Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,6,Mod(45,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.45");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.e (of order \(3\), 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: | \(12.1891703058\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(9\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 2 x^{17} + 1540 x^{16} - 768 x^{15} + 1608492 x^{14} - 1027368 x^{13} + 897054160 x^{12} + \cdots + 80\!\cdots\!36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{16}\cdot 3^{3}\cdot 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 45.3 | ||
Root | \(6.29505 - 10.9033i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 76.45 |
Dual form | 76.6.e.a.49.3 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −6.79505 | − | 11.7694i | −0.435903 | − | 0.755006i | 0.561466 | − | 0.827500i | \(-0.310238\pi\) |
−0.997369 | + | 0.0724940i | \(0.976904\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −47.4871 | − | 82.2500i | −0.849474 | − | 1.47133i | −0.881678 | − | 0.471851i | \(-0.843586\pi\) |
0.0322040 | − | 0.999481i | \(-0.489747\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 189.860 | 1.46449 | 0.732247 | − | 0.681039i | \(-0.238472\pi\) | ||||
0.732247 | + | 0.681039i | \(0.238472\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 29.1546 | − | 50.4972i | 0.119978 | − | 0.207807i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −530.005 | −1.32068 | −0.660341 | − | 0.750966i | \(-0.729588\pi\) | ||||
−0.660341 | + | 0.750966i | \(0.729588\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −353.895 | + | 612.964i | −0.580786 | + | 1.00595i | 0.414600 | + | 0.910004i | \(0.363921\pi\) |
−0.995386 | + | 0.0959473i | \(0.969412\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −645.354 | + | 1117.79i | −0.740576 | + | 1.28272i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −764.589 | − | 1324.31i | −0.641661 | − | 1.11139i | −0.985062 | − | 0.172201i | \(-0.944912\pi\) |
0.343401 | − | 0.939189i | \(-0.388421\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 654.031 | + | 1431.20i | 0.415637 | + | 0.909530i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1290.11 | − | 2234.53i | −0.638377 | − | 1.10570i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 497.425 | − | 861.565i | 0.196068 | − | 0.339600i | −0.751182 | − | 0.660095i | \(-0.770516\pi\) |
0.947250 | + | 0.320495i | \(0.103849\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2947.54 | + | 5105.29i | −0.943213 | + | 1.63369i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4094.82 | −1.08100 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1290.66 | + | 2235.49i | −0.284982 | + | 0.493603i | −0.972605 | − | 0.232465i | \(-0.925321\pi\) |
0.687623 | + | 0.726068i | \(0.258654\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2790.81 | −0.521585 | −0.260793 | − | 0.965395i | \(-0.583984\pi\) | ||||
−0.260793 | + | 0.965395i | \(0.583984\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3601.41 | + | 6237.82i | 0.575689 | + | 0.997122i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9015.88 | − | 15616.0i | −1.24405 | − | 2.15476i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7238.14 | 0.869206 | 0.434603 | − | 0.900622i | \(-0.356889\pi\) | ||||
0.434603 | + | 0.900622i | \(0.356889\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9618.94 | 1.01266 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2181.63 | + | 3778.69i | 0.202685 | + | 0.351060i | 0.949393 | − | 0.314092i | \(-0.101700\pi\) |
−0.746708 | + | 0.665152i | \(0.768367\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3121.70 | − | 5406.94i | −0.257466 | − | 0.445944i | 0.708096 | − | 0.706116i | \(-0.249554\pi\) |
−0.965562 | + | 0.260172i | \(0.916221\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5537.86 | −0.407671 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12320.9 | − | 21340.4i | 0.813576 | − | 1.40915i | −0.0967705 | − | 0.995307i | \(-0.530851\pi\) |
0.910346 | − | 0.413848i | \(-0.135815\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 19239.7 | 1.14474 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10390.8 | + | 17997.5i | −0.559404 | + | 0.968916i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −15497.6 | + | 26842.6i | −0.757833 | + | 1.31261i | 0.186120 | + | 0.982527i | \(0.440409\pi\) |
−0.943953 | + | 0.330079i | \(0.892925\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 25168.4 | + | 43592.9i | 1.12188 | + | 1.94316i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 12400.2 | − | 17422.6i | 0.505523 | − | 0.710275i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −18177.7 | − | 31484.8i | −0.679845 | − | 1.17753i | −0.975027 | − | 0.222085i | \(-0.928714\pi\) |
0.295182 | − | 0.955441i | \(-0.404620\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2886.93 | − | 5000.30i | 0.0993370 | − | 0.172057i | −0.812073 | − | 0.583555i | \(-0.801661\pi\) |
0.911410 | + | 0.411499i | \(0.134994\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5535.27 | − | 9587.38i | 0.175706 | − | 0.304333i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 67221.7 | 1.97345 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 30388.4 | − | 52634.2i | 0.827029 | − | 1.43246i | −0.0733301 | − | 0.997308i | \(-0.523363\pi\) |
0.900359 | − | 0.435148i | \(-0.143304\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −13520.1 | −0.341867 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14829.0 | + | 25684.5i | 0.349112 | + | 0.604680i | 0.986092 | − | 0.166201i | \(-0.0531500\pi\) |
−0.636980 | + | 0.770880i | \(0.719817\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −39002.3 | − | 67553.9i | −0.856609 | − | 1.48369i | −0.875144 | − | 0.483862i | \(-0.839234\pi\) |
0.0185353 | − | 0.999828i | \(-0.494100\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 80114.7 | 1.64460 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −100627. | −1.93413 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −33427.5 | − | 57898.2i | −0.602611 | − | 1.04375i | −0.992424 | − | 0.122858i | \(-0.960794\pi\) |
0.389814 | − | 0.920894i | \(-0.372539\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 20740.0 | + | 35922.7i | 0.351233 | + | 0.608354i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −21919.5 | −0.349250 | −0.174625 | − | 0.984635i | \(-0.555871\pi\) | ||||
−0.174625 | + | 0.984635i | \(0.555871\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −72616.2 | + | 125775.i | −1.09015 | + | 1.88819i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 35080.4 | 0.496898 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −45374.8 | + | 78591.5i | −0.607211 | + | 1.05172i | 0.384487 | + | 0.923131i | \(0.374378\pi\) |
−0.991698 | + | 0.128590i | \(0.958955\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −67190.4 | + | 116377.i | −0.850558 | + | 1.47321i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 18963.7 | + | 32846.0i | 0.227360 | + | 0.393800i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 86658.4 | − | 121758.i | 0.985149 | − | 1.38416i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −30757.3 | − | 53273.1i | −0.331908 | − | 0.574882i | 0.650978 | − | 0.759097i | \(-0.274359\pi\) |
−0.982886 | + | 0.184215i | \(0.941026\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −15452.1 | + | 26763.7i | −0.158452 | + | 0.274447i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5882.91 | − | 10189.5i | 0.0573837 | − | 0.0993915i | −0.835906 | − | 0.548872i | \(-0.815057\pi\) |
0.893290 | + | 0.449480i | \(0.148391\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −57682.4 | −0.535735 | −0.267868 | − | 0.963456i | \(-0.586319\pi\) | ||||
−0.267868 | + | 0.963456i | \(0.586319\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −122527. | + | 212222.i | −1.08457 | + | 1.87853i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −79892.9 | −0.674604 | −0.337302 | − | 0.941397i | \(-0.609514\pi\) | ||||
