.3717i | 0.821105i | 0.911837 | + | 0.410552i | \(0.134664\pi\) | ||||
−0.911837 | + | 0.410552i | \(0.865336\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.59214 | − | 7.59214i | 0.255496 | − | 0.255496i | −0.567723 | − | 0.823219i | \(-0.692176\pi\) |
0.823219 | + | 0.567723i | \(0.192176\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −15.6038 | − | 3.55483i | −0.524517 | − | 0.119494i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10.8301 | − | 40.4184i | −0.363638 | − | 1.35712i | −0.869258 | − | 0.494360i | \(-0.835403\pi\) |
0.505619 | − | 0.862757i | \(-0.331264\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.39665 | − | 55.0062i | 0.0803810 | − | 1.84485i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −20.7181 | − | 6.05226i | −0.694083 | − | 0.202758i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.361864 | − | 1.35049i | 0.0121093 | − | 0.0451925i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 30.7922 | + | 32.1804i | 1.02927 | + | 1.07567i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.620304 | + | 10.3527i | 0.0207113 | + | 0.345665i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.87627 | − | 10.1780i | −0.195984 | − | 0.339455i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −27.7027 | + | 47.9825i | −0.922911 | + | 1.59853i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −13.6795 | + | 8.19804i | −0.455224 | + | 0.272814i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −35.7548 | + | 8.74064i | −1.18853 | + | 0.290549i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.06620 | − | 30.1035i | 0.267834 | − | 0.999570i | −0.692659 | − | 0.721265i | \(-0.743561\pi\) |
0.960493 | − | 0.278304i | \(-0.0897724\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.429476 | − | 3.57104i | −0.0142448 | − | 0.118444i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.16590i | 0.104891i | 0.998624 | + | 0.0524454i | \(0.0167016\pi\) | ||||
−0.998624 | + | 0.0524454i | \(0.983298\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.99274 | − | 2.67755i | −0.330711 | − | 0.0886138i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.95190 | + | 25.7424i | 0.262882 | + | 0.851018i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.71743 | − | 34.7962i | −0.254852 | − | 1.14907i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.7512 | + | 11.9807i | 0.684520 | + | 0.395208i | 0.801556 | − | 0.597920i | \(-0.204006\pi\) |
−0.117036 | + | 0.993128i | \(0.537339\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.4854 | − | 2.76107i | −0.444360 | − | 0.0909803i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 54.0346 | + | 54.0346i | 1.77857 | + | 1.77857i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −41.9880 | + | 38.4402i | −1.38056 | + | 1.26391i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −16.0441 | − | 2.29546i | −0.526957 | − | 0.0753929i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.59475 | + | 4.49423i | −0.0851309 | + | 0.147451i | −0.905447 | − | 0.424459i | \(-0.860464\pi\) |
0.820316 | + | 0.571910i | \(0.193798\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.701040 | + | 1.00157i | −0.0229757 | + | 0.0328252i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 23.4235 | − | 46.8346i | 0.766849 | − | 1.53329i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −23.0914 | + | 12.6617i | −0.755171 | + | 0.414080i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.7185 | − | 22.7185i | −0.742180 | − | 0.742180i | 0.230817 | − | 0.972997i | \(-0.425860\pi\) |
−0.972997 | + | 0.230817i | \(0.925860\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.9032 | + | 12.3313i | 0.453713 | + | 0.402416i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.4705 | + | 8.35457i | −0.471726 | + | 0.272351i | −0.716962 | − | 0.697112i | \(-0.754468\pi\) |
0.245236 | + | 0.969463i | \(0.421135\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.579473 | − | 2.16262i | −0.0188702 | − | 0.0704246i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −12.2436 | + | 28.1974i | −0.398284 | + | 0.917262i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.67673 | + | 28.6499i | 0.249460 | + | 0.930998i | 0.971089 | + | 0.238718i | \(0.0767271\pi\) |
