Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [48,5,Mod(19,48)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(48, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("48.19");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.l (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.96175822802\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 19.13 | ||
Character | \(\chi\) | \(=\) | 48.19 |
Dual form | 48.5.l.a.43.13 |
$q$-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 \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(31\) | \(37\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.43325 | + | 2.05251i | 0.858312 | + | 0.513127i | ||||
\(3\) | −3.67423 | + | 3.67423i | −0.408248 | + | 0.408248i | ||||
\(4\) | 7.57441 | + | 14.0936i | 0.473400 | + | 0.880847i | ||||
\(5\) | −15.8310 | + | 15.8310i | −0.633241 | + | 0.633241i | −0.948880 | − | 0.315638i | \(-0.897781\pi\) |
0.315638 | + | 0.948880i | \(0.397781\pi\) | |||||||
\(6\) | −20.1560 | + | 5.07316i | −0.559888 | + | 0.140921i | ||||
\(7\) | −14.0988 | −0.287730 | −0.143865 | − | 0.989597i | \(-0.545953\pi\) | ||||
−0.143865 | + | 0.989597i | \(0.545953\pi\) | |||||||
\(8\) | −2.92234 | + | 63.9332i | −0.0456615 | + | 0.998957i | ||||
\(9\) | − | 27.0000i | − | 0.333333i | ||||||
\(10\) | −86.8452 | + | 21.8585i | −0.868452 | + | 0.218585i | ||||
\(11\) | 37.6905 | + | 37.6905i | 0.311492 | + | 0.311492i | 0.845487 | − | 0.533996i | \(-0.179310\pi\) |
−0.533996 | + | 0.845487i | \(0.679310\pi\) | |||||||
\(12\) | −79.6132 | − | 23.9529i | −0.552869 | − | 0.166340i | ||||
\(13\) | 127.319 | + | 127.319i | 0.753369 | + | 0.753369i | 0.975106 | − | 0.221737i | \(-0.0711728\pi\) |
−0.221737 | + | 0.975106i | \(0.571173\pi\) | |||||||
\(14\) | −48.4046 | − | 28.9379i | −0.246962 | − | 0.147642i | ||||
\(15\) | − | 116.334i | − | 0.517039i | ||||||
\(16\) | −141.257 | + | 213.501i | −0.551784 | + | 0.833987i | ||||
\(17\) | −81.0525 | −0.280459 | −0.140229 | − | 0.990119i | \(-0.544784\pi\) | ||||
−0.140229 | + | 0.990119i | \(0.544784\pi\) | |||||||
\(18\) | 55.4178 | − | 92.6977i | 0.171042 | − | 0.286104i | ||||
\(19\) | 470.496 | − | 470.496i | 1.30331 | − | 1.30331i | 0.377167 | − | 0.926145i | \(-0.376898\pi\) |
0.926145 | − | 0.377167i | \(-0.123102\pi\) | |||||||
\(20\) | −343.026 | − | 103.205i | −0.857566 | − | 0.258012i | ||||
\(21\) | 51.8022 | − | 51.8022i | 0.117465 | − | 0.117465i | ||||
\(22\) | 52.0408 | + | 206.761i | 0.107522 | + | 0.427192i | ||||
\(23\) | 259.447 | 0.490449 | 0.245224 | − | 0.969466i | \(-0.421138\pi\) | ||||
0.245224 | + | 0.969466i | \(0.421138\pi\) | |||||||
\(24\) | −224.168 | − | 245.643i | −0.389181 | − | 0.426464i | ||||
\(25\) | 123.757i | 0.198011i | ||||||||
\(26\) | 175.795 | + | 698.443i | 0.260052 | + | 1.03320i | ||||
\(27\) | 99.2043 | + | 99.2043i | 0.136083 | + | 0.136083i | ||||
\(28\) | −106.790 | − | 198.702i | −0.136211 | − | 0.253446i | ||||
\(29\) | 708.291 | + | 708.291i | 0.842201 | + | 0.842201i | 0.989145 | − | 0.146944i | \(-0.0469437\pi\) |
−0.146944 | + | 0.989145i | \(0.546944\pi\) | |||||||
\(30\) | 238.776 | − | 399.403i | 0.265307 | − | 0.443781i | ||||
\(31\) | − | 1479.51i | − | 1.53955i | −0.638315 | − | 0.769775i | \(-0.720368\pi\) | ||
0.638315 | − | 0.769775i | \(-0.279632\pi\) | |||||||
\(32\) | −923.182 | + | 443.070i | −0.901545 | + | 0.432686i | ||||
\(33\) | −276.967 | −0.254332 | ||||||||
\(34\) | −278.274 | − | 166.361i | −0.240721 | − | 0.143911i | ||||
\(35\) | 223.198 | − | 223.198i | 0.182202 | − | 0.182202i | ||||
\(36\) | 380.526 | − | 204.509i | 0.293616 | − | 0.157800i | ||||
\(37\) | 564.843 | − | 564.843i | 0.412596 | − | 0.412596i | −0.470046 | − | 0.882642i | \(-0.655763\pi\) |
0.882642 | + | 0.470046i | \(0.155763\pi\) | |||||||
\(38\) | 2581.03 | − | 649.632i | 1.78741 | − | 0.449884i | ||||
\(39\) | −935.602 | −0.615123 | ||||||||
\(40\) | −965.866 | − | 1058.39i | −0.603666 | − | 0.661496i | ||||
\(41\) | 579.599i | 0.344794i | 0.985028 | + | 0.172397i | \(0.0551512\pi\) | ||||
−0.985028 | + | 0.172397i | \(0.944849\pi\) | |||||||
\(42\) | 284.174 | − | 71.5253i | 0.161097 | − | 0.0405472i | ||||
\(43\) | −1348.23 | − | 1348.23i | −0.729170 | − | 0.729170i | 0.241285 | − | 0.970454i | \(-0.422431\pi\) |
−0.970454 | + | 0.241285i | \(0.922431\pi\) | |||||||
\(44\) | −245.710 | + | 816.676i | −0.126916 | + | 0.421837i | ||||
\(45\) | 427.438 | + | 427.438i | 0.211080 | + | 0.211080i | ||||
\(46\) | 890.747 | + | 532.518i | 0.420958 | + | 0.251663i | ||||
\(47\) | 2487.32i | 1.12599i | 0.826459 | + | 0.562997i | \(0.190352\pi\) | ||||
−0.826459 | + | 0.562997i | \(0.809648\pi\) | |||||||
\(48\) | −265.441 | − | 1303.46i | −0.115209 | − | 0.565739i | ||||
\(49\) | −2202.22 | −0.917212 | ||||||||
\(50\) | −254.012 | + | 424.888i | −0.101605 | + | 0.169955i | ||||
\(51\) | 297.806 | − | 297.806i | 0.114497 | − | 0.114497i | ||||
\(52\) | −830.014 | + | 2758.75i | −0.306958 | + | 1.02025i | ||||
\(53\) | −3062.67 | + | 3062.67i | −1.09031 | + | 1.09031i | −0.0948119 | + | 0.995495i | \(0.530225\pi\) |
−0.995495 | + | 0.0948119i | \(0.969775\pi\) | |||||||
\(54\) | 136.975 | + | 544.211i | 0.0469737 | + | 0.186629i | ||||
\(55\) | −1193.36 | −0.394499 | ||||||||
\(56\) | 41.2013 | − | 901.380i | 0.0131382 | − | 0.287430i | ||||
\(57\) | 3457.42i | 1.06415i | ||||||||
\(58\) | 977.966 | + | 3885.51i | 0.290715 | + | 1.15503i | ||||
\(59\) | −851.783 | − | 851.783i | −0.244695 | − | 0.244695i | 0.574094 | − | 0.818789i | \(-0.305354\pi\) |
−0.818789 | + | 0.574094i | \(0.805354\pi\) | |||||||
\(60\) | 1639.56 | − | 881.160i | 0.455433 | − | 0.244767i | ||||
\(61\) | 3221.31 | + | 3221.31i | 0.865711 | + | 0.865711i | 0.991994 | − | 0.126283i | \(-0.0403047\pi\) |
−0.126283 | + | 0.991994i | \(0.540305\pi\) | |||||||
\(62\) | 3036.71 | − | 5079.52i | 0.789986 | − | 1.32142i | ||||
\(63\) | 380.667i | 0.0959100i | ||||||||
\(64\) | −4078.92 | − | 373.669i | −0.995830 | − | 0.0912277i | ||||
\(65\) | −4031.19 | −0.954129 | ||||||||
\(66\) | −950.898 | − | 568.478i | −0.218296 | − | 0.130505i | ||||
\(67\) | 4382.72 | − | 4382.72i | 0.976324 | − | 0.976324i | −0.0234023 | − | 0.999726i | \(-0.507450\pi\) |
0.999726 | + | 0.0234023i | \(0.00744986\pi\) | |||||||
\(68\) | −613.925 | − | 1142.32i | −0.132769 | − | 0.247041i | ||||
\(69\) | −953.270 | + | 953.270i | −0.200225 | + | 0.200225i | ||||
\(70\) | 1224.41 | − | 308.178i | 0.249880 | − | 0.0628935i | ||||
\(71\) | −1927.00 | −0.382265 | −0.191133 | − | 0.981564i | \(-0.561216\pi\) | ||||
−0.191133 | + | 0.981564i | \(0.561216\pi\) | |||||||
\(72\) | 1726.20 | + | 78.9031i | 0.332986 | + | 0.0152205i | ||||
\(73\) | − | 6153.24i | − | 1.15467i | −0.816507 | − | 0.577335i | \(-0.804093\pi\) | ||
0.816507 | − | 0.577335i | \(-0.195907\pi\) | |||||||
\(74\) | 3098.59 | − | 779.902i | 0.565850 | − | 0.142422i | ||||
\(75\) | −454.711 | − | 454.711i | −0.0808376 | − | 0.0808376i | ||||
\(76\) | 10194.7 | + | 3067.23i | 1.76501 | + | 0.531031i | ||||
\(77\) | −531.389 | − | 531.389i | −0.0896255 | − | 0.0896255i | ||||
\(78\) | −3212.16 | − | 1920.33i | −0.527968 | − | 0.315637i | ||||
\(79\) | 3815.82i | 0.611411i | 0.952126 | + | 0.305706i | \(0.0988924\pi\) | ||||
−0.952126 | + | 0.305706i | \(0.901108\pi\) | |||||||
\(80\) | −1143.70 | − | 5616.18i | −0.178703 | − | 0.877528i | ||||
\(81\) | −729.000 | −0.111111 | ||||||||
\(82\) | −1189.63 | + | 1989.91i | −0.176923 | + | 0.295941i | ||||
\(83\) | 6196.26 | − | 6196.26i | 0.899443 | − | 0.899443i | −0.0959439 | − | 0.995387i | \(-0.530587\pi\) |
0.995387 | + | 0.0959439i | \(0.0305870\pi\) | |||||||
\(84\) | 1122.45 | + | 337.706i | 0.159077 | + | 0.0478608i | ||||
\(85\) | 1283.15 | − | 1283.15i | 0.177598 | − | 0.177598i | ||||
\(86\) | −1861.56 | − | 7396.09i | −0.251698 | − | 1.00001i | ||||
\(87\) | −5204.85 | −0.687654 | ||||||||
\(88\) | −2519.82 | + | 2299.53i | −0.325390 | + | 0.296944i | ||||
\(89\) | − | 15002.2i | − | 1.89398i | −0.321263 | − | 0.946990i | \(-0.604107\pi\) | ||
0.321263 | − | 0.946990i | \(-0.395893\pi\) | |||||||
\(90\) | 590.181 | + | 2344.82i | 0.0728618 | + | 0.289484i | ||||
\(91\) | −1795.05 | − | 1795.05i | −0.216767 | − | 0.216767i | ||||
\(92\) | 1965.16 | + | 3656.53i | 0.232179 | + | 0.432010i | ||||
\(93\) | 5436.06 | + | 5436.06i | 0.628519 | + | 0.628519i | ||||
\(94\) | −5105.25 | + | 8539.59i | −0.577778 | + | 0.966455i | ||||
\(95\) | 14896.9i | 1.65062i | ||||||||
\(96\) | 1764.04 | − | 5019.93i | 0.191411 | − | 0.544697i | ||||
\(97\) | 6079.50 | 0.646137 | 0.323068 | − | 0.946376i | \(-0.395286\pi\) | ||||
0.323068 | + | 0.946376i | \(0.395286\pi\) | |||||||
\(98\) | −7560.79 | − | 4520.09i | −0.787254 | − | 0.470646i | ||||
\(99\) | 1017.64 | − | 1017.64i | 0.103831 | − | 0.103831i | ||||
\(100\) | −1744.17 | + | 937.384i | −0.174417 | + | 0.0937384i | ||||
\(101\) | 12060.7 | − | 12060.7i | 1.18230 | − | 1.18230i | 0.203158 | − | 0.979146i | \(-0.434880\pi\) |
0.979146 | − | 0.203158i | \(-0.0651204\pi\) | |||||||
\(102\) | 1633.69 | − | 411.193i | 0.157025 | − | 0.0395226i | ||||
\(103\) | −1018.38 | −0.0959923 | −0.0479962 | − | 0.998848i | \(-0.515284\pi\) | ||||
−0.0479962 | + | 0.998848i | \(0.515284\pi\) | |||||||
\(104\) | −8512.01 | + | 7767.87i | −0.786983 | + | 0.718183i | ||||
\(105\) | 1640.16i | 0.148768i | ||||||||
\(106\) | −16801.1 | + | 4228.75i | −1.49529 | + | 0.376358i | ||||
\(107\) | 13049.5 | + | 13049.5i | 1.13979 | + | 1.13979i | 0.988488 | + | 0.151302i | \(0.0483466\pi\) |
0.151302 | + | 0.988488i | \(0.451653\pi\) | |||||||
\(108\) | −646.728 | + | 2149.56i | −0.0554465 | + | 0.184290i | ||||
\(109\) | 7747.67 | + | 7747.67i | 0.652106 | + | 0.652106i | 0.953500 | − | 0.301394i | \(-0.0974520\pi\) |
−0.301394 | + | 0.953500i | \(0.597452\pi\) | |||||||
\(110\) | −4097.10 | − | 2449.38i | −0.338603 | − | 0.202428i | ||||
\(111\) | 4150.73i | 0.336883i | ||||||||