−0.337302 | + | 0.941397i | \(0.609514\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −98323.4 | − | 170301.i | −0.792667 | − | 1.37294i | −0.924310 | − | 0.381642i | \(-0.875359\pi\) |
0.131643 | − | 0.991297i | \(-0.457975\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −49183.5 | − | 85188.4i | −0.378889 | − | 0.656255i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 205714. | 1.51554 | 0.757770 | − | 0.652521i | \(-0.226289\pi\) | ||||
0.757770 | + | 0.652521i | \(0.226289\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −94484.9 | −0.666220 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 20635.3 | + | 35741.4i | 0.139363 | + | 0.241383i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −145165. | − | 251433.i | −0.939709 | − | 1.62762i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 119854. | 0.744199 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 29648.6 | − | 51352.8i | 0.176702 | − | 0.306056i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 263086. | 1.50599 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −143.620 | + | 248.756i | −0.000790141 | + | 0.00136856i | −0.866420 | − | 0.499316i | \(-0.833585\pi\) |
0.865630 | + | 0.500684i | \(0.166918\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −42424.2 | + | 73480.9i | −0.224460 | + | 0.388777i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −21086.6 | − | 36523.1i | −0.107357 | − | 0.185947i | 0.807342 | − | 0.590084i | \(-0.200905\pi\) |
−0.914699 | + | 0.404137i | \(0.867572\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 124174. | + | 271728.i | 0.608698 | + | 1.33200i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 194451. | + | 336799.i | 0.918281 | + | 1.59051i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −52318.5 | + | 90618.2i | −0.238152 | + | 0.412491i | −0.960184 | − | 0.279369i | \(-0.909875\pi\) |
0.722032 | + | 0.691859i | \(0.243208\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 64404.7 | − | 111552.i | 0.282736 | − | 0.489713i | −0.689322 | − | 0.724455i | \(-0.742091\pi\) |
0.972058 | + | 0.234743i | \(0.0754247\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −334885. | −1.41856 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 187566. | − | 324874.i | 0.767033 | − | 1.32854i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 245159. | 0.968339 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −130735. | − | 226439.i | −0.498997 | − | 0.864288i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −136506. | − | 236435.i | −0.503716 | − | 0.872462i | −0.999991 | − | 0.00429614i | \(-0.998632\pi\) |
0.496275 | − | 0.868165i | \(-0.334701\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 68761.9 | 0.245418 | 0.122709 | − | 0.992443i | \(-0.460842\pi\) | ||||
0.122709 | + | 0.992443i | \(0.460842\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −89165.0 | −0.307940 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 132527. | + | 229544.i | 0.443073 | + | 0.767425i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 275998. | + | 478042.i | 0.893628 | + | 1.54781i | 0.835494 | + | 0.549500i | \(0.185182\pi\) |
0.0581337 | + | 0.998309i | \(0.481485\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 421227. | 1.32137 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 94440.9 | − | 163576.i | 0.287141 | − | 0.497343i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −153395. | −0.452211 | −0.226106 | − | 0.974103i | \(-0.572599\pi\) | ||||
−0.226106 | + | 0.974103i | \(0.572599\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 342041. | − | 592432.i | 0.978065 | − | 1.69406i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 146626. | − | 253963.i | 0.406836 | − | 0.704660i | −0.587697 | − | 0.809081i | \(-0.699965\pi\) |
0.994533 | + | 0.104421i | \(0.0332988\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −64836.9 | − | 112301.i | −0.174625 | − | 0.302459i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 91339.7 | + | 8699.36i | 0.238874 | + | 0.0227508i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −114249. | − | 197885.i | −0.290227 | − | 0.502688i | 0.683636 | − | 0.729823i | \(-0.260398\pi\) |
−0.973863 | + | 0.227135i | \(0.927064\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −559619. | + | 969289.i | −1.38133 | + | 2.39253i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −247037. | + | 427881.i | −0.592693 | + | 1.02657i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 247143. | 0.576521 | 0.288261 | − | 0.957552i | \(-0.406923\pi\) | ||||
0.288261 | + | 0.957552i | \(0.406923\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 353864. | − | 612910.i | 0.802859 | − | 1.39059i | −0.114867 | − | 0.993381i | \(-0.536644\pi\) |
0.917727 | − | 0.397213i | \(-0.130022\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −78467.2 | −0.173205 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −343718. | − | 595337.i | −0.738368 | − | 1.27889i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 405236. | + | 701889.i | 0.847430 | + | 1.46779i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −777442. | −1.58312 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10502.1 | 0.0208301 | 0.0104151 | − | 0.999946i | \(-0.496685\pi\) | ||||
0.0104151 | + | 0.999946i | \(0.496685\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 496794. | + | 860472.i | 0.960025 | + | 1.66281i | 0.722424 | + | 0.691450i | \(0.243028\pi\) |
0.237601 | + | 0.971363i | \(0.423639\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −456775. | − | 791158.i | −0.860233 | − | 1.48997i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −185300. | −0.340182 | −0.170091 | − | 0.985428i | \(-0.554406\pi\) | ||||
−0.170091 | + | 0.985428i | \(0.554406\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 43149.9 | − | 74737.8i | 0.0772408 | − | 0.133785i | −0.824818 | − | 0.565399i | \(-0.808722\pi\) |
0.902059 | + | 0.431614i | \(0.142056\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −825963. | −1.44202 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −245045. | + | 424430.i | −0.417354 | + | 0.722879i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 207198. | − | 358878.i | 0.344351 | − | 0.596433i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −29004.4 | − | 50237.1i | −0.0470476 | − | 0.0814889i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −346640. | − | 758544.i | −0.548924 | − | 1.20120i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 151234. | + | 261945.i | 0.233853 | + | 0.405045i | 0.958939 | − | 0.283613i | \(-0.0915332\pi\) |
−0.725086 | + | 0.688659i | \(0.758200\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 201527. | − | 349055.i | 0.304358 | − | 0.527163i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −296481. | + | 513519.i | −0.437422 | + | 0.757636i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −529861. | −0.763858 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −530045. | + | 918064.i | −0.746796 | + | 1.29349i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.08234e6 | 1.49067 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −339486. | − | 588007.i | −0.457151 | − | 0.791809i | 0.541658 | − | 0.840599i | \(-0.317797\pi\) |
−0.998809 | + | 0.0487901i | \(0.984463\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 171868. | + | 297685.i | 0.226329 | + | 0.392013i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 231581. | 0.298289 | 0.149145 | − | 0.988815i | \(-0.452348\pi\) | ||||
0.149145 | + | 0.988815i | \(0.452348\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 33377.9 | 0.0420601 | 0.0210300 | − | 0.999779i | \(-0.493305\pi\) | ||||
0.0210300 | + | 0.999779i | \(0.493305\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 683762. | + | 1.18431e6i | 0.843093 | + | 1.46028i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 542190. | + | 939100.i | 0.654277 | + | 1.13324i | 0.982075 | + | 0.188493i | \(0.0603602\pi\) |
