Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [13,5,Mod(2,13)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(13, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("13.2");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 13 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 13.f (of order \(12\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.34380952009\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 152 x^{14} + 9190 x^{12} + 285720 x^{10} + 4862025 x^{8} + 43573680 x^{6} + 169417008 x^{4} + \cdots + 3779136 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{2}\cdot 13^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 6.2 | ||
Root | \(-7.09996i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 13.6 |
Dual form | 13.5.f.a.11.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/13\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{5}{12}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.387376 | − | 1.44571i | −0.0968440 | − | 0.361427i | 0.900449 | − | 0.434963i | \(-0.143238\pi\) |
−0.997293 | + | 0.0735357i | \(0.976572\pi\) | |||||||
\(3\) | 3.29308 | − | 5.70378i | 0.365898 | − | 0.633753i | −0.623022 | − | 0.782204i | \(-0.714095\pi\) |
0.988920 | + | 0.148451i | \(0.0474287\pi\) | |||||||
\(4\) | 11.9164 | − | 6.87993i | 0.744775 | − | 0.429996i | ||||
\(5\) | −10.5663 | + | 10.5663i | −0.422650 | + | 0.422650i | −0.886115 | − | 0.463465i | \(-0.846606\pi\) |
0.463465 | + | 0.886115i | \(0.346606\pi\) | |||||||
\(6\) | −9.52166 | − | 2.55132i | −0.264490 | − | 0.0708700i | ||||
\(7\) | −14.3010 | + | 53.3722i | −0.291858 | + | 1.08923i | 0.651823 | + | 0.758372i | \(0.274005\pi\) |
−0.943681 | + | 0.330858i | \(0.892662\pi\) | |||||||
\(8\) | −31.4958 | − | 31.4958i | −0.492122 | − | 0.492122i | ||||
\(9\) | 18.8113 | + | 32.5821i | 0.232238 | + | 0.402248i | ||||
\(10\) | 19.3688 | + | 11.1826i | 0.193688 | + | 0.111826i | ||||
\(11\) | −52.6981 | + | 14.1204i | −0.435521 | + | 0.116698i | −0.469917 | − | 0.882711i | \(-0.655716\pi\) |
0.0343956 | + | 0.999408i | \(0.489049\pi\) | |||||||
\(12\) | − | 90.6246i | − | 0.629338i | ||||||
\(13\) | 115.664 | − | 123.219i | 0.684401 | − | 0.729106i | ||||
\(14\) | 82.7005 | 0.421941 | ||||||||
\(15\) | 25.4721 | + | 95.0631i | 0.113209 | + | 0.422503i | ||||
\(16\) | 76.7460 | − | 132.928i | 0.299789 | − | 0.519250i | ||||
\(17\) | −171.531 | + | 99.0336i | −0.593534 | + | 0.342677i | −0.766494 | − | 0.642252i | \(-0.778000\pi\) |
0.172960 | + | 0.984929i | \(0.444667\pi\) | |||||||
\(18\) | 39.8171 | − | 39.8171i | 0.122892 | − | 0.122892i | ||||
\(19\) | −106.721 | − | 28.5959i | −0.295627 | − | 0.0792130i | 0.107957 | − | 0.994156i | \(-0.465569\pi\) |
−0.403584 | + | 0.914943i | \(0.632236\pi\) | |||||||
\(20\) | −53.2166 | + | 198.607i | −0.133041 | + | 0.496517i | ||||
\(21\) | 257.329 | + | 257.329i | 0.583512 | + | 0.583512i | ||||
\(22\) | 40.8279 | + | 70.7161i | 0.0843553 | + | 0.146108i | ||||
\(23\) | −761.646 | − | 439.737i | −1.43979 | − | 0.831260i | −0.441951 | − | 0.897039i | \(-0.645714\pi\) |
−0.997834 | + | 0.0657787i | \(0.979047\pi\) | |||||||
\(24\) | −283.363 | + | 75.9269i | −0.491950 | + | 0.131818i | ||||
\(25\) | 401.708i | 0.642733i | ||||||||
\(26\) | −222.944 | − | 119.484i | −0.329799 | − | 0.176751i | ||||
\(27\) | 781.267 | 1.07170 | ||||||||
\(28\) | 196.781 | + | 734.395i | 0.250996 | + | 0.936728i | ||||
\(29\) | 398.637 | − | 690.460i | 0.474004 | − | 0.820999i | −0.525553 | − | 0.850761i | \(-0.676142\pi\) |
0.999557 | + | 0.0297621i | \(0.00947496\pi\) | |||||||
\(30\) | 127.566 | − | 73.6504i | 0.141740 | − | 0.0818337i | ||||
\(31\) | 1101.81 | − | 1101.81i | 1.14652 | − | 1.14652i | 0.159290 | − | 0.987232i | \(-0.449079\pi\) |
0.987232 | − | 0.159290i | \(-0.0509205\pi\) | |||||||
\(32\) | −910.290 | − | 243.911i | −0.888955 | − | 0.238195i | ||||
\(33\) | −92.9992 | + | 347.078i | −0.0853987 | + | 0.318712i | ||||
\(34\) | 209.621 | + | 209.621i | 0.181333 | + | 0.181333i | ||||
\(35\) | −412.836 | − | 715.053i | −0.337009 | − | 0.583717i | ||||
\(36\) | 448.325 | + | 258.841i | 0.345930 | + | 0.199723i | ||||
\(37\) | −1201.99 | + | 322.072i | −0.878005 | + | 0.235261i | −0.669546 | − | 0.742771i | \(-0.733511\pi\) |
−0.208459 | + | 0.978031i | \(0.566845\pi\) | |||||||
\(38\) | 165.365i | 0.114519i | ||||||||
\(39\) | −321.924 | − | 1065.49i | −0.211653 | − | 0.700519i | ||||
\(40\) | 665.586 | 0.415991 | ||||||||
\(41\) | 802.734 | + | 2995.84i | 0.477534 | + | 1.78218i | 0.611556 | + | 0.791201i | \(0.290544\pi\) |
−0.134022 | + | 0.990978i | \(0.542789\pi\) | |||||||
\(42\) | 272.339 | − | 471.706i | 0.154387 | − | 0.267407i | ||||
\(43\) | −798.822 | + | 461.200i | −0.432029 | + | 0.249432i | −0.700211 | − | 0.713936i | \(-0.746911\pi\) |
0.268181 | + | 0.963368i | \(0.413577\pi\) | |||||||
\(44\) | −530.823 | + | 530.823i | −0.274186 | + | 0.274186i | ||||
\(45\) | −543.036 | − | 145.506i | −0.268166 | − | 0.0718548i | ||||
\(46\) | −340.687 | + | 1271.46i | −0.161005 | + | 0.600880i | ||||
\(47\) | −995.185 | − | 995.185i | −0.450514 | − | 0.450514i | 0.445011 | − | 0.895525i | \(-0.353200\pi\) |
−0.895525 | + | 0.445011i | \(0.853200\pi\) | |||||||
\(48\) | −505.461 | − | 875.484i | −0.219384 | − | 0.379984i | ||||
\(49\) | −564.749 | − | 326.058i | −0.235214 | − | 0.135801i | ||||
\(50\) | 580.753 | − | 155.612i | 0.232301 | − | 0.0622449i | ||||
\(51\) | 1304.50i | 0.501538i | ||||||||
\(52\) | 530.557 | − | 2264.08i | 0.196212 | − | 0.837309i | ||||
\(53\) | 3865.42 | 1.37608 | 0.688042 | − | 0.725671i | \(-0.258471\pi\) | ||||
0.688042 | + | 0.725671i | \(0.258471\pi\) | |||||||
\(54\) | −302.644 | − | 1129.48i | −0.103787 | − | 0.387340i | ||||
\(55\) | 407.622 | − | 706.021i | 0.134751 | − | 0.233395i | ||||
\(56\) | 2131.42 | − | 1230.58i | 0.679663 | − | 0.392404i | ||||
\(57\) | −514.546 | + | 514.546i | −0.158371 | + | 0.158371i | ||||
\(58\) | −1152.63 | − | 308.845i | −0.342635 | − | 0.0918089i | ||||
\(59\) | 216.499 | − | 807.984i | 0.0621944 | − | 0.232113i | −0.927831 | − | 0.373000i | \(-0.878329\pi\) |
0.990026 | + | 0.140888i | \(0.0449957\pi\) | |||||||
\(60\) | 957.564 | + | 957.564i | 0.265990 | + | 0.265990i | ||||
\(61\) | 1383.34 | + | 2396.02i | 0.371766 | + | 0.643917i | 0.989837 | − | 0.142205i | \(-0.0454191\pi\) |
−0.618072 | + | 0.786122i | \(0.712086\pi\) | |||||||
\(62\) | −2019.71 | − | 1166.08i | −0.525418 | − | 0.303350i | ||||
\(63\) | −2008.00 | + | 538.042i | −0.505921 | + | 0.135561i | ||||
\(64\) | − | 1045.37i | − | 0.255218i | ||||||
\(65\) | 79.8300 | + | 2524.10i | 0.0188947 | + | 0.597419i | ||||
\(66\) | 537.798 | 0.123462 | ||||||||
\(67\) | −783.745 | − | 2924.98i | −0.174592 | − | 0.651588i | −0.996621 | − | 0.0821411i | \(-0.973824\pi\) |
0.822028 | − | 0.569447i | \(-0.192842\pi\) | |||||||
\(68\) | −1362.69 | + | 2360.25i | −0.294699 | + | 0.510434i | ||||
\(69\) | −5016.32 | + | 2896.17i | −1.05363 | + | 0.608312i | ||||
\(70\) | −873.835 | + | 873.835i | −0.178334 | + | 0.178334i | ||||
\(71\) | 4083.09 | + | 1094.06i | 0.809977 | + | 0.217033i | 0.639960 | − | 0.768409i | \(-0.278951\pi\) |
0.170017 | + | 0.985441i | \(0.445618\pi\) | |||||||
\(72\) | 433.723 | − | 1618.68i | 0.0836656 | − | 0.312244i | ||||
\(73\) | −918.987 | − | 918.987i | −0.172450 | − | 0.172450i | 0.615605 | − | 0.788055i | \(-0.288912\pi\) |
−0.788055 | + | 0.615605i | \(0.788912\pi\) | |||||||
\(74\) | 931.243 | + | 1612.96i | 0.170059 | + | 0.294551i | ||||
\(75\) | 2291.26 | + | 1322.86i | 0.407334 | + | 0.235175i | ||||
\(76\) | −1468.47 | + | 393.476i | −0.254237 | + | 0.0681225i | ||||
\(77\) | − | 3014.55i | − | 0.508442i | ||||||
\(78\) | −1415.68 | + | 878.153i | −0.232689 | + | 0.144338i | ||||
\(79\) | −7901.53 | −1.26607 | −0.633034 | − | 0.774124i | \(-0.718191\pi\) | ||||
−0.633034 | + | 0.774124i | \(0.718191\pi\) | |||||||
\(80\) | 593.633 | + | 2215.47i | 0.0927551 | + | 0.346167i | ||||
\(81\) | 1049.06 | − | 1817.02i | 0.159893 | − | 0.276943i | ||||
\(82\) | 4020.15 | − | 2321.04i | 0.597881 | − | 0.345187i | ||||
\(83\) | 2976.10 | − | 2976.10i | 0.432007 | − | 0.432007i | −0.457304 | − | 0.889311i | \(-0.651185\pi\) |
0.889311 | + | 0.457304i | \(0.151185\pi\) | |||||||
\(84\) | 4836.84 | + | 1296.03i | 0.685493 | + | 0.183677i | ||||
\(85\) | 766.029 | − | 2858.86i | 0.106025 | − | 0.395690i | ||||
\(86\) | 976.206 | + | 976.206i | 0.131991 | + | 0.131991i | ||||
\(87\) | −2625.49 | − | 4547.48i | −0.346874 | − | 0.600803i | ||||
\(88\) | 2104.50 | + | 1215.03i | 0.271759 | + | 0.156900i | ||||
\(89\) | 12196.3 | − | 3267.99i | 1.53974 | − | 0.412573i | 0.613561 | − | 0.789647i | \(-0.289736\pi\) |
0.926183 | + | 0.377074i | \(0.123070\pi\) | |||||||
\(90\) | 841.436i | 0.103881i | ||||||||
\(91\) | 4922.36 | + | 7935.39i | 0.594416 | + | 0.958265i | ||||
\(92\) | −12101.4 | −1.42975 | ||||||||
\(93\) | −2656.13 | − | 9912.80i | −0.307102 | − | 1.14612i | ||||
\(94\) | −1053.24 | + | 1824.26i | −0.119198 | + | 0.206457i | ||||
\(95\) | 1429.80 | − | 825.493i | 0.158426 | − | 0.0914674i | ||||
\(96\) | −4388.87 | + | 4388.87i | −0.476223 | + | 0.476223i | ||||
\(97\) | −7629.42 | − | 2044.30i | −0.810864 | − | 0.217270i | −0.170516 | − | 0.985355i | \(-0.554543\pi\) |
−0.640348 | + | 0.768085i | \(0.721210\pi\) | |||||||
\(98\) | −252.614 | + | 942.769i | −0.0263030 | + | 0.0981642i | ||||
\(99\) | −1451.39 | − | 1451.39i | −0.148086 | − | 0.148086i | ||||
\(100\) | 2763.73 | + | 4786.92i | 0.276373 | + | 0.478692i | ||||
\(101\) | 6889.37 | + | 3977.58i | 0.675362 | + | 0.389921i | 0.798105 | − | 0.602518i | \(-0.205836\pi\) |
−0.122743 | + | 0.992438i | \(0.539169\pi\) | |||||||
\(102\) | 1885.93 | − | 505.333i | 0.181269 | − | 0.0485710i | ||||
\(103\) | 2165.17i | 0.204088i | 0.994780 | + | 0.102044i | \(0.0325383\pi\) | ||||
−0.994780 | + | 0.102044i | \(0.967462\pi\) | |||||||
\(104\) | −7523.80 | + | 237.957i | −0.695618 | + | 0.0220004i | ||||
\(105\) | −5438.01 | −0.493243 | ||||||||
\(106\) | −1497.37 | − | 5588.26i | −0.133265 | − | 0.497354i | ||||
\(107\) | −9354.92 | + | 16203.2i | −0.817095 | + | 1.41525i | 0.0907190 | + | 0.995877i | \(0.471083\pi\) |
−0.907814 | + | 0.419373i | \(0.862250\pi\) | |||||||