\(112\) | 1991.55 | − | 3010.10i | 0.158765 | − | 0.239963i | ||||
\(113\) | −14420.3 | −1.12932 | −0.564661 | − | 0.825323i | \(-0.690993\pi\) | ||||
−0.564661 | + | 0.825323i | \(0.690993\pi\) | |||||||
\(114\) | −7096.40 | + | 11870.2i | −0.546045 | + | 0.913373i | ||||
\(115\) | −4107.32 | + | 4107.32i | −0.310572 | + | 0.310572i | ||||
\(116\) | −4617.46 | + | 15347.2i | −0.343152 | + | 1.14055i | ||||
\(117\) | 3437.62 | − | 3437.62i | 0.251123 | − | 0.251123i | ||||
\(118\) | −1176.09 | − | 4672.68i | −0.0844650 | − | 0.335584i | ||||
\(119\) | 1142.74 | 0.0806963 | ||||||||
\(120\) | 7437.60 | + | 339.967i | 0.516500 | + | 0.0236088i | ||||
\(121\) | − | 11799.9i | − | 0.805946i | ||||||
\(122\) | 4447.79 | + | 17671.3i | 0.298831 | + | 1.18727i | ||||
\(123\) | −2129.58 | − | 2129.58i | −0.140762 | − | 0.140762i | ||||
\(124\) | 20851.5 | − | 11206.4i | 1.35611 | − | 0.728824i | ||||
\(125\) | −11853.6 | − | 11853.6i | −0.758630 | − | 0.758630i | ||||
\(126\) | −781.322 | + | 1306.92i | −0.0492140 | + | 0.0823207i | ||||
\(127\) | − | 1641.73i | − | 0.101787i | −0.998704 | − | 0.0508937i | \(-0.983793\pi\) | ||
0.998704 | − | 0.0508937i | \(-0.0162070\pi\) | |||||||
\(128\) | −13237.0 | − | 9654.92i | −0.807922 | − | 0.589290i | ||||
\(129\) | 9907.46 | 0.595365 | ||||||||
\(130\) | −13840.1 | − | 8274.07i | −0.818941 | − | 0.489590i | ||||
\(131\) | −6768.96 | + | 6768.96i | −0.394438 | + | 0.394438i | −0.876266 | − | 0.481828i | \(-0.839973\pi\) |
0.481828 | + | 0.876266i | \(0.339973\pi\) | |||||||
\(132\) | −2097.86 | − | 3903.46i | −0.120401 | − | 0.224028i | ||||
\(133\) | −6633.41 | + | 6633.41i | −0.375002 | + | 0.375002i | ||||
\(134\) | 24042.5 | − | 6051.39i | 1.33897 | − | 0.337012i | ||||
\(135\) | −3141.01 | −0.172346 | ||||||||
\(136\) | 236.863 | − | 5181.95i | 0.0128062 | − | 0.280166i | ||||
\(137\) | 8848.71i | 0.471453i | 0.971819 | + | 0.235727i | \(0.0757470\pi\) | ||||
−0.971819 | + | 0.235727i | \(0.924253\pi\) | |||||||
\(138\) | −5229.41 | + | 1316.22i | −0.274596 | + | 0.0691146i | ||||
\(139\) | −15171.3 | − | 15171.3i | −0.785224 | − | 0.785224i | 0.195483 | − | 0.980707i | \(-0.437373\pi\) |
−0.980707 | + | 0.195483i | \(0.937373\pi\) | |||||||
\(140\) | 4836.25 | + | 1455.06i | 0.246747 | + | 0.0742378i | ||||
\(141\) | −9139.00 | − | 9139.00i | −0.459685 | − | 0.459685i | ||||
\(142\) | −6615.87 | − | 3955.18i | −0.328103 | − | 0.196151i | ||||
\(143\) | 9597.46i | 0.469336i | ||||||||
\(144\) | 5764.52 | + | 3813.93i | 0.277996 | + | 0.183928i | ||||
\(145\) | −22426.0 | −1.06663 | ||||||||
\(146\) | 12629.6 | − | 21125.6i | 0.592493 | − | 0.991068i | ||||
\(147\) | 8091.49 | − | 8091.49i | 0.374450 | − | 0.374450i | ||||
\(148\) | 12239.0 | + | 3682.30i | 0.558757 | + | 0.168111i | ||||
\(149\) | 9365.50 | − | 9365.50i | 0.421850 | − | 0.421850i | −0.463990 | − | 0.885840i | \(-0.653583\pi\) |
0.885840 | + | 0.463990i | \(0.153583\pi\) | |||||||
\(150\) | −627.838 | − | 2494.44i | −0.0279039 | − | 0.110864i | ||||
\(151\) | 17852.7 | 0.782981 | 0.391490 | − | 0.920182i | \(-0.371960\pi\) | ||||
0.391490 | + | 0.920182i | \(0.371960\pi\) | |||||||
\(152\) | 28705.4 | + | 31455.3i | 1.24244 | + | 1.36146i | ||||
\(153\) | 2188.42i | 0.0934862i | ||||||||
\(154\) | −733.711 | − | 2915.07i | −0.0309374 | − | 0.122916i | ||||
\(155\) | 23422.1 | + | 23422.1i | 0.974907 | + | 0.974907i | ||||
\(156\) | −7086.63 | − | 13186.0i | −0.291200 | − | 0.541830i | ||||
\(157\) | 25381.0 | + | 25381.0i | 1.02970 | + | 1.02970i | 0.999545 | + | 0.0301510i | \(0.00959882\pi\) |
0.0301510 | + | 0.999545i | \(0.490401\pi\) | |||||||
\(158\) | −7832.00 | + | 13100.7i | −0.313732 | + | 0.524782i | ||||
\(159\) | − | 22506.0i | − | 0.890232i | ||||||
\(160\) | 7600.66 | − | 21629.2i | 0.296901 | − | 0.844890i | ||||
\(161\) | −3657.89 | −0.141117 | ||||||||
\(162\) | −2502.84 | − | 1496.28i | −0.0953680 | − | 0.0570142i | ||||
\(163\) | −29621.2 | + | 29621.2i | −1.11488 | + | 1.11488i | −0.122397 | + | 0.992481i | \(0.539058\pi\) |
−0.992481 | + | 0.122397i | \(0.960942\pi\) | |||||||
\(164\) | −8168.61 | + | 4390.12i | −0.303711 | + | 0.163226i | ||||
\(165\) | 4384.68 | − | 4384.68i | 0.161053 | − | 0.161053i | ||||
\(166\) | 33991.2 | − | 8555.43i | 1.23353 | − | 0.310474i | ||||
\(167\) | −17898.0 | −0.641758 | −0.320879 | − | 0.947120i | \(-0.603978\pi\) | ||||
−0.320879 | + | 0.947120i | \(0.603978\pi\) | |||||||
\(168\) | 3160.50 | + | 3463.26i | 0.111979 | + | 0.122706i | ||||
\(169\) | 3859.44i | 0.135130i | ||||||||
\(170\) | 7039.03 | − | 1771.69i | 0.243565 | − | 0.0613042i | ||||
\(171\) | −12703.4 | − | 12703.4i | −0.434437 | − | 0.434437i | ||||
\(172\) | 8789.35 | − | 29213.5i | 0.297098 | − | 0.987476i | ||||
\(173\) | −21617.0 | − | 21617.0i | −0.722276 | − | 0.722276i | 0.246792 | − | 0.969068i | \(-0.420623\pi\) |
−0.969068 | + | 0.246792i | \(0.920623\pi\) | |||||||
\(174\) | −17869.6 | − | 10683.0i | −0.590222 | − | 0.352854i | ||||
\(175\) | − | 1744.82i | − | 0.0569736i | ||||||
\(176\) | −13371.0 | + | 2722.91i | −0.431656 | + | 0.0879039i | ||||
\(177\) | 6259.30 | 0.199793 | ||||||||
\(178\) | 30792.2 | − | 51506.4i | 0.971853 | − | 1.62563i | ||||
\(179\) | 19481.5 | − | 19481.5i | 0.608017 | − | 0.608017i | −0.334410 | − | 0.942428i | \(-0.608537\pi\) |
0.942428 | + | 0.334410i | \(0.108537\pi\) | |||||||
\(180\) | −2786.53 | + | 9261.71i | −0.0860041 | + | 0.285855i | ||||
\(181\) | −36095.6 | + | 36095.6i | −1.10178 | + | 1.10178i | −0.107589 | + | 0.994195i | \(0.534313\pi\) |
−0.994195 | + | 0.107589i | \(0.965687\pi\) | |||||||
\(182\) | −2478.49 | − | 9847.19i | −0.0748246 | − | 0.297283i | ||||
\(183\) | −23671.7 | −0.706850 | ||||||||
\(184\) | −758.192 | + | 16587.3i | −0.0223946 | + | 0.489937i | ||||
\(185\) | 17884.1i | 0.522545i | ||||||||
\(186\) | 7505.79 | + | 29820.9i | 0.216955 | + | 0.861976i | ||||
\(187\) | −3054.91 | − | 3054.91i | −0.0873605 | − | 0.0873605i | ||||
\(188\) | −35055.2 | + | 18840.0i | −0.991829 | + | 0.533046i | ||||
\(189\) | −1398.66 | − | 1398.66i | −0.0391551 | − | 0.0391551i | ||||
\(190\) | −30576.0 | + | 51144.7i | −0.846980 | + | 1.41675i | ||||
\(191\) | − | 38346.7i | − | 1.05114i | −0.850750 | − | 0.525571i | \(-0.823852\pi\) | ||
0.850750 | − | 0.525571i | \(-0.176148\pi\) | |||||||
\(192\) | 16359.9 | − | 13614.0i | 0.443789 | − | 0.369302i | ||||
\(193\) | 33888.6 | 0.909785 | 0.454893 | − | 0.890546i | \(-0.349678\pi\) | ||||
0.454893 | + | 0.890546i | \(0.349678\pi\) | |||||||
\(194\) | 20872.4 | + | 12478.2i | 0.554587 | + | 0.331551i | ||||
\(195\) | 14811.6 | − | 14811.6i | 0.389521 | − | 0.389521i | ||||
\(196\) | −16680.5 | − | 31037.2i | −0.434208 | − | 0.807923i | ||||
\(197\) | −26521.3 | + | 26521.3i | −0.683380 | + | 0.683380i | −0.960760 | − | 0.277380i | \(-0.910534\pi\) |
0.277380 | + | 0.960760i | \(0.410534\pi\) | |||||||
\(198\) | 5582.55 | − | 1405.10i | 0.142397 | − | 0.0358408i | ||||
\(199\) | 19874.7 | 0.501873 | 0.250936 | − | 0.968004i | \(-0.419262\pi\) | ||||
0.250936 | + | 0.968004i | \(0.419262\pi\) | |||||||
\(200\) | −7912.17 | − | 361.659i | −0.197804 | − | 0.00904147i | ||||
\(201\) | 32206.3i | 0.797165i | ||||||||
\(202\) | 66162.0 | − | 16652.7i | 1.62146 | − | 0.408113i | ||||
\(203\) | −9986.03 | − | 9986.03i | −0.242326 | − | 0.242326i | ||||
\(204\) | 6452.85 | + | 1941.44i | 0.155057 | + | 0.0466514i | ||||
\(205\) | −9175.65 | − | 9175.65i | −0.218338 | − | 0.218338i | ||||
\(206\) | −3496.36 | − | 2090.24i | −0.0823914 | − | 0.0492563i | ||||
\(207\) | − | 7005.08i | − | 0.163483i | ||||||
\(208\) | −45167.5 | + | 9198.05i | −1.04400 | + | 0.212603i | ||||
\(209\) | 35466.4 | 0.811942 | ||||||||
\(210\) | −3366.45 | + | 5631.09i | −0.0763368 | + | 0.127689i | ||||
\(211\) | −29334.4 | + | 29334.4i | −0.658889 | + | 0.658889i | −0.955117 | − | 0.296228i | \(-0.904271\pi\) |
0.296228 | + | 0.955117i | \(0.404271\pi\) | |||||||
\(212\) | −66361.9 | − | 19966.0i | −1.47655 | − | 0.444242i | ||||
\(213\) | 7080.25 | − | 7080.25i | 0.156059 | − | 0.156059i | ||||
\(214\) | 18017.9 | + | 71586.2i | 0.393438 | + | 1.56315i | ||||
\(215\) | 42687.9 | 0.923481 | ||||||||
\(216\) | −6632.36 | + | 6052.55i | −0.142155 | + | 0.129727i | ||||
\(217\) | 20859.2i | 0.442975i | ||||||||
\(218\) | 10697.5 | + | 42501.8i | 0.225097 | + | 0.894324i | ||||
\(219\) | 22608.4 | + | 22608.4i | 0.471392 | + | 0.471392i | ||||
\(220\) | −9038.99 | − | 16818.7i | −0.186756 | − | 0.347493i | ||||
\(221\) | −10319.6 | − | 10319.6i | −0.211289 | − | 0.211289i | ||||
\(222\) | −8519.42 | + | 14250.5i | −0.172864 | + | 0.289151i | ||||
\(223\) | − | 28991.8i | − | 0.582996i | −0.956571 | − | 0.291498i | \(-0.905846\pi\) | ||
0.956571 | − | 0.291498i | \(-0.0941536\pi\) | |||||||
\(224\) | 13015.7 | − | 6246.74i | 0.259401 | − | 0.124497i | ||||
\(225\) | 3341.43 | 0.0660036 | ||||||||
\(226\) | −49508.6 | − | 29597.8i | −0.969311 | − | 0.579486i | ||||
\(227\) | −5936.67 | + | 5936.67i | −0.115210 | + | 0.115210i | −0.762362 | − | 0.647151i | \(-0.775960\pi\) |
0.647151 | + | 0.762362i | \(0.275960\pi\) | |||||||
\(228\) | −48727.4 | + | 26187.9i | −0.937354 | + | 0.503769i | ||||
\(229\) | −8913.92 | + | 8913.92i | −0.169980 | + | 0.169980i | −0.786971 | − | 0.616991i | \(-0.788352\pi\) |
0.616991 | + | 0.786971i | \(0.288352\pi\) | |||||||
\(230\) | −22531.8 | + | 5671.14i | −0.425931 | + | 0.107205i | ||||
\(231\) | 3904.90 | 0.0731789 | ||||||||
\(232\) | −47353.2 | + | 43213.5i | −0.879779 | + | 0.802866i | ||||
\(233\) | 21770.0i | 0.401002i | 0.979694 | + | 0.200501i | \(0.0642569\pi\) | ||||
−0.979694 | + | 0.200501i | \(0.935743\pi\) | |||||||
\(234\) | 18858.0 | − | 4746.46i | 0.344400 | − | 0.0866839i | ||||
\(235\) | −39376.9 | − | 39376.9i | −0.713026 | − | 0.713026i | ||||
\(236\) | 5552.90 | − | 18456.4i | 0.0997002 | − | 0.331378i | ||||
\(237\) | −14020.2 | − | 14020.2i | −0.249608 | − | 0.249608i | ||||
\(238\) | 3923.31 | + | 2345.49i | 0.0692627 | + | 0.0414075i | ||||