−0.327798 | + | 0.944748i | \(0.606306\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.34033e6 | −2.76445 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −454284. | + | 786843.i | −0.525359 | + | 0.909949i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −284041. | −0.321652 | −0.160826 | − | 0.986983i | \(-0.551416\pi\) | ||||
−0.160826 | + | 0.986983i | \(0.551416\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 306804. | − | 531400.i | 0.340266 | − | 0.589357i | −0.644216 | − | 0.764843i | \(-0.722816\pi\) |
0.984482 | + | 0.175486i | \(0.0561497\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −215663. | + | 373539.i | −0.234293 | + | 0.405807i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −913637. | − | 1.58246e6i | −0.972430 | − | 1.68430i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.10873e6 | − | 105598.i | −1.15634 | − | 0.110132i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 148944. | + | 257979.i | 0.152239 | + | 0.263685i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 369089. | − | 639282.i | 0.369783 | − | 0.640484i | −0.619748 | − | 0.784801i | \(-0.712765\pi\) |
0.989531 | + | 0.144317i | \(0.0460986\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −263637. | + | 456633.i | −0.258944 | + | 0.448504i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.97372e6 | 1.90080 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 686359. | − | 1.18881e6i | 0.648214 | − | 1.12274i | −0.335335 | − | 0.942099i | \(-0.608849\pi\) |
0.983549 | − | 0.180641i | \(-0.0578172\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.37423e6 | 1.27295 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 75257.3 | + | 130349.i | 0.0683829 | + | 0.118443i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −146329. | − | 253449.i | −0.130449 | − | 0.225944i | 0.793401 | − | 0.608699i | \(-0.208308\pi\) |
−0.923850 | + | 0.382756i | \(0.874975\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.94373e6 | 2.57504 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.23330e6 | 1.05874 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −977718. | − | 1.69346e6i | −0.823821 | − | 1.42690i | −0.902817 | − | 0.430025i | \(-0.858505\pi\) |
0.0789962 | − | 0.996875i | \(-0.474828\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −713502. | − | 1.23582e6i | −0.590163 | − | 1.02219i | −0.994210 | − | 0.107454i | \(-0.965730\pi\) |
0.404047 | − | 0.914738i | \(-0.367603\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.82625e6 | 1.48304 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.56221e6 | − | 2.70583e6i | 1.24568 | − | 2.15759i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.20887e6 | −0.946629 | −0.473315 | − | 0.880893i | \(-0.656943\pi\) | ||||
−0.473315 | + | 0.880893i | \(0.656943\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −81364.7 | + | 140928.i | −0.0625785 | + | 0.108389i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −996432. | + | 1.72587e6i | −0.752804 | + | 1.30389i | 0.193655 | + | 0.981070i | \(0.437966\pi\) |
−0.946459 | + | 0.322825i | \(0.895367\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 33435.3 | + | 57911.6i | 0.0248164 | + | 0.0429832i | 0.878167 | − | 0.478354i | \(-0.158767\pi\) |
−0.853350 | + | 0.521338i | \(0.825433\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.02186e6 | − | 192566.i | −1.47448 | − | 0.140432i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 414203. | + | 717421.i | 0.296831 | + | 0.514126i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −459264. | + | 795469.i | −0.323458 | + | 0.560246i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −417994. | + | 723987.i | −0.289360 | + | 0.501185i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.98637e6 | 1.35173 | 0.675866 | − | 0.737025i | \(-0.263770\pi\) | ||||
0.675866 | + | 0.737025i | \(0.263770\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.72641e6 | + | 2.99024e6i | −1.15502 | + | 2.00056i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.17027e6 | 1.42766 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 352072. | + | 609807.i | 0.227748 | + | 0.394470i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −592685. | − | 1.02656e6i | −0.377058 | − | 0.653083i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −159899. | −0.100055 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −548366. | −0.337537 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 932152. | + | 1.61454e6i | 0.564470 | + | 0.977691i | 0.997099 | + | 0.0761187i | \(0.0242528\pi\) |
−0.432629 | + | 0.901572i | \(0.642414\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 391955. | + | 678886.i | 0.233528 | + | 0.404483i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.73570e6 | 1.01759 | 0.508796 | − | 0.860887i | \(-0.330091\pi\) | ||||
0.508796 | + | 0.860887i | \(0.330091\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26566.2 | − | 46014.0i | 0.0153274 | − | 0.0265478i | −0.858260 | − | 0.513215i | \(-0.828454\pi\) |
0.873587 | + | 0.486667i | \(0.161788\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.05142e6 | −0.597032 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −690554. | + | 1.19607e6i | −0.385966 | + | 0.668514i | −0.991903 | − | 0.127000i | \(-0.959465\pi\) |
0.605936 | + | 0.795513i | \(0.292799\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 684056. | − | 1.18482e6i | 0.376370 | − | 0.651892i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 542876. | + | 940289.i | 0.294062 | + | 0.509330i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.39529e6 | − | 1.96042e6i | 0.744144 | − | 1.04555i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.08624e6 | − | 3.61347e6i | −1.09561 | − | 1.89765i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.33623e6 | + | 2.31441e6i | −0.691051 | + | 1.19694i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.33924e6 | − | 4.05169e6i | 1.19148 | − | 2.06370i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −79218.6 | −0.0397427 | −0.0198713 | − | 0.999803i | \(-0.506326\pi\) | ||||
−0.0198713 | + | 0.999803i | \(0.506326\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 211025. | − | 365506.i | 0.104285 | − | 0.180627i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.77222e6 | −2.81016 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.06653e6 | + | 1.84729e6i | 0.511563 | + | 0.886053i | 0.999910 | + | 0.0134034i | \(0.00426657\pi\) |
−0.488347 | + | 0.872649i | \(0.662400\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.39784e6 | − | 2.42112e6i | −0.660628 | − | 1.14424i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.47914e6 | 0.688848 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 461871. | 0.211976 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 642030. | + | 1.11203e6i | 0.290407 | + | 0.503000i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 988867. | + | 1.71277e6i | 0.440874 | + | 0.763616i | 0.997755 | − | 0.0669767i | \(-0.0213353\pi\) |
−0.556881 | + | 0.830592i | \(0.688002\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.01158e6 | −0.884043 | −0.442022 | − | 0.897004i | \(-0.645739\pi\) | ||||
−0.442022 | + | 0.897004i | \(0.645739\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.44914e6 | − | 2.50998e6i | 0.627829 | − | 1.08743i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.89132e6 | −1.23498 | −0.617490 | − | 0.786579i | \(-0.711850\pi\) | ||||
−0.617490 | + | 0.786579i | \(0.711850\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.40837e6 | − | 2.43936e6i | 0.593123 | − | 1.02732i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.97280e6 | + | 3.41699e6i | −0.819243 | + | 1.41897i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −371558. | − | 643557.i | −0.152156 | − | 0.263543i | 0.779864 | − | 0.625950i | \(-0.215288\pi\) |