\(108\) | 9309.88 | − | 5375.06i | 0.798172 | − | 0.460825i | ||||
\(109\) | −2940.23 | + | 2940.23i | −0.247474 | + | 0.247474i | −0.819933 | − | 0.572459i | \(-0.805989\pi\) |
0.572459 | + | 0.819933i | \(0.305989\pi\) | |||||||
\(110\) | −1178.60 | − | 315.806i | −0.0974052 | − | 0.0260996i | ||||
\(111\) | −2121.22 | + | 7916.48i | −0.172163 | + | 0.642520i | ||||
\(112\) | 5997.11 | + | 5997.11i | 0.478086 | + | 0.478086i | ||||
\(113\) | −3629.31 | − | 6286.15i | −0.284228 | − | 0.492298i | 0.688194 | − | 0.725527i | \(-0.258404\pi\) |
−0.972422 | + | 0.233230i | \(0.925071\pi\) | |||||||
\(114\) | 943.206 | + | 544.560i | 0.0725767 | + | 0.0419022i | ||||
\(115\) | 12694.1 | − | 3401.38i | 0.959858 | − | 0.257193i | ||||
\(116\) | − | 10970.4i | − | 0.815279i | ||||||
\(117\) | 6190.51 | + | 1450.66i | 0.452225 | + | 0.105973i | ||||
\(118\) | −1251.97 | −0.0899149 | ||||||||
\(119\) | −2832.57 | − | 10571.3i | −0.200026 | − | 0.746507i | ||||
\(120\) | 2191.83 | − | 3796.35i | 0.152210 | − | 0.263636i | ||||
\(121\) | −10101.8 | + | 5832.26i | −0.689965 | + | 0.398352i | ||||
\(122\) | 2928.06 | − | 2928.06i | 0.196726 | − | 0.196726i | ||||
\(123\) | 19731.1 | + | 5286.93i | 1.30419 | + | 0.349457i | ||||
\(124\) | 5549.21 | − | 20709.9i | 0.360901 | − | 1.34690i | ||||
\(125\) | −10848.5 | − | 10848.5i | −0.694302 | − | 0.694302i | ||||
\(126\) | 1555.70 | + | 2694.56i | 0.0979908 | + | 0.169725i | ||||
\(127\) | 3292.61 | + | 1900.99i | 0.204142 | + | 0.117862i | 0.598586 | − | 0.801058i | \(-0.295729\pi\) |
−0.394444 | + | 0.918920i | \(0.629063\pi\) | |||||||
\(128\) | −16075.9 | + | 4307.53i | −0.981197 | + | 0.262911i | ||||
\(129\) | 6075.07i | 0.365067i | ||||||||
\(130\) | 3618.18 | − | 1093.19i | 0.214094 | − | 0.0646855i | ||||
\(131\) | 5278.85 | 0.307607 | 0.153804 | − | 0.988101i | \(-0.450848\pi\) | ||||
0.153804 | + | 0.988101i | \(0.450848\pi\) | |||||||
\(132\) | 1279.66 | + | 4775.74i | 0.0734422 | + | 0.274090i | ||||
\(133\) | 3052.45 | − | 5287.00i | 0.172562 | − | 0.298887i | ||||
\(134\) | −3925.06 | + | 2266.13i | −0.218593 | + | 0.126205i | ||||
\(135\) | −8255.07 | + | 8255.07i | −0.452953 | + | 0.452953i | ||||
\(136\) | 8521.66 | + | 2283.37i | 0.460730 | + | 0.123452i | ||||
\(137\) | 303.931 | − | 1134.29i | 0.0161933 | − | 0.0604341i | −0.957356 | − | 0.288909i | \(-0.906707\pi\) |
0.973550 | + | 0.228475i | \(0.0733740\pi\) | |||||||
\(138\) | 6130.23 | + | 6130.23i | 0.321898 | + | 0.321898i | ||||
\(139\) | 6086.83 | + | 10542.7i | 0.315037 | + | 0.545660i | 0.979445 | − | 0.201710i | \(-0.0646497\pi\) |
−0.664408 | + | 0.747370i | \(0.731316\pi\) | |||||||
\(140\) | −9839.04 | − | 5680.57i | −0.501992 | − | 0.289825i | ||||
\(141\) | −8953.54 | + | 2399.09i | −0.450356 | + | 0.120673i | ||||
\(142\) | − | 6326.77i | − | 0.313766i | ||||||
\(143\) | −4355.35 | + | 8126.62i | −0.212986 | + | 0.397409i | ||||
\(144\) | 5774.76 | 0.278489 | ||||||||
\(145\) | 3083.47 | + | 11507.7i | 0.146658 | + | 0.547333i | ||||
\(146\) | −972.593 | + | 1684.58i | −0.0456274 | + | 0.0790289i | ||||
\(147\) | −3719.52 | + | 2147.47i | −0.172128 | + | 0.0993784i | ||||
\(148\) | −12107.5 | + | 12107.5i | −0.552755 | + | 0.552755i | ||||
\(149\) | −20323.5 | − | 5445.66i | −0.915431 | − | 0.245289i | −0.229800 | − | 0.973238i | \(-0.573807\pi\) |
−0.685631 | + | 0.727949i | \(0.740474\pi\) | |||||||
\(150\) | 1024.89 | − | 3824.93i | 0.0455505 | − | 0.169997i | ||||
\(151\) | −22690.8 | − | 22690.8i | −0.995167 | − | 0.995167i | 0.00482166 | − | 0.999988i | \(-0.498465\pi\) |
−0.999988 | + | 0.00482166i | \(0.998465\pi\) | |||||||
\(152\) | 2460.62 | + | 4261.92i | 0.106502 | + | 0.184467i | ||||
\(153\) | −6453.44 | − | 3725.90i | −0.275682 | − | 0.159165i | ||||
\(154\) | −4358.16 | + | 1167.76i | −0.183764 | + | 0.0492395i | ||||
\(155\) | 23284.0i | 0.969156i | ||||||||
\(156\) | −11166.7 | − | 10482.0i | −0.458854 | − | 0.430719i | ||||
\(157\) | 35324.6 | 1.43310 | 0.716552 | − | 0.697534i | \(-0.245719\pi\) | ||||
0.716552 | + | 0.697534i | \(0.245719\pi\) | |||||||
\(158\) | 3060.86 | + | 11423.3i | 0.122611 | + | 0.457591i | ||||
\(159\) | 12729.1 | − | 22047.5i | 0.503506 | − | 0.872097i | ||||
\(160\) | 12195.6 | − | 7041.12i | 0.476390 | − | 0.275044i | ||||
\(161\) | 34362.1 | − | 34362.1i | 1.32565 | − | 1.32565i | ||||
\(162\) | −3033.26 | − | 812.761i | −0.115579 | − | 0.0309694i | ||||
\(163\) | −5807.75 | + | 21674.8i | −0.218591 | + | 0.815793i | 0.766280 | + | 0.642506i | \(0.222105\pi\) |
−0.984871 | + | 0.173287i | \(0.944561\pi\) | |||||||
\(164\) | 30176.9 | + | 30176.9i | 1.12199 | + | 1.12199i | ||||
\(165\) | −2684.66 | − | 4649.97i | −0.0986101 | − | 0.170798i | ||||
\(166\) | −5455.43 | − | 3149.70i | −0.197976 | − | 0.114302i | ||||
\(167\) | 1455.11 | − | 389.896i | 0.0521751 | − | 0.0139803i | −0.232637 | − | 0.972564i | \(-0.574735\pi\) |
0.284812 | + | 0.958583i | \(0.408069\pi\) | |||||||
\(168\) | − | 16209.6i | − | 0.574318i | ||||||
\(169\) | −1804.80 | − | 28503.9i | −0.0631911 | − | 0.998001i | ||||
\(170\) | −4429.81 | −0.153281 | ||||||||
\(171\) | −1075.85 | − | 4015.13i | −0.0367925 | − | 0.137312i | ||||
\(172\) | −6346.06 | + | 10991.7i | −0.214510 | + | 0.371542i | ||||
\(173\) | 3791.94 | − | 2189.28i | 0.126698 | − | 0.0731491i | −0.435312 | − | 0.900280i | \(-0.643362\pi\) |
0.562010 | + | 0.827131i | \(0.310028\pi\) | |||||||
\(174\) | −5557.27 | + | 5557.27i | −0.183554 | + | 0.183554i | ||||
\(175\) | −21440.1 | − | 5744.85i | −0.700084 | − | 0.187587i | ||||
\(176\) | −2167.37 | + | 8088.73i | −0.0699693 | + | 0.261129i | ||||
\(177\) | −3895.61 | − | 3895.61i | −0.124345 | − | 0.124345i | ||||
\(178\) | −9449.12 | − | 16366.4i | −0.298230 | − | 0.516550i | ||||
\(179\) | 10787.3 | + | 6228.06i | 0.336672 | + | 0.194378i | 0.658800 | − | 0.752319i | \(-0.271065\pi\) |
−0.322127 | + | 0.946696i | \(0.604398\pi\) | |||||||
\(180\) | −7472.10 | + | 2002.14i | −0.230620 | + | 0.0617945i | ||||
\(181\) | 23085.8i | 0.704673i | 0.935873 | + | 0.352336i | \(0.114613\pi\) | ||||
−0.935873 | + | 0.352336i | \(0.885387\pi\) | |||||||
\(182\) | 9565.45 | − | 10190.3i | 0.288777 | − | 0.307640i | ||||
\(183\) | 18221.8 | 0.544113 | ||||||||
\(184\) | 10138.8 | + | 37838.5i | 0.299468 | + | 1.11763i | ||||
\(185\) | 9297.43 | − | 16103.6i | 0.271656 | − | 0.470522i | ||||
\(186\) | −13302.1 | + | 7679.97i | −0.384498 | + | 0.221990i | ||||
\(187\) | 7640.97 | − | 7640.97i | 0.218507 | − | 0.218507i | ||||
\(188\) | −18705.8 | − | 5012.21i | −0.529250 | − | 0.141812i | ||||
\(189\) | −11172.9 | + | 41697.9i | −0.312783 | + | 1.16732i | ||||
\(190\) | −1747.29 | − | 1747.29i | −0.0484014 | − | 0.0484014i | ||||
\(191\) | −30414.3 | − | 52679.1i | −0.833703 | − | 1.44402i | −0.895082 | − | 0.445901i | \(-0.852883\pi\) |
0.0613793 | − | 0.998115i | \(-0.480450\pi\) | |||||||
\(192\) | −5962.57 | − | 3442.49i | −0.161745 | − | 0.0933836i | ||||
\(193\) | −9841.71 | + | 2637.08i | −0.264214 | + | 0.0707959i | −0.388494 | − | 0.921451i | \(-0.627005\pi\) |
0.124280 | + | 0.992247i | \(0.460338\pi\) | |||||||
\(194\) | 11821.8i | 0.314109i | ||||||||
\(195\) | 14659.8 | + | 7856.71i | 0.385530 | + | 0.206620i | ||||
\(196\) | −8973.03 | −0.233575 | ||||||||
\(197\) | 14724.5 | + | 54952.4i | 0.379408 | + | 1.41597i | 0.846795 | + | 0.531919i | \(0.178529\pi\) |
−0.467387 | + | 0.884053i | \(0.654804\pi\) | |||||||
\(198\) | −1536.05 | + | 2660.52i | −0.0391810 | + | 0.0678635i | ||||
\(199\) | −31073.9 | + | 17940.5i | −0.784673 | + | 0.453031i | −0.838084 | − | 0.545541i | \(-0.816324\pi\) |
0.0534105 | + | 0.998573i | \(0.482991\pi\) | |||||||
\(200\) | 12652.1 | − | 12652.1i | 0.316303 | − | 0.316303i | ||||
\(201\) | −19264.4 | − | 5161.87i | −0.476829 | − | 0.127766i | ||||
\(202\) | 3081.64 | − | 11500.8i | 0.0755230 | − | 0.281856i | ||||
\(203\) | 31150.5 | + | 31150.5i | 0.755914 | + | 0.755914i | ||||
\(204\) | 8974.89 | + | 15545.0i | 0.215659 | + | 0.373533i | ||||
\(205\) | −40136.8 | − | 23173.0i | −0.955069 | − | 0.551409i | ||||
\(206\) | 3130.20 | − | 838.735i | 0.0737629 | − | 0.0197647i | ||||
\(207\) | − | 33088.0i | − | 0.772201i | ||||||
\(208\) | −7502.51 | − | 24831.5i | −0.173412 | − | 0.573953i | ||||
\(209\) | 6027.79 | 0.137996 | ||||||||
\(210\) | 2106.56 | + | 7861.77i | 0.0477677 | + | 0.178271i | ||||
\(211\) | 14344.6 | − | 24845.6i | 0.322199 | − | 0.558066i | −0.658742 | − | 0.752369i | \(-0.728911\pi\) |
0.980942 | + | 0.194303i | \(0.0622446\pi\) | |||||||
\(212\) | 46061.9 | − | 26593.8i | 1.02487 | − | 0.591710i | ||||
\(213\) | 19686.2 | − | 19686.2i | 0.433913 | − | 0.433913i | ||||
\(214\) | 27049.0 | + | 7247.75i | 0.590640 | + | 0.158262i | ||||
\(215\) | 3567.40 | − | 13313.7i | 0.0771747 | − | 0.288020i | ||||
\(216\) | −24606.6 | − | 24606.6i | −0.527405 | − | 0.527405i | ||||
\(217\) | 43048.9 | + | 74562.9i | 0.914204 | + | 1.58345i | ||||
\(218\) | 5389.69 | + | 3111.74i | 0.113410 | + | 0.0654773i | ||||
\(219\) | −8267.99 | + | 2215.40i | −0.172390 | + | 0.0461917i | ||||
\(220\) | − | 11217.6i | − | 0.231769i | ||||||
\(221\) | −7637.13 | + | 32590.5i | −0.156367 | + | 0.667277i | ||||
\(222\) | 12266.6 | 0.248897 | ||||||||
\(223\) | −18745.8 | − | 69960.4i | −0.376960 | − | 1.40683i | −0.850460 | − | 0.526039i | \(-0.823676\pi\) |
0.473501 | − | 0.880794i | \(-0.342990\pi\) | |||||||
\(224\) | 26036.2 | − | 45096.0i | 0.518897 | − | 0.898756i | ||||
\(225\) | −13088.5 | + | 7556.65i | −0.258538 | + | 0.149267i | ||||
\(226\) | −7682.02 | + | 7682.02i | −0.150404 | + | 0.150404i | ||||
\(227\) | −3711.35 | − | 994.452i | −0.0720244 | − | 0.0192989i | 0.222627 | − | 0.974904i | \(-0.428537\pi\) |
−0.294651 | + | 0.955605i | \(0.595203\pi\) | |||||||
\(228\) | −2591.49 | + | 9671.58i | −0.0498517 | + | 0.186049i | ||||
\(229\) | −4649.95 | − | 4649.95i | −0.0886701 | − | 0.0886701i | 0.661380 | − | 0.750051i | \(-0.269971\pi\) |
−0.750051 | + | 0.661380i | \(0.769971\pi\) | |||||||
\(230\) | −9834.80 | − | 17034.4i | −0.185913 | − | 0.322011i | ||||
\(231\) | −17194.3 | − | 9927.15i | −0.322226 | − | 0.186038i | ||||
\(232\) | −34302.0 | + | 9191.19i | −0.637299 | + | 0.170764i | ||||
\(233\) | 56025.7i | 1.03199i | 0.856592 | + | 0.515995i | \(0.172578\pi\) | ||||