\(239\) | − | 28051.7i | − | 0.491093i | −0.969385 | − | 0.245546i | \(-0.921033\pi\) | ||
0.969385 | − | 0.245546i | \(-0.0789673\pi\) | |||||||
\(240\) | 24837.4 | + | 16432.9i | 0.431204 | + | 0.285294i | ||||
\(241\) | 34321.7 | 0.590928 | 0.295464 | − | 0.955354i | \(-0.404526\pi\) | ||||
0.295464 | + | 0.955354i | \(0.404526\pi\) | |||||||
\(242\) | 24219.3 | − | 40511.8i | 0.413553 | − | 0.691753i | ||||
\(243\) | 2678.52 | − | 2678.52i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | −21000.2 | + | 69799.3i | −0.352731 | + | 1.17239i | ||||
\(245\) | 34863.5 | − | 34863.5i | 0.580816 | − | 0.580816i | ||||
\(246\) | −2940.40 | − | 11682.4i | −0.0485888 | − | 0.193046i | ||||
\(247\) | 119806. | 1.96375 | ||||||||
\(248\) | 94589.8 | + | 4323.62i | 1.53795 | + | 0.0702982i | ||||
\(249\) | 45533.0i | 0.734392i | ||||||||
\(250\) | −16366.7 | − | 65026.0i | −0.261868 | − | 1.04042i | ||||
\(251\) | −49564.4 | − | 49564.4i | −0.786724 | − | 0.786724i | 0.194232 | − | 0.980956i | \(-0.437779\pi\) |
−0.980956 | + | 0.194232i | \(0.937779\pi\) | |||||||
\(252\) | −5364.95 | + | 2883.32i | −0.0844820 | + | 0.0454038i | ||||
\(253\) | 9778.70 | + | 9778.70i | 0.152771 | + | 0.152771i | ||||
\(254\) | 3369.66 | − | 5636.46i | 0.0522299 | − | 0.0873654i | ||||
\(255\) | 9429.16i | 0.145008i | ||||||||
\(256\) | −25629.1 | − | 60316.8i | −0.391069 | − | 0.920362i | ||||
\(257\) | 94112.3 | 1.42489 | 0.712443 | − | 0.701730i | \(-0.247589\pi\) | ||||
0.712443 | + | 0.701730i | \(0.247589\pi\) | |||||||
\(258\) | 34014.8 | + | 20335.2i | 0.511009 | + | 0.305498i | ||||
\(259\) | −7963.59 | + | 7963.59i | −0.118716 | + | 0.118716i | ||||
\(260\) | −30533.9 | − | 56813.9i | −0.451685 | − | 0.840442i | ||||
\(261\) | 19123.9 | − | 19123.9i | 0.280734 | − | 0.280734i | ||||
\(262\) | −37132.9 | + | 9346.17i | −0.540949 | + | 0.136154i | ||||
\(263\) | −3529.57 | −0.0510282 | −0.0255141 | − | 0.999674i | \(-0.508122\pi\) | ||||
−0.0255141 | + | 0.999674i | \(0.508122\pi\) | |||||||
\(264\) | 809.392 | − | 17707.4i | 0.0116132 | − | 0.254067i | ||||
\(265\) | − | 96970.5i | − | 1.38086i | ||||||
\(266\) | −36389.3 | + | 9159.01i | −0.514293 | + | 0.129445i | ||||
\(267\) | 55121.7 | + | 55121.7i | 0.773214 | + | 0.773214i | ||||
\(268\) | 94964.6 | + | 28571.6i | 1.32218 | + | 0.397800i | ||||
\(269\) | −61684.8 | − | 61684.8i | −0.852459 | − | 0.852459i | 0.137976 | − | 0.990436i | \(-0.455940\pi\) |
−0.990436 | + | 0.137976i | \(0.955940\pi\) | |||||||
\(270\) | −10783.9 | − | 6446.96i | −0.147927 | − | 0.0884357i | ||||
\(271\) | − | 94137.0i | − | 1.28180i | −0.767623 | − | 0.640902i | \(-0.778560\pi\) | ||
0.767623 | − | 0.640902i | \(-0.221440\pi\) | |||||||
\(272\) | 11449.2 | − | 17304.8i | 0.154753 | − | 0.233899i | ||||
\(273\) | 13190.8 | 0.176989 | ||||||||
\(274\) | −18162.1 | + | 30379.8i | −0.241916 | + | 0.404654i | ||||
\(275\) | −4664.45 | + | 4664.45i | −0.0616787 | + | 0.0616787i | ||||
\(276\) | −20655.4 | − | 6214.51i | −0.271154 | − | 0.0815810i | ||||
\(277\) | 325.906 | − | 325.906i | 0.00424749 | − | 0.00424749i | −0.704980 | − | 0.709227i | \(-0.749044\pi\) |
0.709227 | + | 0.704980i | \(0.249044\pi\) | |||||||
\(278\) | −20947.6 | − | 83226.2i | −0.271048 | − | 1.07689i | ||||
\(279\) | −39946.7 | −0.513184 | ||||||||
\(280\) | 13617.5 | + | 14922.0i | 0.173693 | + | 0.190332i | ||||
\(281\) | 100158.i | 1.26845i | 0.773150 | + | 0.634224i | \(0.218680\pi\) | ||||
−0.773150 | + | 0.634224i | \(0.781320\pi\) | |||||||
\(282\) | −12618.6 | − | 50134.4i | −0.158676 | − | 0.630430i | ||||
\(283\) | 54557.6 | + | 54557.6i | 0.681212 | + | 0.681212i | 0.960273 | − | 0.279061i | \(-0.0900232\pi\) |
−0.279061 | + | 0.960273i | \(0.590023\pi\) | |||||||
\(284\) | −14595.9 | − | 27158.3i | −0.180965 | − | 0.336717i | ||||
\(285\) | −54734.6 | − | 54734.6i | −0.673864 | − | 0.673864i | ||||
\(286\) | −19698.9 | + | 32950.5i | −0.240829 | + | 0.402837i | ||||
\(287\) | − | 8171.63i | − | 0.0992075i | ||||||
\(288\) | 11962.9 | + | 24925.9i | 0.144229 | + | 0.300515i | ||||
\(289\) | −76951.5 | −0.921343 | ||||||||
\(290\) | −76993.9 | − | 46029.5i | −0.915504 | − | 0.547319i | ||||
\(291\) | −22337.5 | + | 22337.5i | −0.263784 | + | 0.263784i | ||||
\(292\) | 86721.0 | − | 46607.1i | 1.01709 | − | 0.546621i | ||||
\(293\) | −34394.8 | + | 34394.8i | −0.400643 | + | 0.400643i | −0.878460 | − | 0.477817i | \(-0.841428\pi\) |
0.477817 | + | 0.878460i | \(0.341428\pi\) | |||||||
\(294\) | 44388.0 | − | 11172.2i | 0.513536 | − | 0.129255i | ||||
\(295\) | 26969.2 | 0.309902 | ||||||||
\(296\) | 34461.6 | + | 37762.9i | 0.393325 | + | 0.431005i | ||||
\(297\) | 7478.12i | 0.0847773i | ||||||||
\(298\) | 51376.9 | − | 12931.3i | 0.578542 | − | 0.145616i | ||||
\(299\) | 33032.7 | + | 33032.7i | 0.369489 | + | 0.369489i | ||||
\(300\) | 2964.33 | − | 9852.67i | 0.0329370 | − | 0.109474i | ||||
\(301\) | 19008.4 | + | 19008.4i | 0.209804 | + | 0.209804i | ||||
\(302\) | 61292.9 | + | 36642.9i | 0.672042 | + | 0.401769i | ||||
\(303\) | 88627.5i | 0.965347i | ||||||||
\(304\) | 33990.5 | + | 166912.i | 0.367799 | + | 1.80609i | ||||
\(305\) | −101993. | −1.09641 | ||||||||
\(306\) | −4491.75 | + | 7513.39i | −0.0479703 | + | 0.0802404i | ||||
\(307\) | −99642.0 | + | 99642.0i | −1.05722 | + | 1.05722i | −0.0589602 | + | 0.998260i | \(0.518778\pi\) |
−0.998260 | + | 0.0589602i | \(0.981222\pi\) | |||||||
\(308\) | 3464.21 | − | 11514.1i | 0.0365176 | − | 0.121375i | ||||
\(309\) | 3741.78 | − | 3741.78i | 0.0391887 | − | 0.0391887i | ||||
\(310\) | 32339.9 | + | 128488.i | 0.336523 | + | 1.33703i | ||||
\(311\) | −163414. | −1.68954 | −0.844772 | − | 0.535126i | \(-0.820264\pi\) | ||||
−0.844772 | + | 0.535126i | \(0.820264\pi\) | |||||||
\(312\) | 2734.14 | − | 59816.1i | 0.0280874 | − | 0.614482i | ||||
\(313\) | − | 91968.7i | − | 0.938753i | −0.882998 | − | 0.469376i | \(-0.844479\pi\) | ||
0.882998 | − | 0.469376i | \(-0.155521\pi\) | |||||||
\(314\) | 35044.5 | + | 139234.i | 0.355436 | + | 1.41217i | ||||
\(315\) | −6026.35 | − | 6026.35i | −0.0607342 | − | 0.0607342i | ||||
\(316\) | −53778.5 | + | 28902.6i | −0.538560 | + | 0.289442i | ||||
\(317\) | 92936.2 | + | 92936.2i | 0.924840 | + | 0.924840i | 0.997366 | − | 0.0725266i | \(-0.0231062\pi\) |
−0.0725266 | + | 0.997366i | \(0.523106\pi\) | |||||||
\(318\) | 46193.7 | − | 77268.6i | 0.456802 | − | 0.764097i | ||||
\(319\) | 53391.7i | 0.524677i | ||||||||
\(320\) | 70489.1 | − | 58658.0i | 0.688370 | − | 0.572832i | ||||
\(321\) | −95893.5 | −0.930634 | ||||||||
\(322\) | −12558.4 | − | 7507.85i | −0.121122 | − | 0.0724109i | ||||
\(323\) | −38134.9 | + | 38134.9i | −0.365525 | + | 0.365525i | ||||
\(324\) | −5521.74 | − | 10274.2i | −0.0526000 | − | 0.0978719i | ||||
\(325\) | −15756.6 | + | 15756.6i | −0.149175 | + | 0.149175i | ||||
\(326\) | −162495. | + | 40899.2i | −1.52899 | + | 0.384839i | ||||
\(327\) | −56933.5 | −0.532442 | ||||||||
\(328\) | −37055.6 | − | 1693.78i | −0.344434 | − | 0.0157438i | ||||
\(329\) | − | 35068.1i | − | 0.323982i | ||||||
\(330\) | 24053.3 | − | 6054.10i | 0.220875 | − | 0.0555932i | ||||
\(331\) | −48028.3 | − | 48028.3i | −0.438370 | − | 0.438370i | 0.453093 | − | 0.891463i | \(-0.350320\pi\) |
−0.891463 | + | 0.453093i | \(0.850320\pi\) | |||||||
\(332\) | 134260. | + | 40394.4i | 1.21807 | + | 0.366475i | ||||
\(333\) | −15250.8 | − | 15250.8i | −0.137532 | − | 0.137532i | ||||
\(334\) | −61448.3 | − | 36735.8i | −0.550829 | − | 0.329304i | ||||
\(335\) | 138766.i | 1.23650i | ||||||||
\(336\) | 3742.39 | + | 18377.2i | 0.0331490 | + | 0.162780i | ||||
\(337\) | −17371.9 | −0.152964 | −0.0764819 | − | 0.997071i | \(-0.524369\pi\) | ||||
−0.0764819 | + | 0.997071i | \(0.524369\pi\) | |||||||
\(338\) | −7921.54 | + | 13250.4i | −0.0693387 | + | 0.115983i | ||||
\(339\) | 52983.6 | − | 52983.6i | 0.461044 | − | 0.461044i | ||||
\(340\) | 27803.2 | + | 8365.02i | 0.240512 | + | 0.0723618i | ||||
\(341\) | 55763.4 | − | 55763.4i | 0.479557 | − | 0.479557i | ||||
\(342\) | −17540.1 | − | 69687.7i | −0.149961 | − | 0.595805i | ||||
\(343\) | 64899.8 | 0.551639 | ||||||||
\(344\) | 90137.0 | − | 82257.0i | 0.761704 | − | 0.695114i | ||||
\(345\) | − | 30182.5i | − | 0.253581i | ||||||
\(346\) | −29847.4 | − | 118586.i | −0.249319 | − | 0.990558i | ||||
\(347\) | 53077.0 | + | 53077.0i | 0.440806 | + | 0.440806i | 0.892283 | − | 0.451477i | \(-0.149103\pi\) |
−0.451477 | + | 0.892283i | \(0.649103\pi\) | |||||||
\(348\) | −39423.7 | − | 73354.9i | −0.325536 | − | 0.605718i | ||||
\(349\) | −44311.9 | − | 44311.9i | −0.363806 | − | 0.363806i | 0.501406 | − | 0.865212i | \(-0.332816\pi\) |
−0.865212 | + | 0.501406i | \(0.832816\pi\) | |||||||
\(350\) | 3581.25 | − | 5990.39i | 0.0292347 | − | 0.0489012i | ||||
\(351\) | 25261.3i | 0.205041i | ||||||||
\(352\) | −51494.7 | − | 18095.6i | −0.415602 | − | 0.146046i | ||||
\(353\) | 92437.0 | 0.741816 | 0.370908 | − | 0.928670i | \(-0.379046\pi\) | ||||
0.370908 | + | 0.928670i | \(0.379046\pi\) | |||||||
\(354\) | 21489.7 | + | 12847.3i | 0.171484 | + | 0.102519i | ||||
\(355\) | 30506.4 | − | 30506.4i | 0.242066 | − | 0.242066i | ||||
\(356\) | 211435. | − | 113633.i | 1.66831 | − | 0.896611i | ||||
\(357\) | −4198.70 | + | 4198.70i | −0.0329441 | + | 0.0329441i | ||||
\(358\) | 106871. | − | 26898.9i | 0.833859 | − | 0.209878i | ||||
\(359\) | −138244. | −1.07265 | −0.536324 | − | 0.844012i | \(-0.680187\pi\) | ||||
−0.536324 | + | 0.844012i | \(0.680187\pi\) | |||||||
\(360\) | −28576.6 | + | 26078.4i | −0.220499 | + | 0.201222i | ||||
\(361\) | − | 312412.i | − | 2.39725i | ||||||
\(362\) | −198012. | + | 49838.6i | −1.51103 | + | 0.380319i | ||||
\(363\) | 43355.4 | + | 43355.4i | 0.329026 | + | 0.329026i | ||||
\(364\) | 11702.2 | − | 38895.0i | 0.0883210 | − | 0.293556i | ||||
\(365\) | 97412.1 | + | 97412.1i | 0.731185 | + | 0.731185i | ||||
