Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,6,Mod(193,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.193");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(53.8889634572\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 118x^{6} + 555x^{5} + 12174x^{4} + 28215x^{3} + 199593x^{2} - 283824x + 1679616 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 168) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 289.1 | ||
Root | \(-2.82121 - 4.88647i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.289 |
Dual form | 336.6.q.k.193.1 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 4.50000 | + | 7.79423i | 0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −30.1755 | + | 52.2655i | −0.539796 | + | 0.934954i | 0.459119 | + | 0.888375i | \(0.348165\pi\) |
−0.998915 | + | 0.0465788i | \(0.985168\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 84.0301 | − | 98.7215i | 0.648172 | − | 0.761494i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −40.5000 | + | 70.1481i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.84136 | + | 6.65343i | 0.00957201 | + | 0.0165792i | 0.870772 | − | 0.491687i | \(-0.163620\pi\) |
−0.861200 | + | 0.508267i | \(0.830286\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −42.5391 | −0.0698120 | −0.0349060 | − | 0.999391i | \(-0.511113\pi\) | ||||
−0.0349060 | + | 0.999391i | \(0.511113\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −543.159 | −0.623302 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −68.9458 | − | 119.418i | −0.0578610 | − | 0.100218i | 0.835644 | − | 0.549271i | \(-0.185095\pi\) |
−0.893505 | + | 0.449053i | \(0.851761\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −542.790 | + | 940.140i | −0.344943 | + | 0.597460i | −0.985343 | − | 0.170582i | \(-0.945435\pi\) |
0.640400 | + | 0.768042i | \(0.278769\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1147.59 | + | 210.703i | 0.567858 | + | 0.104261i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1328.93 | + | 2301.78i | −0.523822 | + | 0.907286i | 0.475794 | + | 0.879557i | \(0.342161\pi\) |
−0.999615 | + | 0.0277290i | \(0.991172\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −258.622 | − | 447.946i | −0.0827589 | − | 0.143343i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2635.67 | −0.581963 | −0.290982 | − | 0.956729i | \(-0.593982\pi\) | ||||
−0.290982 | + | 0.956729i | \(0.593982\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1286.72 | + | 2228.66i | 0.240480 | + | 0.416523i | 0.960851 | − | 0.277065i | \(-0.0893619\pi\) |
−0.720371 | + | 0.693589i | \(0.756029\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −34.5722 | + | 59.8808i | −0.00552640 | + | 0.00957201i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2624.08 | + | 7370.85i | 0.362082 | + | 1.01706i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2872.65 | − | 4975.58i | 0.344968 | − | 0.597502i | −0.640380 | − | 0.768058i | \(-0.721223\pi\) |
0.985348 | + | 0.170556i | \(0.0545564\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −191.426 | − | 331.560i | −0.0201530 | − | 0.0349060i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −18194.0 | −1.69032 | −0.845161 | − | 0.534511i | \(-0.820496\pi\) | ||||
−0.845161 | + | 0.534511i | \(0.820496\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1725.55 | −0.142317 | −0.0711585 | − | 0.997465i | \(-0.522670\pi\) | ||||
−0.0711585 | + | 0.997465i | \(0.522670\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2444.22 | − | 4233.51i | −0.179932 | − | 0.311651i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7384.51 | + | 12790.3i | −0.487615 | + | 0.844574i | −0.999899 | − | 0.0142427i | \(-0.995466\pi\) |
0.512284 | + | 0.858816i | \(0.328800\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2684.87 | − | 16591.2i | −0.159747 | − | 0.987158i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 620.512 | − | 1074.76i | 0.0334060 | − | 0.0578610i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9397.31 | − | 16276.6i | −0.459530 | − | 0.795929i | 0.539406 | − | 0.842046i | \(-0.318649\pi\) |
−0.998936 | + | 0.0461167i | \(0.985315\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −463.660 | −0.0206677 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9770.22 | −0.398306 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3977.27 | − | 6888.84i | −0.148750 | − | 0.257642i | 0.782016 | − | 0.623258i | \(-0.214191\pi\) |
−0.930766 | + | 0.365617i | \(0.880858\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 25481.1 | − | 44134.6i | 0.876787 | − | 1.51864i | 0.0219404 | − | 0.999759i | \(-0.493016\pi\) |
