Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [800,2,Mod(209,800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(800, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 5, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("800.209");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 800 = 2^{5} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 800.be (of order \(10\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.38803216170\) |
Analytic rank: | \(0\) |
Dimension: | \(112\) |
Relative dimension: | \(28\) over \(\Q(\zeta_{10})\) |
Twist minimal: | no (minimal twist has level 200) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 529.2 | ||
Character | \(\chi\) | \(=\) | 800.529 |
Dual form | 800.2.be.a.369.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/800\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(351\) | \(577\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{10}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.54275 | − | 1.84742i | −1.46806 | − | 1.06661i | −0.981170 | − | 0.193145i | \(-0.938131\pi\) |
−0.486890 | − | 0.873463i | \(-0.661869\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.08744 | − | 1.95384i | 0.486318 | − | 0.873782i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.17589i | 0.444443i | 0.974996 | + | 0.222222i | \(0.0713308\pi\) | ||||
−0.974996 | + | 0.222222i | \(0.928669\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.12559 | + | 6.54190i | 0.708531 | + | 2.18063i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.77756 | + | 1.22741i | 1.13898 | + | 0.370077i | 0.816981 | − | 0.576664i | \(-0.195646\pi\) |
0.321997 | + | 0.946741i | \(0.395646\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.280944 | + | 0.864656i | 0.0779198 | + | 0.239812i | 0.982427 | − | 0.186645i | \(-0.0597614\pi\) |
−0.904508 | + | 0.426457i | \(0.859761\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.37465 | + | 2.95917i | −1.64593 | + | 0.764054i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.27511 | + | 4.50780i | 0.794331 | + | 1.09330i | 0.993555 | + | 0.113348i | \(0.0361576\pi\) |
−0.199225 | + | 0.979954i | \(0.563842\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.64864 | + | 3.64555i | 0.607641 | + | 0.836346i | 0.996381 | − | 0.0850017i | \(-0.0270896\pi\) |
−0.388740 | + | 0.921348i | \(0.627090\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.17235 | − | 2.98999i | 0.474047 | − | 0.652469i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.07468 | + | 0.674105i | 0.432601 | + | 0.140561i | 0.517220 | − | 0.855853i | \(-0.326967\pi\) |
−0.0846183 | + | 0.996413i | \(0.526967\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.63495 | − | 4.24936i | −0.526990 | − | 0.849871i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.76703 | − | 11.5937i | 0.724966 | − | 2.23122i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.65841 | + | 5.03536i | −0.679349 | + | 0.935044i | −0.999926 | − | 0.0121788i | \(-0.996123\pi\) |
0.320577 | + | 0.947223i | \(0.396123\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.16778 | − | 0.848445i | 0.209740 | − | 0.152385i | −0.477956 | − | 0.878384i | \(-0.658622\pi\) |
0.687696 | + | 0.725999i | \(0.258622\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.33789 | − | 10.0997i | −1.27736 | − | 1.75814i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.29749 | + | 1.27870i | 0.388347 | + | 0.216141i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.16303 | − | 6.65712i | −0.355600 | − | 1.09442i | −0.955661 | − | 0.294470i | \(-0.904857\pi\) |
0.600061 | − | 0.799954i | \(-0.295143\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.883011 | − | 2.71763i | 0.141395 | − | 0.435169i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.97065 | + | 6.06503i | 0.307763 | + | 0.947198i | 0.978632 | + | 0.205622i | \(0.0659216\pi\) |
−0.670868 | + | 0.741577i | \(0.734078\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.96089 | 0.451532 | 0.225766 | − | 0.974182i | \(-0.427512\pi\) | ||||
0.225766 | + | 0.974182i | \(0.427512\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 15.0933 | + | 2.96086i | 2.24997 | + | 0.441379i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.12538 | − | 4.30172i | 0.455884 | − | 0.627470i | −0.517765 | − | 0.855523i | \(-0.673236\pi\) |
0.973649 | + | 0.228053i | \(0.0732359\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.61729 | 0.802470 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 17.5127i | − | 2.45227i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.5708 | − | 7.68016i | −1.45202 | − | 1.05495i | −0.985355 | − | 0.170515i | \(-0.945457\pi\) |
−0.466661 | − | 0.884436i | \(-0.654543\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.50602 | − | 6.04601i | 0.877272 | − | 0.815244i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 14.1629i | − | 1.87592i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.22277 | + | 0.397301i | −0.159191 | + | 0.0517242i | −0.387528 | − | 0.921858i | \(-0.626671\pi\) |
0.228338 | + | 0.973582i | \(0.426671\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.7321 | + | 4.78675i | 1.88625 | + | 0.612881i | 0.982948 | + | 0.183885i | \(0.0588674\pi\) |
0.903306 | + | 0.428996i | \(0.141133\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.69253 | + | 2.49945i | −0.969167 | + | 0.314902i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.99491 | + | 0.391343i | 0.247438 | + | 0.0485401i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.45652 | + | 1.78477i | −0.300112 | + | 0.218044i | −0.727642 | − | 0.685957i | \(-0.759384\pi\) |
0.427530 | + | 0.904001i | \(0.359384\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.03005 | − | 5.54689i | −0.485161 | − | 0.667767i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.58201 | + | 1.14940i | 0.187750 | + | 0.136409i | 0.677690 | − | 0.735348i | \(-0.262981\pi\) |
−0.489940 | + | 0.871756i | \(0.662981\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.01616 | + | 1.30493i | 0.470056 | + | 0.152731i | 0.534461 | − | 0.845193i | \(-0.320515\pi\) |
−0.0644044 | + | 0.997924i | \(0.520515\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.15031 | + | 15.6729i | −0.132826 | + | 1.80975i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.44329 | + | 4.44199i | −0.164478 | + | 0.506211i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.23200 | − | 1.62164i | −0.251119 | − | 0.182449i | 0.455103 | − | 0.890439i | \(-0.349602\pi\) |
−0.706223 | + | 0.707990i | \(0.749602\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −14.3025 | + | 10.3914i | −1.58917 | + | 1.15460i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.65878 | + | 5.56443i | −0.840660 | + | 0.610775i | −0.922555 | − | 0.385866i | \(-0.873903\pi\) |
0.0818950 | + | 0.996641i | \(0.473903\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.3690 | − | 1.49707i | 1.34160 | − | 0.162380i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 18.6049 | − | 6.04509i | 1.99465 | − | 0.648101i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.806910 | − | 2.48341i | 0.0855323 | − | 0.263241i | −0.899139 | − | 0.437664i | \(-0.855806\pi\) |
0.984671 | + | 0.174423i | \(0.0558059\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.01674 | + | 0.330358i | −0.106583 | + | 0.0346309i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.53682 | −0.470447 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 10.0030 | − | 1.21071i | 1.02629 | − | 0.124216i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.171369 | + | 0.235869i | −0.0173999 | + | 0.0239489i | −0.817628 | − | 0.575746i | \(-0.804712\pi\) |
0.800228 | + | 0.599695i | \(0.204712\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 27.3214i | 2.74590i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 7.84171i | − | 0.780280i | −0.920756 | − | 0.390140i | \(-0.872427\pi\) | ||
0.920756 | − | 0.390140i | \(-0.127573\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.73997 | + | 10.6532i | −0.762642 | + | 1.04969i | 0.234347 | + | 0.972153i | \(0.424705\pi\) |
−0.996990 | + | 0.0775342i | \(0.975295\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.47965 | − | 7.49586i | −0.339579 | − | 0.731521i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.00700 | 0.677392 | 0.338696 | − | 0.940896i | \(-0.390014\pi\) | ||||