\(366\) | −81270.9 | − | 48586.4i | −0.606699 | − | 0.362704i | ||||
\(367\) | 118276.i | 0.878140i | 0.898453 | + | 0.439070i | \(0.144692\pi\) | ||||
−0.898453 | + | 0.439070i | \(0.855308\pi\) | |||||||
\(368\) | −36648.7 | + | 55392.2i | −0.270622 | + | 0.409028i | ||||
\(369\) | 15649.2 | 0.114931 | ||||||||
\(370\) | −36707.3 | + | 61400.6i | −0.268132 | + | 0.448507i | ||||
\(371\) | 43179.9 | − | 43179.9i | 0.313714 | − | 0.313714i | ||||
\(372\) | −35438.5 | + | 117788.i | −0.256088 | + | 0.851170i | ||||
\(373\) | 145050. | − | 145050.i | 1.04255 | − | 1.04255i | 0.0435007 | − | 0.999053i | \(-0.486149\pi\) |
0.999053 | − | 0.0435007i | \(-0.0138511\pi\) | |||||||
\(374\) | −4218.04 | − | 16758.5i | −0.0301555 | − | 0.119810i | ||||
\(375\) | 87105.8 | 0.619419 | ||||||||
\(376\) | −159022. | − | 7268.79i | −1.12482 | − | 0.0514146i | ||||
\(377\) | 180358.i | 1.26898i | ||||||||
\(378\) | −1931.18 | − | 7672.70i | −0.0135157 | − | 0.0536988i | ||||
\(379\) | −20605.5 | − | 20605.5i | −0.143451 | − | 0.143451i | 0.631734 | − | 0.775185i | \(-0.282343\pi\) |
−0.775185 | + | 0.631734i | \(0.782343\pi\) | |||||||
\(380\) | −209950. | + | 112835.i | −1.45395 | + | 0.781405i | ||||
\(381\) | 6032.09 | + | 6032.09i | 0.0415545 | + | 0.0415545i | ||||
\(382\) | 78707.0 | − | 131654.i | 0.539370 | − | 0.902208i | ||||
\(383\) | − | 130541.i | − | 0.889915i | −0.895552 | − | 0.444958i | \(-0.853219\pi\) | ||
0.895552 | − | 0.444958i | \(-0.146781\pi\) | |||||||
\(384\) | 84110.3 | − | 13161.4i | 0.570409 | − | 0.0892562i | ||||
\(385\) | 16824.9 | 0.113509 | ||||||||
\(386\) | 116348. | + | 69556.7i | 0.780880 | + | 0.466836i | ||||
\(387\) | −36402.3 | + | 36402.3i | −0.243057 | + | 0.243057i | ||||
\(388\) | 46048.6 | + | 85681.8i | 0.305881 | + | 0.569148i | ||||
\(389\) | −20853.7 | + | 20853.7i | −0.137811 | + | 0.137811i | −0.772647 | − | 0.634836i | \(-0.781068\pi\) |
0.634836 | + | 0.772647i | \(0.281068\pi\) | |||||||
\(390\) | 81252.6 | − | 20450.9i | 0.534205 | − | 0.134457i | ||||
\(391\) | −21028.9 | −0.137551 | ||||||||
\(392\) | 6435.64 | − | 140795.i | 0.0418812 | − | 0.916255i | ||||
\(393\) | − | 49741.5i | − | 0.322058i | ||||||
\(394\) | −145489. | + | 36619.0i | −0.937215 | + | 0.235893i | ||||
\(395\) | −60408.4 | − | 60408.4i | −0.387171 | − | 0.387171i | ||||
\(396\) | 22050.3 | + | 6634.17i | 0.140612 | + | 0.0423054i | ||||
\(397\) | 33470.8 | + | 33470.8i | 0.212366 | + | 0.212366i | 0.805272 | − | 0.592906i | \(-0.202019\pi\) |
−0.592906 | + | 0.805272i | \(0.702019\pi\) | |||||||
\(398\) | 68234.6 | + | 40792.9i | 0.430763 | + | 0.257525i | ||||
\(399\) | − | 48745.4i | − | 0.306188i | ||||||
\(400\) | −26422.1 | − | 17481.5i | −0.165138 | − | 0.109259i | ||||
\(401\) | −71101.8 | −0.442172 | −0.221086 | − | 0.975254i | \(-0.570960\pi\) | ||||
−0.221086 | + | 0.975254i | \(0.570960\pi\) | |||||||
\(402\) | −66103.7 | + | 110572.i | −0.409047 | + | 0.684217i | ||||
\(403\) | 188370. | − | 188370.i | 1.15985 | − | 1.15985i | ||||
\(404\) | 261330. | + | 78625.4i | 1.60113 | + | 0.481726i | ||||
\(405\) | 11540.8 | − | 11540.8i | 0.0703601 | − | 0.0703601i | ||||
\(406\) | −13788.1 | − | 54780.9i | −0.0836474 | − | 0.332336i | ||||
\(407\) | 42578.4 | 0.257040 | ||||||||
\(408\) | 18169.4 | + | 19910.0i | 0.109149 | + | 0.119605i | ||||
\(409\) | 12068.1i | 0.0721429i | 0.999349 | + | 0.0360715i | \(0.0114844\pi\) | ||||
−0.999349 | + | 0.0360715i | \(0.988516\pi\) | |||||||
\(410\) | −12669.2 | − | 50335.4i | −0.0753669 | − | 0.299437i | ||||
\(411\) | −32512.2 | − | 32512.2i | −0.192470 | − | 0.192470i | ||||
\(412\) | −7713.65 | − | 14352.6i | −0.0454428 | − | 0.0845546i | ||||
\(413\) | 12009.1 | + | 12009.1i | 0.0704060 | + | 0.0704060i | ||||
\(414\) | 14378.0 | − | 24050.2i | 0.0838875 | − | 0.140319i | ||||
\(415\) | 196186.i | 1.13913i | ||||||||
\(416\) | −173950. | − | 61127.5i | −1.00517 | − | 0.353224i | ||||
\(417\) | 111486. | 0.641133 | ||||||||
\(418\) | 121765. | + | 72795.2i | 0.696900 | + | 0.416630i | ||||
\(419\) | 204428. | − | 204428.i | 1.16443 | − | 1.16443i | 0.180932 | − | 0.983496i | \(-0.442088\pi\) |
0.983496 | − | 0.180932i | \(-0.0579115\pi\) | |||||||
\(420\) | −23115.7 | + | 12423.3i | −0.131042 | + | 0.0704267i | ||||
\(421\) | −204135. | + | 204135.i | −1.15174 | + | 1.15174i | −0.165531 | + | 0.986205i | \(0.552934\pi\) |
−0.986205 | + | 0.165531i | \(0.947066\pi\) | |||||||
\(422\) | −160921. | + | 40503.2i | −0.903627 | + | 0.227439i | ||||
\(423\) | 67157.7 | 0.375331 | ||||||||
\(424\) | −186856. | − | 204757.i | −1.03938 | − | 1.13895i | ||||
\(425\) | − | 10030.8i | − | 0.0555338i | ||||||
\(426\) | 38840.5 | − | 9775.98i | 0.214026 | − | 0.0538693i | ||||
\(427\) | −45416.5 | − | 45416.5i | −0.249091 | − | 0.249091i | ||||
\(428\) | −85071.3 | + | 282755.i | −0.464404 | + | 1.54356i | ||||
\(429\) | −35263.3 | − | 35263.3i | −0.191606 | − | 0.191606i | ||||
\(430\) | 146558. | + | 87617.3i | 0.792635 | + | 0.473863i | ||||
\(431\) | − | 48651.4i | − | 0.261903i | −0.991389 | − | 0.130952i | \(-0.958197\pi\) | ||
0.991389 | − | 0.130952i | \(-0.0418033\pi\) | |||||||
\(432\) | −35193.5 | + | 7166.91i | −0.188580 | + | 0.0384030i | ||||
\(433\) | −225719. | −1.20391 | −0.601953 | − | 0.798532i | \(-0.705610\pi\) | ||||
−0.601953 | + | 0.798532i | \(0.705610\pi\) | |||||||
\(434\) | −42813.8 | + | 71615.0i | −0.227303 | + | 0.380211i | ||||
\(435\) | 82398.2 | − | 82398.2i | 0.435451 | − | 0.435451i | ||||
\(436\) | −50508.2 | + | 167876.i | −0.265698 | + | 0.883112i | ||||
\(437\) | 122069. | − | 122069.i | 0.639208 | − | 0.639208i | ||||
\(438\) | 31216.4 | + | 124024.i | 0.162718 | + | 0.646486i | ||||
\(439\) | 58516.9 | 0.303635 | 0.151818 | − | 0.988409i | \(-0.451487\pi\) | ||||
0.151818 | + | 0.988409i | \(0.451487\pi\) | |||||||
\(440\) | 3487.40 | − | 76295.3i | 0.0180134 | − | 0.394087i | ||||
\(441\) | 59460.1i | 0.305737i | ||||||||
\(442\) | −14248.6 | − | 56610.6i | −0.0729337 | − | 0.289770i | ||||
\(443\) | −104599. | − | 104599.i | −0.532990 | − | 0.532990i | 0.388471 | − | 0.921461i | \(-0.373003\pi\) |
−0.921461 | + | 0.388471i | \(0.873003\pi\) | |||||||
\(444\) | −58498.6 | + | 31439.3i | −0.296742 | + | 0.159480i | ||||
\(445\) | 237501. | + | 237501.i | 1.19935 | + | 1.19935i | ||||
\(446\) | 59506.0 | − | 99536.1i | 0.299151 | − | 0.500393i | ||||
\(447\) | 68822.1i | 0.344439i | ||||||||
\(448\) | 57507.7 | + | 5268.27i | 0.286530 | + | 0.0262489i | ||||
\(449\) | −58514.6 | −0.290250 | −0.145125 | − | 0.989413i | \(-0.546358\pi\) | ||||
−0.145125 | + | 0.989413i | \(0.546358\pi\) | |||||||
\(450\) | 11472.0 | + | 6858.32i | 0.0566517 | + | 0.0338683i | ||||
\(451\) | −21845.4 | + | 21845.4i | −0.107400 | + | 0.107400i | ||||
\(452\) | −109225. | − | 203234.i | −0.534622 | − | 0.994761i | ||||
\(453\) | −65595.2 | + | 65595.2i | −0.319651 | + | 0.319651i | ||||
\(454\) | −32567.1 | + | 8196.99i | −0.158004 | + | 0.0397688i | ||||
\(455\) | 56834.9 | 0.274531 | ||||||||
\(456\) | −221044. | − | 10103.8i | −1.06304 | − | 0.0485907i | ||||
\(457\) | 295348.i | 1.41417i | 0.707130 | + | 0.707084i | \(0.249990\pi\) | ||||
−0.707130 | + | 0.707084i | \(0.750010\pi\) | |||||||
\(458\) | −48899.6 | + | 12307.8i | −0.233117 | + | 0.0586746i | ||||
\(459\) | −8040.76 | − | 8040.76i | −0.0381656 | − | 0.0381656i | ||||
\(460\) | −88997.2 | − | 26776.2i | −0.420592 | − | 0.126542i | ||||
\(461\) | 72481.0 | + | 72481.0i | 0.341053 | + | 0.341053i | 0.856763 | − | 0.515710i | \(-0.172472\pi\) |
−0.515710 | + | 0.856763i | \(0.672472\pi\) | |||||||
\(462\) | 13406.5 | + | 8014.84i | 0.0628104 | + | 0.0375501i | ||||
\(463\) | − | 120288.i | − | 0.561127i | −0.959835 | − | 0.280564i | \(-0.909479\pi\) | ||
0.959835 | − | 0.280564i | \(-0.0905214\pi\) | |||||||
\(464\) | −251271. | + | 51169.7i | −1.16710 | + | 0.237672i | ||||
\(465\) | −172117. | −0.796008 | ||||||||
\(466\) | −44683.1 | + | 74741.8i | −0.205765 | + | 0.344185i | ||||
\(467\) | 85420.9 | − | 85420.9i | 0.391679 | − | 0.391679i | −0.483606 | − | 0.875286i | \(-0.660673\pi\) |
0.875286 | + | 0.483606i | \(0.160673\pi\) | |||||||
\(468\) | 74486.3 | + | 22410.4i | 0.340083 | + | 0.102319i | ||||
\(469\) | −61790.9 | + | 61790.9i | −0.280918 | + | 0.280918i | ||||
\(470\) | −54369.2 | − | 216012.i | −0.246126 | − | 0.977872i | ||||
\(471\) | −186511. | −0.840744 | ||||||||
\(472\) | 56946.4 | − | 51968.1i | 0.255613 | − | 0.233267i | ||||
\(473\) | − | 101631.i | − | 0.454261i | ||||||
\(474\) | −19358.3 | − | 76911.5i | −0.0861608 | − | 0.342322i | ||||
\(475\) | 58227.0 | + | 58227.0i | 0.258070 | + | 0.258070i | ||||
\(476\) | 8655.58 | + | 16105.3i | 0.0382017 | + | 0.0710811i | ||||
\(477\) | 82692.2 | + | 82692.2i | 0.363436 | + | 0.363436i | ||||
\(478\) | 57576.4 | − | 96308.5i | 0.251993 | − | 0.421511i | ||||
\(479\) | − | 39356.8i | − | 0.171533i | −0.996315 | − | 0.0857666i | \(-0.972666\pi\) | ||
0.996315 | − | 0.0857666i | \(-0.0273339\pi\) | |||||||
\(480\) | 51544.1 | + | 107397.i | 0.223716 | + | 0.466134i | ||||
\(481\) | 143831. | 0.621673 | ||||||||
\(482\) | 117835. | + | 70445.5i | 0.507200 | + | 0.303221i | ||||
\(483\) | 13439.9 | − | 13439.9i | 0.0576106 | − | 0.0576106i | ||||
\(484\) | 166302. | − | 89376.9i | 0.709915 | − | 0.381535i | ||||
\(485\) | −96244.8 | + | 96244.8i | −0.409161 | + | 0.409161i | ||||
\(486\) | 14693.7 | − | 3698.34i | 0.0622098 | − | 0.0156579i | ||||
\(487\) | −158483. | −0.668230 | −0.334115 | − | 0.942532i | \(-0.608437\pi\) | ||||
−0.334115 | + | 0.942532i | \(0.608437\pi\) | |||||||
\(488\) | −215363. | + | 196535.i | −0.904338 | + | 0.825279i | ||||
\(489\) | − | 217671.i | − | 0.910295i | ||||||
\(490\) | 191253. | − | 48137.4i | 0.796555 | − | 0.200489i | ||||
\(491\) | −50847.6 | − | 50847.6i | −0.210915 | − | 0.210915i | 0.593741 | − | 0.804656i | \(-0.297650\pi\) |
−0.804656 | + | 0.593741i | \(0.797650\pi\) | |||||||
\(492\) | 13883.1 | − | 46143.7i | 0.0573529 | − | 0.190626i | ||||
