Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1000,2,Mod(101,1000)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1000, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 5, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1000.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1000 = 2^{3} \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1000.t (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: | \(7.98504020213\) |
Analytic rank: | \(0\) |
Dimension: | \(224\) |
Relative dimension: | \(56\) over \(\Q(\zeta_{10})\) |
Twist minimal: | no (minimal twist has level 200) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 901.47 | ||
Character | \(\chi\) | \(=\) | 1000.901 |
Dual form | 1000.2.t.b.101.47 |
$q$-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 \(\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times\).
\(n\) | \(377\) | \(501\) | \(751\) |
\(\chi(n)\) | \(e\left(\frac{2}{5}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.21863 | − | 0.717591i | 0.861703 | − | 0.507414i | ||||
\(3\) | 1.84742 | + | 2.54275i | 1.06661 | + | 1.46806i | 0.873463 | + | 0.486890i | \(0.161869\pi\) |
0.193145 | + | 0.981170i | \(0.438131\pi\) | |||||||
\(4\) | 0.970125 | − | 1.74896i | 0.485063 | − | 0.874479i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 4.07598 | + | 1.77299i | 1.66401 | + | 0.723819i | ||||
\(7\) | −1.17589 | −0.444443 | −0.222222 | − | 0.974996i | \(-0.571331\pi\) | ||||
−0.222222 | + | 0.974996i | \(0.571331\pi\) | |||||||
\(8\) | −0.0728129 | − | 2.82749i | −0.0257432 | − | 0.999669i | ||||
\(9\) | −2.12559 | + | 6.54190i | −0.708531 | + | 2.18063i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.77756 | − | 1.22741i | 1.13898 | − | 0.370077i | 0.321997 | − | 0.946741i | \(-0.395646\pi\) |
0.816981 | + | 0.576664i | \(0.195646\pi\) | |||||||
\(12\) | 6.23940 | − | 0.764270i | 1.80116 | − | 0.220626i | ||||
\(13\) | 0.864656 | + | 0.280944i | 0.239812 | + | 0.0779198i | 0.426457 | − | 0.904508i | \(-0.359761\pi\) |
−0.186645 | + | 0.982427i | \(0.559761\pi\) | |||||||
\(14\) | −1.43297 | + | 0.843806i | −0.382978 | + | 0.225517i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.11771 | − | 3.39342i | −0.529429 | − | 0.848355i | ||||
\(17\) | 4.50780 | + | 3.27511i | 1.09330 | + | 0.794331i | 0.979954 | − | 0.199225i | \(-0.0638424\pi\) |
0.113348 | + | 0.993555i | \(0.463842\pi\) | |||||||
\(18\) | 2.10410 | + | 9.49747i | 0.495940 | + | 2.23858i | ||||
\(19\) | −2.64864 | + | 3.64555i | −0.607641 | + | 0.836346i | −0.996381 | − | 0.0850017i | \(-0.972910\pi\) |
0.388740 | + | 0.921348i | \(0.372910\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.17235 | − | 2.98999i | −0.474047 | − | 0.652469i | ||||
\(22\) | 3.72268 | − | 4.20650i | 0.793679 | − | 0.896829i | ||||
\(23\) | 0.674105 | + | 2.07468i | 0.140561 | + | 0.432601i | 0.996413 | − | 0.0846183i | \(-0.0269671\pi\) |
−0.855853 | + | 0.517220i | \(0.826967\pi\) | |||||||
\(24\) | 7.05510 | − | 5.40870i | 1.44012 | − | 1.10405i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.25530 | − | 0.278103i | 0.246184 | − | 0.0545404i | ||||
\(27\) | −11.5937 | + | 3.76703i | −2.23122 | + | 0.724966i | ||||
\(28\) | −1.14076 | + | 2.05658i | −0.215583 | + | 0.388656i | ||||
\(29\) | −3.65841 | − | 5.03536i | −0.679349 | − | 0.935044i | 0.320577 | − | 0.947223i | \(-0.396123\pi\) |
−0.999926 | + | 0.0121788i | \(0.996123\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.16778 | − | 0.848445i | −0.209740 | − | 0.152385i | 0.477956 | − | 0.878384i | \(-0.341378\pi\) |
−0.687696 | + | 0.725999i | \(0.741378\pi\) | |||||||
\(32\) | −5.01580 | − | 2.61567i | −0.886677 | − | 0.462390i | ||||
\(33\) | 10.0997 | + | 7.33789i | 1.75814 | + | 1.27736i | ||||
\(34\) | 7.84354 | + | 0.756392i | 1.34516 | + | 0.129720i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 9.37942 | + | 10.0640i | 1.56324 | + | 1.67734i | ||||
\(37\) | 6.65712 | + | 2.16303i | 1.09442 | + | 0.355600i | 0.799954 | − | 0.600061i | \(-0.204857\pi\) |
0.294470 | + | 0.955661i | \(0.404857\pi\) | |||||||
\(38\) | −0.611709 | + | 6.34322i | −0.0992323 | + | 1.02901i | ||||
\(39\) | 0.883011 | + | 2.71763i | 0.141395 | + | 0.435169i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.97065 | − | 6.06503i | 0.307763 | − | 0.947198i | −0.670868 | − | 0.741577i | \(-0.734078\pi\) |
0.978632 | − | 0.205622i | \(-0.0659216\pi\) | |||||||
\(42\) | −4.79289 | − | 2.08483i | −0.739559 | − | 0.321697i | ||||
\(43\) | − | 2.96089i | − | 0.451532i | −0.974182 | − | 0.225766i | \(-0.927512\pi\) | ||
0.974182 | − | 0.225766i | \(-0.0724884\pi\) | |||||||
\(44\) | 1.51803 | − | 7.79754i | 0.228852 | − | 1.17552i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.31026 | + | 2.04454i | 0.340629 | + | 0.301451i | ||||
\(47\) | 4.30172 | − | 3.12538i | 0.627470 | − | 0.455884i | −0.228053 | − | 0.973649i | \(-0.573236\pi\) |
0.855523 | + | 0.517765i | \(0.173236\pi\) | |||||||
\(48\) | 4.71632 | − | 11.6539i | 0.680743 | − | 1.68209i | ||||
\(49\) | −5.61729 | −0.802470 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 17.5127i | 2.45227i | ||||||||
\(52\) | 1.33018 | − | 1.23970i | 0.184463 | − | 0.171915i | ||||
\(53\) | −7.68016 | − | 10.5708i | −1.05495 | − | 1.45202i | −0.884436 | − | 0.466661i | \(-0.845457\pi\) |
−0.170515 | − | 0.985355i | \(-0.554543\pi\) | |||||||
\(54\) | −11.4253 | + | 12.9102i | −1.55479 | + | 1.75685i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.0856196 | + | 3.32481i | 0.0114414 | + | 0.444296i | ||||
\(57\) | −14.1629 | −1.87592 | ||||||||
\(58\) | −8.07158 | − | 3.51101i | −1.05985 | − | 0.461019i | ||||
\(59\) | 1.22277 | + | 0.397301i | 0.159191 | + | 0.0517242i | 0.387528 | − | 0.921858i | \(-0.373329\pi\) |
−0.228338 | + | 0.973582i | \(0.573329\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.7321 | + | 4.78675i | −1.88625 | + | 0.612881i | −0.903306 | + | 0.428996i | \(0.858867\pi\) |
−0.982948 | + | 0.183885i | \(0.941133\pi\) | |||||||
\(62\) | −2.03194 | − | 0.195950i | −0.258056 | − | 0.0248857i | ||||
\(63\) | 2.49945 | − | 7.69253i | 0.314902 | − | 0.969167i | ||||
\(64\) | −7.98940 | + | 0.411755i | −0.998675 | + | 0.0514694i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 17.5735 | + | 1.69470i | 2.16314 | + | 0.208603i | ||||
\(67\) | 1.78477 | − | 2.45652i | 0.218044 | − | 0.300112i | −0.685957 | − | 0.727642i | \(-0.740616\pi\) |
0.904001 | + | 0.427530i | \(0.140616\pi\) | |||||||
\(68\) | 10.1012 | − | 4.70669i | 1.22495 | − | 0.570770i | ||||
\(69\) | −4.03005 | + | 5.54689i | −0.485161 | + | 0.667767i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.58201 | + | 1.14940i | −0.187750 | + | 0.136409i | −0.677690 | − | 0.735348i | \(-0.737019\pi\) |
0.489940 | + | 0.871756i | \(0.337019\pi\) | |||||||
\(72\) | 18.6519 | + | 5.53375i | 2.19815 | + | 0.652159i | ||||
\(73\) | −1.30493 | − | 4.01616i | −0.152731 | − | 0.470056i | 0.845193 | − | 0.534461i | \(-0.179485\pi\) |
−0.997924 | + | 0.0644044i | \(0.979485\pi\) | |||||||
\(74\) | 9.66475 | − | 2.14116i | 1.12350 | − | 0.248905i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.80639 | + | 8.16901i | 0.436623 | + | 0.937049i | ||||
\(77\) | −4.44199 | + | 1.44329i | −0.506211 | + | 0.164478i | ||||
\(78\) | 3.02621 | + | 2.67815i | 0.342651 | + | 0.303240i | ||||
\(79\) | −2.23200 | + | 1.62164i | −0.251119 | + | 0.182449i | −0.706223 | − | 0.707990i | \(-0.749602\pi\) |
0.455103 | + | 0.890439i | \(0.349602\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −14.3025 | − | 10.3914i | −1.58917 | − | 1.15460i | ||||
\(82\) | −1.95072 | − | 8.80515i | −0.215421 | − | 0.972366i | ||||
\(83\) | −5.56443 | + | 7.65878i | −0.610775 | + | 0.840660i | −0.996641 | − | 0.0818950i | \(-0.973903\pi\) |
0.385866 | + | 0.922555i | \(0.373903\pi\) | |||||||
\(84\) | −7.33683 | + | 0.898695i | −0.800513 | + | 0.0980557i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.12471 | − | 3.60824i | −0.229113 | − | 0.389086i | ||||
\(87\) | 6.04509 | − | 18.6049i | 0.648101 | − | 1.99465i | ||||
\(88\) | −3.74553 | − | 10.5917i | −0.399275 | − | 1.12907i | ||||
\(89\) | −0.806910 | − | 2.48341i | −0.0855323 | − | 0.263241i | 0.899139 | − | 0.437664i | \(-0.144194\pi\) |
−0.984671 | + | 0.174423i | \(0.944194\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.01674 | − | 0.330358i | −0.106583 | − | 0.0346309i | ||||
\(92\) | 4.28250 | + | 0.833719i | 0.446482 | + | 0.0869213i | ||||
\(93\) | − | 4.53682i | − | 0.470447i | ||||||
\(94\) | 2.99946 | − | 6.89556i | 0.309371 | − | 0.711223i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.61528 | − | 17.5862i | −0.266920 | − | 1.79488i | ||||
\(97\) | 0.235869 | − | 0.171369i | 0.0239489 | − | 0.0173999i | −0.575746 | − | 0.817628i | \(-0.695288\pi\) |
0.599695 | + | 0.800228i | \(0.295288\pi\) | |||||||
\(98\) | −6.84541 | + | 4.03092i | −0.691491 | + | 0.407184i | ||||
\(99\) | 27.3214i | 2.74590i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 7.84171i | − | 0.780280i | −0.920756 | − | 0.390140i | \(-0.872427\pi\) | ||
0.920756 | − | 0.390140i | \(-0.127573\pi\) | |||||||
\(102\) | 12.5670 | + | 21.3416i | 1.24432 | + | 2.11313i | ||||
\(103\) | 10.6532 | − | 7.73997i | 1.04969 | − | 0.762642i | 0.0775342 | − | 0.996990i | \(-0.475295\pi\) |
0.972153 | + | 0.234347i | \(0.0752953\pi\) | |||||||
\(104\) | 0.731407 | − | 2.46526i | 0.0717204 | − | 0.241739i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −16.9448 | − | 7.37074i | −1.64583 | − | 0.715909i | ||||
\(107\) | 7.00700i | 0.677392i | 0.940896 | + | 0.338696i | \(0.109986\pi\) | ||||
−0.940896 | + | 0.338696i | \(0.890014\pi\) | |||||||
\(108\) | −4.65899 | + | 23.9315i | −0.448312 | + | 2.30281i | ||||