0.338696 | + | 0.940896i | \(0.390014\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.56991 | + | 0.835013i | −0.246152 | + | 0.0799797i | −0.429495 | − | 0.903069i | \(-0.641308\pi\) |
0.183342 | + | 0.983049i | \(0.441308\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.79844 | + | 20.9235i | −0.645280 | + | 1.98597i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.34695 | − | 1.41241i | 0.408926 | − | 0.132868i | −0.0973282 | − | 0.995252i | \(-0.531030\pi\) |
0.506255 | + | 0.862384i | \(0.331030\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.57318 | − | 3.32054i | 0.333201 | − | 0.309642i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.05932 | + | 3.67581i | −0.467734 | + | 0.339829i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.30066 | + | 3.85116i | −0.485911 | + | 0.353035i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.86428 | + | 2.80757i | 0.351299 | + | 0.255233i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.19378 | − | 19.0625i | 0.558474 | − | 1.71881i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.1679 | + | 0.527349i | −0.998887 | + | 0.0471675i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.20787 | + | 2.66690i | 0.728330 | + | 0.236649i | 0.649631 | − | 0.760250i | \(-0.274923\pi\) |
0.0786992 | + | 0.996898i | \(0.474923\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.52882 | − | 5.47001i | −0.662876 | − | 0.481607i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.11250 | − | 7.03676i | −0.446681 | − | 0.614804i | 0.524999 | − | 0.851103i | \(-0.324066\pi\) |
−0.971680 | + | 0.236299i | \(0.924066\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.28675 | + | 3.11451i | −0.371708 | + | 0.270062i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −18.5558 | − | 19.9677i | −1.59703 | − | 1.71854i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.46540 | − | 1.12598i | 0.296069 | − | 0.0961988i | −0.157216 | − | 0.987564i | \(-0.550252\pi\) |
0.453285 | + | 0.891365i | \(0.350252\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.2832 | − | 4.31597i | −1.12666 | − | 0.366075i | −0.314357 | − | 0.949305i | \(-0.601789\pi\) |
−0.812307 | + | 0.583230i | \(0.801789\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −15.8941 | + | 5.16432i | −1.33853 | + | 0.434914i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.61112i | 0.301977i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.85998 | + | 12.6236i | 0.486645 | + | 1.04833i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −14.2834 | − | 10.3775i | −1.17807 | − | 0.855921i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 2.61363i | − | 0.214117i | −0.994253 | − | 0.107059i | \(-0.965857\pi\) | ||
0.994253 | − | 0.107059i | \(-0.0341433\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.6178 | −0.864067 | −0.432034 | − | 0.901857i | \(-0.642204\pi\) | ||||
−0.432034 | + | 0.901857i | \(0.642204\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −22.5280 | + | 31.0072i | −1.82128 | + | 2.50678i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.387828 | − | 3.20429i | −0.0311511 | − | 0.257375i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.90358 | 0.311539 | 0.155770 | − | 0.987793i | \(-0.450214\pi\) | ||||
0.155770 | + | 0.987793i | \(0.450214\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 12.6906 | + | 39.0575i | 1.00643 | + | 3.09746i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.792671 | + | 2.43959i | −0.0624712 | + | 0.192267i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.06584 | + | 18.6687i | 0.475114 | + | 1.46225i | 0.845805 | + | 0.533493i | \(0.179121\pi\) |
−0.370691 | + | 0.928756i | \(0.620879\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −27.7127 | + | 3.35418i | −2.15743 | + | 0.261123i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.89993 | − | 13.6261i | −0.766080 | − | 1.05442i | −0.996684 | − | 0.0813708i | \(-0.974070\pi\) |
0.230604 | − | 0.973048i | \(-0.425930\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.84852 | − | 7.15537i | 0.757579 | − | 0.550413i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −18.2189 | + | 25.0761i | −1.39323 | + | 1.91762i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.14623 | + | 9.68309i | −0.239203 | + | 0.736192i | 0.757333 | + | 0.653029i | \(0.226502\pi\) |
−0.996536 | + | 0.0831625i | \(0.973498\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.99676 | − | 3.09840i | 0.377719 | − | 0.234217i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.84317 | + | 1.24872i | 0.288871 | + | 0.0938598i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.87687 | − | 12.2180i | 0.663488 | − | 0.913214i | −0.336102 | − | 0.941826i | \(-0.609109\pi\) |
0.999591 | + | 0.0286120i | \(0.00910873\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.1217 | + | 15.3077i | 0.826668 | + | 1.13781i | 0.988534 | + | 0.150998i | \(0.0482489\pi\) |
−0.161866 | + | 0.986813i | \(0.551751\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −28.6170 | − | 39.3879i | −2.11543 | − | 2.91164i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −15.3591 | − | 3.01301i | −1.12922 | − | 0.221521i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.83904 | + | 21.0484i | 0.500120 | + | 1.53921i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 13.6329 | + | 4.42960i | 0.991649 | + | 0.322206i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.692493 | + | 2.13127i | 0.0501070 | + | 0.154214i | 0.972979 | − | 0.230893i | \(-0.0741647\pi\) |
−0.922872 | + | 0.385106i | \(0.874165\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 22.6952i | − | 1.63363i | −0.576896 | − | 0.816817i | \(-0.695736\pi\) | ||
0.576896 | − | 0.816817i | \(-0.304264\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.34958 | − | 4.68051i | −0.311480 | − | 0.335179i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.5031 | + | 7.63095i | 0.748315 | + | 0.543682i | 0.895304 | − | 0.445456i | \(-0.146958\pi\) |
−0.146989 | + | 0.989138i | \(0.546958\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.2166 | 1.29134 | 0.645672 | − | 0.763615i | \(-0.276577\pi\) | ||||
0.645672 | + | 0.763615i | \(0.276577\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.54353 | 0.673149 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.92102 | − | 4.30187i | −0.415574 | − | 0.301932i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.9930 | + | 2.74503i | 0.977316 | + | 0.191721i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 15.0052i | 1.04294i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.53086 | + | 17.0222i | 0.382578 | + | 1.17745i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.67102 | − | 0.542946i | −0.115037 | − | 0.0373779i | 0.250933 | − | 0.968005i | \(-0.419263\pi\) |
−0.365970 | + | 0.930627i | \(0.619263\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.89925 | − | 5.84528i | −0.130134 | − | 0.400512i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.21979 | − | 5.78510i | 0.219588 | − | 0.394540i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.997675 | + | 1.37318i | 0.0677266 | + | 0.0932177i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.80136 | − | 10.7377i | −0.527167 | − | 0.725583i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.97757 | + | 4.09828i | −0.200293 | + | 0.275680i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.48230 | + | 0.481630i | 0.0992625 | + | 0.0322523i | 0.358227 | − | 0.933634i | \(-0.383381\pi\) |
−0.258965 | + | 0.965887i | \(0.583381\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 22.1980 | − | 26.2700i | 1.47987 | − | 1.75133i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.84981 | + | 8.77081i | −0.189148 | + | 0.582139i | −0.999995 | − | 0.00311955i | \(-0.999007\pi\) |
0.810847 | + | 0.585259i | \(0.199007\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.64077 | + | 9.14023i | −0.438834 | + | 0.604003i | −0.969953 | − | 0.243294i | \(-0.921772\pi\) |
0.531118 | + | 0.847298i | \(0.321772\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.8761 | − | 8.62852i | 0.781393 | − | 0.567715i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.30682 | − | 10.0570i | −0.478685 | − | 0.658854i | 0.499566 | − | 0.866276i | \(-0.333493\pi\) |