−0.856592 | + | 0.515995i | \(0.827422\pi\) | |||||||
\(234\) | −300.826 | − | 9511.62i | −0.00549393 | − | 0.173709i | ||||
\(235\) | 21030.8 | 0.380820 | ||||||||
\(236\) | −2978.99 | − | 11117.8i | −0.0534866 | − | 0.199615i | ||||
\(237\) | −26020.3 | + | 45068.6i | −0.463251 | + | 0.802374i | ||||
\(238\) | −14185.7 | + | 8190.13i | −0.250437 | + | 0.144590i | ||||
\(239\) | −23621.5 | + | 23621.5i | −0.413534 | + | 0.413534i | −0.882968 | − | 0.469434i | \(-0.844458\pi\) |
0.469434 | + | 0.882968i | \(0.344458\pi\) | |||||||
\(240\) | 14591.4 | + | 3909.76i | 0.253323 | + | 0.0678778i | ||||
\(241\) | 2176.28 | − | 8122.00i | 0.0374698 | − | 0.139839i | −0.944657 | − | 0.328060i | \(-0.893605\pi\) |
0.982127 | + | 0.188221i | \(0.0602720\pi\) | |||||||
\(242\) | 12344.9 | + | 12344.9i | 0.210794 | + | 0.210794i | ||||
\(243\) | 24732.0 | + | 42837.1i | 0.418839 | + | 0.725451i | ||||
\(244\) | 32968.9 | + | 19034.6i | 0.553763 | + | 0.319715i | ||||
\(245\) | 9412.49 | − | 2522.07i | 0.156810 | − | 0.0420170i | ||||
\(246\) | − | 30573.4i | − | 0.505212i | ||||||
\(247\) | −15867.3 | + | 9842.58i | −0.260082 | + | 0.161330i | ||||
\(248\) | −69404.6 | −1.12846 | ||||||||
\(249\) | −7174.47 | − | 26775.5i | −0.115715 | − | 0.431856i | ||||
\(250\) | −11481.3 | + | 19886.1i | −0.183700 | + | 0.318178i | ||||
\(251\) | −25257.5 | + | 14582.4i | −0.400906 | + | 0.231463i | −0.686875 | − | 0.726776i | \(-0.741018\pi\) |
0.285969 | + | 0.958239i | \(0.407685\pi\) | |||||||
\(252\) | −20226.4 | + | 20226.4i | −0.318506 | + | 0.318506i | ||||
\(253\) | 46346.5 | + | 12418.5i | 0.724063 | + | 0.194012i | ||||
\(254\) | 1472.80 | − | 5496.55i | 0.0228284 | − | 0.0851967i | ||||
\(255\) | −13783.7 | − | 13783.7i | −0.211975 | − | 0.211975i | ||||
\(256\) | 4091.89 | + | 7087.36i | 0.0624372 | + | 0.108144i | ||||
\(257\) | 5674.86 | + | 3276.38i | 0.0859189 | + | 0.0496053i | 0.542344 | − | 0.840157i | \(-0.317537\pi\) |
−0.456425 | + | 0.889762i | \(0.650870\pi\) | |||||||
\(258\) | 8782.78 | − | 2353.34i | 0.131945 | − | 0.0353545i | ||||
\(259\) | − | 68758.8i | − | 1.02501i | ||||||
\(260\) | 18316.9 | + | 29528.9i | 0.270960 | + | 0.436818i | ||||
\(261\) | 29995.5 | 0.440327 | ||||||||
\(262\) | −2044.90 | − | 7631.67i | −0.0297899 | − | 0.111178i | ||||
\(263\) | −10037.2 | + | 17384.9i | −0.145111 | + | 0.251340i | −0.929414 | − | 0.369038i | \(-0.879687\pi\) |
0.784303 | + | 0.620378i | \(0.213021\pi\) | |||||||
\(264\) | 13860.6 | − | 8002.41i | 0.198872 | − | 0.114819i | ||||
\(265\) | −40843.0 | + | 40843.0i | −0.581602 | + | 0.581602i | ||||
\(266\) | −8825.91 | − | 2364.90i | −0.124737 | − | 0.0334232i | ||||
\(267\) | 21523.5 | − | 80326.8i | 0.301919 | − | 1.12678i | ||||
\(268\) | −29463.1 | − | 29463.1i | −0.410212 | − | 0.410212i | ||||
\(269\) | −63876.4 | − | 110637.i | −0.882747 | − | 1.52896i | −0.848275 | − | 0.529556i | \(-0.822358\pi\) |
−0.0344720 | − | 0.999406i | \(-0.510975\pi\) | |||||||
\(270\) | 15132.2 | + | 8736.60i | 0.207575 | + | 0.119844i | ||||
\(271\) | 96583.1 | − | 25879.4i | 1.31511 | − | 0.352383i | 0.467967 | − | 0.883746i | \(-0.344986\pi\) |
0.847145 | + | 0.531362i | \(0.178320\pi\) | |||||||
\(272\) | 30401.7i | 0.410923i | ||||||||
\(273\) | 61471.4 | − | 1944.17i | 0.824799 | − | 0.0260861i | ||||
\(274\) | −1757.58 | −0.0234107 | ||||||||
\(275\) | −5672.28 | − | 21169.2i | −0.0750054 | − | 0.279924i | ||||
\(276\) | −39851.0 | + | 69023.9i | −0.523144 | + | 0.906111i | ||||
\(277\) | 58305.7 | − | 33662.8i | 0.759892 | − | 0.438724i | −0.0693651 | − | 0.997591i | \(-0.522097\pi\) |
0.829257 | + | 0.558868i | \(0.188764\pi\) | |||||||
\(278\) | 12883.8 | − | 12883.8i | 0.166707 | − | 0.166707i | ||||
\(279\) | 56625.6 | + | 15172.8i | 0.727452 | + | 0.194920i | ||||
\(280\) | −9518.57 | + | 35523.8i | −0.121410 | + | 0.453110i | ||||
\(281\) | −9761.98 | − | 9761.98i | −0.123630 | − | 0.123630i | 0.642584 | − | 0.766215i | \(-0.277862\pi\) |
−0.766215 | + | 0.642584i | \(0.777862\pi\) | |||||||
\(282\) | 6936.77 | + | 12014.8i | 0.0872287 | + | 0.151084i | ||||
\(283\) | 75924.7 | + | 43835.2i | 0.948004 | + | 0.547331i | 0.892460 | − | 0.451126i | \(-0.148977\pi\) |
0.0555440 | + | 0.998456i | \(0.482311\pi\) | |||||||
\(284\) | 56182.8 | − | 15054.1i | 0.696573 | − | 0.186646i | ||||
\(285\) | − | 10873.7i | − | 0.133871i | ||||||
\(286\) | 13435.9 | + | 3148.51i | 0.164261 | + | 0.0384922i | ||||
\(287\) | −171375. | −2.08057 | ||||||||
\(288\) | −9176.57 | − | 34247.4i | −0.110636 | − | 0.412898i | ||||
\(289\) | −22145.2 | + | 38356.6i | −0.265145 | + | 0.459245i | ||||
\(290\) | 15442.3 | − | 8915.60i | 0.183618 | − | 0.106012i | ||||
\(291\) | −36784.5 | + | 36784.5i | −0.434389 | + | 0.434389i | ||||
\(292\) | −17273.6 | − | 4628.44i | −0.202589 | − | 0.0542837i | ||||
\(293\) | 17014.8 | − | 63500.0i | 0.198194 | − | 0.739671i | −0.793223 | − | 0.608932i | \(-0.791598\pi\) |
0.991417 | − | 0.130739i | \(-0.0417351\pi\) | |||||||
\(294\) | 4545.47 | + | 4545.47i | 0.0525876 | + | 0.0525876i | ||||
\(295\) | 6249.79 | + | 10824.9i | 0.0718160 | + | 0.124389i | ||||
\(296\) | 48001.5 | + | 27713.7i | 0.547862 | + | 0.316308i | ||||
\(297\) | −41171.2 | + | 11031.8i | −0.466746 | + | 0.125064i | ||||
\(298\) | 31491.3i | 0.354616i | ||||||||
\(299\) | −142279. | + | 42987.7i | −1.59147 | + | 0.480841i | ||||
\(300\) | 36404.7 | 0.404496 | ||||||||
\(301\) | −13191.3 | − | 49230.6i | −0.145598 | − | 0.543378i | ||||
\(302\) | −24014.4 | + | 41594.1i | −0.263304 | + | 0.456056i | ||||
\(303\) | 45374.5 | − | 26197.0i | 0.494227 | − | 0.285342i | ||||
\(304\) | −11991.6 | + | 11991.6i | −0.129757 | + | 0.129757i | ||||
\(305\) | −39933.7 | − | 10700.2i | −0.429279 | − | 0.115025i | ||||
\(306\) | −2886.65 | + | 10773.1i | −0.0308284 | + | 0.115053i | ||||
\(307\) | 24442.3 | + | 24442.3i | 0.259337 | + | 0.259337i | 0.824785 | − | 0.565447i | \(-0.191296\pi\) |
−0.565447 | + | 0.824785i | \(0.691296\pi\) | |||||||
\(308\) | −20739.9 | − | 35922.6i | −0.218628 | − | 0.378674i | ||||
\(309\) | 12349.7 | + | 7130.07i | 0.129341 | + | 0.0746753i | ||||
\(310\) | 33661.8 | − | 9019.66i | 0.350279 | − | 0.0938570i | ||||
\(311\) | 82049.3i | 0.848309i | 0.905590 | + | 0.424155i | \(0.139429\pi\) | ||||
−0.905590 | + | 0.424155i | \(0.860571\pi\) | |||||||
\(312\) | −23419.2 | + | 43697.7i | −0.240582 | + | 0.448900i | ||||
\(313\) | −73633.7 | −0.751602 | −0.375801 | − | 0.926700i | \(-0.622632\pi\) | ||||
−0.375801 | + | 0.926700i | \(0.622632\pi\) | |||||||
\(314\) | −13683.9 | − | 51069.0i | −0.138788 | − | 0.517962i | ||||
\(315\) | 15532.0 | − | 26902.1i | 0.156533 | − | 0.271123i | ||||
\(316\) | −94157.7 | + | 54362.0i | −0.942935 | + | 0.544404i | ||||
\(317\) | 88575.1 | − | 88575.1i | 0.881440 | − | 0.881440i | −0.112241 | − | 0.993681i | \(-0.535803\pi\) |
0.993681 | + | 0.112241i | \(0.0358028\pi\) | |||||||
\(318\) | −36805.2 | − | 9861.92i | −0.363961 | − | 0.0975230i | ||||
\(319\) | −11257.8 | + | 42014.8i | −0.110630 | + | 0.412877i | ||||
\(320\) | 11045.7 | + | 11045.7i | 0.107868 | + | 0.107868i | ||||
\(321\) | 61613.0 | + | 106717.i | 0.597946 | + | 1.03567i | ||||
\(322\) | −62988.6 | − | 36366.5i | −0.607505 | − | 0.350743i | ||||
\(323\) | 21138.0 | − | 5663.91i | 0.202609 | − | 0.0542889i | ||||
\(324\) | − | 28869.8i | − | 0.275013i | ||||||
\(325\) | 49498.1 | + | 46463.1i | 0.468621 | + | 0.439887i | ||||
\(326\) | 33585.2 | 0.316019 | ||||||||
\(327\) | 7088.02 | + | 26452.9i | 0.0662872 | + | 0.247387i | ||||
\(328\) | 69073.8 | − | 119639.i | 0.642045 | − | 1.11205i | ||||
\(329\) | 67347.4 | − | 38883.1i | 0.622199 | − | 0.359227i | ||||
\(330\) | −5682.52 | + | 5682.52i | −0.0521811 | + | 0.0521811i | ||||
\(331\) | 138582. | + | 37132.9i | 1.26488 | + | 0.338924i | 0.828068 | − | 0.560628i | \(-0.189440\pi\) |
0.436814 | + | 0.899552i | \(0.356107\pi\) | |||||||
\(332\) | 14989.0 | − | 55939.7i | 0.135987 | − | 0.507509i | ||||
\(333\) | −33104.7 | − | 33104.7i | −0.298539 | − | 0.298539i | ||||
\(334\) | −1127.35 | − | 1952.63i | −0.0101057 | − | 0.0175036i | ||||
\(335\) | 39187.3 | + | 22624.8i | 0.349185 | + | 0.201602i | ||||
\(336\) | 53955.2 | − | 14457.2i | 0.477919 | − | 0.128058i | ||||
\(337\) | − | 165153.i | − | 1.45421i | −0.686527 | − | 0.727104i | \(-0.740866\pi\) | ||
0.686527 | − | 0.727104i | \(-0.259134\pi\) | |||||||
\(338\) | −40509.2 | + | 13651.0i | −0.354585 | + | 0.119489i | ||||
\(339\) | −47806.4 | −0.415994 | ||||||||
\(340\) | −10540.5 | − | 39337.5i | −0.0911804 | − | 0.340290i | ||||
\(341\) | −42505.2 | + | 73621.1i | −0.365538 | + | 0.633131i | ||||
\(342\) | −5387.94 | + | 3110.73i | −0.0460650 | + | 0.0265956i | ||||
\(343\) | −68331.0 | + | 68331.0i | −0.580804 | + | 0.580804i | ||||
\(344\) | 39685.4 | + | 10633.7i | 0.335362 | + | 0.0898600i | ||||
\(345\) | 22402.0 | − | 83605.5i | 0.188213 | − | 0.702420i | ||||
\(346\) | −4633.97 | − | 4633.97i | −0.0387080 | − | 0.0387080i | ||||
\(347\) | −27797.5 | − | 48146.6i | −0.230859 | − | 0.399859i | 0.727202 | − | 0.686423i | \(-0.240820\pi\) |
−0.958061 | + | 0.286564i | \(0.907487\pi\) | |||||||
\(348\) | −62572.7 | − | 36126.4i | −0.516686 | − | 0.298309i | ||||
\(349\) | −168206. | + | 45070.6i | −1.38099 | + | 0.370035i | −0.871480 | − | 0.490431i | \(-0.836840\pi\) |
−0.509509 | + | 0.860465i | \(0.670173\pi\) | |||||||
\(350\) | 33221.5i | 0.271196i | ||||||||
\(351\) | 90364.2 | − | 96266.8i | 0.733470 | − | 0.781380i | ||||
\(352\) | 51414.6 | 0.414955 | ||||||||
\(353\) | 43391.2 | + | 161938.i | 0.348219 | + | 1.29957i | 0.888806 | + | 0.458283i | \(0.151536\pi\) |
−0.540587 | + | 0.841288i | \(0.681798\pi\) | |||||||
\(354\) | −4122.85 | + | 7140.99i | −0.0328996 | + | 0.0569838i | ||||
\(355\) | −54703.1 | + | 31582.9i | −0.434066 | + | 0.250608i | ||||
\(356\) | 122853. | − | 122853.i | 0.969358 | − | 0.969358i | ||||
\(357\) | −69624.2 | − | 18655.7i | −0.546290 | − | 0.146378i | ||||
\(358\) | 4825.20 | − | 18007.9i | 0.0376487 | − | 0.140507i | ||||
\(359\) | 112373. | + | 112373.i | 0.871912 | + | 0.871912i | 0.992681 | − | 0.120769i | \(-0.0385360\pi\) |
−0.120769 | + | 0.992681i | \(0.538536\pi\) | |||||||
\(360\) | 12520.5 | + | 21686.2i | 0.0966089 | + | 0.167332i | ||||