0.854847 | − | 0.518881i | \(-0.173651\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3521.90 | + | 9892.77i | 0.111796 | + | 0.314027i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1283.64 | − | 2223.33i | 0.0376842 | − | 0.0652710i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11682.8 | − | 20235.2i | −0.317951 | − | 0.550707i | 0.662109 | − | 0.749407i | \(-0.269661\pi\) |
−0.980060 | + | 0.198700i | \(0.936328\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −23920.8 | −0.604857 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −60027.2 | −1.41320 | −0.706598 | − | 0.707615i | \(-0.749771\pi\) | ||||
−0.706598 | + | 0.707615i | \(0.749771\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10029.5 | − | 17371.6i | −0.220278 | − | 0.381532i | 0.734614 | − | 0.678485i | \(-0.237363\pi\) |
−0.954892 | + | 0.296952i | \(0.904030\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2327.59 | − | 4031.51i | 0.0477809 | − | 0.0827589i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 979.626 | + | 179.864i | 0.0188293 | + | 0.00345714i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −23591.6 | + | 40861.9i | −0.425295 | + | 0.736632i | −0.996448 | − | 0.0842114i | \(-0.973163\pi\) |
0.571153 | + | 0.820843i | \(0.306496\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3280.50 | − | 5681.99i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 42207.0 | 0.672496 | 0.336248 | − | 0.941773i | \(-0.390842\pi\) | ||||
0.336248 | + | 0.941773i | \(0.390842\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8321.90 | 0.124932 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −11860.5 | − | 20543.0i | −0.167998 | − | 0.290982i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −17189.2 | + | 29772.6i | −0.230029 | + | 0.398421i | −0.957816 | − | 0.287381i | \(-0.907215\pi\) |
0.727788 | + | 0.685803i | \(0.240549\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3574.57 | + | 4199.53i | −0.0452502 | + | 0.0531615i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −11580.4 | + | 20057.9i | −0.138841 | + | 0.240480i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −32757.9 | − | 56738.4i | −0.372398 | − | 0.645012i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −85606.4 | −0.923797 | −0.461899 | − | 0.886933i | \(-0.652832\pi\) | ||||
−0.461899 | + | 0.886933i | \(0.652832\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −622.300 | −0.00638134 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 36100.5 | + | 62528.0i | 0.352136 | + | 0.609917i | 0.986623 | − | 0.163016i | \(-0.0521222\pi\) |
−0.634488 | + | 0.772933i | \(0.718789\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17672.1 | + | 30609.1i | −0.164133 | + | 0.284287i | −0.936347 | − | 0.351076i | \(-0.885816\pi\) |
0.772214 | + | 0.635363i | \(0.219149\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −45641.7 | + | 53621.5i | −0.404007 | + | 0.474641i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 24080.8 | − | 41709.1i | 0.203335 | − | 0.352186i | −0.746266 | − | 0.665648i | \(-0.768155\pi\) |
0.949601 | + | 0.313462i | \(0.101489\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8178.25 | + | 14165.1i | 0.0659316 | + | 0.114197i | 0.897107 | − | 0.441814i | \(-0.145665\pi\) |
−0.831175 | + | 0.556011i | \(0.812331\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 51707.8 | 0.398335 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −146029. | −1.07583 | −0.537913 | − | 0.843000i | \(-0.680787\pi\) | ||||
−0.537913 | + | 0.843000i | \(0.680787\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −80202.4 | − | 138915.i | −0.565514 | − | 0.979498i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1722.83 | − | 2984.04i | 0.0116353 | − | 0.0201530i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −17582.6 | − | 3228.25i | −0.113819 | − | 0.0208977i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 80496.0 | − | 139423.i | 0.499817 | − | 0.865708i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −81873.2 | − | 141809.i | −0.487954 | − | 0.845161i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −157381. | −0.900900 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −348590. | −1.91781 | −0.958905 | − | 0.283727i | \(-0.908429\pi\) | ||||
−0.958905 | + | 0.283727i | \(0.908429\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7764.98 | − | 13449.3i | −0.0410834 | − | 0.0711585i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 149743. | − | 259363.i | 0.762376 | − | 1.32047i | −0.179247 | − | 0.983804i | \(-0.557366\pi\) |