−0.978252 | + | 0.207422i | \(0.933493\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.00619 | − | 10.7843i | −0.326568 | − | 0.703492i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.67957 | + | 8.24687i | 0.174057 | + | 0.535692i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.53966 | − | 26.2824i | 0.552384 | − | 1.70006i | −0.150368 | − | 0.988630i | \(-0.548046\pi\) |
0.702752 | − | 0.711435i | \(-0.251954\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.32369 | − | 4.07389i | −0.0852663 | − | 0.262423i | 0.899329 | − | 0.437273i | \(-0.144056\pi\) |
−0.984595 | + | 0.174851i | \(0.944056\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 18.9940 | 1.21846 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.10846 | − | 10.9753i | 0.390255 | − | 0.701184i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.40802 | + | 3.31436i | −0.153219 | + | 0.210888i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 29.7542 | 1.88560 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.4000i | 0.845800i | 0.906176 | + | 0.422900i | \(0.138988\pi\) | ||||
−0.906176 | + | 0.422900i | \(0.861012\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.00985 | + | 5.09295i | 0.440705 | + | 0.320191i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −34.2170 | − | 19.0440i | −2.14275 | − | 1.19258i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.81899i | 0.487735i | 0.969809 | + | 0.243868i | \(0.0784162\pi\) | ||||
−0.969809 | + | 0.243868i | \(0.921584\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.82802 | − | 2.54348i | 0.486409 | − | 0.158044i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −40.7171 | − | 13.2298i | −2.52033 | − | 0.818904i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 26.0980 | − | 8.47975i | 1.60927 | − | 0.522884i | 0.639894 | − | 0.768463i | \(-0.278978\pi\) |
0.969377 | + | 0.245579i | \(0.0789781\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −26.5009 | + | 12.3020i | −1.62794 | + | 0.755704i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.63968 | + | 4.82401i | −0.406342 | + | 0.295225i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.5408 | − | 17.2610i | −0.764629 | − | 1.05242i | −0.996815 | − | 0.0797498i | \(-0.974588\pi\) |
0.232186 | − | 0.972671i | \(-0.425412\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.864363 | − | 0.627996i | −0.0525063 | − | 0.0381481i | 0.561223 | − | 0.827665i | \(-0.310331\pi\) |
−0.613729 | + | 0.789517i | \(0.710331\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.19562 | + | 1.03832i | 0.193408 | + | 0.0628420i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.73802 | − | 19.2864i | −0.285713 | − | 1.16301i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.48602 | + | 16.8842i | −0.329623 | + | 1.01448i | 0.639687 | + | 0.768635i | \(0.279064\pi\) |
−0.969310 | + | 0.245840i | \(0.920936\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.03268 | + | 5.83608i | 0.480904 | + | 0.349397i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.77867 | + | 6.37807i | −0.523691 | + | 0.380484i | −0.817993 | − | 0.575229i | \(-0.804913\pi\) |
0.294301 | + | 0.955713i | \(0.404913\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.7899 | − | 13.6517i | 1.11695 | − | 0.811509i | 0.133203 | − | 0.991089i | \(-0.457474\pi\) |
0.983743 | + | 0.179580i | \(0.0574739\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −27.6720 | − | 15.4013i | −1.63915 | − | 0.912293i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.13178 | + | 2.31726i | −0.420976 | + | 0.136783i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.34064 | + | 13.3591i | −0.255332 | + | 0.785830i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.871498 | − | 0.283167i | 0.0510881 | − | 0.0165995i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 23.5633 | 1.37658 | 0.688291 | − | 0.725434i | \(-0.258361\pi\) | ||||
0.688291 | + | 0.725434i | \(0.258361\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.553423 | + | 2.82112i | −0.0322215 | + | 0.164252i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 28.4604 | − | 39.1724i | 1.65144 | − | 2.27301i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.98327i | 0.114696i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.48167i | 0.200680i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −14.4869 | + | 19.9396i | −0.832252 | + | 1.14550i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 25.3728 | − | 23.5788i | 1.45284 | − | 1.35012i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 29.1918 | 1.66607 | 0.833033 | − | 0.553223i | \(-0.186602\pi\) | ||||
0.833033 | + | 0.553223i | \(0.186602\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 39.3617 | − | 12.7894i | 2.23921 | − | 0.727563i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.303724 | + | 0.934766i | −0.0172226 | + | 0.0530057i | −0.959298 | − | 0.282394i | \(-0.908871\pi\) |
0.942076 | + | 0.335400i | \(0.108871\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.11237 | + | 2.96079i | −0.515062 | + | 0.167354i | −0.555003 | − | 0.831848i | \(-0.687283\pi\) |
0.0399413 | + | 0.999202i | \(0.487283\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.48163 | + | 17.7479i | −0.196168 | + | 0.999983i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.8949 | + | 10.8218i | −0.836580 | + | 0.607811i | −0.921413 | − | 0.388584i | \(-0.872964\pi\) |
0.0848334 | + | 0.996395i | \(0.472964\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −20.0003 | + | 14.5311i | −1.11980 | + | 0.813584i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −17.8171 | − | 12.9449i | −0.994453 | − | 0.722512i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.75880 | + | 23.8791i | −0.431711 | + | 1.32867i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.93396 | − | 3.47216i | 0.162747 | − | 0.192601i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.07726 | + | 2.62446i | 0.446673 | + | 0.145133i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.05833 | + | 3.67509i | 0.278875 | + | 0.202614i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.25106 | + | 5.85108i | 0.233659 | + | 0.321604i | 0.909705 | − | 0.415255i | \(-0.136308\pi\) |
−0.676046 | + | 0.736860i | \(0.736308\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 38.9525 | − | 28.3007i | 2.13458 | − | 1.55087i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.815824 | + | 6.74046i | 0.0445733 | + | 0.368271i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.66935 | + | 2.81684i | −0.472250 | + | 0.153443i | −0.535466 | − | 0.844557i | \(-0.679864\pi\) |
0.0632165 | + | 0.998000i | \(0.479864\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −13.6625 | − | 4.43923i | −0.742047 | − | 0.241106i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.45277 | − | 1.77171i | 0.295284 | − | 0.0959436i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.8365i | 0.801096i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −15.2202 | + | 1.84216i | −0.819426 | + | 0.0991784i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.27687 | − | 6.01350i | −0.444326 | − | 0.322821i | 0.343026 | − | 0.939326i | \(-0.388548\pi\) |
−0.787351 | + | 0.616505i | \(0.788548\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.76436i | 0.255030i | 0.991837 | + | 0.127515i | \(0.0407001\pi\) | ||||
−0.991837 | + | 0.127515i | \(0.959300\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.0829 | 0.591562 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.7305 | + | 14.7692i | −0.571126 | + | 0.786087i | −0.992687 | − | 0.120713i | \(-0.961482\pi\) |
0.421562 | + | 0.906800i | \(0.361482\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.96608 | − | 1.84109i | 0.210498 | − | 0.0977149i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 20.5930 | 1.08990 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.64467 | − | 17.3725i | −0.297914 | − | 0.916885i | −0.982227 | − | 0.187697i | \(-0.939898\pi\) |
0.684313 | − | 0.729188i | \(-0.260102\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.403370 | + | 1.24145i | −0.0212300 | + | 0.0653393i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.63917 | − | 14.2779i | −0.243493 | − | 0.749396i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.91695 | − | 6.42789i | 0.362050 | − | 0.336451i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.85005 | − | 12.1811i | −0.461969 | − | 0.635846i | 0.512947 | − | 0.858421i | \(-0.328554\pi\) |