\(109\) | −2.56991 | − | 0.835013i | −0.246152 | − | 0.0799797i | 0.183342 | − | 0.983049i | \(-0.441308\pi\) |
−0.429495 | + | 0.903069i | \(0.641308\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.79844 | + | 20.9235i | 0.645280 | + | 1.98597i | ||||
\(112\) | 2.49019 | + | 3.99027i | 0.235301 | + | 0.377045i | ||||
\(113\) | 1.41241 | − | 4.34695i | 0.132868 | − | 0.408926i | −0.862384 | − | 0.506255i | \(-0.831030\pi\) |
0.995252 | + | 0.0973282i | \(0.0310296\pi\) | |||||||
\(114\) | −17.2593 | + | 10.1632i | −1.61649 | + | 0.951868i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −12.3558 | + | 1.51347i | −1.14720 | + | 0.140522i | ||||
\(117\) | −3.67581 | + | 5.05932i | −0.339829 | + | 0.467734i | ||||
\(118\) | 1.77520 | − | 0.393283i | 0.163420 | − | 0.0362047i | ||||
\(119\) | −5.30066 | − | 3.85116i | −0.485911 | − | 0.353035i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.86428 | − | 2.80757i | 0.351299 | − | 0.255233i | ||||
\(122\) | −14.5181 | + | 16.4049i | −1.31441 | + | 1.48523i | ||||
\(123\) | 19.0625 | − | 6.19378i | 1.71881 | − | 0.558474i | ||||
\(124\) | −2.61679 | + | 1.21931i | −0.234995 | + | 0.109497i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.47418 | − | 11.1679i | −0.220417 | − | 0.994919i | ||||
\(127\) | −2.66690 | − | 8.20787i | −0.236649 | − | 0.728330i | −0.996898 | − | 0.0786992i | \(-0.974923\pi\) |
0.760250 | − | 0.649631i | \(-0.225077\pi\) | |||||||
\(128\) | −9.44066 | + | 6.23490i | −0.834444 | + | 0.551093i | ||||
\(129\) | 7.52882 | − | 5.47001i | 0.662876 | − | 0.481607i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.11250 | + | 7.03676i | −0.446681 | + | 0.614804i | −0.971680 | − | 0.236299i | \(-0.924066\pi\) |
0.524999 | + | 0.851103i | \(0.324066\pi\) | |||||||
\(132\) | 22.6317 | − | 10.5454i | 1.96983 | − | 0.917855i | ||||
\(133\) | 3.11451 | − | 4.28675i | 0.270062 | − | 0.371708i | ||||
\(134\) | 0.412194 | − | 4.27432i | 0.0356082 | − | 0.369245i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.93211 | − | 12.9842i | 0.765922 | − | 1.11339i | ||||
\(137\) | −1.12598 | + | 3.46540i | −0.0961988 | + | 0.296069i | −0.987564 | − | 0.157216i | \(-0.949748\pi\) |
0.891365 | + | 0.453285i | \(0.149748\pi\) | |||||||
\(138\) | −0.930747 | + | 9.65155i | −0.0792305 | + | 0.821594i | ||||
\(139\) | 13.2832 | − | 4.31597i | 1.12666 | − | 0.366075i | 0.314357 | − | 0.949305i | \(-0.398211\pi\) |
0.812307 | + | 0.583230i | \(0.198211\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15.8941 | + | 5.16432i | 1.33853 | + | 0.434914i | ||||
\(142\) | −1.10309 | + | 2.53593i | −0.0925693 | + | 0.212811i | ||||
\(143\) | 3.61112 | 0.301977 | ||||||||
\(144\) | 26.7008 | − | 6.64085i | 2.22507 | − | 0.553404i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.47219 | − | 3.95781i | −0.370121 | − | 0.327551i | ||||
\(147\) | −10.3775 | − | 14.2834i | −0.855921 | − | 1.17807i | ||||
\(148\) | 10.2413 | − | 9.54463i | 0.841829 | − | 0.784563i | ||||
\(149\) | 2.61363i | 0.214117i | 0.994253 | + | 0.107059i | \(0.0341433\pi\) | ||||
−0.994253 | + | 0.107059i | \(0.965857\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.6178 | 0.864067 | 0.432034 | − | 0.901857i | \(-0.357796\pi\) | ||||
0.432034 | + | 0.901857i | \(0.357796\pi\) | |||||||
\(152\) | 10.5006 | + | 7.22357i | 0.851711 | + | 0.585909i | ||||
\(153\) | −31.0072 | + | 22.5280i | −2.50678 | + | 1.82128i | ||||
\(154\) | −4.37745 | + | 4.94637i | −0.352745 | + | 0.398590i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 5.60965 | + | 1.09209i | 0.449132 | + | 0.0874372i | ||||
\(157\) | − | 3.90358i | − | 0.311539i | −0.987793 | − | 0.155770i | \(-0.950214\pi\) | ||
0.987793 | − | 0.155770i | \(-0.0497857\pi\) | |||||||
\(158\) | −1.55631 | + | 3.57784i | −0.123813 | + | 0.284638i | ||||
\(159\) | 12.6906 | − | 39.0575i | 1.00643 | − | 3.09746i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.792671 | − | 2.43959i | −0.0624712 | − | 0.192267i | ||||
\(162\) | −24.8863 | − | 2.39991i | −1.95525 | − | 0.188555i | ||||
\(163\) | −18.6687 | − | 6.06584i | −1.46225 | − | 0.475114i | −0.533493 | − | 0.845805i | \(-0.679121\pi\) |
−0.928756 | + | 0.370691i | \(0.879121\pi\) | |||||||
\(164\) | −8.69571 | − | 9.33042i | −0.679021 | − | 0.728583i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.28511 | + | 13.3262i | −0.0997441 | + | 1.03431i | ||||
\(167\) | 13.6261 | + | 9.89993i | 1.05442 | + | 0.766080i | 0.973048 | − | 0.230604i | \(-0.0740702\pi\) |
0.0813708 | + | 0.996684i | \(0.474070\pi\) | |||||||
\(168\) | −8.29599 | + | 6.36002i | −0.640050 | + | 0.490686i | ||||
\(169\) | −9.84852 | − | 7.15537i | −0.757579 | − | 0.550413i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −18.2189 | − | 25.0761i | −1.39323 | − | 1.91762i | ||||
\(172\) | −5.17848 | − | 2.87244i | −0.394855 | − | 0.219021i | ||||
\(173\) | 9.68309 | − | 3.14623i | 0.736192 | − | 0.239203i | 0.0831625 | − | 0.996536i | \(-0.473498\pi\) |
0.653029 | + | 0.757333i | \(0.273498\pi\) | |||||||
\(174\) | −5.98396 | − | 27.0104i | −0.453643 | − | 2.04765i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −12.1649 | − | 10.2196i | −0.916964 | − | 0.770328i | ||||
\(177\) | 1.24872 | + | 3.84317i | 0.0938598 | + | 0.288871i | ||||
\(178\) | −2.76540 | − | 2.44733i | −0.207276 | − | 0.183435i | ||||
\(179\) | −8.87687 | − | 12.2180i | −0.663488 | − | 0.913214i | 0.336102 | − | 0.941826i | \(-0.390891\pi\) |
−0.999591 | + | 0.0286120i | \(0.990891\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.1217 | + | 15.3077i | −0.826668 | + | 1.13781i | 0.161866 | + | 0.986813i | \(0.448249\pi\) |
−0.988534 | + | 0.150998i | \(0.951751\pi\) | |||||||
\(182\) | −1.47609 | + | 0.327017i | −0.109415 | + | 0.0242401i | ||||
\(183\) | −39.3879 | − | 28.6170i | −2.91164 | − | 2.11543i | ||||
\(184\) | 5.81706 | − | 2.05709i | 0.428839 | − | 0.151651i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −3.25559 | − | 5.52872i | −0.238711 | − | 0.405385i | ||||
\(187\) | 21.0484 | + | 6.83904i | 1.53921 | + | 0.500120i | ||||
\(188\) | −1.29296 | − | 10.5555i | −0.0942986 | − | 0.769841i | ||||
\(189\) | 13.6329 | − | 4.42960i | 0.991649 | − | 0.322206i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.692493 | + | 2.13127i | −0.0501070 | + | 0.154214i | −0.972979 | − | 0.230893i | \(-0.925835\pi\) |
0.922872 | + | 0.385106i | \(0.125835\pi\) | |||||||
\(192\) | −15.8068 | − | 19.5544i | −1.14075 | − | 1.41122i | ||||
\(193\) | 22.6952 | 1.63363 | 0.816817 | − | 0.576896i | \(-0.195736\pi\) | ||||
0.816817 | + | 0.576896i | \(0.195736\pi\) | |||||||
\(194\) | 0.164465 | − | 0.378093i | 0.0118079 | − | 0.0271455i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.44948 | + | 9.82441i | −0.389248 | + | 0.701744i | ||||
\(197\) | −7.63095 | − | 10.5031i | −0.543682 | − | 0.748315i | 0.445456 | − | 0.895304i | \(-0.353042\pi\) |
−0.989138 | + | 0.146989i | \(0.953042\pi\) | |||||||
\(198\) | 19.6056 | + | 33.2947i | 1.39331 | + | 2.36615i | ||||
\(199\) | 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 | ||||||||
\(202\) | −5.62715 | − | 9.55616i | −0.395925 | − | 0.672369i | ||||
\(203\) | 4.30187 | + | 5.92102i | 0.301932 | + | 0.415574i | ||||
\(204\) | 30.6290 | + | 16.9895i | 2.14446 | + | 1.18951i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 7.42814 | − | 17.0768i | 0.517543 | − | 1.18980i | ||||
\(207\) | −15.0052 | −1.04294 | ||||||||
\(208\) | −0.877735 | − | 3.52910i | −0.0608599 | − | 0.244699i | ||||
\(209\) | −5.53086 | + | 17.0222i | −0.382578 | + | 1.17745i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.67102 | + | 0.542946i | −0.115037 | + | 0.0373779i | −0.365970 | − | 0.930627i | \(-0.619263\pi\) |
0.250933 | + | 0.968005i | \(0.419263\pi\) | |||||||
\(212\) | −25.9387 | + | 3.17725i | −1.78148 | + | 0.218215i | ||||
\(213\) | −5.84528 | − | 1.89925i | −0.400512 | − | 0.130134i | ||||
\(214\) | 5.02816 | + | 8.53895i | 0.343718 | + | 0.583711i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 11.4954 | + | 32.5069i | 0.782165 | + | 2.21181i | ||||
\(217\) | 1.37318 | + | 0.997675i | 0.0932177 | + | 0.0677266i | ||||
\(218\) | −3.73097 | + | 0.826569i | −0.252693 | + | 0.0559823i | ||||
\(219\) | 7.80136 | − | 10.7377i | 0.527167 | − | 0.725583i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.97757 | + | 4.09828i | 0.200293 | + | 0.275680i | ||||
\(222\) | 23.2993 | + | 20.6195i | 1.56375 | + | 1.38389i | ||||
\(223\) | 0.481630 | + | 1.48230i | 0.0322523 | + | 0.0992625i | 0.965887 | − | 0.258965i | \(-0.0833813\pi\) |
−0.933634 | + | 0.358227i | \(0.883381\pi\) | |||||||
\(224\) | 5.89801 | + | 3.07573i | 0.394077 | + | 0.205506i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.39813 | − | 6.31086i | −0.0930020 | − | 0.419792i | ||||
\(227\) | 8.77081 | − | 2.84981i | 0.582139 | − | 0.189148i | −0.00311955 | − | 0.999995i | \(-0.500993\pi\) |
0.585259 | + | 0.810847i | \(0.300993\pi\) | |||||||
\(228\) | −13.7398 | + | 24.7703i | −0.909939 | + | 1.64045i | ||||
\(229\) | −6.64077 | − | 9.14023i | −0.438834 | − | 0.604003i | 0.531118 | − | 0.847298i | \(-0.321772\pi\) |
−0.969953 | + | 0.243294i | \(0.921772\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −11.8761 | − | 8.62852i | −0.781393 | − | 0.567715i | ||||
\(232\) | −13.9711 | + | 10.7107i | −0.917245 | + | 0.703195i | ||||
\(233\) | 10.0570 | + | 7.30682i | 0.658854 | + | 0.478685i | 0.866276 | − | 0.499566i | \(-0.166507\pi\) |
−0.207422 | + | 0.978252i | \(0.566507\pi\) | |||||||
\(234\) | −0.848934 | + | 8.80318i | −0.0554966 | + | 0.575482i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.88110 | − | 1.75314i | 0.122449 | − | 0.114119i | ||||