0.941623 | − | 0.336669i | \(-0.109300\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 47201.3 | + | 132585.i | 0.231380 | + | 0.649929i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 21997.9 | − | 38101.5i | 0.103884 | − | 0.179932i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −49324.5 | − | 85432.5i | −0.224523 | − | 0.388885i | 0.731653 | − | 0.681677i | \(-0.238749\pi\) |
−0.956176 | + | 0.292792i | \(0.905416\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −297028. | −1.30395 | −0.651974 | − | 0.758241i | \(-0.726059\pi\) | ||||
−0.651974 | + | 0.758241i | \(0.726059\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −132921. | −0.563049 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −163.408 | − | 283.031i | −0.000668241 | − | 0.00115743i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 79532.6 | − | 137754.i | 0.314141 | − | 0.544109i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 117233. | − | 95586.7i | 0.447464 | − | 0.364842i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −65087.1 | + | 112734.i | −0.240176 | + | 0.415997i | −0.960764 | − | 0.277366i | \(-0.910538\pi\) |
0.720588 | + | 0.693363i | \(0.243872\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −82198.7 | − | 142372.i | −0.293375 | − | 0.508140i | 0.681231 | − | 0.732069i | \(-0.261445\pi\) |
−0.974606 | + | 0.223929i | \(0.928112\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 11169.2 | 0.0385740 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −155309. | −0.519240 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 41102.3 | + | 71191.2i | 0.133081 | + | 0.230503i | 0.924863 | − | 0.380301i | \(-0.124180\pi\) |
−0.791782 | + | 0.610804i | \(0.790846\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 84575.8 | − | 146490.i | 0.265310 | − | 0.459530i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 115565. | + | 324613.i | 0.351367 | + | 0.986964i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −216939. | + | 375749.i | −0.639541 | + | 1.10772i | 0.345992 | + | 0.938237i | \(0.387542\pi\) |
−0.985534 | + | 0.169480i | \(0.945791\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2086.47 | − | 3613.87i | −0.00596626 | − | 0.0103339i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 353734. | 0.981488 | 0.490744 | − | 0.871304i | \(-0.336725\pi\) | ||||
0.490744 | + | 0.871304i | \(0.336725\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −369483. | −0.995126 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −43966.0 | − | 76151.3i | −0.114981 | − | 0.199153i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −201313. | + | 348685.i | −0.511396 | + | 0.885763i | 0.488517 | + | 0.872554i | \(0.337538\pi\) |
−0.999913 | + | 0.0132089i | \(0.995795\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −65953.9 | − | 12109.4i | −0.162797 | − | 0.0298902i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 35795.5 | − | 61999.6i | 0.0858806 | − | 0.148750i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 206755. | + | 358111.i | 0.482308 | + | 0.835382i | 0.999794 | − | 0.0203099i | \(-0.00646529\pi\) |
−0.517486 | + | 0.855692i | \(0.673132\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 552811. | 1.25424 | 0.627119 | − | 0.778923i | \(-0.284234\pi\) | ||||
0.627119 | + | 0.778923i | \(0.284234\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 458660. | 1.01243 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 173367. | + | 300281.i | 0.372425 | + | 0.645058i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 529.691 | − | 917.452i | 0.00110769 | − | 0.00191858i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −61258.0 | + | 71968.0i | −0.124741 | + | 0.146550i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −395164. | + | 684444.i | −0.783779 | + | 1.35755i | 0.145947 | + | 0.989292i | \(0.453377\pi\) |
−0.929726 | + | 0.368253i | \(0.879956\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −235888. | − | 408569.i | −0.455839 | − | 0.789537i | 0.542897 | − | 0.839800i | \(-0.317328\pi\) |
−0.998736 | + | 0.0502625i | \(0.983994\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 23105.5 | 0.0435140 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 188443. | 0.345951 | 0.172976 | − | 0.984926i | \(-0.444662\pi\) | ||||
0.172976 | + | 0.984926i | \(0.444662\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 533185. | + | 923504.i | 0.954433 | + | 1.65313i | 0.735660 | + | 0.677351i | \(0.236872\pi\) |
0.218773 | + | 0.975776i | \(0.429794\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 105145. | − | 182117.i | 0.183569 | − | 0.317951i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −221476. | + | 260197.i | −0.377212 | + | 0.443162i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 549014. | − | 950921.i | 0.912429 | − | 1.58037i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −107644. | − | 186444.i | −0.174607 | − | 0.302429i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8340.20 | −0.0132072 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 69397.7 | 0.107310 | 0.0536548 | − | 0.998560i | \(-0.482913\pi\) | ||||