−0.932020 | + | 0.362407i | \(0.881955\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.62059e6 | + | 1.87210e6i | −0.654491 | + | 0.756070i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −814414. | − | 1.41061e6i | −0.324398 | − | 0.561875i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.70420e6 | + | 6.41587e6i | −1.45533 | + | 2.52071i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.21010e6 | − | 3.82801e6i | 0.856540 | − | 1.48357i | −0.0186695 | − | 0.999826i | \(-0.505943\pi\) |
0.875209 | − | 0.483745i | \(-0.160724\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 254418. | 0.0972705 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.94236e6 | + | 5.09632e6i | −1.10984 | + | 1.92230i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.07890e6 | −0.773680 | −0.386840 | − | 0.922147i | \(-0.626433\pi\) | ||||
−0.386840 | + | 0.922147i | \(0.626433\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.78768e6 | − | 3.09636e6i | −0.656466 | − | 1.13703i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −913517. | − | 1.58226e6i | −0.331027 | − | 0.573355i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.87208e6 | 1.38467 | 0.692335 | − | 0.721576i | \(-0.256582\pi\) | ||||
0.692335 | + | 0.721576i | \(0.256582\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3903.61 | 0.00137770 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −72504.1 | − | 125581.i | −0.0252560 | − | 0.0437448i | 0.853121 | − | 0.521713i | \(-0.174707\pi\) |
−0.878377 | + | 0.477968i | \(0.841373\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.77846e6 | + | 8.27653e6i | 1.64299 | + | 2.84575i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −364047. | −0.123561 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 670618. | − | 1.16154e6i | 0.224699 | − | 0.389190i | −0.731530 | − | 0.681809i | \(-0.761193\pi\) |
0.956229 | + | 0.292619i | \(0.0945268\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.52130e6 | −0.503238 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −286570. | + | 496353.i | −0.0935942 | + | 0.162110i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.17475e6 | + | 5.49883e6i | −1.02380 | + | 1.77328i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −635788. | − | 1.10122e6i | −0.202458 | − | 0.350668i | 0.746862 | − | 0.664980i | \(-0.231560\pi\) |
−0.949320 | + | 0.314311i | \(0.898226\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.35430e6 | − | 3.30786e6i | 0.740336 | − | 1.04019i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 722427. | + | 1.25128e6i | 0.224354 | + | 0.388592i | 0.956125 | − | 0.292958i | \(-0.0946396\pi\) |
−0.731772 | + | 0.681550i | \(0.761306\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 987652. | − | 1.71066e6i | 0.302929 | − | 0.524689i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.96976e6 | − | 3.41172e6i | 0.596727 | − | 1.03356i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.83625e6 | −1.14794 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 306511. | − | 530893.i | 0.0906020 | − | 0.156927i | −0.817163 | − | 0.576407i | \(-0.804454\pi\) |
0.907765 | + | 0.419480i | \(0.137788\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.42203e6 | 0.415244 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.45122e6 | − | 5.97769e6i | −0.995629 | − | 1.72448i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.04089e6 | + | 1.80288e6i | 0.296679 | + | 0.513862i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.75053e6 | −0.492981 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.30914e6 | 1.75564 | 0.877820 | − | 0.478991i | \(-0.158997\pi\) | ||||
0.877820 | + | 0.478991i | \(0.158997\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.28732e6 | − | 2.22970e6i | −0.353981 | − | 0.613113i | 0.632962 | − | 0.774183i | \(-0.281839\pi\) |
−0.986943 | + | 0.161070i | \(0.948506\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −718421. | − | 1.24434e6i | −0.195222 | − | 0.338134i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.01463e6 | 2.42089 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 548111. | − | 949356.i | 0.145478 | − | 0.251976i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.09808e6 | −1.33741 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −921074. | + | 1.59535e6i | −0.238837 | + | 0.413678i | −0.960381 | − | 0.278691i | \(-0.910099\pi\) |
0.721544 | + | 0.692369i | \(0.243433\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.48716e6 | + | 4.30788e6i | −0.637505 | + | 1.10419i | 0.348474 | + | 0.937318i | \(0.386700\pi\) |
−0.985979 | + | 0.166872i | \(0.946633\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.66587e6 | − | 2.88537e6i | −0.422102 | − | 0.731101i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.55841e6 | + | 148425.i | 0.390370 | + | 0.0371796i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.97430e6 | + | 3.41959e6i | 0.488936 | + | 0.846863i | 0.999919 | − | 0.0127283i | \(-0.00405165\pi\) |
−0.510983 | + | 0.859591i | \(0.670718\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 560925. | − | 971550.i | 0.137344 | − | 0.237886i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.42436e6 | − | 5.93117e6i | 0.829031 | − | 1.43592i | −0.0697689 | − | 0.997563i | \(-0.522226\pi\) |
0.898799 | − | 0.438360i | \(-0.144440\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.61886e6 | 2.06324 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.85513e6 | + | 3.21318e6i | −0.439142 | + | 0.760617i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.05530e6 | −0.715216 | −0.357608 | − | 0.933872i | \(-0.616408\pi\) | ||||
−0.357608 | + | 0.933872i | \(0.616408\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.15627e6 | − | 2.00272e6i | −0.267682 | − | 0.463639i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −467241. | − | 809285.i | −0.106978 | − | 0.185292i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.27627e7 | 2.89011 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.86875e6 | −1.31448 | −0.657242 | − | 0.753680i | \(-0.728277\pi\) | ||||
−0.657242 | + | 0.753680i | \(0.728277\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.13086e6 | + | 5.42280e6i | 0.693636 | + | 1.20141i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 970738. | + | 1.68137e6i | 0.212740 | + | 0.368477i | 0.952571 | − | 0.304316i | \(-0.0984279\pi\) |
−0.739831 | + | 0.672793i | \(0.765095\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.37394e6 | 0.514656 | 0.257328 | − | 0.966324i | \(-0.417158\pi\) | ||||
0.257328 | + | 0.966324i | \(0.417158\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.80106e6 | − | 3.11952e6i | 0.386274 | − | 0.669046i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.72608e6 | −0.578425 | −0.289212 | − | 0.957265i | \(-0.593393\pi\) | ||||
−0.289212 | + | 0.957265i | \(0.593393\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.76953e6 | − | 9.99312e6i | 1.21118 | − | 2.09782i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.75084e6 | − | 6.49664e6i | 0.779069 | − | 1.34939i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.65452e6 | + | 2.86570e6i | 0.340031 | + | 0.588950i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.23449e6 | − | 879510.i | −1.87793 | − | 0.178857i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 903649. | + | 1.56517e6i | 0.181846 | + | 0.314967i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.64917e6 | + | 4.58849e6i | −0.527558 | + | 0.913757i | 0.471926 | + | 0.881638i | \(0.343559\pi\) |
−0.999484 | + | 0.0321192i | \(0.989774\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.56154e6 | + | 4.43672e6i | −0.504823 | + | 0.874378i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.56692e6 | −0.500662 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.92114e6 | + | 5.05957e6i | −0.563895 | + | 0.976695i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.45937e6 | 1.04309 | 0.521543 | − | 0.853225i | \(-0.325356\pi\) | ||||