\(237\) | −8.24687 | − | 2.67957i | −0.535692 | − | 0.174057i | ||||
\(238\) | −9.22311 | − | 0.889430i | −0.597845 | − | 0.0576532i | ||||
\(239\) | 8.53966 | + | 26.2824i | 0.552384 | + | 1.70006i | 0.702752 | + | 0.711435i | \(0.251954\pi\) |
−0.150368 | + | 0.988630i | \(0.548046\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.32369 | + | 4.07389i | −0.0852663 | + | 0.262423i | −0.984595 | − | 0.174851i | \(-0.944056\pi\) |
0.899329 | + | 0.437273i | \(0.144056\pi\) | |||||||
\(242\) | 2.69445 | − | 6.19437i | 0.173206 | − | 0.398189i | ||||
\(243\) | − | 18.9940i | − | 1.21846i | ||||||
\(244\) | −5.92016 | + | 30.4096i | −0.378999 | + | 1.94678i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 18.7855 | − | 21.2270i | 1.19772 | − | 1.35338i | ||||
\(247\) | −3.31436 | + | 2.40802i | −0.210888 | + | 0.153219i | ||||
\(248\) | −2.31394 | + | 3.36368i | −0.146935 | + | 0.213594i | ||||
\(249\) | −29.7542 | −1.88560 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 13.4000i | − | 0.845800i | −0.906176 | − | 0.422900i | \(-0.861012\pi\) | ||
0.906176 | − | 0.422900i | \(-0.138988\pi\) | |||||||
\(252\) | −11.0291 | − | 11.8342i | −0.694770 | − | 0.745482i | ||||
\(253\) | 5.09295 | + | 7.00985i | 0.320191 | + | 0.440705i | ||||
\(254\) | −9.13986 | − | 8.08862i | −0.573486 | − | 0.507525i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7.03057 | + | 14.3726i | −0.439411 | + | 0.898286i | ||||
\(257\) | 7.81899 | 0.487735 | 0.243868 | − | 0.969809i | \(-0.421584\pi\) | ||||
0.243868 | + | 0.969809i | \(0.421584\pi\) | |||||||
\(258\) | 5.24963 | − | 12.0685i | 0.326827 | − | 0.751355i | ||||
\(259\) | −7.82802 | − | 2.54348i | −0.486409 | − | 0.158044i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 40.7171 | − | 13.2298i | 2.52033 | − | 0.818904i | ||||
\(262\) | −1.18074 | + | 12.2439i | −0.0729464 | + | 0.756431i | ||||
\(263\) | −8.47975 | + | 26.0980i | −0.522884 | + | 1.60927i | 0.245579 | + | 0.969377i | \(0.421022\pi\) |
−0.768463 | + | 0.639894i | \(0.778978\pi\) | |||||||
\(264\) | 20.0124 | − | 29.0912i | 1.23168 | − | 1.79044i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.719300 | − | 7.45891i | 0.0441031 | − | 0.457335i | ||||
\(267\) | 4.82401 | − | 6.63968i | 0.295225 | − | 0.406342i | ||||
\(268\) | −2.56490 | − | 5.50461i | −0.156676 | − | 0.336248i | ||||
\(269\) | −12.5408 | + | 17.2610i | −0.764629 | + | 1.05242i | 0.232186 | + | 0.972671i | \(0.425412\pi\) |
−0.996815 | + | 0.0797498i | \(0.974588\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.864363 | − | 0.627996i | 0.0525063 | − | 0.0381481i | −0.561223 | − | 0.827665i | \(-0.689669\pi\) |
0.613729 | + | 0.789517i | \(0.289669\pi\) | |||||||
\(272\) | 1.56758 | − | 22.2326i | 0.0950485 | − | 1.34805i | ||||
\(273\) | −1.03832 | − | 3.19562i | −0.0628420 | − | 0.193408i | ||||
\(274\) | 1.11459 | + | 5.03104i | 0.0673350 | + | 0.303936i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 5.79163 | + | 12.4296i | 0.348615 | + | 0.748173i | ||||
\(277\) | −16.8842 | + | 5.48602i | −1.01448 | + | 0.329623i | −0.768635 | − | 0.639687i | \(-0.779064\pi\) |
−0.245840 | + | 0.969310i | \(0.579064\pi\) | |||||||
\(278\) | 13.0902 | − | 14.7915i | 0.785098 | − | 0.887133i | ||||
\(279\) | 8.03268 | − | 5.83608i | 0.480904 | − | 0.349397i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.77867 | − | 6.37807i | −0.523691 | − | 0.380484i | 0.294301 | − | 0.955713i | \(-0.404913\pi\) |
−0.817993 | + | 0.575229i | \(0.804913\pi\) | |||||||
\(282\) | 23.0750 | − | 5.11210i | 1.37410 | − | 0.304421i | ||||
\(283\) | 13.6517 | − | 18.7899i | 0.811509 | − | 1.11695i | −0.179580 | − | 0.983743i | \(-0.557474\pi\) |
0.991089 | − | 0.133203i | \(-0.0425261\pi\) | |||||||
\(284\) | 0.475502 | + | 3.88193i | 0.0282158 | + | 0.230350i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.40063 | − | 2.59131i | 0.260215 | − | 0.153228i | ||||
\(287\) | −2.31726 | + | 7.13178i | −0.136783 | + | 0.420976i | ||||
\(288\) | 27.7730 | − | 27.2530i | 1.63654 | − | 1.60590i | ||||
\(289\) | 4.34064 | + | 13.3591i | 0.255332 | + | 0.785830i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.871498 | + | 0.283167i | 0.0510881 | + | 0.0165995i | ||||
\(292\) | −8.29005 | − | 1.61391i | −0.485138 | − | 0.0944470i | ||||
\(293\) | 23.5633i | 1.37658i | 0.725434 | + | 0.688291i | \(0.241639\pi\) | ||||
−0.725434 | + | 0.688291i | \(0.758361\pi\) | |||||||
\(294\) | −22.8960 | − | 9.95939i | −1.33532 | − | 0.580844i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.63122 | − | 18.9804i | 0.327308 | − | 1.10322i | ||||
\(297\) | −39.1724 | + | 28.4604i | −2.27301 | + | 1.65144i | ||||
\(298\) | 1.87552 | + | 3.18506i | 0.108646 | + | 0.184505i | ||||
\(299\) | 1.98327i | 0.114696i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.48167i | 0.200680i | ||||||||
\(302\) | 12.9392 | − | 7.61927i | 0.744569 | − | 0.438440i | ||||
\(303\) | 19.9396 | − | 14.4869i | 1.14550 | − | 0.832252i | ||||
\(304\) | 17.9799 | + | 1.26773i | 1.03122 | + | 0.0727094i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −21.6204 | + | 49.7038i | −1.23596 | + | 2.84138i | ||||
\(307\) | 29.1918i | 1.66607i | 0.553223 | + | 0.833033i | \(0.313398\pi\) | ||||
−0.553223 | + | 0.833033i | \(0.686602\pi\) | |||||||
\(308\) | −1.78503 | + | 9.16902i | −0.101712 | + | 0.522453i | ||||
\(309\) | 39.3617 | + | 12.7894i | 2.23921 | + | 0.727563i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.303724 | + | 0.934766i | 0.0172226 | + | 0.0530057i | 0.959298 | − | 0.282394i | \(-0.0911286\pi\) |
−0.942076 | + | 0.335400i | \(0.891129\pi\) | |||||||
\(312\) | 7.61977 | − | 2.69458i | 0.431385 | − | 0.152551i | ||||
\(313\) | −2.96079 | + | 9.11237i | −0.167354 | + | 0.515062i | −0.999202 | − | 0.0399413i | \(-0.987283\pi\) |
0.831848 | + | 0.555003i | \(0.187283\pi\) | |||||||
\(314\) | −2.80117 | − | 4.75702i | −0.158079 | − | 0.268454i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.670866 | + | 5.47686i | 0.0377392 | + | 0.308098i | ||||
\(317\) | −10.8218 | + | 14.8949i | −0.607811 | + | 0.836580i | −0.996395 | − | 0.0848334i | \(-0.972964\pi\) |
0.388584 | + | 0.921413i | \(0.372964\pi\) | |||||||
\(318\) | −12.5622 | − | 56.7034i | −0.704455 | − | 3.17977i | ||||
\(319\) | −20.0003 | − | 14.5311i | −1.11980 | − | 0.813584i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −17.8171 | + | 12.9449i | −0.994453 | + | 0.722512i | ||||
\(322\) | −2.71660 | − | 2.40415i | −0.151390 | − | 0.133978i | ||||
\(323\) | −23.8791 | + | 7.75880i | −1.32867 | + | 0.431711i | ||||
\(324\) | −32.0494 | + | 14.9336i | −1.78052 | + | 0.829643i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −27.1031 | + | 6.00450i | −1.50110 | + | 0.332559i | ||||
\(327\) | −2.62446 | − | 8.07726i | −0.145133 | − | 0.446673i | ||||
\(328\) | −17.2923 | − | 5.13037i | −0.954807 | − | 0.283277i | ||||
\(329\) | −5.05833 | + | 3.67509i | −0.278875 | + | 0.202614i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.25106 | − | 5.85108i | 0.233659 | − | 0.321604i | −0.676046 | − | 0.736860i | \(-0.736308\pi\) |
0.909705 | + | 0.415255i | \(0.136308\pi\) | |||||||
\(332\) | 7.99669 | + | 17.1619i | 0.438876 | + | 0.941883i | ||||
\(333\) | −28.3007 | + | 38.9525i | −1.55087 | + | 2.13458i | ||||
\(334\) | 23.7093 | + | 2.28641i | 1.29731 | + | 0.125107i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −5.54586 | + | 13.7037i | −0.302551 | + | 0.747596i | ||||
\(337\) | 2.81684 | − | 8.66935i | 0.153443 | − | 0.472250i | −0.844557 | − | 0.535466i | \(-0.820136\pi\) |
0.998000 | + | 0.0632165i | \(0.0201359\pi\) | |||||||
\(338\) | −17.1363 | − | 1.65254i | −0.932094 | − | 0.0898865i | ||||
\(339\) | 13.6625 | − | 4.43923i | 0.742047 | − | 0.241106i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.45277 | − | 1.77171i | −0.295284 | − | 0.0959436i | ||||
\(342\) | −40.1965 | − | 17.4848i | −2.17358 | − | 0.945472i | ||||
\(343\) | 14.8365 | 0.801096 | ||||||||
\(344\) | −8.37189 | + | 0.215591i | −0.451382 | + | 0.0116239i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.54241 | − | 10.7826i | 0.513003 | − | 0.579676i | ||||
\(347\) | −6.01350 | − | 8.27687i | −0.322821 | − | 0.444326i | 0.616505 | − | 0.787351i | \(-0.288548\pi\) |
−0.939326 | + | 0.343026i | \(0.888548\pi\) | |||||||
\(348\) | −26.6746 | − | 28.6216i | −1.42991 | − | 1.53428i | ||||
\(349\) | − | 4.76436i | − | 0.255030i | −0.991837 | − | 0.127515i | \(-0.959300\pi\) | ||
0.991837 | − | 0.127515i | \(-0.0407001\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.0829 | −0.591562 | ||||||||
\(352\) | −22.1580 | − | 3.72445i | −1.18103 | − | 0.198514i | ||||
\(353\) | −14.7692 | + | 10.7305i | −0.786087 | + | 0.571126i | −0.906800 | − | 0.421562i | \(-0.861482\pi\) |
0.120713 | + | 0.992687i | \(0.461482\pi\) | |||||||
\(354\) | 4.27956 | + | 3.78734i | 0.227456 | + | 0.201295i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −5.12619 | − | 0.997969i | −0.271688 | − | 0.0528923i | ||||
\(357\) | − | 20.5930i | − | 1.08990i | ||||||
\(358\) | −19.5851 | − | 8.51923i | −1.03511 | − | 0.450255i | ||||
\(359\) | −5.64467 | + | 17.3725i | −0.297914 | + | 0.916885i | 0.684313 | + | 0.729188i | \(0.260102\pi\) |
−0.982227 | + | 0.187697i | \(0.939898\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.403370 | − | 1.24145i | −0.0212300 | − | 0.0653393i | ||||
\(362\) | −2.56857 | + | 26.6353i | −0.135001 | + | 1.39992i | ||||
\(363\) | 14.2779 | + | 4.63917i | 0.749396 | + | 0.243493i | ||||
\(364\) | −1.56414 | + | 1.45774i | −0.0819834 | + | 0.0764065i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −68.5347 | − | 6.60914i | −3.58237 | − | 0.345466i | ||||