\(493\) | −57408.8 | − | 57408.8i | −0.236203 | − | 0.236203i | ||||
\(494\) | 411325. | + | 245904.i | 1.68551 | + | 1.00765i | ||||
\(495\) | 32220.7i | 0.131500i | ||||||||
\(496\) | 315876. | + | 208991.i | 1.28397 | + | 0.849500i | ||||
\(497\) | 27168.3 | 0.109989 | ||||||||
\(498\) | −93457.0 | + | 156326.i | −0.376837 | + | 0.630338i | ||||
\(499\) | −193612. | + | 193612.i | −0.777555 | + | 0.777555i | −0.979414 | − | 0.201860i | \(-0.935301\pi\) |
0.201860 | + | 0.979414i | \(0.435301\pi\) | |||||||
\(500\) | 77275.4 | − | 256843.i | 0.309101 | − | 1.02737i | ||||
\(501\) | 65761.4 | − | 65761.4i | 0.261997 | − | 0.261997i | ||||
\(502\) | −68435.5 | − | 271898.i | −0.271565 | − | 1.07894i | ||||
\(503\) | −353152. | −1.39581 | −0.697904 | − | 0.716192i | \(-0.745884\pi\) | ||||
−0.697904 | + | 0.716192i | \(0.745884\pi\) | |||||||
\(504\) | −24337.3 | − | 1112.44i | −0.0958099 | − | 0.00437939i | ||||
\(505\) | 381866.i | 1.49737i | ||||||||
\(506\) | 13501.8 | + | 53643.6i | 0.0527341 | + | 0.209516i | ||||
\(507\) | −14180.5 | − | 14180.5i | −0.0551665 | − | 0.0551665i | ||||
\(508\) | 23137.8 | − | 12435.1i | 0.0896591 | − | 0.0481862i | ||||
\(509\) | −37267.3 | − | 37267.3i | −0.143844 | − | 0.143844i | 0.631518 | − | 0.775362i | \(-0.282432\pi\) |
−0.775362 | + | 0.631518i | \(0.782432\pi\) | |||||||
\(510\) | −19353.4 | + | 32372.6i | −0.0744077 | + | 0.124462i | ||||
\(511\) | 86753.1i | 0.332233i | ||||||||
\(512\) | 35809.8 | − | 259687.i | 0.136604 | − | 0.990626i | ||||
\(513\) | 93350.4 | 0.354717 | ||||||||
\(514\) | 323111. | + | 193166.i | 1.22300 | + | 0.731148i | ||||
\(515\) | 16122.1 | − | 16122.1i | 0.0607863 | − | 0.0607863i | ||||
\(516\) | 75043.1 | + | 139631.i | 0.281846 | + | 0.524425i | ||||
\(517\) | −93748.3 | + | 93748.3i | −0.350738 | + | 0.350738i | ||||
\(518\) | −43686.4 | + | 10995.6i | −0.162812 | + | 0.0409790i | ||||
\(519\) | 158852. | 0.589736 | ||||||||
\(520\) | 11780.5 | − | 257727.i | 0.0435669 | − | 0.953134i | ||||
\(521\) | − | 454022.i | − | 1.67264i | −0.548245 | − | 0.836318i | \(-0.684704\pi\) | ||
0.548245 | − | 0.836318i | \(-0.315296\pi\) | |||||||
\(522\) | 104909. | − | 26405.1i | 0.385009 | − | 0.0969050i | ||||
\(523\) | 119641. | + | 119641.i | 0.437399 | + | 0.437399i | 0.891136 | − | 0.453737i | \(-0.149909\pi\) |
−0.453737 | + | 0.891136i | \(0.649909\pi\) | |||||||
\(524\) | −146670. | − | 44127.9i | −0.534167 | − | 0.160713i | ||||
\(525\) | 6410.87 | + | 6410.87i | 0.0232594 | + | 0.0232594i | ||||
\(526\) | −12117.9 | − | 7244.47i | −0.0437981 | − | 0.0261840i | ||||
\(527\) | 119918.i | 0.431780i | ||||||||
\(528\) | 39123.5 | − | 59132.7i | 0.140336 | − | 0.212110i | ||||
\(529\) | −212528. | −0.759460 | ||||||||
\(530\) | 199033. | − | 332924.i | 0.708555 | − | 1.18521i | ||||
\(531\) | −22998.1 | + | 22998.1i | −0.0815650 | + | 0.0815650i | ||||
\(532\) | −143732. | − | 43244.2i | −0.507846 | − | 0.152793i | ||||
\(533\) | −73794.1 | + | 73794.1i | −0.259757 | + | 0.259757i | ||||
\(534\) | 76108.7 | + | 302384.i | 0.266902 | + | 1.06042i | ||||
\(535\) | −413173. | −1.44352 | ||||||||
\(536\) | 267394. | + | 293009.i | 0.930725 | + | 1.01989i | ||||
\(537\) | 143159.i | 0.496444i | ||||||||
\(538\) | −85170.7 | − | 338388.i | −0.294256 | − | 1.16910i | ||||
\(539\) | −83002.9 | − | 83002.9i | −0.285704 | − | 0.285704i | ||||
\(540\) | −23791.3 | − | 44268.1i | −0.0815889 | − | 0.151811i | ||||
\(541\) | 190892. | + | 190892.i | 0.652218 | + | 0.652218i | 0.953527 | − | 0.301309i | \(-0.0974235\pi\) |
−0.301309 | + | 0.953527i | \(0.597423\pi\) | |||||||
\(542\) | 193217. | − | 323196.i | 0.657729 | − | 1.10019i | ||||
\(543\) | − | 265247.i | − | 0.899603i | ||||||
\(544\) | 74826.2 | − | 35912.0i | 0.252846 | − | 0.121350i | ||||
\(545\) | −245307. | −0.825880 | ||||||||
\(546\) | 45287.4 | + | 27074.3i | 0.151912 | + | 0.0908181i | ||||
\(547\) | 278955. | − | 278955.i | 0.932308 | − | 0.932308i | −0.0655419 | − | 0.997850i | \(-0.520878\pi\) |
0.997850 | + | 0.0655419i | \(0.0208776\pi\) | |||||||
\(548\) | −124710. | + | 67023.7i | −0.415279 | + | 0.223186i | ||||
\(549\) | 86975.4 | − | 86975.4i | 0.288570 | − | 0.288570i | ||||
\(550\) | −25588.1 | + | 6440.40i | −0.0845887 | + | 0.0212906i | ||||
\(551\) | 666496. | 2.19530 | ||||||||
\(552\) | −58159.9 | − | 63731.4i | −0.190873 | − | 0.209158i | ||||
\(553\) | − | 53798.3i | − | 0.175921i | ||||||
\(554\) | 1787.84 | − | 449.991i | 0.00582518 | − | 0.00146617i | ||||
\(555\) | −65710.4 | − | 65710.4i | −0.213328 | − | 0.213328i | ||||
\(556\) | 98904.1 | − | 328732.i | 0.319937 | − | 1.06339i | ||||
\(557\) | −230862. | − | 230862.i | −0.744118 | − | 0.744118i | 0.229250 | − | 0.973368i | \(-0.426373\pi\) |
−0.973368 | + | 0.229250i | \(0.926373\pi\) | |||||||
\(558\) | −137147. | − | 81991.0i | −0.440472 | − | 0.263329i | ||||
\(559\) | − | 343313.i | − | 1.09867i | ||||||
\(560\) | 16124.7 | + | 79181.1i | 0.0514181 | + | 0.252491i | ||||
\(561\) | 22448.9 | 0.0713296 | ||||||||
\(562\) | −205575. | + | 343867.i | −0.650875 | + | 1.08872i | ||||
\(563\) | −393297. | + | 393297.i | −1.24081 | + | 1.24081i | −0.281138 | + | 0.959667i | \(0.590712\pi\) |
−0.959667 | + | 0.281138i | \(0.909288\pi\) | |||||||
\(564\) | 59578.5 | − | 198024.i | 0.187297 | − | 0.622528i | ||||
\(565\) | 228289. | − | 228289.i | 0.715134 | − | 0.715134i | ||||
\(566\) | 75329.9 | + | 299290.i | 0.235144 | + | 0.934242i | ||||
\(567\) | 10278.0 | 0.0319700 | ||||||||
\(568\) | 5631.34 | − | 123199.i | 0.0174548 | − | 0.381866i | ||||
\(569\) | − | 36240.2i | − | 0.111935i | −0.998433 | − | 0.0559675i | \(-0.982176\pi\) | ||
0.998433 | − | 0.0559675i | \(-0.0178243\pi\) | |||||||
\(570\) | −75574.2 | − | 300261.i | −0.232608 | − | 0.924164i | ||||
\(571\) | −10226.1 | − | 10226.1i | −0.0313644 | − | 0.0313644i | 0.691251 | − | 0.722615i | \(-0.257060\pi\) |
−0.722615 | + | 0.691251i | \(0.757060\pi\) | |||||||
\(572\) | −135262. | + | 72695.1i | −0.413414 | + | 0.222184i | ||||
\(573\) | 140895. | + | 140895.i | 0.429127 | + | 0.429127i | ||||
\(574\) | 16772.3 | − | 28055.2i | 0.0509061 | − | 0.0851511i | ||||
\(575\) | 32108.3i | 0.0971141i | ||||||||
\(576\) | −10089.1 | + | 110131.i | −0.0304092 | + | 0.331943i | ||||
\(577\) | 225041. | 0.675942 | 0.337971 | − | 0.941157i | \(-0.390259\pi\) | ||||
0.337971 | + | 0.941157i | \(0.390259\pi\) | |||||||
\(578\) | −264194. | − | 157944.i | −0.790800 | − | 0.472766i | ||||
\(579\) | −124515. | + | 124515.i | −0.371418 | + | 0.371418i | ||||
\(580\) | −169863. | − | 316062.i | −0.504944 | − | 0.939541i | ||||
\(581\) | −87359.6 | + | 87359.6i | −0.258797 | + | 0.258797i | ||||
\(582\) | −122538. | + | 30842.3i | −0.361764 | + | 0.0910543i | ||||
\(583\) | −230867. | −0.679243 | ||||||||
\(584\) | 393397. | + | 17981.8i | 1.15347 | + | 0.0527240i | ||||
\(585\) | 108842.i | 0.318043i | ||||||||
\(586\) | −188682. | + | 47490.3i | −0.549458 | + | 0.138296i | ||||
\(587\) | 456085. | + | 456085.i | 1.32364 | + | 1.32364i | 0.910807 | + | 0.412832i | \(0.135460\pi\) |
0.412832 | + | 0.910807i | \(0.364540\pi\) | |||||||
\(588\) | 175326. | + | 52749.6i | 0.507098 | + | 0.152569i | ||||
\(589\) | −696102. | − | 696102.i | −2.00652 | − | 2.00652i | ||||
\(590\) | 92592.0 | + | 55354.6i | 0.265993 | + | 0.159019i | ||||
\(591\) | − | 194891.i | − | 0.557978i | ||||||
\(592\) | 40806.5 | + | 200382.i | 0.116436 | + | 0.571763i | ||||
\(593\) | 33923.9 | 0.0964709 | 0.0482355 | − | 0.998836i | \(-0.484640\pi\) | ||||
0.0482355 | + | 0.998836i | \(0.484640\pi\) | |||||||
\(594\) | −15348.9 | + | 25674.3i | −0.0435016 | + | 0.0727654i | ||||
\(595\) | −18090.8 | + | 18090.8i | −0.0511003 | + | 0.0511003i | ||||
\(596\) | 202931. | + | 61055.1i | 0.571290 | + | 0.171882i | ||||
\(597\) | −73024.1 | + | 73024.1i | −0.204889 | + | 0.204889i | ||||
\(598\) | 45609.5 | + | 181209.i | 0.127542 | + | 0.506732i | ||||
\(599\) | 612011. | 1.70571 | 0.852856 | − | 0.522146i | \(-0.174868\pi\) | ||||
0.852856 | + | 0.522146i | \(0.174868\pi\) | |||||||
\(600\) | 30400.0 | − | 27742.4i | 0.0844444 | − | 0.0770621i | ||||
\(601\) | 470989.i | 1.30395i | 0.758240 | + | 0.651976i | \(0.226060\pi\) | ||||
−0.758240 | + | 0.651976i | \(0.773940\pi\) | |||||||
\(602\) | 26245.7 | + | 104276.i | 0.0724212 | + | 0.287733i | ||||
\(603\) | −118333. | − | 118333.i | −0.325441 | − | 0.325441i | ||||
\(604\) | 135224. | + | 251609.i | 0.370663 | + | 0.689687i | ||||
\(605\) | 186804. | + | 186804.i | 0.510358 | + | 0.510358i | ||||
\(606\) | −181909. | + | 304280.i | −0.495346 | + | 0.828569i | ||||
\(607\) | 211710.i | 0.574598i | 0.957841 | + | 0.287299i | \(0.0927573\pi\) | ||||
−0.957841 | + | 0.287299i | \(0.907243\pi\) | |||||||
\(608\) | −225890. | + | 642816.i | −0.611070 | + | 1.73892i | ||||
\(609\) | 73382.0 | 0.197859 | ||||||||
\(610\) | −350169. | − | 209342.i | −0.941061 | − | 0.562597i | ||||
\(611\) | −316684. | + | 316684.i | −0.848289 | + | 0.848289i | ||||
\(612\) | −30842.6 | + | 16576.0i | −0.0823471 | + | 0.0442564i | ||||
\(613\) | 310327. | − | 310327.i | 0.825846 | − | 0.825846i | −0.161094 | − | 0.986939i | \(-0.551502\pi\) |
0.986939 | + | 0.161094i | \(0.0515021\pi\) | |||||||
\(614\) | −546612. | + | 137580.i | −1.44991 | + | 0.364937i | ||||
\(615\) | 67427.0 | 0.178272 | ||||||||
\(616\) | 35526.3 | − | 32420.6i | 0.0936244 | − | 0.0854396i | ||||
\(617\) | 61142.3i | 0.160610i | 0.996770 | + | 0.0803048i | \(0.0255894\pi\) | ||||
−0.996770 | + | 0.0803048i | \(0.974411\pi\) | |||||||
\(618\) | 20526.5 | − | 5166.42i | 0.0537450 | − | 0.0135274i | ||||
\(619\) | 95031.3 | + | 95031.3i | 0.248019 | + | 0.248019i | 0.820157 | − | 0.572138i | \(-0.193886\pi\) |
−0.572138 | + | 0.820157i | \(0.693886\pi\) | |||||||
\(620\) | −152693. | + | 507510.i | −0.397223 | + | 1.32027i | ||||
\(621\) | 25738.3 | + | 25738.3i | 0.0667416 | + | 0.0667416i | ||||