−0.974916 | + | 0.222575i | \(0.928554\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −35.4880 | + | 25.7835i | −1.84743 | + | 1.34224i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.03100 | − | 12.4301i | 0.468866 | − | 0.645339i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.219092 | − | 0.674295i | 0.0113441 | − | 0.0349137i | −0.945224 | − | 0.326422i | \(-0.894157\pi\) |
0.956568 | + | 0.291508i | \(0.0941570\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 29.3715 | + | 19.2909i | 1.51674 | + | 0.996176i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.38166 | − | 1.74861i | −0.277170 | − | 0.0900579i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.8210 | − | 14.8938i | 0.555838 | − | 0.765045i | −0.434952 | − | 0.900454i | \(-0.643235\pi\) |
0.990790 | + | 0.135408i | \(0.0432347\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15.9437 | − | 21.9446i | −0.816821 | − | 1.12426i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.5490 | + | 14.5194i | 0.539027 | + | 0.741907i | 0.988472 | − | 0.151401i | \(-0.0483783\pi\) |
−0.449445 | + | 0.893308i | \(0.648378\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.10942 | + | 7.65034i | 0.362330 | + | 0.389897i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.29365 | + | 19.3699i | 0.319924 | + | 0.984625i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.7077 | − | 7.37819i | −1.15133 | − | 0.374089i | −0.329685 | − | 0.944091i | \(-0.606942\pi\) |
−0.821643 | + | 0.570002i | \(0.806942\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.75608 | + | 11.5600i | 0.189953 | + | 0.584616i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 27.3377i | 1.37900i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.59558 | + | 2.59752i | −0.281544 | + | 0.130695i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.16804 | − | 0.848630i | −0.0586222 | − | 0.0425915i | 0.558088 | − | 0.829782i | \(-0.311535\pi\) |
−0.616710 | + | 0.787190i | \(0.711535\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 16.6539 | 0.833740 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −26.0682 | −1.30178 | −0.650891 | − | 0.759171i | \(-0.725605\pi\) | ||||
−0.650891 | + | 0.759171i | \(0.725605\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.06170 | + | 0.771367i | 0.0528868 | + | 0.0384245i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.74996 | + | 39.2448i | 0.236027 | + | 1.95009i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 27.8026i | − | 1.37813i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.312601 | + | 0.962088i | 0.0154571 | + | 0.0475722i | 0.958488 | − | 0.285134i | \(-0.0920382\pi\) |
−0.943030 | + | 0.332706i | \(0.892038\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.8918 | − | 3.53897i | −0.537254 | − | 0.174564i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.467180 | − | 1.43783i | −0.0229884 | − | 0.0707512i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.54353 | + | 21.0150i | 0.124857 | + | 1.03158i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 25.8025 | + | 35.5140i | 1.26355 | + | 1.73913i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.6696 | − | 27.0728i | −0.960920 | − | 1.32259i | −0.946502 | − | 0.322697i | \(-0.895410\pi\) |
−0.0144183 | − | 0.999896i | \(-0.504590\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.1696 | − | 22.2556i | 0.788060 | − | 1.08467i | −0.206287 | − | 0.978492i | \(-0.566138\pi\) |
0.994347 | − | 0.106180i | \(-0.0338621\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 34.7847 | + | 11.3022i | 1.69129 | + | 0.549533i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 10.5255 | − | 25.7949i | 0.510562 | − | 1.25124i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.62868 | + | 17.3233i | −0.272391 | + | 0.838333i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.67126 | − | 9.18220i | 0.322092 | − | 0.443321i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.6348 | + | 15.7186i | −1.04211 | + | 0.757138i | −0.970696 | − | 0.240309i | \(-0.922751\pi\) |
−0.0714143 | + | 0.997447i | \(0.522751\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.1996 | − | 16.7912i | −0.586273 | − | 0.806936i | 0.408092 | − | 0.912941i | \(-0.366194\pi\) |
−0.994366 | + | 0.106005i | \(0.966194\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.42055 | − | 42.9245i | 0.403734 | − | 2.05807i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.03762 | + | 9.34882i | 0.145309 | + | 0.447215i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.0935999 | + | 0.288071i | −0.00446728 | + | 0.0137489i | −0.953265 | − | 0.302134i | \(-0.902301\pi\) |
0.948798 | + | 0.315883i | \(0.102301\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.9401 | + | 36.7478i | 0.568575 | + | 1.74989i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −33.9046 | −1.61086 | −0.805428 | − | 0.592693i | \(-0.798065\pi\) | ||||
−0.805428 | + | 0.592693i | \(0.798065\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.97472 | − | 4.27713i | −0.188420 | − | 0.202755i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.82848 | + | 6.64583i | −0.228379 | + | 0.314337i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.6049 | −0.594860 | −0.297430 | − | 0.954744i | \(-0.596129\pi\) | ||||
−0.297430 | + | 0.954744i | \(0.596129\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 25.3298i | 1.19273i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 26.9986 | + | 19.6156i | 1.26850 | + | 0.921621i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.460174 | + | 2.34578i | −0.0215733 | + | 0.109972i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 2.58934i | − | 0.121124i | −0.998164 | − | 0.0605622i | \(-0.980711\pi\) | ||
0.998164 | − | 0.0605622i | \(-0.0192893\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 64.5997 | − | 20.9897i | 3.01526 | − | 0.979716i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.49523 | − | 2.11043i | −0.302513 | − | 0.0982925i | 0.153827 | − | 0.988098i | \(-0.450840\pi\) |
−0.456340 | + | 0.889805i | \(0.650840\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.7530 | + | 6.74304i | −0.964472 | + | 0.313376i | −0.748582 | − | 0.663042i | \(-0.769265\pi\) |
−0.215889 | + | 0.976418i | \(0.569265\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.93352 | + | 8.86421i | −0.228787 | + | 0.411068i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.43118 | − | 1.76636i | 0.112502 | − | 0.0817373i | −0.530112 | − | 0.847928i | \(-0.677850\pi\) |
0.642614 | + | 0.766190i | \(0.277850\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.09868 | − | 2.88859i | −0.0969081 | − | 0.133383i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.92583 | − | 7.21154i | −0.457358 | − | 0.332290i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.1850 | + | 3.63421i | 0.514285 | + | 0.167101i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.51217 | − | 20.8609i | 0.390565 | − | 0.957163i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 27.7736 | − | 85.4782i | 1.27166 | − | 3.91378i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15.3717 | − | 11.1682i | −0.702349 | − | 0.510287i | 0.178347 | − | 0.983968i | \(-0.442925\pi\) |
−0.880697 | + | 0.473681i | \(0.842925\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.14843 | − | 3.74055i | 0.234748 | − | 0.170555i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.52251 | − | 4.73888i | 0.296785 | − | 0.215627i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.274496 | + | 0.591320i | 0.0124642 | + | 0.0268504i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.80539 | − | 0.586607i | 0.0818101 | − | 0.0265817i | −0.267826 | − | 0.963467i | \(-0.586305\pi\) |
0.349636 | + | 0.936886i | \(0.386305\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 19.0651 | − | 58.6762i | 0.862151 | − | 2.65343i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.3750 | − | 9.54451i | 1.32567 | − | 0.430738i | 0.441234 | − | 0.897392i | \(-0.354541\pi\) |
0.884440 | + | 0.466654i | \(0.154541\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −34.6801 | −1.56191 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 53.3816 | + | 29.7104i | 2.39932 | + | 1.33538i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.35156 | + | 1.86027i | −0.0606258 | + | 0.0834443i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 10.5948i | − | 0.474289i | −0.971474 | − | 0.237145i | \(-0.923788\pi\) | ||