\(367\) | 12.1811 | + | 8.85005i | 0.635846 | + | 0.461969i | 0.858421 | − | 0.512947i | \(-0.171446\pi\) |
−0.222575 | + | 0.974916i | \(0.571446\pi\) | |||||||
\(368\) | 5.61270 | − | 6.68111i | 0.292582 | − | 0.348277i | ||||
\(369\) | 35.4880 | + | 25.7835i | 1.84743 | + | 1.34224i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.03100 | + | 12.4301i | 0.468866 | + | 0.645339i | ||||
\(372\) | −7.93472 | − | 4.40129i | −0.411396 | − | 0.228196i | ||||
\(373\) | −0.674295 | + | 0.219092i | −0.0349137 | + | 0.0113441i | −0.326422 | − | 0.945224i | \(-0.605843\pi\) |
0.291508 | + | 0.956568i | \(0.405843\pi\) | |||||||
\(374\) | 30.5579 | − | 6.76988i | 1.58011 | − | 0.350062i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.15020 | − | 11.9355i | −0.471886 | − | 0.615526i | ||||
\(377\) | −1.74861 | − | 5.38166i | −0.0900579 | − | 0.277170i | ||||
\(378\) | 13.4349 | − | 15.1809i | 0.691015 | − | 0.780822i | ||||
\(379\) | −10.8210 | − | 14.8938i | −0.555838 | − | 0.765045i | 0.434952 | − | 0.900454i | \(-0.356765\pi\) |
−0.990790 | + | 0.135408i | \(0.956765\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.9437 | − | 21.9446i | 0.816821 | − | 1.12426i | ||||
\(382\) | 0.685490 | + | 3.09416i | 0.0350727 | + | 0.158311i | ||||
\(383\) | 14.5194 | + | 10.5490i | 0.741907 | + | 0.539027i | 0.893308 | − | 0.449445i | \(-0.148378\pi\) |
−0.151401 | + | 0.988472i | \(0.548378\pi\) | |||||||
\(384\) | −33.2947 | − | 12.4868i | −1.69906 | − | 0.637214i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 27.6571 | − | 16.2859i | 1.40771 | − | 0.828929i | ||||
\(387\) | 19.3699 | + | 6.29365i | 0.984625 | + | 0.319924i | ||||
\(388\) | −0.0708946 | − | 0.578774i | −0.00359913 | − | 0.0293828i | ||||
\(389\) | −22.7077 | + | 7.37819i | −1.15133 | + | 0.374089i | −0.821643 | − | 0.570002i | \(-0.806942\pi\) |
−0.329685 | + | 0.944091i | \(0.606942\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.75608 | + | 11.5600i | −0.189953 | + | 0.584616i | ||||
\(392\) | 0.409011 | + | 15.8828i | 0.0206582 | + | 0.802204i | ||||
\(393\) | −27.3377 | −1.37900 | ||||||||
\(394\) | −16.8362 | − | 7.32350i | −0.848198 | − | 0.368953i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 47.7840 | + | 26.5052i | 2.40124 | + | 1.33194i | ||||
\(397\) | 0.848630 | + | 1.16804i | 0.0425915 | + | 0.0586222i | 0.829782 | − | 0.558088i | \(-0.188465\pi\) |
−0.787190 | + | 0.616710i | \(0.788465\pi\) | |||||||
\(398\) | 22.1994 | − | 13.0721i | 1.11275 | − | 0.655246i | ||||
\(399\) | 16.6539 | 0.833740 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −26.0682 | −1.30178 | −0.650891 | − | 0.759171i | \(-0.725605\pi\) | ||||
−0.650891 | + | 0.759171i | \(0.725605\pi\) | |||||||
\(402\) | 11.6300 | − | 6.84836i | 0.580054 | − | 0.341565i | ||||
\(403\) | −0.771367 | − | 1.06170i | −0.0384245 | − | 0.0528868i | ||||
\(404\) | −13.7148 | − | 7.60744i | −0.682338 | − | 0.378484i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 9.49126 | + | 4.12855i | 0.471043 | + | 0.204897i | ||||
\(407\) | 27.8026 | 1.37813 | ||||||||
\(408\) | 49.5171 | − | 1.27515i | 2.45146 | − | 0.0631294i | ||||
\(409\) | −0.312601 | + | 0.962088i | −0.0154571 | + | 0.0475722i | −0.958488 | − | 0.285134i | \(-0.907962\pi\) |
0.943030 | + | 0.332706i | \(0.107962\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.8918 | + | 3.53897i | −0.537254 | + | 0.174564i | ||||
\(412\) | −3.20200 | − | 26.1407i | −0.157751 | − | 1.28786i | ||||
\(413\) | −1.43783 | − | 0.467180i | −0.0707512 | − | 0.0229884i | ||||
\(414\) | −18.2859 | + | 10.7676i | −0.898701 | + | 0.529200i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.60208 | − | 3.67081i | −0.176607 | − | 0.179976i | ||||
\(417\) | 35.5140 | + | 25.8025i | 1.73913 | + | 1.26355i | ||||
\(418\) | 5.47494 | + | 24.7127i | 0.267788 | + | 1.20874i | ||||
\(419\) | 19.6696 | − | 27.0728i | 0.960920 | − | 1.32259i | 0.0144183 | − | 0.999896i | \(-0.495410\pi\) |
0.946502 | − | 0.322697i | \(-0.104590\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.1696 | − | 22.2556i | −0.788060 | − | 1.08467i | −0.994347 | − | 0.106180i | \(-0.966138\pi\) |
0.206287 | − | 0.978492i | \(-0.433862\pi\) | |||||||
\(422\) | −1.64674 | + | 1.86076i | −0.0801620 | + | 0.0905803i | ||||
\(423\) | 11.3022 | + | 34.7847i | 0.549533 | + | 1.69129i | ||||
\(424\) | −29.3297 | + | 22.4853i | −1.42438 | + | 1.09198i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −8.48612 | + | 1.88004i | −0.411154 | + | 0.0910883i | ||||
\(427\) | 17.3233 | − | 5.62868i | 0.838333 | − | 0.272391i | ||||
\(428\) | 12.2550 | + | 6.79767i | 0.592366 | + | 0.328578i | ||||
\(429\) | 6.67126 | + | 9.18220i | 0.322092 | + | 0.443321i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.6348 | + | 15.7186i | 1.04211 | + | 0.757138i | 0.970696 | − | 0.240309i | \(-0.0772488\pi\) |
0.0714143 | + | 0.997447i | \(0.477249\pi\) | |||||||
\(432\) | 37.3354 | + | 31.3649i | 1.79630 | + | 1.50904i | ||||
\(433\) | 16.7912 | + | 12.1996i | 0.806936 | + | 0.586273i | 0.912941 | − | 0.408092i | \(-0.133806\pi\) |
−0.106005 | + | 0.994366i | \(0.533806\pi\) | |||||||
\(434\) | 2.38933 | + | 0.230415i | 0.114691 | + | 0.0110603i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.95353 | + | 3.68459i | −0.189340 | + | 0.176460i | ||||
\(437\) | −9.34882 | − | 3.03762i | −0.447215 | − | 0.145309i | ||||
\(438\) | 1.80174 | − | 18.6834i | 0.0860903 | − | 0.892729i | ||||
\(439\) | −0.0935999 | − | 0.288071i | −0.00446728 | − | 0.0137489i | 0.948798 | − | 0.315883i | \(-0.102301\pi\) |
−0.953265 | + | 0.302134i | \(0.902301\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.9401 | − | 36.7478i | 0.568575 | − | 1.74989i | ||||
\(442\) | 6.56946 | + | 2.85761i | 0.312477 | + | 0.135923i | ||||
\(443\) | 33.9046i | 1.61086i | 0.592693 | + | 0.805428i | \(0.298065\pi\) | ||||
−0.592693 | + | 0.805428i | \(0.701935\pi\) | |||||||
\(444\) | 43.1896 | + | 8.40817i | 2.04969 | + | 0.399034i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.65062 | + | 1.46077i | 0.0781591 | + | 0.0691694i | ||||
\(447\) | −6.64583 | + | 4.82848i | −0.314337 | + | 0.228379i | ||||
\(448\) | 9.39462 | − | 0.484177i | 0.443854 | − | 0.0228752i | ||||
\(449\) | 12.6049 | 0.594860 | 0.297430 | − | 0.954744i | \(-0.403871\pi\) | ||||
0.297430 | + | 0.954744i | \(0.403871\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 25.3298i | − | 1.19273i | ||||||
\(452\) | −6.23242 | − | 6.68733i | −0.293148 | − | 0.314545i | ||||
\(453\) | 19.6156 | + | 26.9986i | 0.921621 | + | 1.26850i | ||||
\(454\) | 8.64339 | − | 9.76672i | 0.405654 | − | 0.458375i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.03124 | + | 40.0454i | 0.0482923 | + | 1.87530i | ||||
\(457\) | −2.58934 | −0.121124 | −0.0605622 | − | 0.998164i | \(-0.519289\pi\) | ||||
−0.0605622 | + | 0.998164i | \(0.519289\pi\) | |||||||
\(458\) | −14.6516 | − | 6.37322i | −0.684624 | − | 0.297801i | ||||
\(459\) | −64.5997 | − | 20.9897i | −3.01526 | − | 0.979716i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.49523 | − | 2.11043i | 0.302513 | − | 0.0982925i | −0.153827 | − | 0.988098i | \(-0.549160\pi\) |
0.456340 | + | 0.889805i | \(0.349160\pi\) | |||||||
\(462\) | −20.6644 | − | 1.99277i | −0.961394 | − | 0.0927121i | ||||
\(463\) | 6.74304 | − | 20.7530i | 0.313376 | − | 0.964472i | −0.663042 | − | 0.748582i | \(-0.730735\pi\) |
0.976418 | − | 0.215889i | \(-0.0692651\pi\) | |||||||
\(464\) | −9.33964 | + | 23.0780i | −0.433582 | + | 1.07137i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 17.4990 | + | 1.68752i | 0.810628 | + | 0.0781729i | ||||
\(467\) | −1.76636 | + | 2.43118i | −0.0817373 | + | 0.112502i | −0.847928 | − | 0.530112i | \(-0.822150\pi\) |
0.766190 | + | 0.642614i | \(0.222150\pi\) | |||||||
\(468\) | 5.28254 | + | 11.3370i | 0.244186 | + | 0.524054i | ||||
\(469\) | −2.09868 | + | 2.88859i | −0.0969081 | + | 0.133383i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.92583 | − | 7.21154i | 0.457358 | − | 0.332290i | ||||
\(472\) | 1.03433 | − | 3.48629i | 0.0476089 | − | 0.160469i | ||||
\(473\) | −3.63421 | − | 11.1850i | −0.167101 | − | 0.514285i | ||||
\(474\) | −11.9727 | + | 2.65247i | −0.549926 | + | 0.121832i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −11.8778 | + | 5.53453i | −0.544419 | + | 0.253675i | ||||
\(477\) | 85.4782 | − | 27.7736i | 3.91378 | − | 1.27166i | ||||
\(478\) | 29.2667 | + | 25.9005i | 1.33863 | + | 1.18466i | ||||
\(479\) | −15.3717 | + | 11.1682i | −0.702349 | + | 0.510287i | −0.880697 | − | 0.473681i | \(-0.842925\pi\) |
0.178347 | + | 0.983968i | \(0.442925\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.14843 | + | 3.74055i | 0.234748 | + | 0.170555i | ||||
\(482\) | 1.31030 | + | 5.91444i | 0.0596827 | + | 0.269395i | ||||
\(483\) | 4.73888 | − | 6.52251i | 0.215627 | − | 0.296785i | ||||
\(484\) | −1.16148 | − | 9.48216i | −0.0527945 | − | 0.431007i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −13.6299 | − | 23.1466i | −0.618265 | − | 1.04995i | ||||
\(487\) | 0.586607 | − | 1.80539i | 0.0265817 | − | 0.0818101i | −0.936886 | − | 0.349636i | \(-0.886305\pi\) |
0.963467 | + | 0.267826i | \(0.0863052\pi\) | |||||||
\(488\) | 14.6072 | + | 41.3064i | 0.661236 | + | 1.86985i | ||||
\(489\) | −19.0651 | − | 58.6762i | −0.862151 | − | 2.65343i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.3750 | + | 9.54451i | 1.32567 | + | 0.430738i | 0.884440 | − | 0.466654i | \(-0.154541\pi\) |
0.441234 | + | 0.897392i | \(0.354541\pi\) | |||||||
\(492\) | 7.66034 | − | 39.3482i | 0.345355 | − | 1.77396i | ||||
\(493\) | − | 34.6801i | − | 1.56191i | ||||||