\(361\) | −102290. | − | 59056.9i | −0.784905 | − | 0.453165i | ||||
\(362\) | 33375.3 | − | 8942.89i | 0.254688 | − | 0.0682434i | ||||
\(363\) | 76824.4i | 0.583023i | ||||||||
\(364\) | 113252. | + | 60695.8i | 0.854756 | + | 0.458095i | ||||
\(365\) | 19420.5 | 0.145772 | ||||||||
\(366\) | −7058.69 | − | 26343.4i | −0.0526941 | − | 0.196657i | ||||
\(367\) | 36242.1 | − | 62773.1i | 0.269080 | − | 0.466060i | −0.699545 | − | 0.714589i | \(-0.746614\pi\) |
0.968624 | + | 0.248529i | \(0.0799472\pi\) | |||||||
\(368\) | −116907. | + | 67496.0i | −0.863263 | + | 0.498405i | ||||
\(369\) | −82510.4 | + | 82510.4i | −0.605977 | + | 0.605977i | ||||
\(370\) | −26882.7 | − | 7203.20i | −0.196368 | − | 0.0526165i | ||||
\(371\) | −55279.5 | + | 206306.i | −0.401621 | + | 1.49887i | ||||
\(372\) | −99850.9 | − | 99850.9i | −0.721550 | − | 0.721550i | ||||
\(373\) | 19788.5 | + | 34274.7i | 0.142231 | + | 0.246352i | 0.928337 | − | 0.371741i | \(-0.121239\pi\) |
−0.786105 | + | 0.618093i | \(0.787906\pi\) | |||||||
\(374\) | −14006.5 | − | 8086.68i | −0.100135 | − | 0.0578132i | ||||
\(375\) | −97602.1 | + | 26152.4i | −0.694059 | + | 0.185973i | ||||
\(376\) | 62688.3i | 0.443415i | ||||||||
\(377\) | −38969.9 | − | 128981.i | −0.274186 | − | 0.907491i | ||||
\(378\) | 64611.2 | 0.452193 | ||||||||
\(379\) | 3636.15 | + | 13570.3i | 0.0253141 | + | 0.0944737i | 0.977427 | − | 0.211273i | \(-0.0677608\pi\) |
−0.952113 | + | 0.305746i | \(0.901094\pi\) | |||||||
\(380\) | 11358.7 | − | 19673.8i | 0.0786612 | − | 0.136245i | ||||
\(381\) | 21685.7 | − | 12520.2i | 0.149390 | − | 0.0862506i | ||||
\(382\) | −64376.8 | + | 64376.8i | −0.441167 | + | 0.441167i | ||||
\(383\) | −41441.5 | − | 11104.2i | −0.282513 | − | 0.0756991i | 0.114780 | − | 0.993391i | \(-0.463384\pi\) |
−0.397293 | + | 0.917692i | \(0.630050\pi\) | |||||||
\(384\) | −28370.1 | + | 105879.i | −0.192397 | + | 0.718035i | ||||
\(385\) | 31852.5 | + | 31852.5i | 0.214893 | + | 0.214893i | ||||
\(386\) | 7624.88 | + | 13206.7i | 0.0511751 | + | 0.0886379i | ||||
\(387\) | −30053.7 | − | 17351.5i | −0.200667 | − | 0.115855i | ||||
\(388\) | −104980. | + | 28129.3i | −0.697336 | + | 0.186851i | ||||
\(389\) | − | 204736.i | − | 1.35299i | −0.736446 | − | 0.676497i | \(-0.763497\pi\) | ||
0.736446 | − | 0.676497i | \(-0.236503\pi\) | |||||||
\(390\) | 5679.66 | − | 24237.2i | 0.0373416 | − | 0.159351i | ||||
\(391\) | 174195. | 1.13941 | ||||||||
\(392\) | 7517.76 | + | 28056.7i | 0.0489234 | + | 0.182585i | ||||
\(393\) | 17383.7 | − | 30109.4i | 0.112553 | − | 0.194947i | ||||
\(394\) | 73741.3 | − | 42574.5i | 0.475027 | − | 0.274257i | ||||
\(395\) | 83489.6 | − | 83489.6i | 0.535104 | − | 0.535104i | ||||
\(396\) | −27280.8 | − | 7309.87i | −0.173967 | − | 0.0466143i | ||||
\(397\) | −19570.6 | + | 73038.4i | −0.124172 | + | 0.463415i | −0.999809 | − | 0.0195546i | \(-0.993775\pi\) |
0.875637 | + | 0.482970i | \(0.160442\pi\) | |||||||
\(398\) | 37974.0 | + | 37974.0i | 0.239729 | + | 0.239729i | ||||
\(399\) | −20103.9 | − | 34821.0i | −0.126280 | − | 0.218724i | ||||
\(400\) | 53398.2 | + | 30829.5i | 0.333739 | + | 0.192684i | ||||
\(401\) | 210254. | − | 56337.5i | 1.30754 | − | 0.350355i | 0.463246 | − | 0.886229i | \(-0.346684\pi\) |
0.844298 | + | 0.535874i | \(0.180018\pi\) | |||||||
\(402\) | 29850.2i | 0.184712i | ||||||||
\(403\) | −8324.36 | − | 263203.i | −0.0512555 | − | 1.62062i | ||||
\(404\) | 109462. | 0.670657 | ||||||||
\(405\) | 8114.51 | + | 30283.8i | 0.0494712 | + | 0.184629i | ||||
\(406\) | 32967.5 | − | 57101.4i | 0.200002 | − | 0.346413i | ||||
\(407\) | 58794.7 | − | 33945.1i | 0.354935 | − | 0.204922i | ||||
\(408\) | 41086.3 | − | 41086.3i | 0.246818 | − | 0.246818i | ||||
\(409\) | −220545. | − | 59094.7i | −1.31841 | − | 0.353266i | −0.470026 | − | 0.882652i | \(-0.655756\pi\) |
−0.848381 | + | 0.529386i | \(0.822422\pi\) | |||||||
\(410\) | −17953.3 | + | 67002.7i | −0.106801 | + | 0.398588i | ||||
\(411\) | −5468.86 | − | 5468.86i | −0.0323752 | − | 0.0323752i | ||||
\(412\) | 14896.2 | + | 25801.0i | 0.0877570 | + | 0.152000i | ||||
\(413\) | 40027.7 | + | 23110.0i | 0.234672 | + | 0.135488i | ||||
\(414\) | −47835.6 | + | 12817.5i | −0.279094 | + | 0.0747831i | ||||
\(415\) | 62892.4i | 0.365176i | ||||||||
\(416\) | −135342. | + | 83953.2i | −0.782070 | + | 0.485122i | ||||
\(417\) | 80177.6 | 0.461085 | ||||||||
\(418\) | −2335.02 | − | 8714.42i | −0.0133641 | − | 0.0498754i | ||||
\(419\) | 55459.9 | − | 96059.4i | 0.315901 | − | 0.547157i | −0.663727 | − | 0.747975i | \(-0.731026\pi\) |
0.979629 | + | 0.200818i | \(0.0643598\pi\) | |||||||
\(420\) | −64801.5 | + | 37413.1i | −0.367355 | + | 0.212093i | ||||
\(421\) | 24030.5 | − | 24030.5i | 0.135581 | − | 0.135581i | −0.636059 | − | 0.771640i | \(-0.719437\pi\) |
0.771640 | + | 0.636059i | \(0.219437\pi\) | |||||||
\(422\) | −41476.3 | − | 11113.5i | −0.232903 | − | 0.0624062i | ||||
\(423\) | 13704.5 | − | 51145.9i | 0.0765918 | − | 0.285845i | ||||
\(424\) | −121744. | − | 121744.i | −0.677201 | − | 0.677201i | ||||
\(425\) | −39782.6 | − | 68905.5i | −0.220250 | − | 0.381484i | ||||
\(426\) | −36086.5 | − | 20834.5i | −0.198850 | − | 0.114806i | ||||
\(427\) | −147664. | + | 39566.4i | −0.809876 | + | 0.217006i | ||||
\(428\) | 257445.i | 1.40539i | ||||||||
\(429\) | 32009.9 | + | 51603.5i | 0.173928 | + | 0.280392i | ||||
\(430\) | −20629.7 | −0.111572 | ||||||||
\(431\) | 92790.6 | + | 346299.i | 0.499516 | + | 1.86422i | 0.503103 | + | 0.864226i | \(0.332192\pi\) |
−0.00358674 | + | 0.999994i | \(0.501142\pi\) | |||||||
\(432\) | 59959.1 | − | 103852.i | 0.321283 | − | 0.556478i | ||||
\(433\) | 117899. | − | 68068.7i | 0.628829 | − | 0.363055i | −0.151469 | − | 0.988462i | \(-0.548401\pi\) |
0.780298 | + | 0.625407i | \(0.215067\pi\) | |||||||
\(434\) | 91120.1 | − | 91120.1i | 0.483765 | − | 0.483765i | ||||
\(435\) | 75791.4 | + | 20308.2i | 0.400536 | + | 0.107323i | ||||
\(436\) | −14808.4 | + | 55265.6i | −0.0778994 | + | 0.290725i | ||||
\(437\) | 68709.2 | + | 68709.2i | 0.359793 | + | 0.359793i | ||||
\(438\) | 6405.65 | + | 11094.9i | 0.0333899 | + | 0.0578330i | ||||
\(439\) | −102882. | − | 59398.8i | −0.533837 | − | 0.308211i | 0.208740 | − | 0.977971i | \(-0.433064\pi\) |
−0.742578 | + | 0.669760i | \(0.766397\pi\) | |||||||
\(440\) | −35075.1 | + | 9398.34i | −0.181173 | + | 0.0485451i | ||||
\(441\) | − | 24534.3i | − | 0.126152i | ||||||
\(442\) | 50074.8 | − | 1583.72i | 0.256315 | − | 0.00810653i | ||||
\(443\) | −112001. | −0.570710 | −0.285355 | − | 0.958422i | \(-0.592112\pi\) | ||||
−0.285355 | + | 0.958422i | \(0.592112\pi\) | |||||||
\(444\) | 29187.6 | + | 108930.i | 0.148058 | + | 0.552562i | ||||
\(445\) | −94339.0 | + | 163400.i | −0.476399 | + | 0.825148i | ||||
\(446\) | −93880.6 | + | 54202.0i | −0.471961 | + | 0.272487i | ||||
\(447\) | −97987.6 | + | 97987.6i | −0.490407 | + | 0.490407i | ||||
\(448\) | 55793.9 | + | 14949.9i | 0.277991 | + | 0.0744874i | ||||
\(449\) | 67319.2 | − | 251239.i | 0.333923 | − | 1.24622i | −0.571109 | − | 0.820874i | \(-0.693487\pi\) |
0.905032 | − | 0.425343i | \(-0.139847\pi\) | |||||||
\(450\) | 15994.9 | + | 15994.9i | 0.0789870 | + | 0.0789870i | ||||
\(451\) | −84605.1 | − | 146540.i | −0.415952 | − | 0.720450i | ||||
\(452\) | −86496.6 | − | 49938.8i | −0.423372 | − | 0.244434i | ||||
\(453\) | −204146. | + | 54700.7i | −0.994819 | + | 0.266561i | ||||
\(454\) | 5750.75i | 0.0279005i | ||||||||
\(455\) | −135858. | − | 31836.5i | −0.656241 | − | 0.153781i | ||||
\(456\) | 32412.1 | 0.155875 | ||||||||
\(457\) | 42203.5 | + | 157506.i | 0.202077 | + | 0.754161i | 0.990321 | + | 0.138798i | \(0.0443238\pi\) |
−0.788244 | + | 0.615363i | \(0.789009\pi\) | |||||||
\(458\) | −4921.19 | + | 8523.74i | −0.0234606 | + | 0.0406349i | ||||
\(459\) | −134012. | + | 77371.7i | −0.636088 | + | 0.367246i | ||||
\(460\) | 127867. | − | 127867.i | 0.604286 | − | 0.604286i | ||||
\(461\) | −118521. | − | 31757.7i | −0.557693 | − | 0.149433i | −0.0310467 | − | 0.999518i | \(-0.509884\pi\) |
−0.526646 | + | 0.850085i | \(0.676551\pi\) | |||||||
\(462\) | −7691.08 | + | 28703.5i | −0.0360332 | + | 0.134478i | ||||
\(463\) | 93433.1 | + | 93433.1i | 0.435852 | + | 0.435852i | 0.890613 | − | 0.454762i | \(-0.150276\pi\) |
−0.454762 | + | 0.890613i | \(0.650276\pi\) | |||||||
\(464\) | −61187.6 | − | 105980.i | −0.284202 | − | 0.492253i | ||||
\(465\) | 132807. | + | 76675.9i | 0.614206 | + | 0.354612i | ||||
\(466\) | 80996.8 | − | 21703.0i | 0.372989 | − | 0.0999421i | ||||
\(467\) | − | 40338.7i | − | 0.184964i | −0.995714 | − | 0.0924821i | \(-0.970520\pi\) | ||
0.995714 | − | 0.0924821i | \(-0.0294801\pi\) | |||||||
\(468\) | 83749.0 | − | 25303.7i | 0.382374 | − | 0.115529i | ||||
\(469\) | 167321. | 0.760685 | ||||||||
\(470\) | −8146.82 | − | 30404.3i | −0.0368801 | − | 0.137638i | ||||
\(471\) | 116327. | − | 201483.i | 0.524369 | − | 0.908234i | ||||
\(472\) | −32266.9 | + | 18629.3i | −0.144835 | + | 0.0836205i | ||||
\(473\) | 35584.1 | − | 35584.1i | 0.159050 | − | 0.159050i | ||||
\(474\) | 75235.6 | + | 20159.3i | 0.334863 | + | 0.0897262i | ||||
\(475\) | 11487.2 | − | 42870.8i | 0.0509128 | − | 0.190009i | ||||
\(476\) | −106484. | − | 106484.i | −0.469969 | − | 0.469969i | ||||
\(477\) | 72713.5 | + | 125943.i | 0.319579 | + | 0.553527i | ||||
\(478\) | 43300.1 | + | 24999.3i | 0.189511 | + | 0.109414i | ||||
\(479\) | 100333. | − | 26884.1i | 0.437292 | − | 0.117172i | −0.0334553 | − | 0.999440i | \(-0.510651\pi\) |
0.470747 | + | 0.882268i | \(0.343984\pi\) | |||||||
\(480\) | − | 92747.9i | − | 0.402552i | ||||||
\(481\) | −99341.1 | + | 185360.i | −0.429377 | + | 0.801171i | ||||
\(482\) | −12585.1 | −0.0541703 | ||||||||
\(483\) | −82836.7 | − | 309151.i | −0.355082 | − | 1.32518i | ||||
\(484\) | −80251.2 | + | 138999.i | −0.342579 | + | 0.593364i | ||||
\(485\) | 102215. | − | 59013.9i | 0.434541 | − | 0.250883i | ||||
\(486\) | 52349.4 | − | 52349.4i | 0.221635 | − | 0.221635i | ||||
\(487\) | 335714. | + | 89954.3i | 1.41550 | + | 0.379283i | 0.883887 | − | 0.467701i | \(-0.154918\pi\) |
0.531618 | + | 0.846984i | \(0.321584\pi\) | |||||||
\(488\) | 31895.0 | − | 119034.i | 0.133932 | − | 0.499840i | ||||