0.521543 | + | 0.853225i | \(0.325356\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.04233e6 | + | 1.80536e6i | 0.197120 | + | 0.341422i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.95495e6 | − | 6.85017e6i | −0.740350 | − | 1.28232i | −0.952336 | − | 0.305051i | \(-0.901326\pi\) |
0.211986 | − | 0.977273i | \(-0.432007\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.94730e6 | 0.731447 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.93509e6 | 0.538404 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.81542e6 | + | 4.87645e6i | 0.511272 | + | 0.885550i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.75343e6 | − | 8.23318e6i | −0.854586 | − | 1.48019i | −0.877029 | − | 0.480438i | \(-0.840478\pi\) |
0.0224433 | − | 0.999748i | \(-0.492855\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.98532e6 | −0.709363 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.72038e6 | + | 6.44389e6i | −0.655643 | + | 1.13561i | 0.326090 | + | 0.945339i | \(0.394269\pi\) |
−0.981732 | + | 0.190268i | \(0.939064\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.11745e6 | −0.194984 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −881141. | + | 1.52618e6i | −0.152239 | + | 0.263685i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 513257. | − | 888987.i | 0.0878092 | − | 0.152090i | −0.818776 | − | 0.574114i | \(-0.805347\pi\) |
0.906585 | + | 0.422024i | \(0.138680\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.40496e6 | − | 1.28258e7i | −1.25450 | − | 2.17286i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.67814e6 | − | 5.86052e6i | −0.449304 | − | 0.983202i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.73917e6 | + | 4.74438e6i | 0.455093 | + | 0.788245i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.53014e6 | + | 1.13105e7i | −1.07447 | + | 1.86104i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.55266e6 | + | 2.68928e6i | −0.253022 | + | 0.438246i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.83600e6 | 0.941936 | 0.470968 | − | 0.882150i | \(-0.343905\pi\) | ||||
0.470968 | + | 0.882150i | \(0.343905\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.68243e6 | − | 2.91406e6i | 0.268958 | − | 0.465848i | −0.699635 | − | 0.714500i | \(-0.746654\pi\) |
0.968593 | + | 0.248652i | \(0.0799875\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.52106e7 | 2.40850 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.13382e6 | + | 3.69588e6i | 0.334681 | + | 0.579684i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.72331e6 | + | 4.71691e6i | 0.423114 | + | 0.732856i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.11986e6 | −0.326265 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.08827e6 | −0.470866 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.79388e6 | + | 6.57119e6i | 0.573058 | + | 0.992566i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.67935e6 | − | 2.90872e6i | −0.251307 | − | 0.435277i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.01971e7 | −1.51184 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.79104e6 | − | 8.29833e6i | 0.703780 | − | 1.21898i | −0.263350 | − | 0.964700i | \(-0.584827\pi\) |
0.967130 | − | 0.254282i | \(-0.0818393\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9.61809e6 | −1.39987 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.33818e6 | + | 1.61742e7i | −1.34670 | + | 2.33255i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.53036e6 | + | 4.38271e6i | −0.361588 | + | 0.626289i | −0.988222 | − | 0.153024i | \(-0.951099\pi\) |
0.626634 | + | 0.779314i | \(0.284432\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −168334. | − | 291563.i | −0.0238364 | − | 0.0412859i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.04357e6 | − | 385117.i | −0.567396 | − | 0.0540398i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.34654e6 | − | 1.09925e7i | −0.882520 | − | 1.52857i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.67116e6 | + | 8.09069e6i | −0.643713 | + | 1.11494i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.89885e6 | + | 6.75300e6i | −0.532474 | + | 0.922271i | 0.466807 | + | 0.884359i | \(0.345404\pi\) |
−0.999281 | + | 0.0379124i | \(0.987929\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.41902e6 | 0.598131 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.50720e6 | − | 9.53874e6i | 0.738794 | − | 1.27963i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.30439e6 | 0.572323 | 0.286161 | − | 0.958181i | \(-0.407621\pi\) | ||||
0.286161 | + | 0.958181i | \(0.407621\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.76875e6 | − | 1.69200e7i | −1.28741 | − | 2.22986i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.93768e6 | + | 6.82027e6i | 0.514379 | + | 0.890930i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.79289e6 | −1.26803 | −0.634016 | − | 0.773320i | \(-0.718595\pi\) | ||||
−0.634016 | + | 0.773320i | \(0.718595\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.14671e6 | −0.788955 | −0.394477 | − | 0.918906i | \(-0.629074\pi\) | ||||
−0.394477 | + | 0.918906i | \(0.629074\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −71362.1 | − | 123603.i | −0.00907990 | − | 0.0157269i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.93236e6 | + | 5.07899e6i | 0.369869 | + | 0.640631i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −704051. | −0.0880369 | −0.0440185 | − | 0.999031i | \(-0.514016\pi\) | ||||
−0.0440185 | + | 0.999031i | \(0.514016\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.75148e6 | − | 1.16939e7i | 0.836955 | − | 1.44965i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.16163e6 | −0.511474 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.21378e6 | − | 1.42267e7i | 1.00086 | − | 1.73353i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.95982e6 | − | 3.39451e6i | 0.236770 | − | 0.410097i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.80763e6 | + | 8.32707e6i | 0.575885 | + | 0.997463i | 0.995945 | + | 0.0899662i | \(0.0286759\pi\) |
−0.420059 | + | 0.907497i | \(0.637991\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.82527e6 | − | 3.99421e6i | −0.216790 | − | 0.474398i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.25913e6 | + | 2.18087e6i | 0.148286 | + | 0.256839i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.57887e6 | − | 9.66289e6i | 0.651493 | − | 1.12842i | −0.331268 | − | 0.943537i | \(-0.607476\pi\) |
0.982761 | − | 0.184882i | \(-0.0591903\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.37869e7 | + | 2.38796e7i | −1.59652 | + | 2.76525i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.17282e6 | −0.134678 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.00898e6 | − | 6.94376e6i | 0.456528 | − | 0.790729i | −0.542247 | − | 0.840219i | \(-0.682426\pi\) |
0.998775 | + | 0.0494902i | \(0.0157597\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.34115e7 | 1.51458 | 0.757290 | − | 0.653079i | \(-0.226523\pi\) | ||||
0.757290 | + | 0.653079i | \(0.226523\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.77192e6 | − | 3.06905e6i | −0.198450 | − | 0.343725i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.69151e6 | − | 9.85799e6i | −0.632178 | − | 1.09496i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.14504e6 | 0.346461 | 0.173231 | − | 0.984881i | \(-0.444579\pi\) | ||||
0.173231 | + | 0.984881i | \(0.444579\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.66036e6 | 0.727704 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.72061e6 | + | 1.51045e7i | 0.945027 | + | 1.63683i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.86161e6 | + | 3.22440e6i | 0.200095 | + | 0.346575i | 0.948559 | − | 0.316601i | \(-0.102542\pi\) |
−0.748464 | + | 0.663176i | \(0.769208\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.63169e6 | −0.600414 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −650699. | + | 1.12704e6i | −0.0688125 | + | 0.119187i | −0.898379 | − | 0.439221i | \(-0.855254\pi\) |