\(494\) | −2.31101 | + | 5.31285i | −0.103977 | + | 0.239036i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.406095 | + | 5.75955i | −0.0182342 | + | 0.258611i | ||||
\(497\) | 1.86027 | − | 1.35156i | 0.0834443 | − | 0.0606258i | ||||
\(498\) | −36.2594 | + | 21.3514i | −1.62482 | + | 0.956778i | ||||
\(499\) | − | 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 | ||||||||
\(502\) | −9.61572 | − | 16.3297i | −0.429171 | − | 0.728828i | ||||
\(503\) | 21.4189 | − | 15.5618i | 0.955024 | − | 0.693865i | 0.00303389 | − | 0.999995i | \(-0.499034\pi\) |
0.951990 | + | 0.306130i | \(0.0990343\pi\) | |||||||
\(504\) | −21.9325 | − | 6.50707i | −0.976953 | − | 0.289848i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 11.2366 | + | 4.88776i | 0.499529 | + | 0.217288i | ||||
\(507\) | − | 38.2613i | − | 1.69925i | ||||||
\(508\) | −16.9424 | − | 3.29836i | −0.751699 | − | 0.146341i | ||||
\(509\) | −17.5095 | − | 5.68919i | −0.776096 | − | 0.252169i | −0.105923 | − | 0.994374i | \(-0.533780\pi\) |
−0.670172 | + | 0.742205i | \(0.733780\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.53445 | + | 4.72255i | 0.0678800 | + | 0.208913i | ||||
\(512\) | 1.74596 | + | 22.5600i | 0.0771615 | + | 0.997019i | ||||
\(513\) | 16.9748 | − | 52.2431i | 0.749456 | − | 2.30659i | ||||
\(514\) | 9.52847 | − | 5.61084i | 0.420283 | − | 0.247484i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.26292 | − | 18.4742i | −0.0996196 | − | 0.813281i | ||||
\(517\) | 12.4139 | − | 17.0863i | 0.545963 | − | 0.751453i | ||||
\(518\) | −11.3646 | + | 2.51776i | −0.499334 | + | 0.110624i | ||||
\(519\) | 25.8888 | + | 18.8093i | 1.13639 | + | 0.825637i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.7039 | − | 23.7608i | 1.43278 | − | 1.04098i | 0.443295 | − | 0.896376i | \(-0.353809\pi\) |
0.989490 | − | 0.144603i | \(-0.0461906\pi\) | |||||||
\(522\) | 40.1256 | − | 45.3405i | 1.75625 | − | 1.98450i | ||||
\(523\) | −16.5534 | + | 5.37852i | −0.723828 | + | 0.235186i | −0.647682 | − | 0.761911i | \(-0.724262\pi\) |
−0.0761461 | + | 0.997097i | \(0.524262\pi\) | |||||||
\(524\) | 7.34723 | + | 15.7681i | 0.320965 | + | 0.688832i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.39400 | + | 37.8888i | 0.365996 | + | 1.65203i | ||||
\(527\) | −2.48539 | − | 7.64925i | −0.108265 | − | 0.333206i | ||||
\(528\) | 3.51216 | − | 49.8122i | 0.152847 | − | 2.16780i | ||||
\(529\) | 14.7575 | − | 10.7220i | 0.641630 | − | 0.466172i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.19820 | + | 7.15471i | −0.225583 | + | 0.310488i | ||||
\(532\) | −4.47589 | − | 9.60582i | −0.194054 | − | 0.416465i | ||||
\(533\) | 3.40786 | − | 4.69052i | 0.147611 | − | 0.203169i | ||||
\(534\) | 1.11411 | − | 11.5530i | 0.0482124 | − | 0.499947i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −7.07573 | − | 4.86754i | −0.305625 | − | 0.210246i | ||||
\(537\) | 14.6680 | − | 45.1434i | 0.632970 | − | 1.94808i | ||||
\(538\) | −2.89633 | + | 30.0340i | −0.124870 | + | 1.29486i | ||||
\(539\) | −21.2197 | + | 6.89469i | −0.913996 | + | 0.296975i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.69917 | − | 2.50161i | −0.331013 | − | 0.107553i | 0.138795 | − | 0.990321i | \(-0.455677\pi\) |
−0.469808 | + | 0.882768i | \(0.655677\pi\) | |||||||
\(542\) | 0.602695 | − | 1.38556i | 0.0258880 | − | 0.0595147i | ||||
\(543\) | −59.4701 | −2.55211 | ||||||||
\(544\) | −14.0436 | − | 28.2182i | −0.602115 | − | 1.20985i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −3.55848 | − | 3.14920i | −0.152289 | − | 0.134773i | ||||
\(547\) | 15.0486 | + | 20.7126i | 0.643431 | + | 0.885607i | 0.998793 | − | 0.0491221i | \(-0.0156423\pi\) |
−0.355362 | + | 0.934729i | \(0.615642\pi\) | |||||||
\(548\) | 4.96851 | + | 5.33117i | 0.212244 | + | 0.227736i | ||||
\(549\) | − | 106.551i | − | 4.54747i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 28.0465 | 1.19482 | ||||||||
\(552\) | 15.9772 | + | 10.9911i | 0.680036 | + | 0.467810i | ||||
\(553\) | 2.62457 | − | 1.90686i | 0.111608 | − | 0.0810881i | ||||
\(554\) | −16.6389 | + | 18.8014i | −0.706921 | + | 0.798796i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.33790 | − | 27.4188i | 0.226377 | − | 1.16281i | ||||
\(557\) | − | 1.74254i | − | 0.0738336i | −0.999318 | − | 0.0369168i | \(-0.988246\pi\) | ||
0.999318 | − | 0.0369168i | \(-0.0117537\pi\) | |||||||
\(558\) | 5.60095 | − | 12.8762i | 0.237107 | − | 0.545094i | ||||
\(559\) | 0.831844 | − | 2.56015i | 0.0351832 | − | 0.108283i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 21.4952 | + | 66.1555i | 0.907529 | + | 2.79309i | ||||
\(562\) | −15.2748 | − | 1.47303i | −0.644329 | − | 0.0621359i | ||||
\(563\) | 24.4440 | + | 7.94233i | 1.03019 | + | 0.334729i | 0.774866 | − | 0.632126i | \(-0.217817\pi\) |
0.255325 | + | 0.966855i | \(0.417817\pi\) | |||||||
\(564\) | 24.4515 | − | 22.7882i | 1.02959 | − | 0.959555i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 3.15288 | − | 32.6943i | 0.132525 | − | 1.37425i | ||||
\(567\) | 16.8181 | + | 12.2191i | 0.706296 | + | 0.513154i | ||||
\(568\) | 3.36510 | + | 4.38943i | 0.141197 | + | 0.184176i | ||||
\(569\) | 11.5604 | + | 8.39915i | 0.484639 | + | 0.352111i | 0.803119 | − | 0.595819i | \(-0.203172\pi\) |
−0.318480 | + | 0.947930i | \(0.603172\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.7151 | + | 16.1245i | 0.490263 | + | 0.674789i | 0.980436 | − | 0.196836i | \(-0.0630666\pi\) |
−0.490174 | + | 0.871625i | \(0.663067\pi\) | |||||||
\(572\) | 3.50324 | − | 6.31571i | 0.146478 | − | 0.264073i | ||||
\(573\) | −6.69863 | + | 2.17652i | −0.279839 | + | 0.0909253i | ||||
\(574\) | 2.29382 | + | 10.3539i | 0.0957424 | + | 0.432162i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 14.2885 | − | 53.1410i | 0.595356 | − | 2.21421i | ||||
\(577\) | 4.76100 | + | 14.6528i | 0.198203 | + | 0.610006i | 0.999924 | + | 0.0123079i | \(0.00391783\pi\) |
−0.801721 | + | 0.597698i | \(0.796082\pi\) | |||||||
\(578\) | 14.8760 | + | 13.1650i | 0.618761 | + | 0.547593i | ||||
\(579\) | 41.9275 | + | 57.7083i | 1.74245 | + | 2.39827i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.54313 | − | 9.00585i | 0.271455 | − | 0.373626i | ||||
\(582\) | 1.26523 | − | 0.280303i | 0.0524456 | − | 0.0116189i | ||||
\(583\) | −41.9870 | − | 30.5054i | −1.73892 | − | 1.26340i | ||||
\(584\) | −11.2606 | + | 3.98210i | −0.465969 | + | 0.164781i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16.9088 | + | 28.7150i | 0.698497 | + | 1.18620i | ||||
\(587\) | −13.0914 | − | 4.25364i | −0.540338 | − | 0.175567i | 0.0261173 | − | 0.999659i | \(-0.491686\pi\) |
−0.566455 | + | 0.824092i | \(0.691686\pi\) | |||||||
\(588\) | −35.0485 | + | 4.29313i | −1.44538 | + | 0.177046i | ||||
\(589\) | 6.18610 | − | 2.00998i | 0.254894 | − | 0.0828200i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12.6092 | − | 38.8072i | 0.518675 | − | 1.59632i | ||||
\(592\) | −6.75782 | − | 27.1711i | −0.277745 | − | 1.11672i | ||||
\(593\) | 6.37493 | 0.261787 | 0.130894 | − | 0.991396i | \(-0.458215\pi\) | ||||
0.130894 | + | 0.991396i | \(0.458215\pi\) | |||||||
\(594\) | −27.3138 | + | 62.7926i | −1.12070 | + | 2.57641i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.57114 | + | 2.53555i | 0.187241 | + | 0.103860i | ||||
\(597\) | 33.6538 | + | 46.3205i | 1.37736 | + | 1.89577i | ||||
\(598\) | 1.42318 | + | 2.41688i | 0.0581981 | + | 0.0988335i | ||||
\(599\) | −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 | \(0.184198\pi\) | |||||||
\(602\) | 2.49842 | + | 4.24287i | 0.101828 | + | 0.172927i | ||||
\(603\) | 12.2766 | + | 16.8973i | 0.499942 | + | 0.688112i | ||||
\(604\) | 10.3006 | − | 18.5702i | 0.419127 | − | 0.755609i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 13.9033 | − | 31.9627i | 0.564782 | − | 1.29840i | ||||
\(607\) | −28.6948 | −1.16469 | −0.582343 | − | 0.812943i | \(-0.697864\pi\) | ||||
−0.582343 | + | 0.812943i | \(0.697864\pi\) | |||||||
\(608\) | 22.8206 | − | 11.3574i | 0.925499 | − | 0.460601i | ||||
\(609\) | −7.10833 | + | 21.8772i | −0.288044 | + | 0.886509i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.59756 | − | 1.49384i | 0.185997 | − | 0.0604342i | ||||
\(612\) | 9.31976 | + | 76.0853i | 0.376729 | + | 3.07557i | ||||
\(613\) | 7.10423 | + | 2.30831i | 0.286937 | + | 0.0932316i | 0.448949 | − | 0.893557i | \(-0.351798\pi\) |
−0.162012 | + | 0.986789i | \(0.551798\pi\) | |||||||
\(614\) | 20.9478 | + | 35.5741i | 0.845385 | + | 1.43565i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.40432 | + | 12.4546i | 0.177455 | + | 0.501809i | ||||
\(617\) | −32.7837 | − | 23.8187i | −1.31982 | − | 0.958906i | −0.999934 | − | 0.0114498i | \(-0.996355\pi\) |
−0.319886 | − | 0.947456i | \(-0.603645\pi\) | |||||||
\(618\) | 57.1450 | − | 12.6601i | 2.29871 | − | 0.509263i | ||||
\(619\) | 5.89273 | − | 8.11065i | 0.236849 | − | 0.325994i | −0.674003 | − | 0.738729i | \(-0.735426\pi\) |
0.910851 | + | 0.412735i | \(0.135426\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −15.6308 | − | 21.5140i | −0.627242 | − | 0.863325i | ||||
\(622\) | 1.04091 | + | 0.921185i | 0.0417366 | + | 0.0369362i | ||||
\(623\) | 0.948834 | + | 2.92021i | 0.0380142 | + | 0.116996i | ||||
\(624\) | 7.35208 | − | 8.75159i | 0.294319 | − | 0.350344i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.93085 | + | 13.2293i | 0.117140 | + | 0.528748i | ||||
\(627\) | −53.5012 | + | 17.3836i | −2.13663 | + | 0.694234i | ||||
\(628\) | −6.82719 | − | 3.78696i | −0.272435 | − | 0.151116i | ||||
\(629\) | 22.9248 | + | 31.5533i | 0.914073 | + | 1.25811i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.4964 | − | 17.7976i | −0.975184 | − | 0.708513i | −0.0185571 | − | 0.999828i | \(-0.505907\pi\) |