\(489\) | 104503. | + | 104503.i | 0.437030 | + | 0.437030i | ||||
\(490\) | −7292.35 | − | 12630.7i | −0.0303721 | − | 0.0526061i | ||||
\(491\) | −177842. | − | 102677.i | −0.737685 | − | 0.425902i | 0.0835422 | − | 0.996504i | \(-0.473377\pi\) |
−0.821227 | + | 0.570602i | \(0.806710\pi\) | |||||||
\(492\) | 271497. | − | 72747.5i | 1.12159 | − | 0.300530i | ||||
\(493\) | 157914.i | 0.649721i | ||||||||
\(494\) | 20376.1 | + | 19126.8i | 0.0834964 | + | 0.0783768i | ||||
\(495\) | 30671.5 | 0.125177 | ||||||||
\(496\) | −61901.7 | − | 231020.i | −0.251617 | − | 0.939046i | ||||
\(497\) | −116785. | + | 202278.i | −0.472796 | + | 0.818907i | ||||
\(498\) | −35930.3 | + | 20744.4i | −0.144878 | + | 0.0836454i | ||||
\(499\) | −84685.9 | + | 84685.9i | −0.340102 | + | 0.340102i | −0.856406 | − | 0.516303i | \(-0.827308\pi\) |
0.516303 | + | 0.856406i | \(0.327308\pi\) | |||||||
\(500\) | −203911. | − | 54637.9i | −0.815645 | − | 0.218552i | ||||
\(501\) | 2567.92 | − | 9583.59i | 0.0102307 | − | 0.0381815i | ||||
\(502\) | 30866.1 | + | 30866.1i | 0.122482 | + | 0.122482i | ||||
\(503\) | −2971.77 | − | 5147.25i | −0.0117457 | − | 0.0203441i | 0.860093 | − | 0.510138i | \(-0.170406\pi\) |
−0.871839 | + | 0.489793i | \(0.837072\pi\) | |||||||
\(504\) | 80189.6 | + | 46297.5i | 0.315687 | + | 0.182262i | ||||
\(505\) | −114823. | + | 30766.7i | −0.450242 | + | 0.120642i | ||||
\(506\) | − | 71814.2i | − | 0.280485i | ||||||
\(507\) | −168523. | − | 83571.4i | −0.655608 | − | 0.325119i | ||||
\(508\) | 52314.8 | 0.202720 | ||||||||
\(509\) | −18497.0 | − | 69031.7i | −0.0713946 | − | 0.266448i | 0.920997 | − | 0.389570i | \(-0.127376\pi\) |
−0.992392 | + | 0.123121i | \(0.960710\pi\) | |||||||
\(510\) | −14587.7 | + | 25266.7i | −0.0560851 | + | 0.0971422i | ||||
\(511\) | 62190.9 | − | 35905.9i | 0.238169 | − | 0.137507i | ||||
\(512\) | −179633. | + | 179633.i | −0.685247 | + | 0.685247i | ||||
\(513\) | −83377.8 | − | 22341.0i | −0.316822 | − | 0.0848923i | ||||
\(514\) | 2538.38 | − | 9473.38i | 0.00960796 | − | 0.0358574i | ||||
\(515\) | −22877.8 | − | 22877.8i | −0.0862579 | − | 0.0862579i | ||||
\(516\) | 41796.1 | + | 72393.0i | 0.156977 | + | 0.271892i | ||||
\(517\) | 66496.7 | + | 38391.9i | 0.248782 | + | 0.143634i | ||||
\(518\) | −99405.1 | + | 26635.5i | −0.370467 | + | 0.0992662i | ||||
\(519\) | − | 28837.9i | − | 0.107060i | ||||||
\(520\) | 76984.1 | − | 82012.7i | 0.284705 | − | 0.303302i | ||||
\(521\) | −445916. | −1.64277 | −0.821386 | − | 0.570373i | \(-0.806799\pi\) | ||||
−0.821386 | + | 0.570373i | \(0.806799\pi\) | |||||||
\(522\) | −11619.5 | − | 43364.7i | −0.0426430 | − | 0.159146i | ||||
\(523\) | 14899.9 | − | 25807.4i | 0.0544729 | − | 0.0943499i | −0.837503 | − | 0.546433i | \(-0.815985\pi\) |
0.891976 | + | 0.452083i | \(0.149319\pi\) | |||||||
\(524\) | 62904.9 | − | 36318.1i | 0.229098 | − | 0.132270i | ||||
\(525\) | −103371. | + | 103371.i | −0.375043 | + | 0.375043i | ||||
\(526\) | 29021.7 | + | 7776.35i | 0.104894 | + | 0.0281063i | ||||
\(527\) | −79878.4 | + | 298110.i | −0.287613 | + | 1.07339i | ||||
\(528\) | 38999.0 | + | 38999.0i | 0.139890 | + | 0.139890i | ||||
\(529\) | 246816. | + | 427499.i | 0.881988 | + | 1.52765i | ||||
\(530\) | 74868.7 | + | 43225.4i | 0.266531 | + | 0.153882i | ||||
\(531\) | 30398.4 | − | 8145.23i | 0.107811 | − | 0.0288878i | ||||
\(532\) | − | 84002.7i | − | 0.296804i | ||||||
\(533\) | 461992. | + | 247599.i | 1.62622 | + | 0.871553i | ||||
\(534\) | −124467. | −0.436487 | ||||||||
\(535\) | −72360.7 | − | 270054.i | −0.252810 | − | 0.943501i | ||||
\(536\) | −67439.8 | + | 116809.i | −0.234740 | + | 0.406581i | ||||
\(537\) | 71047.0 | − | 41019.0i | 0.246375 | − | 0.142245i | ||||
\(538\) | −135205. | + | 135205.i | −0.467119 | + | 0.467119i | ||||
\(539\) | 34365.2 | + | 9208.14i | 0.118288 | + | 0.0316952i | ||||
\(540\) | −41576.3 | + | 155165.i | −0.142580 | + | 0.532116i | ||||
\(541\) | −382857. | − | 382857.i | −1.30810 | − | 1.30810i | −0.922782 | − | 0.385322i | \(-0.874090\pi\) |
−0.385322 | − | 0.922782i | \(-0.625910\pi\) | |||||||
\(542\) | −74828.0 | − | 129606.i | −0.254722 | − | 0.441191i | ||||
\(543\) | 131676. | + | 76023.3i | 0.446589 | + | 0.257838i | ||||
\(544\) | 180299. | − | 48310.8i | 0.609248 | − | 0.163248i | ||||
\(545\) | − | 62134.5i | − | 0.209190i | ||||||
\(546\) | −26623.3 | − | 88116.6i | −0.0893050 | − | 0.295578i | ||||
\(547\) | −83576.4 | −0.279325 | −0.139662 | − | 0.990199i | \(-0.544602\pi\) | ||||
−0.139662 | + | 0.990199i | \(0.544602\pi\) | |||||||
\(548\) | −4182.06 | − | 15607.7i | −0.0139261 | − | 0.0519728i | ||||
\(549\) | −52044.8 | + | 90144.2i | −0.172676 | + | 0.299084i | ||||
\(550\) | −28407.2 | + | 16400.9i | −0.0939082 | + | 0.0542179i | ||||
\(551\) | −62287.4 | + | 62287.4i | −0.205162 | + | 0.205162i | ||||
\(552\) | 249210. | + | 66775.7i | 0.817877 | + | 0.219150i | ||||
\(553\) | 113000. | − | 421722.i | 0.369512 | − | 1.37904i | ||||
\(554\) | −71252.9 | − | 71252.9i | −0.232158 | − | 0.232158i | ||||
\(555\) | −61234.3 | − | 106061.i | −0.198797 | − | 0.344326i | ||||
\(556\) | 145066. | + | 83754.0i | 0.469263 | + | 0.270929i | ||||
\(557\) | 461816. | − | 123743.i | 1.48853 | − | 0.398851i | 0.579291 | − | 0.815121i | \(-0.303329\pi\) |
0.909241 | + | 0.416270i | \(0.136663\pi\) | |||||||
\(558\) | − | 87741.6i | − | 0.281798i | ||||||
\(559\) | −35566.2 | + | 151774.i | −0.113819 | + | 0.485707i | ||||
\(560\) | −126734. | −0.404127 | ||||||||
\(561\) | −18420.1 | − | 68744.7i | −0.0585283 | − | 0.218431i | ||||
\(562\) | −10331.4 | + | 17894.5i | −0.0327105 | + | 0.0566562i | ||||
\(563\) | 102499. | − | 59178.1i | 0.323374 | − | 0.186700i | −0.329522 | − | 0.944148i | \(-0.606887\pi\) |
0.652895 | + | 0.757448i | \(0.273554\pi\) | |||||||
\(564\) | −90188.3 | + | 90188.3i | −0.283525 | + | 0.283525i | ||||
\(565\) | 104769. | + | 28072.9i | 0.328199 | + | 0.0879406i | ||||
\(566\) | 33961.4 | − | 126746.i | 0.106011 | − | 0.395640i | ||||
\(567\) | 81975.9 | + | 81975.9i | 0.254988 | + | 0.254988i | ||||
\(568\) | −94141.9 | − | 163059.i | −0.291801 | − | 0.505414i | ||||
\(569\) | 28871.9 | + | 16669.2i | 0.0891766 | + | 0.0514861i | 0.543925 | − | 0.839134i | \(-0.316938\pi\) |
−0.454749 | + | 0.890620i | \(0.650271\pi\) | |||||||
\(570\) | −15720.1 | + | 4212.20i | −0.0483845 | + | 0.0129646i | ||||
\(571\) | − | 534672.i | − | 1.63989i | −0.572440 | − | 0.819947i | \(-0.694003\pi\) | ||
0.572440 | − | 0.819947i | \(-0.305997\pi\) | |||||||
\(572\) | 4010.47 | + | 126805.i | 0.0122575 | + | 0.387563i | ||||
\(573\) | −400627. | −1.22020 | ||||||||
\(574\) | 66386.5 | + | 247758.i | 0.201491 | + | 0.751976i | ||||
\(575\) | 176646. | − | 305960.i | 0.534279 | − | 0.925398i | ||||
\(576\) | 34060.4 | − | 19664.8i | 0.102661 | − | 0.0592713i | ||||
\(577\) | 201296. | − | 201296.i | 0.604622 | − | 0.604622i | −0.336914 | − | 0.941535i | \(-0.609383\pi\) |
0.941535 | + | 0.336914i | \(0.109383\pi\) | |||||||
\(578\) | 64030.9 | + | 17157.0i | 0.191661 | + | 0.0513555i | ||||
\(579\) | −17368.2 | + | 64819.0i | −0.0518081 | + | 0.193350i | ||||
\(580\) | 115916. | + | 115916.i | 0.344578 | + | 0.344578i | ||||
\(581\) | 116280. | + | 201402.i | 0.344470 | + | 0.596639i | ||||
\(582\) | 67429.0 | + | 38930.2i | 0.199068 | + | 0.114932i | ||||
\(583\) | −203700. | + | 54581.3i | −0.599313 | + | 0.160586i | ||||
\(584\) | 57888.5i | 0.169733i | ||||||||
\(585\) | −80738.6 | + | 50082.5i | −0.235923 | + | 0.146344i | ||||
\(586\) | −98393.6 | −0.286531 | ||||||||
\(587\) | −100815. | − | 376246.i | −0.292582 | − | 1.09193i | −0.943119 | − | 0.332457i | \(-0.892122\pi\) |
0.650536 | − | 0.759475i | \(-0.274544\pi\) | |||||||
\(588\) | −29548.9 | + | 51180.2i | −0.0854646 | + | 0.148029i | ||||
\(589\) | −149094. | + | 86079.2i | −0.429762 | + | 0.248123i | ||||
\(590\) | 13228.7 | − | 13228.7i | 0.0380026 | − | 0.0380026i | ||||
\(591\) | 361925. | + | 96977.6i | 1.03620 | + | 0.277649i | ||||
\(592\) | −49435.4 | + | 184495.i | −0.141057 | + | 0.526432i | ||||
\(593\) | 29431.4 | + | 29431.4i | 0.0836955 | + | 0.0836955i | 0.747715 | − | 0.664020i | \(-0.231151\pi\) |
−0.664020 | + | 0.747715i | \(0.731151\pi\) | |||||||
\(594\) | 31897.5 | + | 55248.1i | 0.0904032 | + | 0.156583i | ||||
\(595\) | 141629. | + | 81769.3i | 0.400053 | + | 0.230971i | ||||
\(596\) | −279648. | + | 74931.6i | −0.787263 | + | 0.210947i | ||||
\(597\) | 236318.i | 0.663052i | ||||||||
\(598\) | 117263. | + | 189041.i | 0.327913 | + | 0.528632i | ||||
\(599\) | 109234. | 0.304442 | 0.152221 | − | 0.988346i | \(-0.451357\pi\) | ||||
0.152221 | + | 0.988346i | \(0.451357\pi\) | |||||||
\(600\) | −30500.5 | − | 113829.i | −0.0847236 | − | 0.316193i | ||||
\(601\) | −311032. | + | 538723.i | −0.861104 | + | 1.49148i | 0.00975940 | + | 0.999952i | \(0.496893\pi\) |
−0.870864 | + | 0.491524i | \(0.836440\pi\) | |||||||
\(602\) | −66063.0 | + | 38141.5i | −0.182291 | + | 0.105246i | ||||
\(603\) | 80558.6 | − | 80558.6i | 0.221553 | − | 0.221553i | ||||
\(604\) | −426504. | − | 114281.i | −1.16909 | − | 0.313257i | ||||
\(605\) | 45112.8 | − | 168363.i | 0.123251 | − | 0.459977i | ||||
\(606\) | −55450.1 | − | 55450.1i | −0.150993 | − | 0.150993i | ||||
\(607\) | −125630. | − | 217598.i | −0.340971 | − | 0.590579i | 0.643642 | − | 0.765327i | \(-0.277423\pi\) |
−0.984613 | + | 0.174747i | \(0.944089\pi\) | |||||||
\(608\) | 90172.4 | + | 52061.1i | 0.243931 | + | 0.140834i | ||||
\(609\) | 280256. | − | 75094.4i | 0.755650 | − | 0.202476i | ||||
\(610\) | 61877.4i | 0.166292i | ||||||||
\(611\) | −237732. | + | 7518.80i | −0.636804 | + | 0.0201403i | ||||
\(612\) | −102536. | −0.273761 | ||||||||
\(613\) | −74439.2 | − | 277811.i | −0.198098 | − | 0.739313i | −0.991443 | − | 0.130540i | \(-0.958329\pi\) |
0.793345 | − | 0.608773i | \(-0.208338\pi\) | |||||||
\(614\) | 25868.0 | − | 44804.8i | 0.0686162 | − | 0.118847i | ||||
\(615\) | −264347. | + | 152621.i | −0.698915 | + | 0.403519i | ||||
\(616\) | −94945.7 | + | 94945.7i | −0.250215 | + | 0.250215i | ||||
\(617\) | −24959.6 | − | 6687.91i | −0.0655643 | − | 0.0175679i | 0.225888 | − | 0.974153i | \(-0.427472\pi\) |
−0.291452 | + | 0.956585i | \(0.594138\pi\) | |||||||