0.0536548 | + | 0.998560i | \(0.482913\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −270122. | − | 467866.i | −0.407954 | − | 0.706598i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 52069.4 | − | 90186.8i | 0.0768221 | − | 0.133060i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 328139. | + | 60247.9i | 0.473052 | + | 0.0868545i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 90265.2 | − | 156344.i | 0.127177 | − | 0.220278i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2932.89 | + | 5079.92i | 0.00403939 | + | 0.00699643i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.15636e6 | 1.55715 | 0.778574 | − | 0.627553i | \(-0.215943\pi\) | ||||
0.778574 | + | 0.627553i | \(0.215943\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 41896.7 | 0.0551726 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 309983. | + | 536906.i | 0.399275 | + | 0.691565i | 0.993637 | − | 0.112633i | \(-0.0359284\pi\) |
−0.594361 | + | 0.804198i | \(0.702595\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 324585. | − | 562198.i | 0.409016 | − | 0.708436i | −0.585764 | − | 0.810482i | \(-0.699205\pi\) |
0.994780 | + | 0.102045i | \(0.0325387\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3006.42 | + | 8444.82i | 0.00370697 | + | 0.0104126i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 133434. | − | 231115.i | 0.161019 | − | 0.278893i | −0.774215 | − | 0.632922i | \(-0.781855\pi\) |
0.935234 | + | 0.354029i | \(0.115189\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −445662. | − | 771910.i | −0.526425 | − | 0.911794i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −424649. | −0.491088 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 504518. | 0.571323 | 0.285661 | − | 0.958331i | \(-0.407787\pi\) | ||||
0.285661 | + | 0.958331i | \(0.407787\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −452336. | − | 783469.i | −0.501670 | − | 0.868918i | −0.999998 | − | 0.00192971i | \(-0.999386\pi\) |
0.498328 | − | 0.866989i | \(-0.333948\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 29524.5 | − | 51137.9i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 948163. | + | 360320.i | 1.00918 | + | 0.383507i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 23089.8 | − | 39992.7i | 0.0240812 | − | 0.0417099i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 189932. | + | 328971.i | 0.194133 | + | 0.336248i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.43747e6 | 1.44018 | 0.720089 | − | 0.693882i | \(-0.244101\pi\) | ||||
0.720089 | + | 0.693882i | \(0.244101\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −20419.6 | −0.0200561 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 37448.5 | + | 64862.8i | 0.0360649 | + | 0.0624662i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −550635. | + | 953728.i | −0.520033 | + | 0.900724i | 0.479695 | + | 0.877435i | \(0.340747\pi\) |
−0.999729 | + | 0.0232892i | \(0.992586\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −249807. | − | 701691.i | −0.231396 | − | 0.649975i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 106745. | − | 184887.i | 0.0969939 | − | 0.167998i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 630499. | + | 1.09206e6i | 0.562076 | + | 0.973544i | 0.997315 | + | 0.0732293i | \(0.0233305\pi\) |
−0.435239 | + | 0.900315i | \(0.643336\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.13427e6 | 0.992209 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −309406. | −0.265614 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −241521. | − | 418327.i | −0.203505 | − | 0.352481i | 0.746150 | − | 0.665777i | \(-0.231900\pi\) |
−0.949655 | + | 0.313297i | \(0.898567\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −259591. | + | 449624.i | −0.214717 | + | 0.371900i | −0.953185 | − | 0.302388i | \(-0.902216\pi\) |
0.738468 | + | 0.674288i | \(0.235549\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −48817.6 | − | 8963.13i | −0.0396433 | − | 0.00727869i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1986.92 | − | 3441.44i | 0.00158434 | − | 0.00274415i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.18853e6 | + | 2.05860e6i | 0.930704 | + | 1.61203i | 0.782122 | + | 0.623126i | \(0.214138\pi\) |
0.148582 | + | 0.988900i | \(0.452529\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −208448. | −0.160320 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 940528. | 0.710568 | 0.355284 | − | 0.934758i | \(-0.384384\pi\) | ||||