−0.956627 | + | 0.291315i | \(0.905907\pi\) | |||||||
\(632\) | 4.74769 | + | 6.19287i | 0.188853 | + | 0.246339i | ||||
\(633\) | −4.46765 | − | 3.24593i | −0.177573 | − | 0.129014i | ||||
\(634\) | −2.49930 | + | 25.9170i | −0.0992600 | + | 1.02929i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −55.9986 | − | 60.0860i | −2.22049 | − | 2.38256i | ||||
\(637\) | −4.85702 | − | 1.57814i | −0.192442 | − | 0.0625283i | ||||
\(638\) | −34.8004 | − | 3.35597i | −1.37776 | − | 0.132864i | ||||
\(639\) | −4.15654 | − | 12.7925i | −0.164430 | − | 0.506064i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.1688 | + | 37.4516i | −0.480637 | + | 1.47925i | 0.357564 | + | 0.933889i | \(0.383607\pi\) |
−0.838201 | + | 0.545361i | \(0.816393\pi\) | |||||||
\(642\) | −12.4233 | + | 28.5604i | −0.490310 | + | 1.12719i | ||||
\(643\) | 15.6623i | 0.617660i | 0.951117 | + | 0.308830i | \(0.0999375\pi\) | ||||
−0.951117 | + | 0.308830i | \(0.900063\pi\) | |||||||
\(644\) | −5.03573 | − | 0.980359i | −0.198436 | − | 0.0386316i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −23.5322 | + | 26.5906i | −0.925862 | + | 1.04619i | ||||
\(647\) | −26.8579 | + | 19.5134i | −1.05589 | + | 0.767152i | −0.973324 | − | 0.229434i | \(-0.926313\pi\) |
−0.0825693 | + | 0.996585i | \(0.526313\pi\) | |||||||
\(648\) | −28.3402 | + | 41.1969i | −1.11331 | + | 1.61837i | ||||
\(649\) | 5.10673 | 0.200457 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.33479i | 0.209087i | ||||||||
\(652\) | −28.7199 | + | 26.7662i | −1.12476 | + | 1.04825i | ||||
\(653\) | −2.28117 | − | 3.13976i | −0.0892690 | − | 0.122868i | 0.762047 | − | 0.647522i | \(-0.224195\pi\) |
−0.851316 | + | 0.524654i | \(0.824195\pi\) | |||||||
\(654\) | −8.99442 | − | 7.95991i | −0.351710 | − | 0.311257i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −24.7544 | + | 6.15677i | −0.966499 | + | 0.240381i | ||||
\(657\) | 29.0471 | 1.13323 | ||||||||
\(658\) | −3.52702 | + | 8.10839i | −0.137498 | + | 0.316098i | ||||
\(659\) | 38.7539 | + | 12.5919i | 1.50964 | + | 0.490511i | 0.942811 | − | 0.333327i | \(-0.108171\pi\) |
0.566826 | + | 0.823838i | \(0.308171\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −35.9253 | + | 11.6728i | −1.39733 | + | 0.454020i | −0.908327 | − | 0.418261i | \(-0.862640\pi\) |
−0.489004 | + | 0.872282i | \(0.662640\pi\) | |||||||
\(662\) | 0.981789 | − | 10.1808i | 0.0381583 | − | 0.395689i | ||||
\(663\) | −4.92009 | + | 15.1425i | −0.191081 | + | 0.588085i | ||||
\(664\) | 22.0603 | + | 15.1757i | 0.856105 | + | 0.588931i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −6.53608 | + | 67.7771i | −0.253268 | + | 2.62631i | ||||
\(667\) | 7.98063 | − | 10.9844i | 0.309011 | − | 0.425318i | ||||
\(668\) | 30.5336 | − | 14.2273i | 1.18138 | − | 0.550471i | ||||
\(669\) | −2.87936 | + | 3.96311i | −0.111323 | + | 0.153223i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −49.7762 | + | 36.1645i | −1.92159 | + | 1.39612i | ||||
\(672\) | 3.07527 | + | 20.6794i | 0.118631 | + | 0.797724i | ||||
\(673\) | −0.512274 | − | 1.57662i | −0.0197467 | − | 0.0607742i | 0.940698 | − | 0.339246i | \(-0.110172\pi\) |
−0.960444 | + | 0.278472i | \(0.910172\pi\) | |||||||
\(674\) | −2.78836 | − | 12.5861i | −0.107404 | − | 0.484798i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −22.0687 | + | 10.2831i | −0.848798 | + | 0.395502i | ||||
\(677\) | −0.215778 | + | 0.0701106i | −0.00829304 | + | 0.00269457i | −0.313161 | − | 0.949700i | \(-0.601388\pi\) |
0.304868 | + | 0.952395i | \(0.401388\pi\) | |||||||
\(678\) | 13.4640 | − | 15.2139i | 0.517083 | − | 0.584286i | ||||
\(679\) | −0.277355 | + | 0.201510i | −0.0106439 | + | 0.00773325i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 23.4497 | + | 17.0372i | 0.898596 | + | 0.652868i | ||||
\(682\) | −7.91628 | + | 1.75380i | −0.303130 | + | 0.0671563i | ||||
\(683\) | −17.4833 | + | 24.0637i | −0.668981 | + | 0.920773i | −0.999737 | − | 0.0229435i | \(-0.992696\pi\) |
0.330756 | + | 0.943716i | \(0.392696\pi\) | |||||||
\(684\) | −61.5317 | + | 7.53707i | −2.35272 | + | 0.288187i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 18.0802 | − | 10.6465i | 0.690306 | − | 0.406487i | ||||
\(687\) | 10.9731 | − | 33.7717i | 0.418649 | − | 1.28847i | ||||
\(688\) | −10.0475 | + | 6.27032i | −0.383059 | + | 0.239054i | ||||
\(689\) | −3.67089 | − | 11.2978i | −0.139850 | − | 0.430413i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.9436 | + | 9.72925i | 1.13911 | + | 0.370118i | 0.817030 | − | 0.576595i | \(-0.195619\pi\) |
0.322077 | + | 0.946714i | \(0.395619\pi\) | |||||||
\(692\) | 3.89119 | − | 19.9876i | 0.147921 | − | 0.759813i | ||||
\(693\) | − | 32.1269i | − | 1.22040i | ||||||
\(694\) | −13.2676 | − | 5.77122i | −0.503633 | − | 0.219072i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −53.0452 | − | 15.7377i | −2.01067 | − | 0.596538i | ||||
\(697\) | 28.7469 | − | 20.8859i | 1.08887 | − | 0.791108i | ||||
\(698\) | −3.41886 | − | 5.80600i | −0.129406 | − | 0.219760i | ||||
\(699\) | 39.0712i | 1.47781i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 2.30506i | − | 0.0870611i | −0.999052 | − | 0.0435305i | \(-0.986139\pi\) | ||
0.999052 | − | 0.0435305i | \(-0.0138606\pi\) | |||||||
\(702\) | −13.5060 | + | 7.95301i | −0.509751 | + | 0.300167i | ||||
\(703\) | −25.5178 | + | 18.5398i | −0.962422 | + | 0.699240i | ||||
\(704\) | −29.6751 | + | 11.3617i | −1.11842 | + | 0.428209i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10.2982 | + | 23.6748i | −0.387576 | + | 0.891012i | ||||
\(707\) | 9.22096i | 0.346790i | ||||||||
\(708\) | 7.93297 | + | 1.54440i | 0.298139 | + | 0.0580419i | ||||
\(709\) | 25.4956 | + | 8.28402i | 0.957508 | + | 0.311113i | 0.745763 | − | 0.666212i | \(-0.232085\pi\) |
0.211745 | + | 0.977325i | \(0.432085\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.86429 | − | 18.0484i | −0.219928 | − | 0.676869i | ||||
\(712\) | −6.96307 | + | 2.46235i | −0.260952 | + | 0.0922806i | ||||
\(713\) | 0.973045 | − | 2.99472i | 0.0364408 | − | 0.112153i | ||||
\(714\) | −14.7773 | − | 25.0953i | −0.553028 | − | 0.939166i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −29.9804 | + | 3.67233i | −1.12042 | + | 0.137241i | ||||
\(717\) | −51.0533 | + | 70.2688i | −1.90662 | + | 2.62424i | ||||
\(718\) | 5.58759 | + | 25.2212i | 0.208527 | + | 0.941248i | ||||
\(719\) | −12.3313 | − | 8.95922i | −0.459880 | − | 0.334123i | 0.333604 | − | 0.942713i | \(-0.391735\pi\) |
−0.793484 | + | 0.608591i | \(0.791735\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.5269 | + | 9.10133i | −0.466526 | + | 0.338951i | ||||
\(722\) | −1.38241 | − | 1.22341i | −0.0514480 | − | 0.0455306i | ||||
\(723\) | −12.8043 | + | 4.16038i | −0.476198 | + | 0.154726i | ||||
\(724\) | 15.9831 | + | 34.3017i | 0.594007 | + | 1.27481i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 20.7285 | − | 4.59226i | 0.769308 | − | 0.170435i | ||||
\(727\) | −0.688107 | − | 2.11778i | −0.0255205 | − | 0.0785440i | 0.937485 | − | 0.348025i | \(-0.113148\pi\) |
−0.963006 | + | 0.269481i | \(0.913148\pi\) | |||||||
\(728\) | −0.860052 | + | 2.89887i | −0.0318756 | + | 0.107439i | ||||
\(729\) | 5.38937 | − | 3.91560i | 0.199606 | − | 0.145022i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.69724 | − | 13.3471i | 0.358665 | − | 0.493661i | ||||
\(732\) | −88.2612 | + | 41.1258i | −3.26223 | + | 1.52005i | ||||
\(733\) | 29.0933 | − | 40.0434i | 1.07458 | − | 1.47904i | 0.209237 | − | 0.977865i | \(-0.432902\pi\) |
0.865347 | − | 0.501173i | \(-0.167098\pi\) | |||||||
\(734\) | 21.1949 | + | 2.04393i | 0.782319 | + | 0.0754430i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.04551 | − | 12.1694i | 0.0753986 | − | 0.448571i | ||||
\(737\) | 3.72692 | − | 11.4703i | 0.137283 | − | 0.422513i | ||||
\(738\) | 61.7488 | + | 5.95475i | 2.27301 | + | 0.219197i | ||||
\(739\) | 17.2361 | − | 5.60033i | 0.634039 | − | 0.206012i | 0.0256753 | − | 0.999670i | \(-0.491826\pi\) |
0.608363 | + | 0.793659i | \(0.291826\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −12.2460 | − | 3.97897i | −0.449869 | − | 0.146171i | ||||
\(742\) | 19.9252 | + | 8.66715i | 0.731477 | + | 0.318181i | ||||
\(743\) | 15.5632 | 0.570959 | 0.285479 | − | 0.958385i | \(-0.407847\pi\) | ||||
0.285479 | + | 0.958385i | \(0.407847\pi\) | |||||||
\(744\) | −12.8278 | + | 0.330339i | −0.470291 | + | 0.0121108i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −0.664499 | + | 0.750860i | −0.0243290 | + | 0.0274910i | ||||
\(747\) | −38.2752 | − | 52.6813i | −1.40042 | − | 1.92751i | ||||
\(748\) | 32.3808 | − | 30.1781i | 1.18396 | − | 1.10342i | ||||
\(749\) | − | 8.23944i | − | 0.301062i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 41.5803 | 1.51729 | 0.758643 | − | 0.651507i | \(-0.225863\pi\) | ||||
0.758643 | + | 0.651507i | \(0.225863\pi\) | |||||||
\(752\) | −19.7155 | − | 7.97886i | −0.718951 | − | 0.290959i | ||||
\(753\) | 34.0729 | − | 24.7554i | 1.24169 | − | 0.902137i | ||||
\(754\) | −5.99274 | − | 5.30348i | −0.218243 | − | 0.193141i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.47844 | − | 28.1407i | 0.199249 | − | 1.02347i | ||||
\(757\) | − | 1.83755i | − | 0.0667870i | −0.999442 | − | 0.0333935i | \(-0.989369\pi\) | ||
0.999442 | − | 0.0333935i | \(-0.0106315\pi\) | |||||||
\(758\) | −23.8745 | − | 10.3850i | −0.867161 | − | 0.377202i | ||||
\(759\) | −8.41550 | + | 25.9003i | −0.305463 | + | 0.940120i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.18935 | − | 28.2819i | −0.333114 | − | 1.02522i | −0.967644 | − | 0.252320i | \(-0.918806\pi\) |
0.634530 | − | 0.772898i | \(-0.281194\pi\) | |||||||
\(762\) | 3.68223 | − | 38.1835i | 0.133393 | − | 1.38324i | ||||