0.971474 | − | 0.237145i | \(-0.0762115\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 52.9371i | 2.36506i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.5618 | + | 21.4189i | −0.693865 | + | 0.955024i | 0.306130 | + | 0.951990i | \(0.400966\pi\) |
−0.999995 | + | 0.00303389i | \(0.999034\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.3214 | − | 8.52739i | −0.681794 | − | 0.379464i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −38.2613 | −1.69925 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.5095 | + | 5.68919i | −0.776096 | + | 0.252169i | −0.670172 | − | 0.742205i | \(-0.733780\pi\) |
−0.105923 | + | 0.994374i | \(0.533780\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.53445 | + | 4.72255i | −0.0678800 | + | 0.208913i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 52.2431 | − | 16.9748i | 2.30659 | − | 0.749456i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12.3978 | + | 26.7073i | 0.546311 | + | 1.17686i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17.0863 | − | 12.4139i | 0.751453 | − | 0.545963i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 25.8888 | − | 18.8093i | 1.13639 | − | 0.825637i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.7039 | + | 23.7608i | 1.43278 | + | 1.04098i | 0.989490 | + | 0.144603i | \(0.0461906\pi\) |
0.443295 | + | 0.896376i | \(0.353809\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.37852 | + | 16.5534i | −0.235186 | + | 0.723828i | 0.761911 | + | 0.647682i | \(0.224262\pi\) |
−0.997097 | + | 0.0761461i | \(0.975738\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −18.4296 | − | 1.35263i | −0.804333 | − | 0.0590336i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.64925 | + | 2.48539i | 0.333206 | + | 0.108265i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.7575 | − | 10.7220i | −0.641630 | − | 0.466172i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.19820 | − | 7.15471i | −0.225583 | − | 0.310488i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.69052 | + | 3.40786i | −0.203169 | + | 0.147611i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.61969 | − | 13.6905i | 0.329428 | − | 0.591893i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −45.1434 | + | 14.6680i | −1.94808 | + | 0.632970i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 21.2197 | + | 6.89469i | 0.913996 | + | 0.296975i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.69917 | − | 2.50161i | 0.331013 | − | 0.107553i | −0.138795 | − | 0.990321i | \(-0.544323\pi\) |
0.469808 | + | 0.882768i | \(0.344323\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 59.4701i | − | 2.55211i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.16314 | + | 5.92920i | −0.0498233 | + | 0.253979i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.7126 | + | 15.0486i | 0.885607 | + | 0.643431i | 0.934729 | − | 0.355362i | \(-0.115642\pi\) |
−0.0491221 | + | 0.998793i | \(0.515642\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 106.551i | 4.54747i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −28.0465 | −1.19482 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.90686 | − | 2.62457i | 0.0810881 | − | 0.111608i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 33.4881 | + | 36.0360i | 1.42149 | + | 1.52964i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.74254 | 0.0738336 | 0.0369168 | − | 0.999318i | \(-0.488246\pi\) | ||||
0.0369168 | + | 0.999318i | \(0.488246\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.831844 | + | 2.56015i | 0.0351832 | + | 0.108283i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 21.4952 | − | 66.1555i | 0.907529 | − | 2.79309i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.94233 | − | 24.4440i | −0.334729 | − | 1.03019i | −0.966855 | − | 0.255325i | \(-0.917817\pi\) |
0.632126 | − | 0.774866i | \(-0.282183\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.96742 | − | 10.0291i | 0.0827702 | − | 0.421929i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −12.2191 | − | 16.8181i | −0.513154 | − | 0.706296i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11.5604 | + | 8.39915i | −0.484639 | + | 0.352111i | −0.803119 | − | 0.595819i | \(-0.796828\pi\) |
0.318480 | + | 0.947930i | \(0.396828\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.7151 | − | 16.1245i | 0.490263 | − | 0.674789i | −0.490174 | − | 0.871625i | \(-0.663067\pi\) |
0.980436 | + | 0.196836i | \(0.0630666\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.17652 | − | 6.69863i | 0.0909253 | − | 0.279839i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.60218 | − | 10.5923i | −0.108518 | − | 0.441729i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.6528 | + | 4.76100i | 0.610006 | + | 0.198203i | 0.597698 | − | 0.801721i | \(-0.296082\pi\) |
0.0123079 | + | 0.999924i | \(0.496082\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −41.9275 | + | 57.7083i | −1.74245 | + | 2.39827i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.54313 | − | 9.00585i | −0.271455 | − | 0.373626i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −30.5054 | − | 41.9870i | −1.26340 | − | 1.73892i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.68023 | + | 13.8823i | 0.0694690 | + | 0.573963i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.25364 | − | 13.0914i | −0.175567 | − | 0.540338i | 0.824092 | − | 0.566455i | \(-0.191686\pi\) |
−0.999659 | + | 0.0261173i | \(0.991686\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.18610 | + | 2.00998i | 0.254894 | + | 0.0828200i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.6092 | − | 38.8072i | −0.518675 | − | 1.59632i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 6.37493i | − | 0.261787i | −0.991396 | − | 0.130894i | \(-0.958215\pi\) | ||
0.991396 | − | 0.130894i | \(-0.0417846\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.76038 | + | 14.5445i | 0.0721686 | + | 0.596267i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −46.3205 | − | 33.6538i | −1.89577 | − | 1.37736i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −38.8351 | −1.58676 | −0.793380 | − | 0.608727i | \(-0.791681\pi\) | ||||
−0.793380 | + | 0.608727i | \(0.791681\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 41.0478 | 1.67438 | 0.837188 | − | 0.546916i | \(-0.184198\pi\) | ||||
0.837188 | + | 0.546916i | \(0.184198\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −16.8973 | − | 12.2766i | −0.688112 | − | 0.499942i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.68770 | − | 4.49712i | 0.393861 | − | 0.182834i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.6948i | 1.16469i | 0.812943 | + | 0.582343i | \(0.197864\pi\) | ||||
−0.812943 | + | 0.582343i | \(0.802136\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.10833 | + | 21.8772i | 0.288044 | + | 0.886509i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.59756 | + | 1.49384i | 0.185997 | + | 0.0604342i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.30831 | + | 7.10423i | 0.0932316 | + | 0.286937i | 0.986789 | − | 0.162012i | \(-0.0517983\pi\) |
−0.893557 | + | 0.448949i | \(0.851798\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −30.5096 | − | 32.8309i | −1.23027 | − | 1.32387i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23.8187 | − | 32.7837i | −0.958906 | − | 1.31982i | −0.947456 | − | 0.319886i | \(-0.896355\pi\) |
−0.0114498 | − | 0.999934i | \(-0.503645\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.89273 | − | 8.11065i | −0.236849 | − | 0.325994i | 0.674003 | − | 0.738729i | \(-0.264574\pi\) |
−0.910851 | + | 0.412735i | \(0.864574\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 15.6308 | − | 21.5140i | 0.627242 | − | 0.863325i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.92021 | + | 0.948834i | 0.116996 | + | 0.0380142i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.1141 | + | 22.3937i | −0.444562 | + | 0.895748i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 17.3836 | − | 53.5012i | 0.694234 | − | 2.13663i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 22.9248 | − | 31.5533i | 0.914073 | − | 1.25811i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.4964 | − | 17.7976i | 0.975184 | − | 0.708513i | 0.0185571 | − | 0.999828i | \(-0.494093\pi\) |