0.829566 | + | 0.558408i | \(0.188588\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.44161e7 | 1.51224 | 0.756118 | − | 0.654435i | \(-0.227093\pi\) | ||||
0.756118 | + | 0.654435i | \(0.227093\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.03687e6 | + | 3.52795e6i | −0.211950 | + | 0.367108i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.61485e6 | + | 1.49214e7i | −0.889257 | + | 1.54024i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.28211e6 | − | 5.68478e6i | −0.336088 | − | 0.582122i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.57216e6 | + | 9.23408e6i | −0.667635 | + | 0.938047i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.53420e6 | − | 9.58552e6i | −0.557736 | − | 0.966026i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.56517e6 | − | 2.71095e6i | 0.156490 | − | 0.271049i | −0.777110 | − | 0.629364i | \(-0.783315\pi\) |
0.933601 | + | 0.358315i | \(0.116649\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.05528e6 | − | 3.55986e6i | 0.203874 | − | 0.353121i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 27280.3 | 0.00268482 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.80883e6 | + | 1.17932e7i | −0.664851 | + | 1.15156i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.72933e6 | 0.167542 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.12325e6 | − | 3.67757e6i | −0.204106 | − | 0.353522i | 0.745742 | − | 0.666235i | \(-0.232095\pi\) |
−0.949848 | + | 0.312713i | \(0.898762\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.08032e6 | + | 8.79938e6i | 0.484578 | + | 0.839314i | 0.999843 | − | 0.0177168i | \(-0.00563972\pi\) |
−0.515265 | + | 0.857031i | \(0.672306\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.05840e6 | 0.762693 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.33300e6 | 0.313022 | 0.156511 | − | 0.987676i | \(-0.449975\pi\) | ||||
0.156511 | + | 0.987676i | \(0.449975\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.63429e6 | + | 1.66871e7i | 0.897859 | + | 1.55514i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.60044e6 | + | 6.23614e6i | 0.332968 | + | 0.576718i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.56244e6 | −0.326938 | −0.163469 | − | 0.986549i | \(-0.552268\pi\) | ||||
−0.163469 | + | 0.986549i | \(0.552268\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.00269e6 | + | 3.46875e6i | −0.182394 | + | 0.315915i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.54837e6 | −0.411096 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.65732e6 | − | 1.67270e7i | 0.866249 | − | 1.50039i | 0.000448081 | − | 1.00000i | \(-0.499857\pi\) |
0.865801 | − | 0.500388i | \(-0.166809\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.55793e6 | − | 9.62662e6i | 0.494777 | − | 0.856979i | −0.505205 | − | 0.863000i | \(-0.668583\pi\) |
0.999982 | + | 0.00602036i | \(0.00191635\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.35454e6 | − | 1.27384e7i | −0.649788 | − | 1.12547i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.64529e7 | − | 2.31169e7i | 1.44274 | − | 2.02710i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.28401e6 | + | 2.22398e6i | 0.111752 | + | 0.193560i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.61365e6 | + | 7.99108e6i | −0.398547 | + | 0.690303i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.53008e6 | + | 2.65018e6i | −0.131193 | + | 0.227232i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.82842e6 | 0.410929 | 0.205465 | − | 0.978665i | \(-0.434129\pi\) | ||||
0.205465 | + | 0.978665i | \(0.434129\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.20697e7 | − | 2.09052e7i | 1.01961 | − | 1.76602i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.20527e6 | −0.268777 | −0.134389 | − | 0.990929i | \(-0.542907\pi\) | ||||
−0.134389 | + | 0.990929i | \(0.542907\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.83956e6 | − | 1.01144e7i | −0.486078 | − | 0.841912i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.57360e6 | − | 2.72556e6i | −0.130025 | − | 0.225210i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.29678e7 | 1.88395 | 0.941973 | − | 0.335688i | \(-0.108969\pi\) | ||||
0.941973 | + | 0.335688i | \(0.108969\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.93780e6 | 0.809215 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −226804. | − | 392837.i | −0.0183341 | − | 0.0317556i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.09690e7 | − | 1.89989e7i | −0.880278 | − | 1.52469i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.10876e6 | 0.566368 | 0.283184 | − | 0.959066i | \(-0.408609\pi\) | ||||
0.283184 | + | 0.959066i | \(0.408609\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.93372e6 | + | 5.08135e6i | −0.232052 | + | 0.401926i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.22336e7 | −0.960707 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.33610e6 | − | 5.77829e6i | 0.260110 | − | 0.450523i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.36841e6 | − | 1.27625e7i | 0.570402 | − | 0.987965i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.73351e6 | + | 1.33948e7i | 0.594403 | + | 1.02954i | 0.993631 | + | 0.112685i | \(0.0359451\pi\) |
−0.399227 | + | 0.916852i | \(0.630722\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.73397e6 | + | 1.03592e7i | 0.361274 | + | 0.790569i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.59027e7 | + | 2.75443e7i | 1.20503 | + | 2.08717i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.11693e6 | − | 1.93458e6i | 0.0840381 | − | 0.145558i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.30537e6 | − | 1.09212e7i | 0.471081 | − | 0.815936i | −0.528372 | − | 0.849013i | \(-0.677197\pi\) |
0.999453 | + | 0.0330772i | \(0.0105307\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.89826e6 | −0.289199 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.38822e6 | + | 2.40446e6i | −0.102266 | + | 0.177131i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.56278e7 | −2.60630 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.93007e6 | + | 3.34298e6i | 0.140209 | + | 0.242849i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.02749e7 | − | 1.77967e7i | −0.741234 | − | 1.28386i | −0.951934 | − | 0.306304i | \(-0.900907\pi\) |
0.210699 | − | 0.977551i | \(-0.432426\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.09516e7 | −0.784581 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.33899e6 | −0.593291 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.60855e6 | − | 1.31784e7i | −0.537597 | − | 0.931146i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.28557e6 | − | 1.43510e7i | −0.581415 | − | 1.00704i | −0.995312 | − | 0.0967169i | \(-0.969166\pi\) |
0.413897 | − | 0.910324i | \(-0.364167\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.59414e7 | 1.11098 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.77363e6 | + | 8.26818e6i | −0.330412 | + | 0.572290i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.52568e7 | 1.73628 | 0.868139 | − | 0.496321i | \(-0.165316\pi\) | ||||
0.868139 | + | 0.496321i | \(0.165316\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.24164e7 | + | 2.15059e7i | −0.847770 | + | 1.46838i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.61060e7 | + | 2.78964e7i | −1.09224 | + | 1.89182i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.54248e6 | + | 1.13319e7i | 0.440688 | + | 0.763294i | 0.997741 | − | 0.0671833i | \(-0.0214012\pi\) |
−0.557053 | + | 0.830477i | \(0.688068\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.29109e6 | + | 1.37667e7i | 0.420901 | + | 0.921049i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.18603e6 | + | 2.05426e6i | 0.0788177 | + | 0.136516i | 0.902740 | − | 0.430186i | \(-0.141552\pi\) |