\(622\) | −561042. | − | 335410.i | −1.45016 | − | 0.866952i | ||||
\(623\) | 211513.i | 0.544955i | ||||||||
\(624\) | 132160. | − | 199752.i | 0.339415 | − | 0.513005i | ||||
\(625\) | 297961. | 0.762781 | ||||||||
\(626\) | 188767. | − | 315751.i | 0.481700 | − | 0.805743i | ||||
\(627\) | −130312. | + | 130312.i | −0.331474 | + | 0.331474i | ||||
\(628\) | −165462. | + | 549954.i | −0.419547 | + | 1.39446i | ||||
\(629\) | −45782.0 | + | 45782.0i | −0.115716 | + | 0.115716i | ||||
\(630\) | −8320.82 | − | 33059.1i | −0.0209645 | − | 0.0832932i | ||||
\(631\) | 268083. | 0.673303 | 0.336651 | − | 0.941629i | \(-0.390706\pi\) | ||||
0.336651 | + | 0.941629i | \(0.390706\pi\) | |||||||
\(632\) | −243958. | − | 11151.1i | −0.610774 | − | 0.0279180i | ||||
\(633\) | − | 215563.i | − | 0.537981i | ||||||
\(634\) | 128321. | + | 509826.i | 0.319241 | + | 1.26836i | ||||
\(635\) | 25990.3 | + | 25990.3i | 0.0644560 | + | 0.0644560i | ||||
\(636\) | 317189. | − | 170469.i | 0.784159 | − | 0.421436i | ||||
\(637\) | −280386. | − | 280386.i | −0.690999 | − | 0.690999i | ||||
\(638\) | −109587. | + | 183307.i | −0.269226 | + | 0.450337i | ||||
\(639\) | 52029.0i | 0.127422i | ||||||||
\(640\) | 362403. | − | 56707.9i | 0.884772 | − | 0.138447i | ||||
\(641\) | 791424. | 1.92616 | 0.963081 | − | 0.269211i | \(-0.0867629\pi\) | ||||
0.963081 | + | 0.269211i | \(0.0867629\pi\) | |||||||
\(642\) | −329226. | − | 196822.i | −0.798775 | − | 0.477534i | ||||
\(643\) | −228349. | + | 228349.i | −0.552303 | + | 0.552303i | −0.927105 | − | 0.374802i | \(-0.877711\pi\) |
0.374802 | + | 0.927105i | \(0.377711\pi\) | |||||||
\(644\) | −27706.3 | − | 51552.6i | −0.0668047 | − | 0.124302i | ||||
\(645\) | −156845. | + | 156845.i | −0.377009 | + | 0.377009i | ||||
\(646\) | −209199. | + | 52654.3i | −0.501296 | + | 0.126174i | ||||
\(647\) | −88355.9 | −0.211070 | −0.105535 | − | 0.994416i | \(-0.533656\pi\) | ||||
−0.105535 | + | 0.994416i | \(0.533656\pi\) | |||||||
\(648\) | 2130.38 | − | 46607.3i | 0.00507350 | − | 0.110995i | ||||
\(649\) | − | 64208.2i | − | 0.152441i | ||||||
\(650\) | −86437.1 | + | 21755.8i | −0.204585 | + | 0.0514930i | ||||
\(651\) | −76641.7 | − | 76641.7i | −0.180844 | − | 0.180844i | ||||
\(652\) | −641831. | − | 193105.i | −1.50982 | − | 0.454254i | ||||
\(653\) | −539514. | − | 539514.i | −1.26525 | − | 1.26525i | −0.948514 | − | 0.316735i | \(-0.897413\pi\) |
−0.316735 | − | 0.948514i | \(-0.602587\pi\) | |||||||
\(654\) | −195467. | − | 116857.i | −0.457002 | − | 0.273211i | ||||
\(655\) | − | 214319.i | − | 0.499549i | ||||||
\(656\) | −123745. | − | 81872.2i | −0.287554 | − | 0.190252i | ||||
\(657\) | −166137. | −0.384890 | ||||||||
\(658\) | 71977.7 | − | 120398.i | 0.166244 | − | 0.278078i | ||||
\(659\) | −27362.6 | + | 27362.6i | −0.0630066 | + | 0.0630066i | −0.737908 | − | 0.674901i | \(-0.764186\pi\) |
0.674901 | + | 0.737908i | \(0.264186\pi\) | |||||||
\(660\) | 95007.1 | + | 28584.4i | 0.218106 | + | 0.0656207i | ||||
\(661\) | 466632. | − | 466632.i | 1.06800 | − | 1.06800i | 0.0704871 | − | 0.997513i | \(-0.477545\pi\) |
0.997513 | − | 0.0704871i | \(-0.0224554\pi\) | |||||||
\(662\) | −66314.5 | − | 263471.i | −0.151319 | − | 0.601198i | ||||
\(663\) | 75833.0 | 0.172517 | ||||||||
\(664\) | 378040. | + | 414255.i | 0.857435 | + | 0.939575i | ||||
\(665\) | − | 210027.i | − | 0.474933i | ||||||
\(666\) | −21057.3 | − | 83662.0i | −0.0474739 | − | 0.188617i | ||||
\(667\) | 183764. | + | 183764.i | 0.413056 | + | 0.413056i | ||||
\(668\) | −135567. | − | 252246.i | −0.303809 | − | 0.565291i | ||||
\(669\) | 106523. | + | 106523.i | 0.238007 | + | 0.238007i | ||||
\(670\) | −284818. | + | 476418.i | −0.634481 | + | 1.06130i | ||||
\(671\) | 242826.i | 0.539324i | ||||||||
\(672\) | −24870.8 | + | 70774.8i | −0.0550746 | + | 0.156726i | ||||
\(673\) | 723002. | 1.59628 | 0.798141 | − | 0.602471i | \(-0.205817\pi\) | ||||
0.798141 | + | 0.602471i | \(0.205817\pi\) | |||||||
\(674\) | −59642.2 | − | 35656.1i | −0.131291 | − | 0.0784899i | ||||
\(675\) | −12277.2 | + | 12277.2i | −0.0269459 | + | 0.0269459i | ||||
\(676\) | −54393.2 | + | 29233.0i | −0.119029 | + | 0.0639704i | ||||
\(677\) | 157815. | − | 157815.i | 0.344326 | − | 0.344326i | −0.513665 | − | 0.857991i | \(-0.671712\pi\) |
0.857991 | + | 0.513665i | \(0.171712\pi\) | |||||||
\(678\) | 290655. | − | 73156.6i | 0.632294 | − | 0.159145i | ||||
\(679\) | −85713.4 | −0.185913 | ||||||||
\(680\) | 78285.9 | + | 85785.4i | 0.169303 | + | 0.185522i | ||||
\(681\) | − | 43625.4i | − | 0.0940687i | ||||||
\(682\) | 305905. | − | 76994.8i | 0.657684 | − | 0.165536i | ||||
\(683\) | −53616.3 | − | 53616.3i | −0.114936 | − | 0.114936i | 0.647300 | − | 0.762236i | \(-0.275898\pi\) |
−0.762236 | + | 0.647300i | \(0.775898\pi\) | |||||||
\(684\) | 82815.3 | − | 275257.i | 0.177010 | − | 0.588336i | ||||
\(685\) | −140084. | − | 140084.i | −0.298544 | − | 0.298544i | ||||
\(686\) | 222817. | + | 133207.i | 0.473479 | + | 0.283061i | ||||
\(687\) | − | 65503.7i | − | 0.138788i | ||||||
\(688\) | 478296. | − | 97401.8i | 1.01046 | − | 0.205774i | ||||
\(689\) | −779875. | −1.64281 | ||||||||
\(690\) | 61949.9 | − | 103624.i | 0.130119 | − | 0.217652i | ||||
\(691\) | 222699. | − | 222699.i | 0.466404 | − | 0.466404i | −0.434344 | − | 0.900747i | \(-0.643020\pi\) |
0.900747 | + | 0.434344i | \(0.143020\pi\) | |||||||
\(692\) | 140924. | − | 468396.i | 0.294289 | − | 0.978140i | ||||
\(693\) | −14347.5 | + | 14347.5i | −0.0298752 | + | 0.0298752i | ||||
\(694\) | 73285.5 | + | 291167.i | 0.152159 | + | 0.604538i | ||||
\(695\) | 480355. | 0.994473 | ||||||||
\(696\) | 15210.3 | − | 332763.i | 0.0313993 | − | 0.686937i | ||||
\(697\) | − | 46977.9i | − | 0.0967005i | ||||||
\(698\) | −61183.2 | − | 243085.i | −0.125580 | − | 0.498938i | ||||
\(699\) | −79988.0 | − | 79988.0i | −0.163708 | − | 0.163708i | ||||
\(700\) | 24590.7 | − | 13216.0i | 0.0501851 | − | 0.0269713i | ||||
\(701\) | −7694.62 | − | 7694.62i | −0.0156585 | − | 0.0156585i | 0.699234 | − | 0.714893i | \(-0.253524\pi\) |
−0.714893 | + | 0.699234i | \(0.753524\pi\) | |||||||
\(702\) | −51849.0 | + | 86728.2i | −0.105212 | + | 0.175989i | ||||
\(703\) | − | 531513.i | − | 1.07548i | ||||||
\(704\) | −139653. | − | 167820.i | −0.281776 | − | 0.338609i | ||||
\(705\) | 289360. | 0.582183 | ||||||||
\(706\) | 317359. | + | 189728.i | 0.636710 | + | 0.380646i | ||||
\(707\) | −170041. | + | 170041.i | −0.340184 | + | 0.340184i | ||||
\(708\) | 47410.5 | + | 88215.8i | 0.0945819 | + | 0.175987i | ||||
\(709\) | −352000. | + | 352000.i | −0.700245 | + | 0.700245i | −0.964463 | − | 0.264218i | \(-0.914886\pi\) |
0.264218 | + | 0.964463i | \(0.414886\pi\) | |||||||
\(710\) | 167351. | − | 42121.4i | 0.331979 | − | 0.0835576i | ||||
\(711\) | 103027. | 0.203804 | ||||||||
\(712\) | 959140. | + | 43841.5i | 1.89200 | + | 0.0864820i | ||||
\(713\) | − | 383854.i | − | 0.755070i | ||||||
\(714\) | −23033.0 | + | 5797.31i | −0.0451809 | + | 0.0113718i | ||||
\(715\) | −151938. | − | 151938.i | −0.297203 | − | 0.297203i | ||||
\(716\) | 422124. | + | 127003.i | 0.823406 | + | 0.247735i | ||||
\(717\) | 103069. | + | 103069.i | 0.200488 | + | 0.200488i | ||||
\(718\) | −474626. | − | 283747.i | −0.920667 | − | 0.550405i | ||||
\(719\) | − | 42870.7i | − | 0.0829284i | −0.999140 | − | 0.0414642i | \(-0.986798\pi\) | ||
0.999140 | − | 0.0414642i | \(-0.0132022\pi\) | |||||||
\(720\) | −151637. | + | 30879.8i | −0.292509 | + | 0.0595675i | ||||
\(721\) | 14357.9 | 0.0276199 | ||||||||
\(722\) | 641228. | − | 1.07259e6i | 1.23009 | − | 2.05759i | ||||
\(723\) | −126106. | + | 126106.i | −0.241245 | + | 0.241245i | ||||
\(724\) | −782117. | − | 235312.i | −1.49209 | − | 0.448919i | ||||
\(725\) | −87655.8 | + | 87655.8i | −0.166765 | + | 0.166765i | ||||
\(726\) | 59862.6 | + | 237837.i | 0.113575 | + | 0.451239i | ||||
\(727\) | −457506. | −0.865622 | −0.432811 | − | 0.901485i | \(-0.642478\pi\) | ||||
−0.432811 | + | 0.901485i | \(0.642478\pi\) | |||||||
\(728\) | 120009. | − | 109517.i | 0.226439 | − | 0.206643i | ||||
\(729\) | 19683.0i | 0.0370370i | ||||||||
\(730\) | 134501. | + | 534379.i | 0.252394 | + | 1.00278i | ||||
\(731\) | 109278. | + | 109278.i | 0.204502 | + | 0.204502i | ||||
\(732\) | −179299. | − | 333619.i | −0.334623 | − | 0.622627i | ||||
\(733\) | 152573. | + | 152573.i | 0.283969 | + | 0.283969i | 0.834690 | − | 0.550721i | \(-0.185647\pi\) |
−0.550721 | + | 0.834690i | \(0.685647\pi\) | |||||||
\(734\) | −242762. | + | 406070.i | −0.450598 | + | 0.753719i | ||||
\(735\) | 256193.i | 0.474234i | ||||||||
\(736\) | −239517. | + | 114953.i | −0.442161 | + | 0.212210i | ||||
\(737\) | 330374. | 0.608234 | ||||||||
\(738\) | 53727.5 | + | 32120.1i | 0.0986470 | + | 0.0589744i | ||||
\(739\) | 567943. | − | 567943.i | 1.03996 | − | 1.03996i | 0.0407903 | − | 0.999168i | \(-0.487012\pi\) |
0.999168 | − | 0.0407903i | \(-0.0129876\pi\) | |||||||
\(740\) | −252051. | + | 135461.i | −0.460282 | + | 0.247373i | ||||
\(741\) | −440197. | + | 440197.i | −0.801698 | + | 0.801698i | ||||
\(742\) | 236875. | − | 59620.2i | 0.430240 | − | 0.108289i | ||||
\(743\) | −566258. | −1.02574 | −0.512869 | − | 0.858467i | \(-0.671417\pi\) | ||||
−0.512869 | + | 0.858467i | \(0.671417\pi\) | |||||||
\(744\) | −363431. | + | 331659.i | −0.656563 | + | 0.599164i | ||||
\(745\) | 296531.i | 0.534266i | ||||||||
\(746\) | 795707. | − | 200276.i | 1.42980 | − | 0.359874i | ||||
\(747\) | −167299. | − | 167299.i | −0.299814 | − | 0.299814i | ||||
\(748\) | 19915.4 | − | 66193.7i | 0.0355948 | − | 0.118308i | ||||
\(749\) | −183981. | − | 183981.i | −0.327952 | − | 0.327952i | ||||
\(750\) | 299056. | + | 178785.i | 0.531655 | + | 0.317841i | ||||
\(751\) | 303992.i | 0.538991i | 0.963002 | + | 0.269496i | \(0.0868570\pi\) | ||||
−0.963002 | + | 0.269496i | \(0.913143\pi\) | |||||||
\(752\) | −531045. | − | 351351.i | −0.939064 | − | 0.621306i | ||||