0.956627 | + | 0.291315i | \(0.0940927\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.24593 | + | 4.46765i | 0.129014 | + | 0.177573i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.1362 | − | 13.1367i | 0.560979 | − | 0.521316i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.57814 | + | 4.85702i | 0.0625283 | + | 0.192442i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.15654 | + | 12.7925i | −0.164430 | + | 0.506064i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.1688 | − | 37.4516i | −0.480637 | − | 1.47925i | −0.838201 | − | 0.545361i | \(-0.816393\pi\) |
0.357564 | − | 0.933889i | \(-0.383607\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.6623 | −0.617660 | −0.308830 | − | 0.951117i | \(-0.599937\pi\) | ||||
−0.308830 | + | 0.951117i | \(0.599937\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −18.8746 | + | 8.76178i | −0.743188 | + | 0.344995i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −19.5134 | + | 26.8579i | −0.767152 | + | 1.05589i | 0.229434 | + | 0.973324i | \(0.426313\pi\) |
−0.996585 | + | 0.0825693i | \(0.973687\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.10673 | −0.200457 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 5.33479i | − | 0.209087i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.13976 | − | 2.28117i | −0.122868 | − | 0.0892690i | 0.524654 | − | 0.851316i | \(-0.324195\pi\) |
−0.647522 | + | 0.762047i | \(0.724195\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −19.3082 | + | 2.33695i | −0.754434 | + | 0.0913121i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 29.0471i | 1.13323i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −38.7539 | + | 12.5919i | −1.50964 | + | 0.490511i | −0.942811 | − | 0.333327i | \(-0.891829\pi\) |
−0.566826 | + | 0.823838i | \(0.691829\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.9253 | + | 11.6728i | 1.39733 | + | 0.454020i | 0.908327 | − | 0.418261i | \(-0.137360\pi\) |
0.489004 | + | 0.872282i | \(0.337360\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 15.1425 | − | 4.92009i | 0.588085 | − | 0.191081i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.42365 | + | 11.7624i | 0.0552070 | + | 0.456128i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.9844 | + | 7.98063i | −0.425318 | + | 0.309011i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.87936 | − | 3.96311i | −0.111323 | − | 0.153223i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 49.7762 | + | 36.1645i | 1.92159 | + | 1.39612i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.57662 | + | 0.512274i | 0.0607742 | + | 0.0197467i | 0.339246 | − | 0.940698i | \(-0.389828\pi\) |
−0.278472 | + | 0.960444i | \(0.589828\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −59.1919 | + | 14.5415i | −2.27830 | + | 0.559702i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −0.0701106 | + | 0.215778i | −0.00269457 | + | 0.00829304i | −0.952395 | − | 0.304868i | \(-0.901388\pi\) |
0.949700 | + | 0.313161i | \(0.101388\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.277355 | − | 0.201510i | −0.0106439 | − | 0.00773325i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 23.4497 | − | 17.0372i | 0.898596 | − | 0.652868i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24.0637 | + | 17.4833i | −0.920773 | + | 0.668981i | −0.943716 | − | 0.330756i | \(-0.892696\pi\) |
0.0229435 | + | 0.999737i | \(0.492696\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.56844 | − | 7.99527i | 0.0599270 | − | 0.305483i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 33.7717 | − | 10.9731i | 1.28847 | − | 0.418649i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.67089 | − | 11.2978i | 0.139850 | − | 0.430413i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.9436 | − | 9.72925i | 1.13911 | − | 0.370118i | 0.322077 | − | 0.946714i | \(-0.395619\pi\) |
0.817030 | + | 0.576595i | \(0.195619\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −32.1269 | −1.22040 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −22.8773 | + | 21.2598i | −0.867787 | + | 0.806430i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.8859 | + | 28.7469i | −0.791108 | + | 1.08887i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 39.0712i | 1.47781i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 2.30506i | − | 0.0870611i | −0.999052 | − | 0.0435305i | \(-0.986139\pi\) | ||
0.999052 | − | 0.0435305i | \(-0.0138606\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.5398 | − | 25.5178i | 0.699240 | − | 0.962422i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.19368 | + | 36.6704i | −0.270930 | + | 1.38109i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.22096 | 0.346790 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.4956 | − | 8.28402i | 0.957508 | − | 0.311113i | 0.211745 | − | 0.977325i | \(-0.432085\pi\) |
0.745763 | + | 0.666212i | \(0.232085\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.86429 | − | 18.0484i | 0.219928 | − | 0.676869i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.99472 | − | 0.973045i | 0.112153 | − | 0.0364408i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.05555 | + | 3.92688i | 0.263862 | + | 0.146857i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −70.2688 | + | 51.0533i | −2.62424 | + | 1.90662i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.3313 | + | 8.95922i | −0.459880 | + | 0.334123i | −0.793484 | − | 0.608591i | \(-0.791735\pi\) |
0.333604 | + | 0.942713i | \(0.391735\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.5269 | − | 9.10133i | −0.466526 | − | 0.338951i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.16038 | + | 12.8043i | −0.154726 | + | 0.476198i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 31.0368 | + | 2.27793i | 1.15268 | + | 0.0846001i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.11778 | + | 0.688107i | 0.0785440 | + | 0.0255205i | 0.348025 | − | 0.937485i | \(-0.386852\pi\) |
−0.269481 | + | 0.963006i | \(0.586852\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −5.38937 | − | 3.91560i | −0.199606 | − | 0.145022i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.69724 | + | 13.3471i | 0.358665 | + | 0.493661i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −40.0434 | + | 29.0933i | −1.47904 | + | 1.07458i | −0.501173 | + | 0.865347i | \(0.667098\pi\) |
−0.977865 | + | 0.209237i | \(0.932902\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −35.8082 | + | 16.6225i | −1.32081 | + | 0.613131i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −11.4703 | + | 3.72692i | −0.422513 | + | 0.137283i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.2361 | − | 5.60033i | −0.634039 | − | 0.206012i | −0.0256753 | − | 0.999670i | \(-0.508174\pi\) |
−0.608363 | + | 0.793659i | \(0.708174\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.2460 | − | 3.97897i | 0.449869 | − | 0.146171i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.5632i | 0.570959i | 0.958385 | + | 0.285479i | \(0.0921528\pi\) | ||||
−0.958385 | + | 0.285479i | \(0.907847\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.10661 | − | 2.84217i | −0.187092 | − | 0.104129i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −52.6813 | − | 38.2752i | −1.92751 | − | 1.40042i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.23944i | 0.301062i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −41.5803 | −1.51729 | −0.758643 | − | 0.651507i | \(-0.774137\pi\) | ||||
−0.758643 | + | 0.651507i | \(0.774137\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 24.7554 | − | 34.0729i | 0.902137 | − | 1.24169i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11.5463 | + | 20.7455i | −0.420211 | + | 0.755007i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.83755 | 0.0667870 | 0.0333935 | − | 0.999442i | \(-0.489369\pi\) | ||||
0.0333935 | + | 0.999442i | \(0.489369\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.41550 | − | 25.9003i | −0.305463 | − | 0.940120i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.18935 | + | 28.2819i | −0.333114 | + | 1.02522i | 0.634530 | + | 0.772898i | \(0.281194\pi\) |