\(763\) | 3.02192 | + | 0.981880i | 0.109401 | + | 0.0355464i | ||||
\(764\) | 3.05570 | + | 3.27874i | 0.110552 | + | 0.118621i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 25.2637 | + | 2.43630i | 0.912813 | + | 0.0880272i | ||||
\(767\) | 0.945653 | + | 0.687057i | 0.0341455 | + | 0.0248082i | ||||
\(768\) | −49.5344 | + | 8.67516i | −1.78742 | + | 0.313038i | ||||
\(769\) | −7.63237 | − | 5.54524i | −0.275230 | − | 0.199966i | 0.441604 | − | 0.897210i | \(-0.354410\pi\) |
−0.716834 | + | 0.697244i | \(0.754410\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.4450 | + | 19.8818i | 0.520222 | + | 0.716025i | ||||
\(772\) | 22.0172 | − | 39.6929i | 0.792415 | − | 1.42858i | ||||
\(773\) | 23.0787 | − | 7.49873i | 0.830084 | − | 0.269711i | 0.137003 | − | 0.990571i | \(-0.456253\pi\) |
0.693081 | + | 0.720860i | \(0.256253\pi\) | |||||||
\(774\) | 28.1210 | − | 6.23000i | 1.01079 | − | 0.223933i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −0.501718 | − | 0.654439i | −0.0180106 | − | 0.0234930i | ||||
\(777\) | −7.99420 | − | 24.6036i | −0.286790 | − | 0.882649i | ||||
\(778\) | −22.3778 | + | 25.2862i | −0.802284 | + | 0.906553i | ||||
\(779\) | 16.8908 | + | 23.2482i | 0.605176 | + | 0.832953i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.56537 | + | 6.28370i | −0.163362 | + | 0.224848i | ||||
\(782\) | 3.71810 | + | 16.7827i | 0.132959 | + | 0.600150i | ||||
\(783\) | 61.3830 | + | 44.5974i | 2.19365 | + | 1.59378i | ||||
\(784\) | 11.8958 | + | 19.0618i | 0.424851 | + | 0.680779i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −33.3146 | + | 19.6173i | −1.18829 | + | 0.699725i | ||||
\(787\) | 35.4350 | + | 11.5135i | 1.26312 | + | 0.410413i | 0.862606 | − | 0.505877i | \(-0.168831\pi\) |
0.400515 | + | 0.916290i | \(0.368831\pi\) | |||||||
\(788\) | −25.7725 | + | 3.15689i | −0.918106 | + | 0.112460i | ||||
\(789\) | −82.0264 | + | 26.6520i | −2.92022 | + | 0.948837i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.66083 | + | 5.11151i | −0.0590524 | + | 0.181745i | ||||
\(792\) | 77.2510 | − | 1.98935i | 2.74499 | − | 0.0706885i | ||||
\(793\) | −14.0830 | −0.500103 | ||||||||
\(794\) | 1.87234 | + | 0.814440i | 0.0664469 | + | 0.0289034i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 17.6724 | − | 31.8602i | 0.626383 | − | 1.12925i | ||||
\(797\) | 2.93174 | + | 4.03520i | 0.103848 | + | 0.142934i | 0.857778 | − | 0.514020i | \(-0.171844\pi\) |
−0.753930 | + | 0.656954i | \(0.771844\pi\) | |||||||
\(798\) | 20.2950 | − | 11.9507i | 0.718436 | − | 0.423051i | ||||
\(799\) | 29.6272 | 1.04814 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 17.9614 | 0.634635 | ||||||||
\(802\) | −31.7675 | + | 18.7063i | −1.12175 | + | 0.660542i | ||||
\(803\) | −9.85892 | − | 13.5696i | −0.347914 | − | 0.478862i | ||||
\(804\) | 9.25842 | − | 16.6912i | 0.326519 | − | 0.588655i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.70187 | − | 0.740289i | −0.0599460 | − | 0.0260756i | ||||
\(807\) | −67.0587 | −2.36058 | ||||||||
\(808\) | −22.1724 | + | 0.570978i | −0.780021 | + | 0.0200869i | ||||
\(809\) | 2.74204 | − | 8.43914i | 0.0964051 | − | 0.296704i | −0.891212 | − | 0.453587i | \(-0.850144\pi\) |
0.987617 | + | 0.156882i | \(0.0501443\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.7338 | + | 6.73681i | −0.728062 | + | 0.236562i | −0.649515 | − | 0.760349i | \(-0.725028\pi\) |
−0.0785467 | + | 0.996910i | \(0.525028\pi\) | |||||||
\(812\) | 14.5290 | − | 1.77967i | 0.509867 | − | 0.0624541i | ||||
\(813\) | 3.19368 | + | 1.03769i | 0.112007 | + | 0.0363934i | ||||
\(814\) | 33.8812 | − | 19.9509i | 1.18753 | − | 0.699280i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 59.4280 | − | 37.0870i | 2.08040 | − | 1.29830i | ||||
\(817\) | 10.7941 | + | 7.84235i | 0.377637 | + | 0.274369i | ||||
\(818\) | 0.309440 | + | 1.39675i | 0.0108193 | + | 0.0488362i | ||||
\(819\) | 4.32233 | − | 5.94918i | 0.151035 | − | 0.207881i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.5298 | + | 29.6332i | 0.751394 | + | 1.03420i | 0.997881 | + | 0.0650589i | \(0.0207235\pi\) |
−0.246488 | + | 0.969146i | \(0.579276\pi\) | |||||||
\(822\) | −10.7336 | + | 12.1286i | −0.374377 | + | 0.423033i | ||||
\(823\) | 1.83068 | + | 5.63427i | 0.0638136 | + | 0.196398i | 0.977880 | − | 0.209166i | \(-0.0670750\pi\) |
−0.914066 | + | 0.405564i | \(0.867075\pi\) | |||||||
\(824\) | −22.6604 | − | 29.5581i | −0.789412 | − | 1.02971i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.08743 | + | 0.462456i | −0.0726311 | + | 0.0160909i | ||||
\(827\) | −14.4864 | + | 4.70692i | −0.503742 | + | 0.163676i | −0.549854 | − | 0.835261i | \(-0.685317\pi\) |
0.0461123 | + | 0.998936i | \(0.485317\pi\) | |||||||
\(828\) | −14.5570 | + | 26.2435i | −0.505889 | + | 0.912026i | ||||
\(829\) | −25.2244 | − | 34.7183i | −0.876078 | − | 1.20582i | −0.977492 | − | 0.210974i | \(-0.932337\pi\) |
0.101414 | − | 0.994844i | \(-0.467663\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −45.1419 | − | 32.7975i | −1.56595 | − | 1.13773i | ||||
\(832\) | −7.02376 | − | 1.88854i | −0.243505 | − | 0.0654735i | ||||
\(833\) | −25.3216 | − | 18.3972i | −0.877343 | − | 0.637427i | ||||
\(834\) | 61.7941 | + | 5.95912i | 2.13976 | + | 0.206347i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 24.4056 | + | 26.1870i | 0.844085 | + | 0.905695i | ||||
\(837\) | 16.7351 | + | 5.43757i | 0.578450 | + | 0.187950i | ||||
\(838\) | 4.54271 | − | 47.1065i | 0.156925 | − | 1.62727i | ||||
\(839\) | −14.0891 | − | 43.3617i | −0.486409 | − | 1.49701i | −0.829930 | − | 0.557868i | \(-0.811620\pi\) |
0.343521 | − | 0.939145i | \(-0.388380\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.00946 | + | 9.26218i | −0.103775 | + | 0.319385i | ||||
\(842\) | −35.6753 | − | 15.5182i | −1.22945 | − | 0.534792i | ||||
\(843\) | − | 34.1050i | − | 1.17464i | ||||||
\(844\) | −0.671504 | + | 3.44926i | −0.0231141 | + | 0.118729i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 38.7344 | + | 34.2793i | 1.33172 | + | 1.17855i | ||||
\(847\) | −4.54396 | + | 3.30138i | −0.156132 | + | 0.113437i | ||||
\(848\) | −19.6069 | + | 48.4480i | −0.673303 | + | 1.66371i | ||||
\(849\) | 72.9986 | 2.50531 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15.2695i | 0.523433i | ||||||||
\(852\) | −8.99235 | + | 8.38064i | −0.308073 | + | 0.287116i | ||||
\(853\) | −28.9855 | − | 39.8951i | −0.992445 | − | 1.36598i | −0.929848 | − | 0.367944i | \(-0.880062\pi\) |
−0.0625971 | − | 0.998039i | \(-0.519938\pi\) | |||||||
\(854\) | 17.0716 | − | 19.2903i | 0.584179 | − | 0.660101i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 19.8122 | − | 0.510200i | 0.677168 | − | 0.0174383i | ||||
\(857\) | −57.0345 | −1.94826 | −0.974130 | − | 0.225989i | \(-0.927439\pi\) | ||||
−0.974130 | + | 0.225989i | \(0.927439\pi\) | |||||||
\(858\) | 14.7189 | + | 6.40248i | 0.502494 | + | 0.218577i | ||||
\(859\) | −20.6564 | − | 6.71166i | −0.704786 | − | 0.228999i | −0.0653714 | − | 0.997861i | \(-0.520823\pi\) |
−0.639415 | + | 0.768862i | \(0.720823\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −22.4153 | + | 7.28318i | −0.763912 | + | 0.248210i | ||||
\(862\) | 37.6443 | + | 3.63023i | 1.28217 | + | 0.123646i | ||||
\(863\) | −5.84794 | + | 17.9981i | −0.199066 | + | 0.612663i | 0.800839 | + | 0.598880i | \(0.204387\pi\) |
−0.999905 | + | 0.0137830i | \(0.995613\pi\) | |||||||
\(864\) | 68.0052 | + | 11.4307i | 2.31358 | + | 0.388881i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 29.2166 | + | 2.81751i | 0.992822 | + | 0.0957428i | ||||
\(867\) | −25.9500 | + | 35.7171i | −0.881307 | + | 1.21302i | ||||
\(868\) | 3.07705 | − | 1.43377i | 0.104442 | − | 0.0486653i | ||||
\(869\) | −6.44110 | + | 8.86542i | −0.218499 | + | 0.300739i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.23335 | − | 1.62262i | 0.0756742 | − | 0.0549805i | ||||
\(872\) | −2.17387 | + | 7.32718i | −0.0736165 | + | 0.248130i | ||||
\(873\) | 0.619716 | + | 1.90729i | 0.0209742 | + | 0.0645520i | ||||
\(874\) | −13.5725 | + | 3.00690i | −0.459098 | + | 0.101710i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −11.2114 | − | 24.0611i | −0.378799 | − | 0.812950i | ||||
\(877\) | 13.2478 | − | 4.30447i | 0.447347 | − | 0.145352i | −0.0766761 | − | 0.997056i | \(-0.524431\pi\) |
0.524023 | + | 0.851704i | \(0.324431\pi\) | |||||||
\(878\) | −0.320781 | − | 0.283886i | −0.0108258 | − | 0.00958068i | ||||
\(879\) | −59.9157 | + | 43.5313i | −2.02091 | + | 1.46827i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −32.7294 | − | 23.7793i | −1.10268 | − | 0.801145i | −0.121186 | − | 0.992630i | \(-0.538670\pi\) |
−0.981496 | + | 0.191485i | \(0.938670\pi\) | |||||||
\(882\) | −11.8193 | − | 53.3501i | −0.397977 | − | 1.79639i | ||||
\(883\) | 2.40648 | − | 3.31224i | 0.0809845 | − | 0.111466i | −0.766603 | − | 0.642122i | \(-0.778054\pi\) |
0.847587 | + | 0.530656i | \(0.178054\pi\) | |||||||
\(884\) | 10.0563 | − | 1.23181i | 0.338231 | − | 0.0414303i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 24.3297 | + | 41.3172i | 0.817371 | + | 1.38808i | ||||
\(887\) | −1.75339 | + | 5.39637i | −0.0588730 | + | 0.181192i | −0.976168 | − | 0.217016i | \(-0.930368\pi\) |
0.917295 | + | 0.398208i | \(0.130368\pi\) | |||||||
\(888\) | 58.6658 | − | 20.7460i | 1.96870 | − | 0.696191i | ||||
\(889\) | 3.13597 | + | 9.65152i | 0.105177 | + | 0.323701i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −66.7832 | − | 21.6992i | −2.23732 | − | 0.726950i | ||||
\(892\) | 3.05973 | + | 0.595670i | 0.102447 | + | 0.0199445i | ||||
\(893\) | 23.9601i | 0.801795i | ||||||||