\(753\) | 364222. | 0.642357 | ||||||||
\(754\) | −370187. | + | 619215.i | −0.651146 | + | 1.08918i | ||||
\(755\) | −282627. | + | 282627.i | −0.495816 | + | 0.495816i | ||||
\(756\) | 9118.07 | − | 30306.1i | 0.0159536 | − | 0.0530257i | ||||
\(757\) | −19158.8 | + | 19158.8i | −0.0334331 | + | 0.0334331i | −0.723626 | − | 0.690193i | \(-0.757526\pi\) |
0.690193 | + | 0.723626i | \(0.257526\pi\) | |||||||
\(758\) | −28450.8 | − | 113037.i | −0.0495172 | − | 0.196735i | ||||
\(759\) | −71858.4 | −0.124737 | ||||||||
\(760\) | −952405. | − | 43533.7i | −1.64890 | − | 0.0753699i | ||||
\(761\) | 506267.i | 0.874199i | 0.899413 | + | 0.437100i | \(0.143994\pi\) | ||||
−0.899413 | + | 0.437100i | \(0.856006\pi\) | |||||||
\(762\) | 8328.75 | + | 33090.6i | 0.0143440 | + | 0.0569895i | ||||
\(763\) | −109233. | − | 109233.i | −0.187630 | − | 0.187630i | ||||
\(764\) | 540442. | − | 290454.i | 0.925896 | − | 0.497611i | ||||
\(765\) | −34644.9 | − | 34644.9i | −0.0591993 | − | 0.0591993i | ||||
\(766\) | 267936. | − | 448179.i | 0.456640 | − | 0.763825i | ||||
\(767\) | − | 216897.i | − | 0.368691i | ||||||
\(768\) | 315785. | + | 127451.i | 0.535389 | + | 0.216083i | ||||
\(769\) | −79751.5 | −0.134861 | −0.0674305 | − | 0.997724i | \(-0.521480\pi\) | ||||
−0.0674305 | + | 0.997724i | \(0.521480\pi\) | |||||||
\(770\) | 57764.0 | + | 34533.2i | 0.0974263 | + | 0.0582446i | ||||
\(771\) | −345791. | + | 345791.i | −0.581707 | + | 0.581707i | ||||
\(772\) | 256686. | + | 477611.i | 0.430693 | + | 0.801382i | ||||
\(773\) | −618926. | + | 618926.i | −1.03581 | + | 1.03581i | −0.0364753 | + | 0.999335i | \(0.511613\pi\) |
−0.999335 | + | 0.0364753i | \(0.988387\pi\) | |||||||
\(774\) | −199694. | + | 50262.2i | −0.333337 | + | 0.0838995i | ||||
\(775\) | 183099. | 0.304848 | ||||||||
\(776\) | −17766.3 | + | 388682.i | −0.0295036 | + | 0.645463i | ||||
\(777\) | − | 58520.2i | − | 0.0969313i | ||||||
\(778\) | −114398. | + | 28793.5i | −0.188999 | + | 0.0475703i | ||||
\(779\) | 272699. | + | 272699.i | 0.449374 | + | 0.449374i | ||||
\(780\) | 320936. | + | 96558.7i | 0.527509 | + | 0.158709i | ||||
\(781\) | −72629.5 | − | 72629.5i | −0.119072 | − | 0.119072i | ||||
\(782\) | −72197.3 | − | 43161.9i | −0.118061 | − | 0.0705810i | ||||
\(783\) | 140531.i | 0.229218i | ||||||||
\(784\) | 311079. | − | 470176.i | 0.506103 | − | 0.764942i | ||||
\(785\) | −803614. | −1.30409 | ||||||||
\(786\) | 102095. | − | 170775.i | 0.165257 | − | 0.276426i | ||||
\(787\) | −78356.7 | + | 78356.7i | −0.126511 | + | 0.126511i | −0.767527 | − | 0.641017i | \(-0.778513\pi\) |
0.641017 | + | 0.767527i | \(0.278513\pi\) | |||||||
\(788\) | −574663. | − | 172896.i | −0.925466 | − | 0.278441i | ||||
\(789\) | 12968.5 | − | 12968.5i | 0.0208322 | − | 0.0208322i | ||||
\(790\) | −83408.2 | − | 331386.i | −0.133646 | − | 0.530982i | ||||
\(791\) | 203309. | 0.324940 | ||||||||
\(792\) | 62087.4 | + | 68035.1i | 0.0989812 | + | 0.108463i | ||||
\(793\) | 820271.i | 1.30440i | ||||||||
\(794\) | 46214.4 | + | 183613.i | 0.0733055 | + | 0.291247i | ||||
\(795\) | 356293. | + | 356293.i | 0.563732 | + | 0.563732i | ||||
\(796\) | 150539. | + | 280105.i | 0.237587 | + | 0.442073i | ||||
\(797\) | 585144. | + | 585144.i | 0.921184 | + | 0.921184i | 0.997113 | − | 0.0759296i | \(-0.0241924\pi\) |
−0.0759296 | + | 0.997113i | \(0.524192\pi\) | |||||||
\(798\) | 100050. | − | 167355.i | 0.157113 | − | 0.262805i | ||||
\(799\) | − | 201604.i | − | 0.315795i | ||||||
\(800\) | −54832.9 | − | 114250.i | −0.0856765 | − | 0.178516i | ||||
\(801\) | −405060. | −0.631327 | ||||||||
\(802\) | −244110. | − | 145937.i | −0.379522 | − | 0.226891i | ||||
\(803\) | 231919. | − | 231919.i | 0.359670 | − | 0.359670i | ||||
\(804\) | −453901. | + | 243943.i | −0.702181 | + | 0.377378i | ||||
\(805\) | 57908.1 | − | 57908.1i | 0.0893609 | − | 0.0893609i | ||||
\(806\) | 1.03335e6 | − | 260090.i | 1.59066 | − | 0.400363i | ||||
\(807\) | 453289. | 0.696030 | ||||||||
\(808\) | 735833. | + | 806324.i | 1.12708 | + | 1.23506i | ||||
\(809\) | − | 113161.i | − | 0.172901i | −0.996256 | − | 0.0864506i | \(-0.972448\pi\) | ||
0.996256 | − | 0.0864506i | \(-0.0275525\pi\) | |||||||
\(810\) | 63310.2 | − | 15934.9i | 0.0964947 | − | 0.0242873i | ||||
\(811\) | −156533. | − | 156533.i | −0.237993 | − | 0.237993i | 0.578025 | − | 0.816019i | \(-0.303823\pi\) |
−0.816019 | + | 0.578025i | \(0.803823\pi\) | |||||||
\(812\) | 65100.4 | − | 216377.i | 0.0987351 | − | 0.328170i | ||||
\(813\) | 345881. | + | 345881.i | 0.523294 | + | 0.523294i | ||||
\(814\) | 146182. | + | 87392.7i | 0.220621 | + | 0.131894i | ||||
\(815\) | − | 937869.i | − | 1.41197i | ||||||
\(816\) | 21514.7 | + | 105649.i | 0.0323113 | + | 0.158666i | ||||
\(817\) | −1.26868e6 | −1.90067 | ||||||||
\(818\) | −24770.0 | + | 41433.0i | −0.0370185 | + | 0.0619212i | ||||
\(819\) | −48466.2 | + | 48466.2i | −0.0722556 | + | 0.0722556i | ||||
\(820\) | 59817.4 | − | 198818.i | 0.0889611 | − | 0.295683i | ||||
\(821\) | 727942. | − | 727942.i | 1.07997 | − | 1.07997i | 0.0834551 | − | 0.996512i | \(-0.473404\pi\) |
0.996512 | − | 0.0834551i | \(-0.0265955\pi\) | |||||||
\(822\) | −44890.9 | − | 178354.i | −0.0664378 | − | 0.263961i | ||||
\(823\) | −1.29556e6 | −1.91275 | −0.956375 | − | 0.292142i | \(-0.905632\pi\) | ||||
−0.956375 | + | 0.292142i | \(0.905632\pi\) | |||||||
\(824\) | 2976.06 | − | 65108.5i | 0.00438315 | − | 0.0958922i | ||||
\(825\) | − | 34276.6i | − | 0.0503605i | ||||||
\(826\) | 16581.4 | + | 65879.0i | 0.0243031 | + | 0.0965576i | ||||
\(827\) | −885753. | − | 885753.i | −1.29509 | − | 1.29509i | −0.931594 | − | 0.363500i | \(-0.881582\pi\) |
−0.363500 | − | 0.931594i | \(-0.618418\pi\) | |||||||
\(828\) | 98726.4 | − | 53059.3i | 0.144003 | − | 0.0773928i | ||||
\(829\) | −113239. | − | 113239.i | −0.164773 | − | 0.164773i | 0.619904 | − | 0.784677i | \(-0.287171\pi\) |
−0.784677 | + | 0.619904i | \(0.787171\pi\) | |||||||
\(830\) | −402675. | + | 673557.i | −0.584518 | + | 0.977728i | ||||
\(831\) | 2394.91i | 0.00346806i | ||||||||
\(832\) | −471750. | − | 566901.i | −0.681499 | − | 0.818956i | ||||
\(833\) | 178496. | 0.257240 | ||||||||
\(834\) | 382759. | + | 228826.i | 0.550292 | + | 0.328983i | ||||
\(835\) | 283344. | − | 283344.i | 0.406388 | − | 0.406388i | ||||
\(836\) | 268637. | + | 499848.i | 0.384374 | + | 0.715197i | ||||
\(837\) | 146774. | − | 146774.i | 0.209506 | − | 0.209506i | ||||
\(838\) | 1.12144e6 | − | 282262.i | 1.59694 | − | 0.401943i | ||||
\(839\) | −524009. | −0.744414 | −0.372207 | − | 0.928150i | \(-0.621399\pi\) | ||||
−0.372207 | + | 0.928150i | \(0.621399\pi\) | |||||||
\(840\) | −104861. | − | 4793.11i | −0.148613 | − | 0.00679295i | ||||
\(841\) | 296071.i | 0.418605i | ||||||||
\(842\) | −1.11983e6 | + | 281857.i | −1.57954 | + | 0.397562i | ||||
\(843\) | −368004. | − | 368004.i | −0.517842 | − | 0.517842i | ||||
\(844\) | −635617. | − | 191235.i | −0.892299 | − | 0.268462i | ||||
\(845\) | −61098.9 | − | 61098.9i | −0.0855697 | − | 0.0855697i | ||||
\(846\) | 230569. | + | 137842.i | 0.322152 | + | 0.192593i | ||||
\(847\) | 166363.i | 0.231895i | ||||||||
\(848\) | −221260. | − | 1.08651e6i | −0.307688 | − | 1.51092i | ||||
\(849\) | −400915. | −0.556208 | ||||||||
\(850\) | 20588.3 | − | 34438.2i | 0.0284959 | − | 0.0476654i | ||||
\(851\) | 146547. | − | 146547.i | 0.202357 | − | 0.202357i | ||||
\(852\) | 153415. | + | 46157.2i | 0.211343 | + | 0.0635858i | ||||
\(853\) | −331577. | + | 331577.i | −0.455708 | + | 0.455708i | −0.897244 | − | 0.441536i | \(-0.854434\pi\) |
0.441536 | + | 0.897244i | \(0.354434\pi\) | |||||||
\(854\) | −62708.4 | − | 249144.i | −0.0859825 | − | 0.341613i | ||||
\(855\) | 402215. | 0.550208 | ||||||||
\(856\) | −872429. | + | 796159.i | −1.19065 | + | 1.08656i | ||||
\(857\) | 731561.i | 0.996068i | 0.867157 | + | 0.498034i | \(0.165945\pi\) | ||||
−0.867157 | + | 0.498034i | \(0.834055\pi\) | |||||||
\(858\) | −48689.5 | − | 193446.i | −0.0661394 | − | 0.262776i | ||||
\(859\) | 308744. | + | 308744.i | 0.418420 | + | 0.418420i | 0.884659 | − | 0.466239i | \(-0.154391\pi\) |
−0.466239 | + | 0.884659i | \(0.654391\pi\) | |||||||
\(860\) | 323336. | + | 601624.i | 0.437176 | + | 0.813446i | ||||
\(861\) | 30024.5 | + | 30024.5i | 0.0405013 | + | 0.0405013i | ||||
\(862\) | 99857.5 | − | 167033.i | 0.134390 | − | 0.224795i | ||||
\(863\) | − | 38525.4i | − | 0.0517280i | −0.999665 | − | 0.0258640i | \(-0.991766\pi\) | ||
0.999665 | − | 0.0258640i | \(-0.00823369\pi\) | |||||||
\(864\) | −135538. | − | 47629.1i | −0.181566 | − | 0.0638036i | ||||
\(865\) | 684439. | 0.914750 | ||||||||
\(866\) | −774950. | − | 463291.i | −1.03333 | − | 0.617757i | ||||
\(867\) | 282738. | − | 282738.i | 0.376137 | − | 0.376137i | ||||
\(868\) | −293981. | + | 157996.i | −0.390193 | + | 0.209704i | ||||
\(869\) | −143820. | + | 143820.i | −0.190450 | + | 0.190450i | ||||
\(870\) | 452017. | − | 113771.i | 0.597195 | − | 0.150311i | ||||
\(871\) | 1.11601e6 | 1.47106 | ||||||||
\(872\) | −517975. | + | 472692.i | −0.681202 | + | 0.621649i | ||||
\(873\) | − | 164147.i | − | 0.215379i | ||||||
\(874\) | 669640. | − | 168545.i | 0.876635 | − | 0.220645i | ||||
\(875\) | 167121. | + | 167121.i | 0.218281 | + | 0.218281i | ||||
\(876\) | −147388. | + | 489879.i | −0.192067 | + | 0.638382i | ||||
\(877\) | 220189. | + | 220189.i | 0.286283 | + | 0.286283i | 0.835609 | − | 0.549325i | \(-0.185115\pi\) |
−0.549325 | + | 0.835609i | \(0.685115\pi\) | |||||||
\(878\) | 200903. | + | 120107.i | 0.260614 | + | 0.155804i | ||||
\(879\) | − | 252749.i | − | 0.327124i | ||||||
\(880\) | 168570. | − | 254783.i | 0.217678 | − | 0.329007i | ||||
\(881\) | 141526. | 0.182341 | 0.0911703 | − | 0.995835i | \(-0.470939\pi\) | ||||
0.0911703 | + | 0.995835i | \(0.470939\pi\) | |||||||
\(882\) | −122042. | + | 204141.i | −0.156882 | + | 0.262418i | ||||