\(618\) | 5524.04 | − | 20616.0i | 0.0144637 | − | 0.0539793i | ||||
\(619\) | 236220. | + | 236220.i | 0.616502 | + | 0.616502i | 0.944632 | − | 0.328130i | \(-0.106419\pi\) |
−0.328130 | + | 0.944632i | \(0.606419\pi\) | |||||||
\(620\) | 160192. | + | 277461.i | 0.416733 | + | 0.721803i | ||||
\(621\) | −595049. | − | 343552.i | −1.54301 | − | 0.890859i | ||||
\(622\) | 118619. | − | 31783.9i | 0.306602 | − | 0.0821537i | ||||
\(623\) | 697680.i | 1.79755i | ||||||||
\(624\) | −166340. | − | 38979.4i | −0.427195 | − | 0.100107i | ||||
\(625\) | −21812.3 | −0.0558394 | ||||||||
\(626\) | 28523.9 | + | 106453.i | 0.0727882 | + | 0.271649i | ||||
\(627\) | 19850.0 | − | 34381.2i | 0.0504923 | − | 0.0874552i | ||||
\(628\) | 420941. | − | 243031.i | 1.06734 | − | 0.616229i | ||||
\(629\) | 174283. | − | 174283.i | 0.440507 | − | 0.440507i | ||||
\(630\) | −44909.3 | − | 12033.4i | −0.113150 | − | 0.0303185i | ||||
\(631\) | −34896.2 | + | 130234.i | −0.0876434 | + | 0.327090i | −0.995802 | − | 0.0915374i | \(-0.970822\pi\) |
0.908158 | + | 0.418627i | \(0.137489\pi\) | |||||||
\(632\) | 248865. | + | 248865.i | 0.623060 | + | 0.623060i | ||||
\(633\) | −94476.0 | − | 163637.i | −0.235784 | − | 0.408390i | ||||
\(634\) | −162366. | − | 93741.8i | −0.403939 | − | 0.233214i | ||||
\(635\) | −54877.0 | + | 14704.2i | −0.136095 | + | 0.0364666i | ||||
\(636\) | − | 350302.i | − | 0.866021i | ||||||
\(637\) | −105497. | + | 31874.7i | −0.259994 | + | 0.0785537i | ||||
\(638\) | 65102.2 | 0.159939 | ||||||||
\(639\) | 41161.4 | + | 153616.i | 0.100806 | + | 0.376215i | ||||
\(640\) | 124348. | − | 215377.i | 0.303584 | − | 0.525823i | ||||
\(641\) | 273381. | − | 157836.i | 0.665352 | − | 0.384141i | −0.128961 | − | 0.991650i | \(-0.541164\pi\) |
0.794313 | + | 0.607508i | \(0.207831\pi\) | |||||||
\(642\) | 130414. | − | 130414.i | 0.316413 | − | 0.316413i | ||||
\(643\) | −234488. | − | 62830.7i | −0.567150 | − | 0.151967i | −0.0361607 | − | 0.999346i | \(-0.511513\pi\) |
−0.530989 | + | 0.847379i | \(0.678180\pi\) | |||||||
\(644\) | 173063. | − | 645881.i | 0.417285 | − | 1.55733i | ||||
\(645\) | −64190.8 | − | 64190.8i | −0.154296 | − | 0.154296i | ||||
\(646\) | −16376.7 | − | 28365.3i | −0.0392429 | − | 0.0679708i | ||||
\(647\) | 170861. | + | 98646.7i | 0.408164 | + | 0.235653i | 0.690000 | − | 0.723809i | \(-0.257610\pi\) |
−0.281837 | + | 0.959462i | \(0.590944\pi\) | |||||||
\(648\) | −90269.5 | + | 24187.6i | −0.214977 | + | 0.0576028i | ||||
\(649\) | 45636.2i | 0.108348i | ||||||||
\(650\) | 47997.7 | − | 89558.4i | 0.113604 | − | 0.211973i | ||||
\(651\) | 567054. | 1.33802 | ||||||||
\(652\) | 79913.9 | + | 298243.i | 0.187987 | + | 0.701576i | ||||
\(653\) | −69052.8 | + | 119603.i | −0.161940 | + | 0.280489i | −0.935565 | − | 0.353156i | \(-0.885109\pi\) |
0.773624 | + | 0.633645i | \(0.218442\pi\) | |||||||
\(654\) | 35497.4 | − | 20494.4i | 0.0829928 | − | 0.0479159i | ||||
\(655\) | −55777.7 | + | 55777.7i | −0.130010 | + | 0.130010i | ||||
\(656\) | 459838. | + | 123213.i | 1.06856 | + | 0.286319i | ||||
\(657\) | 12655.2 | − | 47229.8i | 0.0293182 | − | 0.109417i | ||||
\(658\) | −82302.3 | − | 82302.3i | −0.190090 | − | 0.190090i | ||||
\(659\) | −75236.5 | − | 130313.i | −0.173244 | − | 0.300067i | 0.766308 | − | 0.642473i | \(-0.222092\pi\) |
−0.939552 | + | 0.342406i | \(0.888758\pi\) | |||||||
\(660\) | −63982.9 | − | 36940.6i | −0.146885 | − | 0.0848038i | ||||
\(661\) | 401796. | − | 107661.i | 0.919608 | − | 0.246408i | 0.232190 | − | 0.972670i | \(-0.425411\pi\) |
0.687418 | + | 0.726262i | \(0.258744\pi\) | |||||||
\(662\) | − | 214733.i | − | 0.489985i | ||||||
\(663\) | 160739. | + | 150884.i | 0.365675 | + | 0.343253i | ||||
\(664\) | −187469. | −0.425200 | ||||||||
\(665\) | 23610.8 | + | 88116.9i | 0.0533910 | + | 0.199258i | ||||
\(666\) | −35035.8 | + | 60683.7i | −0.0789883 | + | 0.136812i | ||||
\(667\) | −607241. | + | 350591.i | −1.36493 | + | 0.788041i | ||||
\(668\) | 14657.2 | − | 14657.2i | 0.0328472 | − | 0.0328472i | ||||
\(669\) | −460770. | − | 123463.i | −1.02951 | − | 0.275857i | ||||
\(670\) | 17528.6 | − | 65417.7i | 0.0390480 | − | 0.145729i | ||||
\(671\) | −106732. | − | 106732.i | −0.237055 | − | 0.237055i | ||||
\(672\) | −171478. | − | 297009.i | −0.379726 | − | 0.657706i | ||||
\(673\) | 16660.0 | + | 9618.68i | 0.0367829 | + | 0.0212366i | 0.518279 | − | 0.855212i | \(-0.326573\pi\) |
−0.481496 | + | 0.876448i | \(0.659906\pi\) | |||||||
\(674\) | −238763. | + | 63976.4i | −0.525590 | + | 0.140831i | ||||
\(675\) | 313841.i | 0.688815i | ||||||||
\(676\) | −217612. | − | 327247.i | −0.476200 | − | 0.716114i | ||||
\(677\) | 600314. | 1.30979 | 0.654895 | − | 0.755720i | \(-0.272713\pi\) | ||||
0.654895 | + | 0.755720i | \(0.272713\pi\) | |||||||
\(678\) | 18519.1 | + | 69114.1i | 0.0402865 | + | 0.150351i | ||||
\(679\) | 218217. | − | 377964.i | 0.473315 | − | 0.819805i | ||||
\(680\) | −114169. | + | 65915.4i | −0.246905 | + | 0.142551i | ||||
\(681\) | −17893.9 | + | 17893.9i | −0.0385843 | + | 0.0385843i | ||||
\(682\) | 122900. | + | 32931.0i | 0.264231 | + | 0.0708004i | ||||
\(683\) | −179215. | + | 668838.i | −0.384178 | + | 1.43377i | 0.455282 | + | 0.890348i | \(0.349539\pi\) |
−0.839459 | + | 0.543423i | \(0.817128\pi\) | |||||||
\(684\) | −40444.1 | − | 40444.1i | −0.0864456 | − | 0.0864456i | ||||
\(685\) | 8773.76 | + | 15196.6i | 0.0186984 | + | 0.0323866i | ||||
\(686\) | 125256. | + | 72316.8i | 0.266166 | + | 0.153671i | ||||
\(687\) | −41834.9 | + | 11209.6i | −0.0886391 | + | 0.0237508i | ||||
\(688\) | 141581.i | 0.299108i | ||||||||
\(689\) | 447089. | − | 476293.i | 0.941793 | − | 1.00331i | ||||
\(690\) | −129547. | −0.272101 | ||||||||
\(691\) | 219977. | + | 820967.i | 0.460704 | + | 1.71937i | 0.670753 | + | 0.741681i | \(0.265971\pi\) |
−0.210049 | + | 0.977691i | \(0.567362\pi\) | |||||||
\(692\) | 30124.2 | − | 52176.7i | 0.0629077 | − | 0.108959i | ||||
\(693\) | 98220.3 | − | 56707.5i | 0.204520 | − | 0.118079i | ||||
\(694\) | −58837.9 | + | 58837.9i | −0.122163 | + | 0.122163i | ||||
\(695\) | −175712. | − | 47081.9i | −0.363774 | − | 0.0974730i | ||||
\(696\) | −60534.6 | + | 225918.i | −0.124964 | + | 0.466372i | ||||
\(697\) | −434383. | − | 434383.i | −0.894144 | − | 0.894144i | ||||
\(698\) | 130318. | + | 225717.i | 0.267481 | + | 0.463291i | ||||
\(699\) | 319558. | + | 184497.i | 0.654027 | + | 0.377603i | ||||
\(700\) | −295013. | + | 79048.4i | −0.602066 | + | 0.161323i | ||||
\(701\) | − | 318525.i | − | 0.648198i | −0.946023 | − | 0.324099i | \(-0.894939\pi\) | ||
0.946023 | − | 0.324099i | \(-0.105061\pi\) | |||||||
\(702\) | −174179. | − | 93348.8i | −0.353444 | − | 0.189424i | ||||
\(703\) | 137488. | 0.278198 | ||||||||
\(704\) | 14761.1 | + | 55089.1i | 0.0297833 | + | 0.111153i | ||||
\(705\) | 69255.9 | − | 119955.i | 0.139341 | − | 0.241346i | ||||
\(706\) | 217307. | − | 125462.i | 0.435977 | − | 0.251712i | ||||
\(707\) | −310818. | + | 310818.i | −0.621823 | + | 0.621823i | ||||
\(708\) | −73223.2 | − | 19620.1i | −0.146077 | − | 0.0391413i | ||||
\(709\) | −81416.6 | + | 303851.i | −0.161965 | + | 0.604461i | 0.836443 | + | 0.548054i | \(0.184631\pi\) |
−0.998408 | + | 0.0564071i | \(0.982036\pi\) | |||||||
\(710\) | 66850.3 | + | 66850.3i | 0.132613 | + | 0.132613i | ||||
\(711\) | −148638. | − | 257448.i | −0.294029 | − | 0.509273i | ||||
\(712\) | −487061. | − | 281205.i | −0.960778 | − | 0.554706i | ||||
\(713\) | −1.32369e6 | + | 354683.i | −2.60380 | + | 0.697687i | ||||
\(714\) | 107883.i | 0.211620i | ||||||||
\(715\) | −39848.1 | − | 131888.i | −0.0779464 | − | 0.257984i | ||||
\(716\) | 171395. | 0.334327 | ||||||||
\(717\) | 56944.3 | + | 212519.i | 0.110767 | + | 0.413389i | ||||
\(718\) | 118928. | − | 205989.i | 0.230693 | − | 0.399572i | ||||
\(719\) | −341956. | + | 197428.i | −0.661473 | + | 0.381902i | −0.792838 | − | 0.609433i | \(-0.791397\pi\) |
0.131365 | + | 0.991334i | \(0.458064\pi\) | |||||||
\(720\) | −61017.6 | + | 61017.6i | −0.117704 | + | 0.117704i | ||||
\(721\) | −115560. | − | 30964.2i | −0.222299 | − | 0.0595648i | ||||
\(722\) | −45754.5 | + | 170758.i | −0.0877727 | + | 0.327572i | ||||
\(723\) | −39159.4 | − | 39159.4i | −0.0749134 | − | 0.0749134i | ||||
\(724\) | 158829. | + | 275099.i | 0.303007 | + | 0.524823i | ||||
\(725\) | 277363. | + | 160136.i | 0.527683 | + | 0.304658i | ||||
\(726\) | 111066. | − | 29759.9i | 0.210720 | − | 0.0564623i | ||||
\(727\) | 77095.4i | 0.145868i | 0.997337 | + | 0.0729339i | \(0.0232362\pi\) | ||||
−0.997337 | + | 0.0729339i | \(0.976764\pi\) | |||||||
\(728\) | 94898.0 | − | 404965.i | 0.179058 | − | 0.764108i | ||||
\(729\) | 495726. | 0.932795 | ||||||||
\(730\) | −7523.04 | − | 28076.4i | −0.0141172 | − | 0.0526860i | ||||
\(731\) | 91348.7 | − | 158221.i | 0.170949 | − | 0.296093i | ||||
\(732\) | 217138. | − | 125365.i | 0.405241 | − | 0.233966i | ||||
\(733\) | 549893. | − | 549893.i | 1.02346 | − | 1.02346i | 0.0237405 | − | 0.999718i | \(-0.492442\pi\) |
0.999718 | − | 0.0237405i | \(-0.00755755\pi\) | |||||||
\(734\) | −104791. | − | 28078.6i | −0.194505 | − | 0.0521175i | ||||
\(735\) | 16610.7 | − | 61992.1i | 0.0307478 | − | 0.114752i | ||||
\(736\) | 586062. | + | 586062.i | 1.08190 | + | 1.08190i | ||||
\(737\) | 82603.7 | + | 143074.i | 0.152077 | + | 0.263406i | ||||
\(738\) | 151248. | + | 87323.4i | 0.277702 | + | 0.160331i | ||||
\(739\) | 638068. | − | 170970.i | 1.16836 | − | 0.313062i | 0.378062 | − | 0.925780i | \(-0.376591\pi\) |
0.790301 | + | 0.612718i | \(0.209924\pi\) | |||||||
\(740\) | − | 255863.i | − | 0.467244i | ||||||
\(741\) | 3887.49 | + | 122916.i | 0.00708000 | + | 0.223858i | ||||
\(742\) | 319672. | 0.580627 | ||||||||
\(743\) | −182602. | − | 681479.i | −0.330771 | − | 1.23445i | −0.908382 | − | 0.418142i | \(-0.862681\pi\) |
0.577611 | − | 0.816312i | \(-0.303985\pi\) | |||||||
\(744\) | −228555. | + | 395869.i | −0.412900 | + | 0.715163i | ||||
\(745\) | 272283. | − | 157203.i | 0.490579 | − | 0.283236i | ||||
\(746\) | 41885.5 | − | 41885.5i | 0.0752639 | − | 0.0752639i | ||||
\(747\) | 152952. | + | 40983.2i | 0.274102 | + | 0.0734455i | ||||
\(748\) | 38483.4 | − | 143622.i | 0.0687814 | − | 0.256696i | ||||