−0.967644 | + | 0.252320i | \(0.918806\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.981880 | − | 3.02192i | −0.0355464 | − | 0.109401i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 36.0851 | + | 77.7345i | 1.30466 | + | 2.81050i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.687057 | − | 0.945653i | −0.0248082 | − | 0.0341455i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.63237 | − | 5.54524i | 0.275230 | − | 0.199966i | −0.441604 | − | 0.897210i | \(-0.645590\pi\) |
0.716834 | + | 0.697244i | \(0.245590\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.4450 | − | 19.8818i | 0.520222 | − | 0.716025i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.49873 | + | 23.0787i | −0.269711 | + | 0.830084i | 0.720860 | + | 0.693081i | \(0.243747\pi\) |
−0.990571 | + | 0.137003i | \(0.956253\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.68240 | − | 2.72672i | −0.240039 | − | 0.0979467i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −24.6036 | − | 7.99420i | −0.882649 | − | 0.286790i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −16.8908 | + | 23.2482i | −0.605176 | + | 0.832953i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.56537 | + | 6.28370i | 0.163362 | + | 0.224848i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 44.5974 | + | 61.3830i | 1.59378 | + | 2.19365i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.24490 | − | 7.62695i | 0.151507 | − | 0.272217i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.5135 | + | 35.4350i | 0.410413 | + | 1.26312i | 0.916290 | + | 0.400515i | \(0.131169\pi\) |
−0.505877 | + | 0.862606i | \(0.668831\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −82.0264 | − | 26.6520i | −2.92022 | − | 0.948837i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.66083 | + | 5.11151i | 0.0590524 | + | 0.181745i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.0830i | 0.500103i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 90.1123 | + | 17.6774i | 3.19595 | + | 0.626953i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.03520 | − | 2.93174i | −0.142934 | − | 0.103848i | 0.514020 | − | 0.857778i | \(-0.328156\pi\) |
−0.656954 | + | 0.753930i | \(0.728156\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 29.6272 | 1.04814 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 17.9614 | 0.634635 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13.5696 | + | 9.85892i | 0.478862 | + | 0.347914i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.90458 | + | 4.20166i | 0.137618 | + | 0.148089i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 67.0587i | 2.36058i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.74204 | − | 8.43914i | −0.0964051 | − | 0.296704i | 0.891212 | − | 0.453587i | \(-0.149856\pi\) |
−0.987617 | + | 0.156882i | \(0.949856\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.7338 | − | 6.73681i | −0.728062 | − | 0.236562i | −0.0785467 | − | 0.996910i | \(-0.525028\pi\) |
−0.649515 | + | 0.760349i | \(0.725028\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.03769 | + | 3.19368i | 0.0363934 | + | 0.112007i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 43.0719 | + | 8.44946i | 1.50874 | + | 0.295972i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.84235 | + | 10.7941i | 0.274369 | + | 0.377637i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.32233 | − | 5.94918i | −0.151035 | − | 0.207881i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.5298 | + | 29.6332i | −0.751394 | + | 1.03420i | 0.246488 | + | 0.969146i | \(0.420724\pi\) |
−0.997881 | + | 0.0650589i | \(0.979276\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.63427 | + | 1.83068i | 0.196398 | + | 0.0638136i | 0.405564 | − | 0.914066i | \(-0.367075\pi\) |
−0.209166 | + | 0.977880i | \(0.567075\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −23.5824 | + | 57.7936i | −0.821033 | + | 2.01212i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.70692 | − | 14.4864i | 0.163676 | − | 0.503742i | −0.835261 | − | 0.549854i | \(-0.814683\pi\) |
0.998936 | + | 0.0461123i | \(0.0146832\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25.2244 | + | 34.7183i | −0.876078 | + | 1.20582i | 0.101414 | + | 0.994844i | \(0.467663\pi\) |
−0.977492 | + | 0.210974i | \(0.932337\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 45.1419 | − | 32.7975i | 1.56595 | − | 1.13773i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.3972 | + | 25.3216i | 0.637427 | + | 0.877343i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −37.3887 | + | 4.52531i | −1.29389 | + | 0.156605i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.43757 | − | 16.7351i | −0.187950 | − | 0.578450i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14.0891 | + | 43.3617i | −0.486409 | + | 1.49701i | 0.343521 | + | 0.939145i | \(0.388380\pi\) |
−0.829930 | + | 0.557868i | \(0.811620\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.00946 | − | 9.26218i | −0.103775 | − | 0.319385i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 34.1050 | 1.17464 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.27075 | − | 27.0234i | −0.112517 | − | 0.929634i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.30138 | + | 4.54396i | −0.113437 | + | 0.156132i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −72.9986 | −2.50531 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 15.2695i | − | 0.523433i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −39.8951 | − | 28.9855i | −1.36598 | − | 0.992445i | −0.998039 | − | 0.0625971i | \(-0.980062\pi\) |
−0.367944 | − | 0.929848i | \(-0.619938\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 29.1827 | + | 62.8654i | 0.998028 | + | 2.14995i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 57.0345i | − | 1.94826i | −0.225989 | − | 0.974130i | \(-0.572561\pi\) | ||
0.225989 | − | 0.974130i | \(-0.427439\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.6564 | − | 6.71166i | 0.704786 | − | 0.228999i | 0.0653714 | − | 0.997861i | \(-0.479177\pi\) |
0.639415 | + | 0.768862i | \(0.279177\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 22.4153 | + | 7.28318i | 0.763912 | + | 0.248210i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.9981 | − | 5.84794i | 0.612663 | − | 0.199066i | 0.0137830 | − | 0.999905i | \(-0.495613\pi\) |
0.598880 | + | 0.800839i | \(0.295613\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.4978 | + | 16.6770i | 0.526942 | + | 0.567034i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 35.7171 | − | 25.9500i | 1.21302 | − | 0.881307i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.44110 | − | 8.86542i | −0.218499 | − | 0.300739i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.23335 | − | 1.62262i | −0.0756742 | − | 0.0549805i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.90729 | − | 0.619716i | −0.0645520 | − | 0.0209742i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.620102 | − | 13.1322i | −0.0209633 | − | 0.443949i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.30447 | − | 13.2478i | 0.145352 | − | 0.447347i | −0.851704 | − | 0.524023i | \(-0.824431\pi\) |
0.997056 | + | 0.0766761i | \(0.0244307\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −59.9157 | − | 43.5313i | −2.02091 | − | 1.46827i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −32.7294 | + | 23.7793i | −1.10268 | + | 0.801145i | −0.981496 | − | 0.191485i | \(-0.938670\pi\) |
−0.121186 | + | 0.992630i | \(0.538670\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.31224 | − | 2.40648i | 0.111466 | − | 0.0809845i | −0.530656 | − | 0.847587i | \(-0.678054\pi\) |
0.642122 | + | 0.766603i | \(0.278054\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.61902 | − | 6.15102i | 0.222496 | − | 0.206764i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.39637 | + | 1.75339i | −0.181192 | + | 0.0588730i | −0.398208 | − | 0.917295i | \(-0.630368\pi\) |
0.217016 | + | 0.976168i | \(0.430368\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.13597 | + | 9.65152i | −0.105177 | + | 0.323701i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −66.7832 | + | 21.6992i | −2.23732 | + | 0.726950i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 23.9601 | 0.801795 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.2188 | − | 30.6302i | −0.475284 | − | 1.02386i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.66394 | − | 5.04297i | 0.122335 | − | 0.168380i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.98418i | 0.299639i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 72.8046i | − | 2.42547i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.43211 | − | 8.85304i | 0.214047 | − | 0.294611i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 42.0029 | − | 5.08377i | 1.39622 | − | 0.168990i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −49.8362 | −1.65478 | −0.827392 | − | 0.561625i | \(-0.810176\pi\) | ||||