\(894\) | −4.63394 | + | 10.6531i | −0.154982 | + | 0.356294i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 11.1011 | − | 7.33153i | 0.370863 | − | 0.244929i | ||||
\(897\) | −5.04297 | + | 3.66394i | −0.168380 | + | 0.122335i | ||||
\(898\) | 15.3607 | − | 9.04513i | 0.512592 | − | 0.301840i | ||||
\(899\) | 8.98418i | 0.299639i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 72.8046i | − | 2.42547i | ||||||
\(902\) | −18.1765 | − | 30.8677i | −0.605210 | − | 1.02778i | ||||
\(903\) | −8.85304 | + | 6.43211i | −0.294611 | + | 0.214047i | ||||
\(904\) | −12.3938 | − | 3.67706i | −0.412211 | − | 0.122297i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 43.2781 | + | 18.8253i | 1.43782 | + | 0.625429i | ||||
\(907\) | − | 49.8362i | − | 1.65478i | −0.561625 | − | 0.827392i | \(-0.689824\pi\) | ||
0.561625 | − | 0.827392i | \(-0.310176\pi\) | |||||||
\(908\) | 3.52458 | − | 18.1045i | 0.116967 | − | 0.600817i | ||||
\(909\) | 51.2997 | + | 16.6683i | 1.70150 | + | 0.552852i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.08071 | + | 3.32610i | 0.0358057 | + | 0.110199i | 0.967362 | − | 0.253399i | \(-0.0815485\pi\) |
−0.931556 | + | 0.363597i | \(0.881548\pi\) | |||||||
\(912\) | 29.9930 | + | 48.0606i | 0.993166 | + | 1.59145i | ||||
\(913\) | −11.6196 | + | 35.7613i | −0.384551 | + | 1.18353i | ||||
\(914\) | −3.15545 | + | 1.85809i | −0.104373 | + | 0.0614602i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −22.4283 | + | 2.74726i | −0.741051 | + | 0.0907720i | ||||
\(917\) | 6.01172 | − | 8.27442i | 0.198525 | − | 0.273246i | ||||
\(918\) | −93.7853 | + | 20.7775i | −3.09538 | + | 0.685759i | ||||
\(919\) | 35.2395 | + | 25.6030i | 1.16244 | + | 0.844564i | 0.990085 | − | 0.140471i | \(-0.0448616\pi\) |
0.172357 | + | 0.985034i | \(0.444862\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −74.2277 | + | 53.9296i | −2.44589 | + | 1.77704i | ||||
\(922\) | 6.40087 | − | 7.23276i | 0.210801 | − | 0.238198i | ||||
\(923\) | −1.69081 | + | 0.549378i | −0.0556538 | + | 0.0180830i | ||||
\(924\) | −26.6123 | + | 12.4001i | −0.875479 | + | 0.407935i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −6.67486 | − | 30.1290i | −0.219349 | − | 0.990099i | ||||
\(927\) | 27.9899 | + | 86.1439i | 0.919307 | + | 2.82934i | ||||
\(928\) | 5.17898 | + | 34.8256i | 0.170008 | + | 1.14321i | ||||
\(929\) | 20.6493 | − | 15.0026i | 0.677483 | − | 0.492220i | −0.195039 | − | 0.980795i | \(-0.562483\pi\) |
0.872522 | + | 0.488576i | \(0.162483\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14.8782 | − | 20.4781i | 0.487614 | − | 0.671143i | ||||
\(932\) | 22.5358 | − | 10.5007i | 0.738186 | − | 0.343962i | ||||
\(933\) | −1.81577 | + | 2.49920i | −0.0594458 | + | 0.0818201i | ||||
\(934\) | −0.407943 | + | 4.23024i | −0.0133483 | + | 0.138418i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 14.5728 | + | 10.0249i | 0.476327 | + | 0.327675i | ||||
\(937\) | −1.22309 | + | 3.76427i | −0.0399565 | + | 0.122973i | −0.969045 | − | 0.246884i | \(-0.920593\pi\) |
0.929089 | + | 0.369857i | \(0.120593\pi\) | |||||||
\(938\) | −0.484694 | + | 5.02612i | −0.0158258 | + | 0.164109i | ||||
\(939\) | −28.6403 | + | 9.30581i | −0.934642 | + | 0.303684i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.54079 | + | 2.45015i | 0.245823 | + | 0.0798727i | 0.429337 | − | 0.903144i | \(-0.358747\pi\) |
−0.183514 | + | 0.983017i | \(0.558747\pi\) | |||||||
\(942\) | 6.92099 | − | 15.9109i | 0.225498 | − | 0.518405i | ||||
\(943\) | 13.9114 | 0.453018 | ||||||||
\(944\) | −1.24126 | − | 4.99073i | −0.0403996 | − | 0.162434i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.4550 | − | 11.0225i | −0.404947 | − | 0.358371i | ||||
\(947\) | 0.457976 | + | 0.630350i | 0.0148822 | + | 0.0204836i | 0.816393 | − | 0.577496i | \(-0.195970\pi\) |
−0.801511 | + | 0.597980i | \(0.795970\pi\) | |||||||
\(948\) | −12.6870 | + | 11.8239i | −0.412053 | + | 0.384023i | ||||
\(949\) | − | 3.83921i | − | 0.124626i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −57.8664 | −1.87645 | ||||||||
\(952\) | −10.5031 | + | 15.2680i | −0.340409 | + | 0.494838i | ||||
\(953\) | 8.66334 | − | 6.29429i | 0.280633 | − | 0.203892i | −0.438560 | − | 0.898702i | \(-0.644511\pi\) |
0.719194 | + | 0.694810i | \(0.244511\pi\) | |||||||
\(954\) | 84.2364 | − | 95.1842i | 2.72725 | − | 3.08170i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 54.2513 | + | 10.5617i | 1.75461 | + | 0.341589i | ||||
\(957\) | − | 77.7008i | − | 2.51171i | ||||||
\(958\) | −10.7182 | + | 24.6405i | −0.346290 | + | 0.796097i | ||||
\(959\) | 1.32402 | − | 4.07492i | 0.0427549 | − | 0.131586i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.93566 | − | 27.5011i | −0.288247 | − | 0.887134i | ||||
\(962\) | 8.95823 | + | 0.863887i | 0.288825 | + | 0.0278528i | ||||
\(963\) | −45.8391 | − | 14.8940i | −1.47714 | − | 0.479953i | ||||
\(964\) | 5.84093 | + | 6.26726i | 0.188124 | + | 0.201855i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.09445 | − | 11.3491i | 0.0352134 | − | 0.365152i | ||||
\(967\) | 7.39419 | + | 5.37219i | 0.237781 | + | 0.172758i | 0.700294 | − | 0.713854i | \(-0.253052\pi\) |
−0.462513 | + | 0.886612i | \(0.653052\pi\) | |||||||
\(968\) | −8.21973 | − | 10.7218i | −0.264192 | − | 0.344612i | ||||
\(969\) | −63.8435 | − | 46.3850i | −2.05095 | − | 1.49010i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.2665 | − | 21.0125i | −0.489924 | − | 0.674323i | 0.490450 | − | 0.871469i | \(-0.336833\pi\) |
−0.980374 | + | 0.197147i | \(0.936833\pi\) | |||||||
\(972\) | −33.2196 | − | 18.4265i | −1.06552 | − | 0.591031i | ||||
\(973\) | −15.6195 | + | 5.07508i | −0.500738 | + | 0.162700i | ||||
\(974\) | −0.580675 | − | 2.62105i | −0.0186060 | − | 0.0839839i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 47.4419 | + | 39.8552i | 1.51858 | + | 1.27574i | ||||
\(977\) | 9.43346 | + | 29.0332i | 0.301803 | + | 0.928855i | 0.980851 | + | 0.194760i | \(0.0623929\pi\) |
−0.679048 | + | 0.734094i | \(0.737607\pi\) | |||||||
\(978\) | −65.3388 | − | 57.8237i | −2.08930 | − | 1.84900i | ||||
\(979\) | −6.09631 | − | 8.39085i | −0.194839 | − | 0.268173i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.9251 | − | 15.0372i | 0.348813 | − | 0.480100i | ||||
\(982\) | 42.6463 | − | 9.44799i | 1.36090 | − | 0.301498i | ||||
\(983\) | 32.3674 | + | 23.5163i | 1.03236 | + | 0.750052i | 0.968779 | − | 0.247924i | \(-0.0797485\pi\) |
0.0635791 | + | 0.997977i | \(0.479748\pi\) | |||||||
\(984\) | −18.9008 | − | 53.4480i | −0.602537 | − | 1.70386i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −24.8861 | − | 42.2623i | −0.792536 | − | 1.34590i | ||||
\(987\) | −18.6897 | − | 6.07265i | −0.594900 | − | 0.193295i | ||||
\(988\) | 0.996190 | + | 8.13276i | 0.0316930 | + | 0.258738i | ||||
\(989\) | 6.14291 | − | 1.99595i | 0.195333 | − | 0.0634676i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.8786 | − | 45.7916i | 0.472634 | − | 1.45462i | −0.376488 | − | 0.926422i | \(-0.622868\pi\) |
0.849122 | − | 0.528197i | \(-0.177132\pi\) | |||||||
\(992\) | 3.63812 | + | 7.31018i | 0.115510 | + | 0.232098i | ||||
\(993\) | 22.7314 | 0.721358 | ||||||||
\(994\) | 1.29711 | − | 2.98197i | 0.0411418 | − | 0.0945822i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −28.8653 | + | 52.0389i | −0.914633 | + | 1.64892i | ||||
\(997\) | 0.704471 | + | 0.969621i | 0.0223108 | + | 0.0307082i | 0.820027 | − | 0.572325i | \(-0.193959\pi\) |
−0.797716 | + | 0.603033i | \(0.793959\pi\) | |||||||
\(998\) | −7.60275 | − | 12.9112i | −0.240661 | − | 0.408696i | ||||
\(999\) | −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 | 1000.2.t.b.901.47 | 224 | ||
5.2 | odd | 4 | 1000.2.o.a.349.19 | 112 | |||
5.3 | odd | 4 | 200.2.o.a.69.10 | yes | 112 | ||
5.4 | even | 2 | inner | 1000.2.t.b.901.10 | 224 | ||
8.5 | even | 2 | inner | 1000.2.t.b.901.2 | 224 | ||
20.3 | even | 4 | 800.2.be.a.369.27 | 112 | |||
25.3 | odd | 20 | 1000.2.o.a.149.13 | 112 | |||
25.4 | even | 10 | inner | 1000.2.t.b.101.55 | 224 | ||
25.21 | even | 5 | inner | 1000.2.t.b.101.2 | 224 | ||
25.22 | odd | 20 | 200.2.o.a.29.16 | yes | 112 | ||
40.3 | even | 4 | 800.2.be.a.369.2 | 112 | |||
40.13 | odd | 4 | 200.2.o.a.69.16 | yes | 112 | ||
40.29 | even | 2 | inner | 1000.2.t.b.901.55 | 224 | ||
40.37 | odd | 4 | 1000.2.o.a.349.13 | 112 | |||
100.47 | even | 20 | 800.2.be.a.529.2 | 112 | |||
200.21 | even | 10 | inner | 1000.2.t.b.101.47 | 224 | ||
200.29 | even | 10 | inner | 1000.2.t.b.101.10 | 224 | ||
200.53 | odd | 20 | 1000.2.o.a.149.19 | 112 | |||
200.147 | even | 20 | 800.2.be.a.529.27 | 112 | |||
200.197 | odd | 20 | 200.2.o.a.29.10 | ✓ | 112 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
200.2.o.a.29.10 | ✓ | 112 | 200.197 | odd | 20 | ||
200.2.o.a.29.16 | yes | 112 | 25.22 | odd | 20 | ||
200.2.o.a.69.10 | yes | 112 | 5.3 | odd | 4 | ||
200.2.o.a.69.16 | yes | 112 | 40.13 | odd | 4 | ||
800.2.be.a.369.2 | 112 | 40.3 | even | 4 | |||
800.2.be.a.369.27 | 112 | 20.3 | even | 4 | |||
800.2.be.a.529.2 | 112 | 100.47 | even | 20 | |||
800.2.be.a.529.27 | 112 | 200.147 | even | 20 | |||
1000.2.o.a.149.13 | 112 | 25.3 | odd | 20 | |||
1000.2.o.a.149.19 | 112 | 200.53 | odd | 20 | |||
1000.2.o.a.349.13 | 112 | 40.37 | odd | 4 | |||
1000.2.o.a.349.19 | 112 | 5.2 | odd | 4 | |||
1000.2.t.b.101.2 | 224 | 25.21 | even | 5 | inner | ||
1000.2.t.b.101.10 | 224 | 200.29 | even | 10 | inner | ||
1000.2.t.b.101.47 | 224 | 200.21 | even | 10 | inner | ||
1000.2.t.b.101.55 | 224 | 25.4 | even | 10 | inner | ||
1000.2.t.b.901.2 | 224 | 8.5 | even | 2 | inner | ||
1000.2.t.b.901.10 | 224 | 5.4 | even | 2 | inner | ||
1000.2.t.b.901.47 | 224 | 1.1 | even | 1 | trivial | ||
1000.2.t.b.901.55 | 224 | 40.29 | even | 2 | inner |