\(749\) | −731016. | − | 731016.i | −1.30306 | − | 1.30306i | ||||
\(750\) | 75617.5 | + | 130973.i | 0.134431 | + | 0.232841i | ||||
\(751\) | −343285. | − | 198196.i | −0.608660 | − | 0.351410i | 0.163781 | − | 0.986497i | \(-0.447631\pi\) |
−0.772441 | + | 0.635087i | \(0.780964\pi\) | |||||||
\(752\) | −208664. | + | 55911.4i | −0.368988 | + | 0.0988701i | ||||
\(753\) | 192084.i | 0.338767i | ||||||||
\(754\) | −171373. | + | 106303.i | −0.301438 | + | 0.186983i | ||||
\(755\) | 479514. | 0.841215 | ||||||||
\(756\) | 153738. | + | 573758.i | 0.268991 | + | 1.00389i | ||||
\(757\) | 310425. | − | 537672.i | 0.541708 | − | 0.938266i | −0.457098 | − | 0.889416i | \(-0.651111\pi\) |
0.998806 | − | 0.0488493i | \(-0.0155554\pi\) | |||||||
\(758\) | 18210.1 | − | 10513.6i | 0.0316938 | − | 0.0182984i | ||||
\(759\) | 223455. | − | 223455.i | 0.387889 | − | 0.387889i | ||||
\(760\) | −71032.2 | − | 19033.0i | −0.122978 | − | 0.0329519i | ||||
\(761\) | −87290.5 | + | 325773.i | −0.150729 | + | 0.562529i | 0.848704 | + | 0.528868i | \(0.177383\pi\) |
−0.999433 | + | 0.0336612i | \(0.989283\pi\) | |||||||
\(762\) | −26501.1 | − | 26501.1i | −0.0456408 | − | 0.0456408i | ||||
\(763\) | −114878. | − | 198975.i | −0.197328 | − | 0.341783i | ||||
\(764\) | −724858. | − | 418497.i | −1.24184 | − | 0.716978i | ||||
\(765\) | 107558. | − | 28820.0i | 0.183788 | − | 0.0492459i | ||||
\(766\) | 64213.8i | 0.109439i | ||||||||
\(767\) | −74517.8 | − | 120131.i | −0.126669 | − | 0.204204i | ||||
\(768\) | 53899.6 | 0.0913825 | ||||||||
\(769\) | 70356.3 | + | 262573.i | 0.118973 | + | 0.444015i | 0.999553 | − | 0.0298827i | \(-0.00951336\pi\) |
−0.880580 | + | 0.473898i | \(0.842847\pi\) | |||||||
\(770\) | 33710.5 | − | 58388.3i | 0.0568570 | − | 0.0984792i | ||||
\(771\) | 37375.5 | − | 21578.8i | 0.0628750 | − | 0.0363009i | ||||
\(772\) | −99134.7 | + | 99134.7i | −0.166338 | + | 0.166338i | ||||
\(773\) | −711148. | − | 190552.i | −1.19015 | − | 0.318899i | −0.391204 | − | 0.920304i | \(-0.627941\pi\) |
−0.798944 | + | 0.601405i | \(0.794608\pi\) | |||||||
\(774\) | −13443.1 | + | 50170.5i | −0.0224398 | + | 0.0837464i | ||||
\(775\) | 442605. | + | 442605.i | 0.736908 | + | 0.736908i | ||||
\(776\) | 175908. | + | 304681.i | 0.292120 | + | 0.505967i | ||||
\(777\) | −392185. | − | 226428.i | −0.649604 | − | 0.375049i | ||||
\(778\) | −295989. | + | 79310.0i | −0.489008 | + | 0.131029i | ||||
\(779\) | − | 342675.i | − | 0.564687i | ||||||
\(780\) | 228745. | − | 7234.57i | 0.375978 | − | 0.0118911i | ||||
\(781\) | −230620. | −0.378089 | ||||||||
\(782\) | −67478.9 | − | 251835.i | −0.110346 | − | 0.411815i | ||||
\(783\) | 311442. | − | 539433.i | 0.507988 | − | 0.879861i | ||||
\(784\) | −86684.4 | + | 50047.2i | −0.141029 | + | 0.0814232i | ||||
\(785\) | −373248. | + | 373248.i | −0.605702 | + | 0.605702i | ||||
\(786\) | −50263.4 | − | 13468.0i | −0.0813592 | − | 0.0218001i | ||||
\(787\) | −75848.9 | + | 283072.i | −0.122462 | + | 0.457033i | −0.999736 | − | 0.0229554i | \(-0.992692\pi\) |
0.877275 | + | 0.479988i | \(0.159359\pi\) | |||||||
\(788\) | 553532. | + | 553532.i | 0.891436 | + | 0.891436i | ||||
\(789\) | 66106.6 | + | 114500.i | 0.106192 | + | 0.183929i | ||||
\(790\) | −153043. | − | 88359.6i | −0.245223 | − | 0.141579i | ||||
\(791\) | 387409. | − | 103806.i | 0.619179 | − | 0.165909i | ||||
\(792\) | 91425.4i | 0.145753i | ||||||||
\(793\) | 455237. | + | 106678.i | 0.723921 | + | 0.169641i | ||||
\(794\) | 113173. | 0.179516 | ||||||||
\(795\) | 98460.3 | + | 367459.i | 0.155785 | + | 0.581399i | ||||
\(796\) | −246859. | + | 427572.i | −0.389603 | + | 0.674813i | ||||
\(797\) | −882413. | + | 509462.i | −1.38917 | + | 0.802038i | −0.993222 | − | 0.116235i | \(-0.962917\pi\) |
−0.395948 | + | 0.918273i | \(0.629584\pi\) | |||||||
\(798\) | −42553.2 | + | 42553.2i | −0.0668231 | + | 0.0668231i | ||||
\(799\) | 269262. | + | 72148.6i | 0.421776 | + | 0.113014i | ||||
\(800\) | 97981.2 | − | 365671.i | 0.153096 | − | 0.571361i | ||||
\(801\) | 335906. | + | 335906.i | 0.523544 | + | 0.523544i | ||||
\(802\) | −162895. | − | 282143.i | −0.253256 | − | 0.438652i | ||||
\(803\) | 61405.3 | + | 35452.4i | 0.0952302 | + | 0.0549812i | ||||
\(804\) | −265075. | + | 71026.6i | −0.410069 | + | 0.109878i | ||||
\(805\) | 726157.i | 1.12057i | ||||||||
\(806\) | −377289. | + | 113993.i | −0.580771 | + | 0.175472i | ||||
\(807\) | −841400. | −1.29198 | ||||||||
\(808\) | −91709.2 | − | 342263.i | −0.140472 | − | 0.524249i | ||||
\(809\) | −201736. | + | 349418.i | −0.308239 | + | 0.533885i | −0.977977 | − | 0.208712i | \(-0.933073\pi\) |
0.669738 | + | 0.742597i | \(0.266406\pi\) | |||||||
\(810\) | 40638.1 | − | 23462.4i | 0.0619389 | − | 0.0357604i | ||||
\(811\) | 514105. | − | 514105.i | 0.781646 | − | 0.781646i | −0.198463 | − | 0.980108i | \(-0.563595\pi\) |
0.980108 | + | 0.198463i | \(0.0635949\pi\) | |||||||
\(812\) | 585514. | + | 156888.i | 0.888026 | + | 0.237946i | ||||
\(813\) | 170446. | − | 636112.i | 0.257872 | − | 0.962393i | ||||
\(814\) | −71850.4 | − | 71850.4i | −0.108438 | − | 0.108438i | ||||
\(815\) | −167656. | − | 290388.i | −0.252408 | − | 0.437183i | ||||
\(816\) | 173405. | + | 100115.i | 0.260424 | + | 0.150356i | ||||
\(817\) | 98439.8 | − | 26376.9i | 0.147478 | − | 0.0395166i | ||||
\(818\) | 341735.i | 0.510720i | ||||||||
\(819\) | −165956. | + | 309655.i | −0.247414 | + | 0.461648i | ||||
\(820\) | −637714. | −0.948415 | ||||||||
\(821\) | 141194. | + | 526943.i | 0.209474 | + | 0.781767i | 0.988039 | + | 0.154203i | \(0.0492810\pi\) |
−0.778565 | + | 0.627563i | \(0.784052\pi\) | |||||||
\(822\) | −5787.86 | + | 10024.9i | −0.00856593 | + | 0.0148366i | ||||
\(823\) | −364137. | + | 210235.i | −0.537608 | + | 0.310388i | −0.744109 | − | 0.668058i | \(-0.767126\pi\) |
0.206501 | + | 0.978446i | \(0.433792\pi\) | |||||||
\(824\) | 68193.8 | − | 68193.8i | 0.100436 | − | 0.100436i | ||||
\(825\) | −139424. | − | 37358.5i | −0.204847 | − | 0.0548886i | ||||
\(826\) | 17904.5 | − | 66820.7i | 0.0262424 | − | 0.0979379i | ||||
\(827\) | −558727. | − | 558727.i | −0.816937 | − | 0.816937i | 0.168726 | − | 0.985663i | \(-0.446035\pi\) |
−0.985663 | + | 0.168726i | \(0.946035\pi\) | |||||||
\(828\) | −227644. | − | 394290.i | −0.332043 | − | 0.575116i | ||||
\(829\) | 550395. | + | 317771.i | 0.800877 | + | 0.462386i | 0.843778 | − | 0.536693i | \(-0.180327\pi\) |
−0.0429010 | + | 0.999079i | \(0.513660\pi\) | |||||||
\(830\) | 90924.0 | − | 24363.0i | 0.131984 | − | 0.0353651i | ||||
\(831\) | − | 443417.i | − | 0.642112i | ||||||
\(832\) | −128810. | − | 120912.i | −0.186081 | − | 0.174671i | ||||
\(833\) | 129163. | 0.186143 | ||||||||
\(834\) | −31058.9 | − | 115913.i | −0.0446534 | − | 0.166649i | ||||
\(835\) | −11255.3 | + | 19494.8i | −0.0161431 | + | 0.0279606i | ||||
\(836\) | 71829.6 | − | 41470.8i | 0.102776 | − | 0.0593376i | ||||
\(837\) | 860805. | − | 860805.i | 1.22872 | − | 1.22872i | ||||
\(838\) | −160358. | − | 42967.7i | −0.228350 | − | 0.0611863i | ||||
\(839\) | −85900.8 | + | 320586.i | −0.122032 | + | 0.455429i | −0.999717 | − | 0.0238094i | \(-0.992421\pi\) |
0.877685 | + | 0.479239i | \(0.159087\pi\) | |||||||
\(840\) | 171274. | + | 171274.i | 0.242736 | + | 0.242736i | ||||
\(841\) | 35817.3 | + | 62037.3i | 0.0506408 | + | 0.0877124i | ||||
\(842\) | −44049.9 | − | 25432.2i | −0.0621327 | − | 0.0358723i | ||||
\(843\) | −87827.2 | + | 23533.2i | −0.123587 | + | 0.0331151i | ||||
\(844\) | − | 394761.i | − | 0.554177i | ||||||
\(845\) | 320250. | + | 282110.i | 0.448513 | + | 0.395098i | ||||
\(846\) | −79250.8 | −0.110729 | ||||||||
\(847\) | −166815. | − | 622562.i | −0.232524 | − | 0.867792i | ||||
\(848\) | 296655. | − | 513822.i | 0.412535 | − | 0.714531i | ||||
\(849\) | 500052. | − | 288705.i | 0.693745 | − | 0.400534i | ||||
\(850\) | −84206.4 | + | 84206.4i | −0.116549 | + | 0.116549i | ||||
\(851\) | 1.05712e6 | + | 283254.i | 1.45970 | + | 0.391126i | ||||
\(852\) | 99148.9 | − | 370029.i | 0.136587 | − | 0.509749i | ||||
\(853\) | 359793. | + | 359793.i | 0.494487 | + | 0.494487i | 0.909717 | − | 0.415229i | \(-0.136299\pi\) |
−0.415229 | + | 0.909717i | \(0.636299\pi\) | |||||||
\(854\) | 114403. | + | 198152.i | 0.156863 | + | 0.271695i | ||||
\(855\) | 53792.6 | + | 31057.2i | 0.0735852 | + | 0.0424844i | ||||
\(856\) | 804973. | − | 215692.i | 1.09859 | − | 0.294365i | ||||
\(857\) | − | 870729.i | − | 1.18555i | −0.805367 | − | 0.592777i | \(-0.798032\pi\) | ||
0.805367 | − | 0.592777i | \(-0.201968\pi\) | |||||||
\(858\) | 62203.8 | − | 66266.9i | 0.0844972 | − | 0.0900165i | ||||
\(859\) | −955429. | −1.29483 | −0.647414 | − | 0.762139i | \(-0.724149\pi\) | ||||
−0.647414 | + | 0.762139i | \(0.724149\pi\) | |||||||
\(860\) | −49087.0 | − | 183195.i | −0.0663696 | − | 0.247695i | ||||
\(861\) | −564351. | + | 977484.i | −0.761277 | + | 1.31857i | ||||
\(862\) | 464703. | − | 268296.i | 0.625404 | − | 0.361077i | ||||
\(863\) | −997697. | + | 997697.i | −1.33961 | + | 1.33961i | −0.443166 | + | 0.896439i | \(0.646145\pi\) |
−0.896439 | + | 0.443166i | \(0.853855\pi\) | |||||||
\(864\) | −711179. | − | 190560.i | −0.952689 | − | 0.255272i | ||||
\(865\) | −16934.2 | + | 63199.2i | −0.0226325 | + | 0.0844655i | ||||
\(866\) | −144079. | − | 144079.i | −0.192116 | − | 0.192116i | ||||
\(867\) | 145852. | + | 252622.i | 0.194032 | + | 0.336073i | ||||
\(868\) | 1.02598e6 | + | 592348.i | 1.36175 | + | 0.786208i | ||||
\(869\) | 416395. | − | 111573.i | 0.551399 | − | 0.147747i | ||||
\(870\) | − | 117439.i | − | 0.155158i | ||||||
\(871\) | −451063. | − | 241742.i | −0.594568 | − | 0.318651i | ||||
\(872\) | 185210. | 0.243574 | ||||||||
\(873\) | −76911.7 | − | 287038.i | −0.100917 | − | 0.376627i | ||||
\(874\) | 72717.2 | − | 125950.i | 0.0951950 | − | 0.164883i | ||||
\(875\) | 734151. | − | 423862.i | 0.958892 | − | 0.553616i | ||||
\(876\) | −83282.9 | + | 83282.9i | −0.108529 | + | 0.108529i | ||||
\(877\) | −294738. | − | 78974.8i | −0.383210 | − | 0.102681i | 0.0620710 | − | 0.998072i | \(-0.480229\pi\) |
−0.445281 | + | 0.895391i | \(0.646896\pi\) | |||||||
\(878\) | −46019.3 | + | 171746.i | −0.0596968 | + | 0.222792i | ||||