−0.823922 | + | 0.566703i | \(0.808219\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.29645e7 | + | 2.24552e7i | −0.855787 | + | 1.48227i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −639054. | + | 1.10687e6i | −0.0419021 | + | 0.0725766i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.51684e7 | −0.987953 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.34919e7 | + | 2.33686e7i | −0.872916 | + | 1.51193i | −0.0139493 | + | 0.999903i | \(0.504440\pi\) |
−0.858966 | + | 0.512032i | \(0.828893\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.00319e7 | −0.644758 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.26530e6 | − | 5.65567e6i | −0.208476 | − | 0.361091i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.46311e7 | + | 2.53419e7i | 0.927980 | + | 1.60731i | 0.786697 | + | 0.617340i | \(0.211790\pi\) |
0.141284 | + | 0.989969i | \(0.454877\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.16572e6 | 0.451497 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.62075e7 | −1.64045 | −0.820226 | − | 0.572040i | \(-0.806152\pi\) | ||||
−0.820226 | + | 0.572040i | \(0.806152\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.86677e7 | − | 3.23333e7i | −1.16086 | − | 2.01066i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.23418e6 | + | 7.33382e6i | 0.261587 | + | 0.453082i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.57321e7 | 1.57938 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.54995e6 | − | 4.41664e6i | 0.155495 | − | 0.269325i | −0.777744 | − | 0.628581i | \(-0.783636\pi\) |
0.933239 | + | 0.359256i | \(0.116969\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.86554e7 | −1.13023 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.67472e6 | + | 1.50250e7i | −0.522164 | + | 0.904414i | 0.477504 | + | 0.878630i | \(0.341542\pi\) |
−0.999668 | + | 0.0257842i | \(0.991792\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.22601e6 | − | 1.42479e7i | 0.491966 | − | 0.852110i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −9.33797e6 | − | 1.61738e7i | −0.554881 | − | 0.961082i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.98122e6 | + | 5.59373e6i | −0.235057 | + | 0.330262i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.85942e6 | − | 1.36129e7i | −0.461066 | − | 0.798589i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.28503e6 | − | 9.15394e6i | 0.308065 | − | 0.533585i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.62126e7 | − | 4.54016e7i | 1.51823 | − | 2.62965i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.89085e6 | 0.223928 | 0.111964 | − | 0.993712i | \(-0.464286\pi\) | ||||
0.111964 | + | 0.993712i | \(0.464286\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.98862e6 | + | 3.44439e6i | −0.113726 | + | 0.196979i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.90568e7 | 2.21950 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.04334e6 | + | 3.53917e6i | 0.115387 | + | 0.199856i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.00028e7 | − | 3.46459e7i | −1.12247 | − | 1.94417i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.46516e6 | −0.137467 | −0.0687336 | − | 0.997635i | \(-0.521896\pi\) | ||||
−0.0687336 | + | 0.997635i | \(0.521896\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.76817e7 | −2.08816 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.64576e6 | + | 4.58260e6i | 0.145703 | + | 0.252366i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.06714e7 | + | 3.58039e7i | 1.13131 | + | 1.95948i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.79389e7 | −0.975676 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.32873e7 | + | 2.30143e7i | −0.718212 | + | 1.24398i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.17605e7 | 0.631762 | 0.315881 | − | 0.948799i | \(-0.397700\pi\) | ||||
0.315881 | + | 0.948799i | \(0.397700\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.70469e6 | − | 8.14875e6i | 0.251176 | − | 0.435050i | −0.712674 | − | 0.701496i | \(-0.752516\pi\) |
0.963850 | + | 0.266446i | \(0.0858493\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.69656e6 | + | 1.67949e7i | −0.514507 | + | 0.891153i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.28427e6 | + | 1.26167e7i | 0.384142 | + | 0.665353i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.69674e6 | − | 8.00409e6i | 0.298587 | − | 0.419524i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.91781e6 | + | 6.78585e6i | 0.204096 | + | 0.353504i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.22161e6 | − | 5.57999e6i | 0.166807 | − | 0.288918i | −0.770488 | − | 0.637454i | \(-0.779988\pi\) |
0.937296 | + | 0.348536i | \(0.113321\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.61870e6 | − | 9.73187e6i | 0.289158 | − | 0.500837i | −0.684451 | − | 0.729059i | \(-0.739958\pi\) |
0.973609 | + | 0.228222i | \(0.0732912\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.24612e7 | −2.17199 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.80309e6 | − | 1.00513e7i | 0.295050 | − | 0.511042i | −0.679946 | − | 0.733262i | \(-0.737997\pi\) |
0.974997 | + | 0.222220i | \(0.0713303\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.34279e7 | −1.18399 | −0.591993 | − | 0.805943i | \(-0.701659\pi\) | ||||
−0.591993 | + | 0.805943i | \(0.701659\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.21433e6 | + | 1.42276e7i | 0.412638 | + | 0.714711i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.47105e7 | − | 2.54793e7i | −0.734537 | − | 1.27226i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.78513e7 | −1.38239 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.14278e7 | 0.563833 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.33046e7 | − | 2.30442e7i | −0.652523 | − | 1.13020i | −0.982509 | − | 0.186217i | \(-0.940377\pi\) |
0.329986 | − | 0.943986i | \(-0.392956\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.92396e6 | + | 1.19927e7i | 0.337571 | + | 0.584690i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.70832e7 | 1.31260 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.15783e6 | + | 1.06657e7i | −0.296678 | + | 0.513862i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.27554e7 | 1.08988 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 454389. | − | 787024.i | 0.0216351 | − | 0.0374730i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.60043e6 | − | 6.23613e6i | 0.170424 | − | 0.295183i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.75001e7 | + | 3.03111e7i | 0.823510 | + | 1.42636i | 0.903053 | + | 0.429530i | \(0.141321\pi\) |
−0.0795426 | + | 0.996831i | \(0.525346\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.62193e6 | − | 7.92580e6i | −0.169443 | − | 0.370790i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.77062e6 | − | 8.26296e6i | −0.221882 | − | 0.384312i | 0.733497 | − | 0.679692i | \(-0.237887\pi\) |
−0.955380 | + | 0.295381i | \(0.904553\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.79816e6 | − | 4.84656e6i | 0.129387 | − | 0.224105i | −0.794052 | − | 0.607849i | \(-0.792032\pi\) |
0.923439 | + | 0.383745i | \(0.125366\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.62906e6 | − | 9.74983e6i | 0.258779 | − | 0.448218i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.93765e6 | 0.317092 | 0.158546 | − | 0.987352i | \(-0.449319\pi\) | ||||
0.158546 | + | 0.987352i | \(0.449319\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.08507e7 | + | 1.87940e7i | −0.493081 | + | 0.854041i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.24829e7 | 0.563985 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.77168e7 | + | 3.06863e7i | 0.795856 | + | 1.37846i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.15086e7 | + | 3.72540e7i | 0.960653 | + | 1.66390i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.58686e6 | −0.159286 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.99494e7 | 2.20552 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.50749e6 | − | 9.53926e6i | −0.241799 | − | 0.418809i | 0.719428 | − | 0.694567i | \(-0.244404\pi\) |