−0.721629 | + | 0.692280i | \(0.756606\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.4163 | + | 12.9421i | −0.727665 | + | 0.420117i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −13.7771 | − | 12.2194i | −0.446752 | − | 0.396242i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.59553 | − | 2.59553i | −0.0840774 | − | 0.0840774i | 0.663817 | − | 0.747895i | \(-0.268935\pi\) |
−0.747895 | + | 0.663817i | \(0.768935\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.87585 | − | 1.13065i | −0.125420 | − | 0.0365870i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.64321 | + | 17.2819i | −0.279395 | + | 0.558643i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −16.2510 | − | 31.2111i | −0.524774 | − | 1.00786i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.3085 | − | 21.3189i | 0.397048 | − | 0.687707i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −29.4478 | − | 4.21316i | −0.948942 | − | 0.135767i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.9423 | + | 0.263264i | 0.384436 | + | 0.00847478i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25.3567 | − | 25.3567i | −0.815418 | − | 0.815418i | 0.170022 | − | 0.985440i | \(-0.445616\pi\) |
−0.985440 | + | 0.170022i | \(0.945616\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.45535 | + | 0.297975i | 0.0467525 | + | 0.00957233i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.9980 | + | 6.92703i | 0.385033 | + | 0.222299i | 0.680006 | − | 0.733207i | \(-0.261977\pi\) |
−0.294973 | + | 0.955506i | \(0.595311\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.93756 | + | 8.19125i | −0.286525 | + | 0.262600i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −11.3380 | − | 39.7941i | −0.363108 | − | 1.27443i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12.0931 | + | 3.24035i | 0.386894 | + | 0.103668i | 0.447022 | − | 0.894523i | \(-0.352484\pi\) |
−0.0601286 | + | 0.998191i | \(0.519151\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.3810i | 0.395697i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.43680 | + | 45.2063i | 0.173584 | + | 1.44332i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.827204 | + | 3.08717i | −0.0263837 | + | 0.0984653i | −0.977862 | − | 0.209250i | \(-0.932898\pi\) |
0.951478 | + | 0.307715i | \(0.0995644\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 24.8215 | − | 40.8839i | 0.790879 | − | 1.30267i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.598050 | − | 36.6805i | −0.0190362 | − | 1.16755i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.18070 | − | 3.77708i | 0.0693422 | − | 0.120104i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.1183 | − | 31.3818i | −0.575547 | − | 0.996877i | −0.995982 | − | 0.0895543i | \(-0.971456\pi\) |
0.420435 | − | 0.907323i | \(-0.361878\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.0429895 | + | 0.717480i | 0.00136423 | + | 0.0227685i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.93411 | + | 3.76440i | −0.124720 | + | 0.119340i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.42696 | + | 12.7896i | −0.108533 | + | 0.405051i | −0.998722 | − | 0.0505407i | \(-0.983906\pi\) |
0.890189 | + | 0.455591i | \(0.150572\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 25.2700 | + | 53.4913i | 0.799509 | + | 1.69239i |
(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 | 420.2.bv.c.317.11 | yes | 48 | |
3.2 | odd | 2 | inner | 420.2.bv.c.317.9 | yes | 48 | |
5.3 | odd | 4 | inner | 420.2.bv.c.233.9 | yes | 48 | |
7.4 | even | 3 | inner | 420.2.bv.c.137.2 | yes | 48 | |
15.8 | even | 4 | inner | 420.2.bv.c.233.2 | yes | 48 | |
21.11 | odd | 6 | inner | 420.2.bv.c.137.9 | yes | 48 | |
35.18 | odd | 12 | inner | 420.2.bv.c.53.9 | ✓ | 48 | |
105.53 | even | 12 | inner | 420.2.bv.c.53.11 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.bv.c.53.9 | ✓ | 48 | 35.18 | odd | 12 | inner | |
420.2.bv.c.53.11 | yes | 48 | 105.53 | even | 12 | inner | |
420.2.bv.c.137.2 | yes | 48 | 7.4 | even | 3 | inner | |
420.2.bv.c.137.9 | yes | 48 | 21.11 | odd | 6 | inner | |
420.2.bv.c.233.2 | yes | 48 | 15.8 | even | 4 | inner | |
420.2.bv.c.233.9 | yes | 48 | 5.3 | odd | 4 | inner | |
420.2.bv.c.317.9 | yes | 48 | 3.2 | odd | 2 | inner | |
420.2.bv.c.317.11 | yes | 48 | 1.1 | even | 1 | trivial |