\(879\) | −306159. | − | 306159.i | −0.396250 | − | 0.396250i | ||||
\(880\) | −62566.6 | − | 108369.i | −0.0807937 | − | 0.139939i | ||||
\(881\) | −68696.3 | − | 39661.8i | −0.0885078 | − | 0.0511000i | 0.455093 | − | 0.890444i | \(-0.349606\pi\) |
−0.543601 | + | 0.839344i | \(0.682939\pi\) | |||||||
\(882\) | −35469.4 | + | 9503.99i | −0.0455949 | + | 0.0122171i | ||||
\(883\) | 1.21909e6i | 1.56356i | 0.623554 | + | 0.781781i | \(0.285688\pi\) | ||||
−0.623554 | + | 0.781781i | \(0.714312\pi\) | |||||||
\(884\) | 133213. | + | 440904.i | 0.170468 | + | 0.564209i | ||||
\(885\) | 82324.1 | 0.105109 | ||||||||
\(886\) | 43386.6 | + | 161921.i | 0.0552699 | + | 0.206270i | ||||
\(887\) | −226185. | + | 391763.i | −0.287485 | + | 0.497939i | −0.973209 | − | 0.229923i | \(-0.926153\pi\) |
0.685724 | + | 0.727862i | \(0.259486\pi\) | |||||||
\(888\) | 316145. | − | 182527.i | 0.400923 | − | 0.231473i | ||||
\(889\) | −148548. | + | 148548.i | −0.187959 | + | 0.187959i | ||||
\(890\) | 272773. | + | 73089.3i | 0.344367 | + | 0.0922729i | ||||
\(891\) | −29626.3 | + | 110567.i | −0.0373183 | + | 0.139274i | ||||
\(892\) | −704706. | − | 704706.i | −0.885682 | − | 0.885682i | ||||
\(893\) | 77749.2 | + | 134666.i | 0.0974974 | + | 0.168871i | ||||
\(894\) | 179620. | + | 103703.i | 0.224739 | + | 0.129753i | ||||
\(895\) | −179789. | + | 48174.3i | −0.224449 | + | 0.0601408i | ||||
\(896\) | − | 919611.i | − | 1.14548i | ||||||
\(897\) | −223343. | + | 953088.i | −0.277580 | + | 1.18454i | ||||
\(898\) | −389296. | −0.482755 | ||||||||
\(899\) | −321532. | − | 1.19998e6i | −0.397837 | − | 1.48475i | ||||
\(900\) | −103978. | + | 180096.i | −0.128368 | + | 0.222341i | ||||
\(901\) | −663040. | + | 382806.i | −0.816752 | + | 0.471552i | ||||
\(902\) | −179080. | + | 179080.i | −0.220108 | + | 0.220108i | ||||
\(903\) | −324240. | − | 86879.9i | −0.397641 | − | 0.106548i | ||||
\(904\) | −83679.3 | + | 312295.i | −0.102396 | + | 0.382145i | ||||
\(905\) | −243930. | − | 243930.i | −0.297830 | − | 0.297830i | ||||
\(906\) | 158162. | + | 273945.i | 0.192685 | + | 0.333740i | ||||
\(907\) | 322283. | + | 186070.i | 0.391763 | + | 0.226184i | 0.682924 | − | 0.730490i | \(-0.260708\pi\) |
−0.291161 | + | 0.956674i | \(0.594041\pi\) | |||||||
\(908\) | −51067.6 | + | 13683.5i | −0.0619404 | + | 0.0165969i | ||||
\(909\) | 299293.i | 0.362217i | ||||||||
\(910\) | 6601.99 | + | 208744.i | 0.00797245 | + | 0.252076i | ||||
\(911\) | −106064. | −0.127800 | −0.0639001 | − | 0.997956i | \(-0.520354\pi\) | ||||
−0.0639001 | + | 0.997956i | \(0.520354\pi\) | |||||||
\(912\) | 28908.2 | + | 107887.i | 0.0347561 | + | 0.129712i | ||||
\(913\) | −114811. | + | 198858.i | −0.137734 | + | 0.238562i | ||||
\(914\) | 211359. | − | 122028.i | 0.253004 | − | 0.146072i | ||||
\(915\) | −192536. | + | 192536.i | −0.229969 | + | 0.229969i | ||||
\(916\) | −87402.0 | − | 23419.3i | −0.104167 | − | 0.0279115i | ||||
\(917\) | −75493.1 | + | 281744.i | −0.0897777 | + | 0.335055i | ||||
\(918\) | 163770. | + | 163770.i | 0.194334 | + | 0.194334i | ||||
\(919\) | −232722. | − | 403086.i | −0.275554 | − | 0.477273i | 0.694721 | − | 0.719279i | \(-0.255528\pi\) |
−0.970275 | + | 0.242006i | \(0.922194\pi\) | |||||||
\(920\) | −506941. | − | 292683.i | −0.598938 | − | 0.345797i | ||||
\(921\) | 219904. | − | 58923.0i | 0.259247 | − | 0.0694650i | ||||
\(922\) | 183650.i | 0.216037i | ||||||||
\(923\) | 607075. | − | 376571.i | 0.712588 | − | 0.442021i | ||||
\(924\) | −273192. | −0.319981 | ||||||||
\(925\) | −129379. | − | 482849.i | −0.151210 | − | 0.564323i | ||||
\(926\) | 98883.2 | − | 171271.i | 0.115319 | − | 0.199738i | ||||
\(927\) | −70545.8 | + | 40729.6i | −0.0820940 | + | 0.0473970i | ||||
\(928\) | −531286. | + | 531286.i | −0.616925 | + | 0.616925i | ||||
\(929\) | 1.58177e6 | + | 423834.i | 1.83279 | + | 0.491094i | 0.998210 | − | 0.0597983i | \(-0.0190457\pi\) |
0.834576 | + | 0.550892i | \(0.185712\pi\) | |||||||
\(930\) | 59404.9 | − | 221702.i | 0.0686841 | − | 0.256332i | ||||
\(931\) | 50946.8 | + | 50946.8i | 0.0587784 | + | 0.0587784i | ||||
\(932\) | 385453. | + | 667625.i | 0.443752 | + | 0.768600i | ||||
\(933\) | 467991. | + | 270195.i | 0.537619 | + | 0.310394i | ||||
\(934\) | −58317.9 | + | 15626.2i | −0.0668510 | + | 0.0179127i | ||||
\(935\) | 161473.i | 0.184704i | ||||||||
\(936\) | −149285. | − | 240665.i | −0.170398 | − | 0.274701i | ||||
\(937\) | 291324. | 0.331816 | 0.165908 | − | 0.986141i | \(-0.446945\pi\) | ||||
0.165908 | + | 0.986141i | \(0.446945\pi\) | |||||||
\(938\) | −64816.2 | − | 241897.i | −0.0736678 | − | 0.274932i | ||||
\(939\) | −242481. | + | 419990.i | −0.275009 | + | 0.476330i | ||||
\(940\) | 250611. | − | 144690.i | 0.283625 | − | 0.163751i | ||||
\(941\) | −1.05131e6 | + | 1.05131e6i | −1.18727 | + | 1.18727i | −0.209453 | + | 0.977819i | \(0.567168\pi\) |
−0.977819 | + | 0.209453i | \(0.932832\pi\) | |||||||
\(942\) | −336348. | − | 90124.3i | −0.379042 | − | 0.101564i | ||||
\(943\) | 705983. | − | 2.63477e6i | 0.793910 | − | 2.96291i | ||||
\(944\) | −90788.2 | − | 90788.2i | −0.101879 | − | 0.101879i | ||||
\(945\) | −322535. | − | 558647.i | −0.361172 | − | 0.625568i | ||||
\(946\) | −65228.6 | − | 37659.7i | −0.0728879 | − | 0.0420819i | ||||
\(947\) | 1.12897e6 | − | 302507.i | 1.25888 | − | 0.337315i | 0.433116 | − | 0.901338i | \(-0.357414\pi\) |
0.825759 | + | 0.564023i | \(0.190747\pi\) | |||||||
\(948\) | 716073.i | 0.796784i | ||||||||
\(949\) | −219530. | + | 6943.11i | −0.243759 | + | 0.00770942i | ||||
\(950\) | −66428.6 | −0.0736051 | ||||||||
\(951\) | −213528. | − | 796897.i | −0.236099 | − | 0.881132i | ||||
\(952\) | −243737. | + | 422165.i | −0.268935 | + | 0.465810i | ||||
\(953\) | 171284. | − | 98891.0i | 0.188596 | − | 0.108886i | −0.402729 | − | 0.915319i | \(-0.631938\pi\) |
0.591325 | + | 0.806433i | \(0.298605\pi\) | |||||||
\(954\) | 153910. | − | 153910.i | 0.169110 | − | 0.169110i | ||||
\(955\) | 877987. | + | 235256.i | 0.962679 | + | 0.257949i | ||||
\(956\) | −118969. | + | 443997.i | −0.130172 | + | 0.485808i | ||||
\(957\) | 202570. | + | 202570.i | 0.221183 | + | 0.221183i | ||||
\(958\) | −77733.0 | − | 134637.i | −0.0846982 | − | 0.146702i | ||||
\(959\) | 56192.9 | + | 32443.0i | 0.0611005 | + | 0.0352764i | ||||
\(960\) | 99376.4 | − | 26627.8i | 0.107830 | − | 0.0288930i | ||||
\(961\) | − | 1.50444e6i | − | 1.62903i | ||||||
\(962\) | 306458. | + | 71814.3i | 0.331147 | + | 0.0775998i | ||||
\(963\) | −703912. | −0.759042 | ||||||||
\(964\) | −29945.4 | − | 111758.i | −0.0322237 | − | 0.120261i | ||||
\(965\) | 76126.0 | − | 131854.i | 0.0817482 | − | 0.141592i | ||||
\(966\) | −414853. | + | 239515.i | −0.444569 | + | 0.256672i | ||||
\(967\) | 549664. | − | 549664.i | 0.587820 | − | 0.587820i | −0.349220 | − | 0.937041i | \(-0.613554\pi\) |
0.937041 | + | 0.349220i | \(0.113554\pi\) | |||||||
\(968\) | 501855. | + | 134472.i | 0.535584 | + | 0.143509i | ||||
\(969\) | 37303.4 | − | 139218.i | 0.0397284 | − | 0.148268i | ||||
\(970\) | −124912. | − | 124912.i | −0.132758 | − | 0.132758i | ||||
\(971\) | 664057. | + | 1.15018e6i | 0.704315 | + | 1.21991i | 0.966938 | + | 0.255011i | \(0.0820790\pi\) |
−0.262623 | + | 0.964898i | \(0.584588\pi\) | |||||||
\(972\) | 589433. | + | 340310.i | 0.623882 | + | 0.360198i | ||||
\(973\) | −649736. | + | 174096.i | −0.686295 | + | 0.183892i | ||||
\(974\) | − | 520190.i | − | 0.548333i | ||||||
\(975\) | 428016. | − | 129319.i | 0.450247 | − | 0.136036i | ||||
\(976\) | 424663. | 0.445805 | ||||||||
\(977\) | 157223. | + | 586765.i | 0.164713 | + | 0.614717i | 0.998077 | + | 0.0619919i | \(0.0197453\pi\) |
−0.833364 | + | 0.552725i | \(0.813588\pi\) | |||||||
\(978\) | 110599. | − | 191563.i | 0.115631 | − | 0.200278i | ||||
\(979\) | −596577. | + | 344434.i | −0.622445 | + | 0.359369i | ||||
\(980\) | 94811.3 | − | 94811.3i | 0.0987207 | − | 0.0987207i | ||||
\(981\) | −151108. | − | 40489.4i | −0.157018 | − | 0.0420730i | ||||
\(982\) | −79549.2 | + | 296882.i | −0.0824922 | + | 0.307865i | ||||
\(983\) | −156513. | − | 156513.i | −0.161974 | − | 0.161974i | 0.621467 | − | 0.783441i | \(-0.286537\pi\) |
−0.783441 | + | 0.621467i | \(0.786537\pi\) | |||||||
\(984\) | −454931. | − | 787963.i | −0.469845 | − | 0.813796i | ||||
\(985\) | −736224. | − | 425059.i | −0.758818 | − | 0.438104i | ||||
\(986\) | 228297. | − | 61172.1i | 0.234826 | − | 0.0629216i | ||||
\(987\) | − | 512180.i | − | 0.525761i | ||||||
\(988\) | −121365. | + | 226454.i | −0.124331 | + | 0.231989i | ||||
\(989\) | 811227. | 0.829373 | ||||||||
\(990\) | −11881.4 | − | 44342.1i | −0.0121227 | − | 0.0452424i | ||||
\(991\) | −252070. | + | 436598.i | −0.256669 | + | 0.444564i | −0.965348 | − | 0.260968i | \(-0.915958\pi\) |
0.708678 | + | 0.705532i | \(0.249292\pi\) | |||||||
\(992\) | −1.27171e6 | + | 734221.i | −1.29230 | + | 0.746111i | ||||
\(993\) | 668158. | − | 668158.i | 0.677612 | − | 0.677612i | ||||
\(994\) | 337674. | + | 90479.4i | 0.341763 | + | 0.0915750i | ||||
\(995\) | 138770. | − | 517898.i | 0.140169 | − | 0.523116i | ||||
\(996\) | −269708. | − | 269708.i | −0.271878 | − | 0.271878i | ||||
\(997\) | 186654. | + | 323294.i | 0.187779 | + | 0.325242i | 0.944509 | − | 0.328485i | \(-0.106538\pi\) |
−0.756731 | + | 0.653727i | \(0.773205\pi\) | |||||||
\(998\) | 155236. | + | 89625.7i | 0.155859 | + | 0.0899853i | ||||
\(999\) | −939073. | + | 251624.i | −0.940954 | + | 0.252128i |
(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 | 13.5.f.a.6.2 | ✓ | 16 | |
3.2 | odd | 2 | 117.5.bd.c.19.3 | 16 | |||
13.4 | even | 6 | 169.5.d.c.70.5 | 16 | |||
13.6 | odd | 12 | 169.5.d.c.99.5 | 16 | |||
13.7 | odd | 12 | 169.5.d.d.99.4 | 16 | |||
13.9 | even | 3 | 169.5.d.d.70.4 | 16 | |||
13.11 | odd | 12 | inner | 13.5.f.a.11.2 | yes | 16 | |
39.11 | even | 12 | 117.5.bd.c.37.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.5.f.a.6.2 | ✓ | 16 | 1.1 | even | 1 | trivial | |
13.5.f.a.11.2 | yes | 16 | 13.11 | odd | 12 | inner | |
117.5.bd.c.19.3 | 16 | 3.2 | odd | 2 | |||
117.5.bd.c.37.3 | 16 | 39.11 | even | 12 | |||
169.5.d.c.70.5 | 16 | 13.4 | even | 6 | |||
169.5.d.c.99.5 | 16 | 13.6 | odd | 12 | |||
169.5.d.d.70.4 | 16 | 13.9 | even | 3 | |||
169.5.d.d.99.4 | 16 | 13.7 | odd | 12 |