0.355284 | + | 0.934758i | \(0.384384\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −324746. | − | 562477.i | −0.241034 | − | 0.417483i | 0.719975 | − | 0.694000i | \(-0.244153\pi\) |
−0.961009 | + | 0.276517i | \(0.910820\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 294821. | − | 510646.i | 0.215004 | − | 0.372398i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.52885e6 | + | 1.79614e6i | −1.09562 | + | 1.28717i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 700421. | − | 1.21317e6i | 0.493304 | − | 0.854428i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −385229. | − | 667236.i | −0.266677 | − | 0.461899i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −793396. | −0.539909 | −0.269955 | − | 0.962873i | \(-0.587009\pi\) | ||||
−0.269955 | + | 0.962873i | \(0.587009\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 480065. | 0.321177 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2800.35 | − | 4850.35i | −0.00184213 | − | 0.00319067i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 56531.6 | − | 97915.7i | 0.0365691 | − | 0.0633395i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −144998. | + | 170349.i | −0.0922458 | + | 0.108374i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −324905. | + | 562752.i | −0.203306 | + | 0.352136i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.53781e6 | + | 2.66357e6i | 0.946572 | + | 1.63951i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.08282e6 | 1.26126 | 0.630632 | − | 0.776082i | \(-0.282796\pi\) | ||||
0.630632 | + | 0.776082i | \(0.282796\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −318099. | −0.189525 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 598523. | + | 1.03667e6i | 0.350897 | + | 0.607772i | 0.986407 | − | 0.164321i | \(-0.0525433\pi\) |
−0.635510 | + | 0.772093i | \(0.719210\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.29207e6 | + | 2.23793e6i | −0.745460 | + | 1.29117i | 0.204520 | + | 0.978862i | \(0.434437\pi\) |
−0.949980 | + | 0.312311i | \(0.898897\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −623326. | − | 114445.i | −0.353947 | − | 0.0649863i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −645757. | + | 1.11848e6i | −0.360928 | + | 0.625146i | −0.988114 | − | 0.153724i | \(-0.950873\pi\) |
0.627185 | + | 0.778870i | \(0.284207\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10124.5 | − | 17536.2i | −0.00557056 | − | 0.00964849i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 433454. | 0.234791 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 149692. | 0.0798350 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11001.5 | + | 19055.2i | 0.00577756 | + | 0.0100070i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −73604.2 | + | 127486.i | −0.0380657 | + | 0.0659316i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 642161. | + | 1.80378e6i | 0.327080 | + | 0.918744i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.55407e6 | − | 2.69172e6i | 0.779650 | − | 1.35039i | −0.152493 | − | 0.988305i | \(-0.548730\pi\) |
0.932143 | − | 0.362089i | \(-0.117937\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 232685. | + | 403022.i | 0.114989 | + | 0.199167i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.41014e6 | 0.686515 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.45367e6 | −1.65656 | −0.828278 | − | 0.560318i | \(-0.810679\pi\) | ||||
−0.828278 | + | 0.560318i | \(0.810679\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −657129. | − | 1.13818e6i | −0.310564 | − | 0.537913i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9885.48 | + | 17122.1i | −0.00460375 | + | 0.00797393i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.86351e6 | − | 1.12910e6i | −0.855259 | − | 0.518201i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 721822. | − | 1.25023e6i | 0.326499 | − | 0.565514i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.52325e6 | − | 2.63834e6i | −0.679119 | − | 1.17627i | −0.975246 | − | 0.221121i | \(-0.929028\pi\) |
0.296127 | − | 0.955149i | \(-0.404305\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.94475e6 | −1.73363 | −0.866814 | − | 0.498631i | \(-0.833836\pi\) | ||||
−0.866814 | + | 0.498631i | \(0.833836\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 31011.0 | 0.0134353 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −163086. | − | 282473.i | −0.0696594 | − | 0.120654i | 0.829092 | − | 0.559112i | \(-0.188858\pi\) |