−0.961227 | + | 0.275759i | \(0.911071\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.34975e7 | − | 2.33783e7i | −0.589224 | − | 1.02057i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.01700e7 | −1.30959 | −0.654796 | − | 0.755806i | \(-0.727246\pi\) | ||||
−0.654796 | + | 0.755806i | \(0.727246\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.52557e7 | − | 2.64237e7i | 0.658464 | − | 1.14049i | −0.322550 | − | 0.946552i | \(-0.604540\pi\) |
0.981013 | − | 0.193940i | \(-0.0621267\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.69243e7 | 2.01391 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.89963e6 | − | 6.75436e6i | 0.166423 | − | 0.288254i | −0.770736 | − | 0.637154i | \(-0.780111\pi\) |
0.937160 | + | 0.348900i | \(0.113445\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −27267.6 | + | 47228.8i | −0.00115716 | + | 0.00200425i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.09923e7 | − | 1.90392e7i | −0.463867 | − | 0.803441i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.86007e7 | + | 3.67641e6i | 1.61982 | + | 0.154275i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.17361e7 | − | 2.03275e7i | −0.489740 | − | 0.848254i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.78470e6 | − | 8.28734e6i | 0.198552 | − | 0.343901i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.60198e6 | − | 6.23882e6i | 0.148642 | − | 0.257456i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.73971e7 | 1.94509 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.05465e6 | + | 1.39511e7i | −0.328721 | + | 0.569361i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.72158e7 | −2.72803 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.48982e6 | − | 6.04454e6i | −0.140859 | − | 0.243975i | 0.786961 | − | 0.617002i | \(-0.211653\pi\) |
−0.927820 | + | 0.373027i | \(0.878320\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −343027. | − | 594141.i | −0.0137695 | − | 0.0238495i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.39353e7 | −0.955528 | −0.477764 | − | 0.878488i | \(-0.658553\pi\) | ||||
−0.477764 | + | 0.878488i | \(0.658553\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.16175e7 | 0.461247 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.72618e6 | + | 6.45393e6i | 0.147133 | + | 0.254842i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.00350e6 | − | 6.93427e6i | −0.157223 | − | 0.272319i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.03520e6 | −0.352898 | −0.176449 | − | 0.984310i | \(-0.556461\pi\) | ||||
−0.176449 | + | 0.984310i | \(0.556461\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.26680e7 | − | 2.19417e7i | 0.492108 | − | 0.852356i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.09916e7 | −0.811037 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.13347e7 | + | 3.69528e7i | −0.819846 | + | 1.42002i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.68170e6 | + | 2.91280e6i | −0.0642762 | + | 0.111330i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.55430e6 | − | 2.69212e6i | −0.0590874 | − | 0.102342i | 0.834969 | − | 0.550298i | \(-0.185486\pi\) |
−0.894056 | + | 0.447955i | \(0.852152\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.25834e7 | + | 2.75359e7i | 0.475798 | + | 1.04118i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.17942e7 | − | 2.04281e7i | −0.443571 | − | 0.768288i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.84869e7 | − | 6.66613e7i | 1.43974 | − | 2.49370i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.85807e7 | + | 3.21827e7i | −0.691374 | + | 1.19750i | 0.280013 | + | 0.959996i | \(0.409661\pi\) |
−0.971388 | + | 0.237499i | \(0.923672\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −722074. | −0.0267250 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.14651e6 | − | 1.41102e7i | 0.299915 | − | 0.519467i | −0.676202 | − | 0.736717i | \(-0.736375\pi\) |
0.976116 | + | 0.217249i | \(0.0697085\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.34078e6 | 0.158960 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.69184e7 | + | 6.39446e7i | 1.34482 | + | 2.32929i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.90876e7 | + | 3.30607e7i | 0.691634 | + | 1.19795i | 0.971302 | + | 0.237849i | \(0.0764424\pi\) |
−0.279668 | + | 0.960097i | \(0.590224\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.52108e7 | 1.99003 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.87694e7 | 0.672975 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.93217e6 | − | 6.81072e6i | −0.140249 | − | 0.242919i | 0.787341 | − | 0.616517i | \(-0.211457\pi\) |
−0.927590 | + | 0.373599i | \(0.878124\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −498713. | − | 863795.i | −0.0176946 | − | 0.0306480i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.85928e7 | −0.656243 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.93317e6 | + | 1.72047e7i | −0.348772 | + | 0.604090i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.08406e7 | −0.727949 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.32924e6 | + | 4.03436e6i | −0.0809373 | + | 0.140188i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.71825e7 | − | 8.17225e7i | 1.63103 | − | 2.82503i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.96743e6 | + | 3.40769e6i | 0.0676601 | + | 0.117191i | 0.897871 | − | 0.440259i | \(-0.145113\pi\) |
−0.830211 | + | 0.557450i | \(0.811780\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.25540e7 | − | 3.10050e6i | −1.11377 | − | 0.106077i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.28377e6 | − | 3.95561e6i | −0.0777329 | − | 0.134637i | 0.824539 | − | 0.565806i | \(-0.191435\pi\) |
−0.902271 | + | 0.431168i | \(0.858101\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.22279e7 | − | 2.11793e7i | 0.414065 | − | 0.717181i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.83522e7 | + | 4.91075e7i | −0.955158 | + | 1.65438i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.77743e7 | −0.595739 | −0.297870 | − | 0.954607i | \(-0.596276\pi\) | ||||
−0.297870 | + | 0.954607i | \(0.596276\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.40489e7 | − | 4.16539e7i | 0.801933 | − | 1.38899i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.14663e7 | −0.380409 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.38981e6 | + | 1.62636e7i | 0.309937 | + | 0.536826i | 0.978348 | − | 0.206966i | \(-0.0663588\pi\) |
−0.668412 | + | 0.743792i | \(0.733025\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.79937e6 | + | 1.52410e7i | 0.288975 | + | 0.500520i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.35811e7 | −2.07747 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.21124e6 | −0.201924 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.05047e7 | − | 3.55152e7i | −0.663239 | − | 1.14876i | −0.979760 | − | 0.200178i | \(-0.935848\pi\) |
0.316521 | − | 0.948586i | \(-0.397485\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 538295. | + | 932354.i | 0.0173240 | + | 0.0300060i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.19624e6 | −0.262456 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.23888e7 | + | 2.14579e7i | −0.394720 | + | 0.683676i | −0.993065 | − | 0.117563i | \(-0.962492\pi\) |
0.598345 | + | 0.801239i | \(0.295825\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.96389e7 | −0.939611 |
(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 | 76.6.e.a.45.3 | ✓ | 18 | |
3.2 | odd | 2 | 684.6.k.f.577.9 | 18 | |||
4.3 | odd | 2 | 304.6.i.d.273.7 | 18 | |||
19.11 | even | 3 | inner | 76.6.e.a.49.3 | yes | 18 | |
57.11 | odd | 6 | 684.6.k.f.505.9 | 18 | |||
76.11 | odd | 6 | 304.6.i.d.49.7 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.6.e.a.45.3 | ✓ | 18 | 1.1 | even | 1 | trivial | |
76.6.e.a.49.3 | yes | 18 | 19.11 | even | 3 | inner | |
304.6.i.d.49.7 | 18 | 76.11 | odd | 6 | |||
304.6.i.d.273.7 | 18 | 4.3 | odd | 2 | |||
684.6.k.f.505.9 | 18 | 57.11 | odd | 6 | |||
684.6.k.f.577.9 | 18 | 3.2 | odd | 2 |