\(883\) | 529860. | − | 529860.i | 0.679578 | − | 0.679578i | −0.280327 | − | 0.959905i | \(-0.590443\pi\) |
0.959905 | + | 0.280327i | \(0.0904428\pi\) | |||||||
\(884\) | 67274.8 | − | 223604.i | 0.0860890 | − | 0.286137i | ||||
\(885\) | −99091.2 | + | 99091.2i | −0.126517 | + | 0.126517i | ||||
\(886\) | −144424. | − | 573803.i | −0.183980 | − | 0.730964i | ||||
\(887\) | 415500. | 0.528109 | 0.264054 | − | 0.964508i | \(-0.414940\pi\) | ||||
0.264054 | + | 0.964508i | \(0.414940\pi\) | |||||||
\(888\) | −265370. | − | 12129.8i | −0.336531 | − | 0.0153826i | ||||
\(889\) | 23146.3i | 0.0292873i | ||||||||
\(890\) | 327927. | + | 1.30287e6i | 0.413996 | + | 1.64483i | ||||
\(891\) | −27476.4 | − | 27476.4i | −0.0346102 | − | 0.0346102i | ||||
\(892\) | 408598. | − | 219596.i | 0.513530 | − | 0.275990i | ||||
\(893\) | 1.17027e6 | + | 1.17027e6i | 1.46752 | + | 1.46752i | ||||
\(894\) | −141258. | + | 236283.i | −0.176741 | + | 0.295637i | ||||
\(895\) | 616824.i | 0.770043i | ||||||||
\(896\) | 186625. | + | 136122.i | 0.232463 | + | 0.169556i | ||||
\(897\) | −242739. | −0.301686 | ||||||||
\(898\) | −200895. | − | 120102.i | −0.249125 | − | 0.148935i | ||||
\(899\) | 1.04792e6 | − | 1.04792e6i | 1.29661 | − | 1.29661i | ||||
\(900\) | 25309.4 | + | 47092.7i | 0.0312461 | + | 0.0581391i | ||||
\(901\) | 248237. | − | 248237.i | 0.305786 | − | 0.305786i | ||||
\(902\) | −119838. | + | 30162.8i | −0.147293 | + | 0.0370730i | ||||
\(903\) | −139683. | −0.171304 | ||||||||
\(904\) | 42141.0 | − | 921938.i | 0.0515665 | − | 1.12814i | ||||
\(905\) | − | 1.14286e6i | − | 1.39539i | ||||||
\(906\) | −359839. | + | 90569.9i | −0.438382 | + | 0.110339i | ||||
\(907\) | 377257. | + | 377257.i | 0.458588 | + | 0.458588i | 0.898192 | − | 0.439604i | \(-0.144881\pi\) |
−0.439604 | + | 0.898192i | \(0.644881\pi\) | |||||||
\(908\) | −128635. | − | 38702.0i | −0.156023 | − | 0.0469420i | ||||
\(909\) | −325638. | − | 325638.i | −0.394101 | − | 0.394101i | ||||
\(910\) | 195128. | + | 116654.i | 0.235634 | + | 0.140870i | ||||
\(911\) | 30235.1i | 0.0364313i | 0.999834 | + | 0.0182157i | \(0.00579855\pi\) | ||||
−0.999834 | + | 0.0182157i | \(0.994201\pi\) | |||||||
\(912\) | −738162. | − | 488384.i | −0.887487 | − | 0.587181i | ||||
\(913\) | 467080. | 0.560338 | ||||||||
\(914\) | −606204. | + | 1.01400e6i | −0.725648 | + | 1.21380i | ||||
\(915\) | 374748. | − | 374748.i | 0.447607 | − | 0.447607i | ||||
\(916\) | −193147. | − | 58111.2i | −0.230195 | − | 0.0692579i | ||||
\(917\) | 95433.9 | − | 95433.9i | 0.113492 | − | 0.113492i | ||||
\(918\) | −11102.2 | − | 44109.7i | −0.0131742 | − | 0.0523418i | ||||
\(919\) | 156253. | 0.185011 | 0.0925053 | − | 0.995712i | \(-0.470512\pi\) | ||||
0.0925053 | + | 0.995712i | \(0.470512\pi\) | |||||||
\(920\) | −250591. | − | 274597.i | −0.296067 | − | 0.324430i | ||||
\(921\) | − | 732216.i | − | 0.863217i | ||||||
\(922\) | 100077. | + | 397613.i | 0.117726 | + | 0.467734i | ||||
\(923\) | −245344. | − | 245344.i | −0.287987 | − | 0.287987i | ||||
\(924\) | 29577.3 | + | 55033.9i | 0.0346429 | + | 0.0644594i | ||||
\(925\) | 69903.2 | + | 69903.2i | 0.0816984 | + | 0.0816984i | ||||
\(926\) | 246893. | − | 412980.i | 0.287930 | − | 0.481623i | ||||
\(927\) | 27496.3i | 0.0319974i | ||||||||
\(928\) | −967704. | − | 340059.i | −1.12369 | − | 0.394873i | ||||
\(929\) | −171947. | −0.199234 | −0.0996168 | − | 0.995026i | \(-0.531762\pi\) | ||||
−0.0996168 | + | 0.995026i | \(0.531762\pi\) | |||||||
\(930\) | −590920. | − | 353272.i | −0.683224 | − | 0.408454i | ||||
\(931\) | −1.03614e6 | + | 1.03614e6i | −1.19541 | + | 1.19541i | ||||
\(932\) | −306817. | + | 164895.i | −0.353221 | + | 0.189834i | ||||
\(933\) | 600423. | − | 600423.i | 0.689754 | − | 0.689754i | ||||
\(934\) | 468599. | − | 117944.i | 0.537165 | − | 0.135202i | ||||
\(935\) | 96724.8 | 0.110641 | ||||||||
\(936\) | 209732. | + | 229824.i | 0.239394 | + | 0.262328i | ||||
\(937\) | − | 1.23829e6i | − | 1.41040i | −0.709006 | − | 0.705202i | \(-0.750856\pi\) | ||
0.709006 | − | 0.705202i | \(-0.249144\pi\) | |||||||
\(938\) | −338970. | + | 85317.2i | −0.385262 | + | 0.0969685i | ||||
\(939\) | 337914. | + | 337914.i | 0.383244 | + | 0.383244i | ||||
\(940\) | 256704. | − | 853216.i | 0.290520 | − | 0.965614i | ||||
\(941\) | 795144. | + | 795144.i | 0.897980 | + | 0.897980i | 0.995257 | − | 0.0972772i | \(-0.0310133\pi\) |
−0.0972772 | + | 0.995257i | \(0.531013\pi\) | |||||||
\(942\) | −640340. | − | 382816.i | −0.721621 | − | 0.431409i | ||||
\(943\) | 150375.i | 0.169104i | ||||||||
\(944\) | 302176. | − | 61536.2i | 0.339091 | − | 0.0690536i | ||||
\(945\) | 44284.4 | 0.0495892 | ||||||||
\(946\) | 208599. | − | 348926.i | 0.233094 | − | 0.389898i | ||||
\(947\) | 126444. | − | 126444.i | 0.140993 | − | 0.140993i | −0.633087 | − | 0.774081i | \(-0.718213\pi\) |
0.774081 | + | 0.633087i | \(0.218213\pi\) | |||||||
\(948\) | 91399.9 | − | 303789.i | 0.101702 | − | 0.338031i | ||||
\(949\) | 783426. | − | 783426.i | 0.869893 | − | 0.869893i | ||||
\(950\) | 80396.4 | + | 319419.i | 0.0890819 | + | 0.353927i | ||||
\(951\) | −682939. | −0.755129 | ||||||||
\(952\) | −3339.47 | + | 73059.1i | −0.00368471 | + | 0.0806122i | ||||
\(953\) | 359882.i | 0.396254i | 0.980176 | + | 0.198127i | \(0.0634859\pi\) | ||||
−0.980176 | + | 0.198127i | \(0.936514\pi\) | |||||||
\(954\) | 114176. | + | 453629.i | 0.125453 | + | 0.498430i | ||||
\(955\) | 607068. | + | 607068.i | 0.665627 | + | 0.665627i | ||||
\(956\) | 395348. | − | 212475.i | 0.432578 | − | 0.232483i | ||||
\(957\) | −196174. | − | 196174.i | −0.214199 | − | 0.214199i | ||||
\(958\) | 80780.1 | − | 135122.i | 0.0880184 | − | 0.147229i | ||||
\(959\) | − | 124756.i | − | 0.135651i | ||||||
\(960\) | −43470.3 | + | 474517.i | −0.0471683 | + | 0.514883i | ||||
\(961\) | −1.26542e6 | −1.37022 | ||||||||
\(962\) | 493808. | + | 295214.i | 0.533590 | + | 0.318998i | ||||
\(963\) | 352335. | − | 352335.i | 0.379930 | − | 0.379930i | ||||
\(964\) | 259966. | + | 483714.i | 0.279745 | + | 0.520517i | ||||
\(965\) | −536491. | + | 536491.i | −0.576114 | + | 0.576114i | ||||
\(966\) | 73728.2 | − | 18557.0i | 0.0790095 | − | 0.0198863i | ||||
\(967\) | −1.22648e6 | −1.31162 | −0.655810 | − | 0.754926i | \(-0.727673\pi\) | ||||
−0.655810 | + | 0.754926i | \(0.727673\pi\) | |||||||
\(968\) | 754403. | + | 34483.1i | 0.805105 | + | 0.0368007i | ||||
\(969\) | − | 280233.i | − | 0.298450i | ||||||
\(970\) | −527976. | + | 132889.i | −0.561139 | + | 0.141236i | ||||
\(971\) | −1.03007e6 | − | 1.03007e6i | −1.09251 | − | 1.09251i | −0.995260 | − | 0.0972546i | \(-0.968994\pi\) |
−0.0972546 | − | 0.995260i | \(-0.531006\pi\) | |||||||
\(972\) | 58038.0 | + | 17461.7i | 0.0614299 | + | 0.0184822i | ||||
\(973\) | 213897. | + | 213897.i | 0.225932 | + | 0.225932i | ||||
\(974\) | −544113. | − | 325289.i | −0.573550 | − | 0.342887i | ||||
\(975\) | − | 115787.i | − | 0.121801i | ||||||
\(976\) | −1.14278e6 | + | 232720.i | −1.19968 | + | 0.244306i | ||||
\(977\) | 949908. | 0.995159 | 0.497580 | − | 0.867418i | \(-0.334222\pi\) | ||||
0.497580 | + | 0.867418i | \(0.334222\pi\) | |||||||
\(978\) | 446771. | − | 747317.i | 0.467097 | − | 0.781317i | ||||
\(979\) | 565441. | − | 565441.i | 0.589959 | − | 0.589959i | ||||
\(980\) | 755421. | + | 227280.i | 0.786569 | + | 0.236652i | ||||
\(981\) | 209187. | − | 209187.i | 0.217369 | − | 0.217369i | ||||
\(982\) | −70207.3 | − | 278938.i | −0.0728047 | − | 0.289257i | ||||
\(983\) | −1.15419e6 | −1.19446 | −0.597229 | − | 0.802071i | \(-0.703732\pi\) | ||||
−0.597229 | + | 0.802071i | \(0.703732\pi\) | |||||||
\(984\) | 142374. | − | 129928.i | 0.147042 | − | 0.134187i | ||||
\(985\) | − | 839719.i | − | 0.865489i | ||||||
\(986\) | −79266.6 | − | 314931.i | −0.0815336 | − | 0.323938i | ||||
\(987\) | 128849. | + | 128849.i | 0.132265 | + | 0.132265i | ||||
\(988\) | 907463. | + | 1.68850e6i | 0.929640 | + | 1.72976i | ||||
\(989\) | −349796. | − | 349796.i | −0.357620 | − | 0.357620i | ||||
\(990\) | −66133.3 | + | 110622.i | −0.0674761 | + | 0.112868i | ||||
\(991\) | 1.60156e6i | 1.63078i | 0.578911 | + | 0.815391i | \(0.303478\pi\) | ||||
−0.578911 | + | 0.815391i | \(0.696522\pi\) | |||||||
\(992\) | 655526. | + | 1.36586e6i | 0.666142 | + | 1.38797i | ||||
\(993\) | 352934. | 0.357928 | ||||||||
\(994\) | 93275.6 | + | 55763.2i | 0.0944050 | + | 0.0564384i | ||||
\(995\) | −314636. | + | 314636.i | −0.317806 | + | 0.317806i | ||||
\(996\) | −641722. | + | 344886.i | −0.646887 | + | 0.347661i | ||||
\(997\) | −699293. | + | 699293.i | −0.703508 | + | 0.703508i | −0.965162 | − | 0.261654i | \(-0.915732\pi\) |
0.261654 | + | 0.965162i | \(0.415732\pi\) | |||||||
\(998\) | −1.06211e6 | + | 267328.i | −1.06637 | + | 0.268400i | ||||
\(999\) | 112070. | 0.112294 |
(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 | 48.5.l.a.19.13 | ✓ | 32 | |
3.2 | odd | 2 | 144.5.m.c.19.4 | 32 | |||
4.3 | odd | 2 | 192.5.l.a.175.13 | 32 | |||
8.3 | odd | 2 | 384.5.l.a.223.4 | 32 | |||
8.5 | even | 2 | 384.5.l.b.223.13 | 32 | |||
12.11 | even | 2 | 576.5.m.b.559.12 | 32 | |||
16.3 | odd | 4 | 384.5.l.b.31.13 | 32 | |||
16.5 | even | 4 | 192.5.l.a.79.13 | 32 | |||
16.11 | odd | 4 | inner | 48.5.l.a.43.13 | yes | 32 | |
16.13 | even | 4 | 384.5.l.a.31.4 | 32 | |||
48.5 | odd | 4 | 576.5.m.b.271.12 | 32 | |||
48.11 | even | 4 | 144.5.m.c.91.4 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.5.l.a.19.13 | ✓ | 32 | 1.1 | even | 1 | trivial | |
48.5.l.a.43.13 | yes | 32 | 16.11 | odd | 4 | inner | |
144.5.m.c.19.4 | 32 | 3.2 | odd | 2 | |||
144.5.m.c.91.4 | 32 | 48.11 | even | 4 | |||
192.5.l.a.79.13 | 32 | 16.5 | even | 4 | |||
192.5.l.a.175.13 | 32 | 4.3 | odd | 2 | |||
384.5.l.a.31.4 | 32 | 16.13 | even | 4 | |||
384.5.l.a.223.4 | 32 | 8.3 | odd | 2 | |||
384.5.l.b.31.13 | 32 | 16.3 | odd | 4 | |||
384.5.l.b.223.13 | 32 | 8.5 | even | 2 | |||
576.5.m.b.271.12 | 32 | 48.5 | odd | 4 | |||
576.5.m.b.559.12 | 32 | 12.11 | even | 2 |