−0.827392 | + | 0.561625i | \(0.810176\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 51.2997 | − | 16.6683i | 1.70150 | − | 0.552852i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.08071 | + | 3.32610i | −0.0358057 | + | 0.110199i | −0.967362 | − | 0.253399i | \(-0.918452\pi\) |
0.931556 | + | 0.363597i | \(0.118452\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −35.7613 | + | 11.6196i | −1.18353 | + | 0.384551i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −108.077 | + | 13.0810i | −3.57291 | + | 0.432443i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.27442 | − | 6.01172i | 0.273246 | − | 0.198525i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35.2395 | − | 25.6030i | 1.16244 | − | 0.844564i | 0.172357 | − | 0.985034i | \(-0.444862\pi\) |
0.990085 | + | 0.140471i | \(0.0448616\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −74.2277 | − | 53.9296i | −2.44589 | − | 1.77704i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.549378 | + | 1.69081i | −0.0180830 | + | 0.0556538i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −22.5890 | + | 26.7327i | −0.742722 | + | 0.878965i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −86.1439 | − | 27.9899i | −2.82934 | − | 0.919307i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −20.6493 | − | 15.0026i | −0.677483 | − | 0.492220i | 0.195039 | − | 0.980795i | \(-0.437517\pi\) |
−0.872522 | + | 0.488576i | \(0.837517\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14.8782 | + | 20.4781i | 0.487614 | + | 0.671143i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.49920 | − | 1.81577i | 0.0818201 | − | 0.0594458i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 48.5622 | + | 9.52649i | 1.58815 | + | 0.311549i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.76427 | − | 1.22309i | 0.122973 | − | 0.0399565i | −0.246884 | − | 0.969045i | \(-0.579407\pi\) |
0.369857 | + | 0.929089i | \(0.379407\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 28.6403 | + | 9.30581i | 0.934642 | + | 0.303684i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.54079 | + | 2.45015i | −0.245823 | + | 0.0798727i | −0.429337 | − | 0.903144i | \(-0.641253\pi\) |
0.183514 | + | 0.983017i | \(0.441253\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.9114i | 0.453018i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 23.4797 | − | 21.8196i | 0.763794 | − | 0.709791i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.630350 | + | 0.457976i | 0.0204836 | + | 0.0148822i | 0.597980 | − | 0.801511i | \(-0.295970\pi\) |
−0.577496 | + | 0.816393i | \(0.695970\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.83921i | 0.124626i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 57.8664 | 1.87645 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.29429 | − | 8.66334i | 0.203892 | − | 0.280633i | −0.694810 | − | 0.719194i | \(-0.744511\pi\) |
0.898702 | + | 0.438560i | \(0.144511\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.91720 | + | 0.964613i | 0.159117 | + | 0.0312141i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 77.7008 | 2.51171 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.32402 | + | 4.07492i | 0.0427549 | + | 0.131586i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.93566 | + | 27.5011i | −0.288247 | + | 0.887134i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 14.8940 | + | 45.8391i | 0.479953 | + | 1.47714i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −44.3427 | − | 24.6796i | −1.42744 | − | 0.794465i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.37219 | − | 7.39419i | −0.172758 | − | 0.237781i | 0.713854 | − | 0.700294i | \(-0.246948\pi\) |
−0.886612 | + | 0.462513i | \(0.846948\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 63.8435 | − | 46.3850i | 2.05095 | − | 1.49010i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.2665 | + | 21.0125i | −0.489924 | + | 0.674323i | −0.980374 | − | 0.197147i | \(-0.936833\pi\) |
0.490450 | + | 0.871469i | \(0.336833\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.07508 | − | 15.6195i | 0.162700 | − | 0.500738i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −13.8749 | + | 3.40859i | −0.444351 | + | 0.109162i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 29.0332 | + | 9.43346i | 0.928855 | + | 0.301803i | 0.734094 | − | 0.679048i | \(-0.237607\pi\) |
0.194760 | + | 0.980851i | \(0.437607\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.09631 | − | 8.39085i | 0.194839 | − | 0.268173i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.9251 | − | 15.0372i | −0.348813 | − | 0.480100i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 23.5163 | + | 32.3674i | 0.750052 | + | 1.03236i | 0.997977 | + | 0.0635791i | \(0.0202515\pi\) |
−0.247924 | + | 0.968779i | \(0.579748\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 26.3311 | − | 12.2231i | 0.838978 | − | 0.389462i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.07265 | − | 18.6897i | −0.193295 | − | 0.594900i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.14291 | + | 1.99595i | 0.195333 | + | 0.0634676i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14.8786 | − | 45.7916i | −0.472634 | − | 1.45462i | −0.849122 | − | 0.528197i | \(-0.822868\pi\) |
0.376488 | − | 0.926422i | \(-0.377132\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 22.7314i | − | 0.721358i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19.8095 | − | 35.5923i | 0.628003 | − | 1.12835i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.969621 | − | 0.704471i | −0.0307082 | − | 0.0223108i | 0.572325 | − | 0.820027i | \(-0.306041\pi\) |
−0.603033 | + | 0.797716i | \(0.706041\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −85.3292 | −2.69970 |
(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 | 800.2.be.a.529.2 | 112 | ||
4.3 | odd | 2 | 200.2.o.a.29.16 | yes | 112 | ||
8.3 | odd | 2 | 200.2.o.a.29.10 | ✓ | 112 | ||
8.5 | even | 2 | inner | 800.2.be.a.529.27 | 112 | ||
20.3 | even | 4 | 1000.2.t.b.101.2 | 224 | |||
20.7 | even | 4 | 1000.2.t.b.101.55 | 224 | |||
20.19 | odd | 2 | 1000.2.o.a.149.13 | 112 | |||
25.19 | even | 10 | inner | 800.2.be.a.369.27 | 112 | ||
40.3 | even | 4 | 1000.2.t.b.101.47 | 224 | |||
40.19 | odd | 2 | 1000.2.o.a.149.19 | 112 | |||
40.27 | even | 4 | 1000.2.t.b.101.10 | 224 | |||
100.19 | odd | 10 | 200.2.o.a.69.10 | yes | 112 | ||
100.31 | odd | 10 | 1000.2.o.a.349.19 | 112 | |||
100.67 | even | 20 | 1000.2.t.b.901.10 | 224 | |||
100.83 | even | 20 | 1000.2.t.b.901.47 | 224 | |||
200.19 | odd | 10 | 200.2.o.a.69.16 | yes | 112 | ||
200.67 | even | 20 | 1000.2.t.b.901.55 | 224 | |||
200.69 | even | 10 | inner | 800.2.be.a.369.2 | 112 | ||
200.83 | even | 20 | 1000.2.t.b.901.2 | 224 | |||
200.131 | odd | 10 | 1000.2.o.a.349.13 | 112 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
200.2.o.a.29.10 | ✓ | 112 | 8.3 | odd | 2 | ||
200.2.o.a.29.16 | yes | 112 | 4.3 | odd | 2 | ||
200.2.o.a.69.10 | yes | 112 | 100.19 | odd | 10 | ||
200.2.o.a.69.16 | yes | 112 | 200.19 | odd | 10 | ||
800.2.be.a.369.2 | 112 | 200.69 | even | 10 | inner | ||
800.2.be.a.369.27 | 112 | 25.19 | even | 10 | inner | ||
800.2.be.a.529.2 | 112 | 1.1 | even | 1 | trivial | ||
800.2.be.a.529.27 | 112 | 8.5 | even | 2 | inner | ||
1000.2.o.a.149.13 | 112 | 20.19 | odd | 2 | |||
1000.2.o.a.149.19 | 112 | 40.19 | odd | 2 | |||
1000.2.o.a.349.13 | 112 | 200.131 | odd | 10 | |||
1000.2.o.a.349.19 | 112 | 100.31 | odd | 10 | |||
1000.2.t.b.101.2 | 224 | 20.3 | even | 4 | |||
1000.2.t.b.101.10 | 224 | 40.27 | even | 4 | |||
1000.2.t.b.101.47 | 224 | 40.3 | even | 4 | |||
1000.2.t.b.101.55 | 224 | 20.7 | even | 4 | |||
1000.2.t.b.901.2 | 224 | 200.83 | even | 20 | |||
1000.2.t.b.901.10 | 224 | 100.67 | even | 20 | |||
1000.2.t.b.901.47 | 224 | 100.83 | even | 20 | |||
1000.2.t.b.901.55 | 224 | 200.67 | even | 20 |