−0.898751 | + | 0.438459i | \(0.855525\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.81135e6 | − | 3.13735e6i | 0.762837 | − | 1.32127i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −53960.1 | − | 151570.i | −0.0224079 | − | 0.0629423i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.83256e6 | + | 3.17408e6i | −0.750450 | + | 1.29982i | 0.197155 | + | 0.980372i | \(0.436830\pi\) |
−0.947605 | + | 0.319445i | \(0.896504\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 648807. | + | 1.12377e6i | 0.262028 | + | 0.453846i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.44893e6 | 0.577139 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.21058e6 | 0.475620 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 419401. | + | 726423.i | 0.162541 | + | 0.281530i | 0.935779 | − | 0.352586i | \(-0.114698\pi\) |
−0.773238 | + | 0.634116i | \(0.781364\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 736859. | − | 1.27628e6i | 0.281720 | − | 0.487954i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.39651e6 | − | 440010.i | −0.903950 | − | 0.165969i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 883385. | − | 1.53007e6i | 0.328759 | − | 0.569427i | −0.653507 | − | 0.756921i | \(-0.726703\pi\) |
0.982266 | + | 0.187493i | \(0.0600362\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −708213. | − | 1.22666e6i | −0.260067 | − | 0.450450i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 112119. | 0.0406280 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.02568e6 | −0.366786 | −0.183393 | − | 0.983040i | \(-0.558708\pi\) | ||||
−0.183393 | + | 0.983040i | \(0.558708\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.56866e6 | − | 2.71699e6i | −0.553624 | − | 0.958905i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −981203. | + | 1.69949e6i | −0.341792 | + | 0.592001i | −0.984766 | − | 0.173887i | \(-0.944367\pi\) |
0.642974 | + | 0.765888i | \(0.277701\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −38961.4 | + | 45773.2i | −0.0133962 | + | 0.0157383i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 69884.8 | − | 121044.i | 0.0237195 | − | 0.0410834i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.81474e6 | + | 3.14322e6i | 0.608052 | + | 1.05318i | 0.991561 | + | 0.129640i | \(0.0413821\pi\) |
−0.383509 | + | 0.923537i | \(0.625285\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 366498. | 0.121235 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.69538e6 | 0.880316 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.42378e6 | − | 2.46606e6i | −0.459145 | − | 0.795262i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.49711e6 | + | 2.59307e6i | −0.476735 | + | 0.825728i | −0.999645 | − | 0.0266595i | \(-0.991513\pi\) |
0.522910 | + | 0.852388i | \(0.324846\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −820993. | + | 964531.i | −0.258171 | + | 0.303308i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.13003e6 | − | 3.68931e6i | 0.661491 | − | 1.14574i | −0.318733 | − | 0.947845i | \(-0.603257\pi\) |
0.980224 | − | 0.197892i | \(-0.0634094\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −54735.8 | − | 94805.2i | −0.0167884 | − | 0.0290783i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 395963. | 0.119955 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 44139.6 | 0.0132081 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.44228e6 | − | 2.49811e6i | −0.426326 | − | 0.738419i | 0.570217 | − | 0.821494i | \(-0.306859\pi\) |
−0.996543 | + | 0.0830751i | \(0.973526\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 443920. | − | 768893.i | 0.129628 | − | 0.224523i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.01429e6 | − | 186228.i | −0.292608 | − | 0.0537241i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.27362e6 | + | 2.20597e6i | −0.363010 | + | 0.628753i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.33663e6 | − | 2.31510e6i | −0.376417 | − | 0.651974i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −232038. | −0.0645690 | −0.0322845 | − | 0.999479i | \(-0.510278\pi\) | ||||
−0.0322845 | + | 0.999479i | \(0.510278\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.39524e6 | −0.933609 | −0.466805 | − | 0.884360i | \(-0.654595\pi\) | ||||
−0.466805 | + | 0.884360i | \(0.654595\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −598145. | − | 1.03602e6i | −0.162538 | − | 0.281525i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −35661.7 | + | 61768.0i | −0.00957702 | + | 0.0165879i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.21585e6 | − | 6.22417e6i | −0.588127 | − | 1.65201i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1470.67 | − | 2547.28i | 0.000385809 | − | 0.000668241i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.43893e6 | + | 4.22435e6i | 0.632421 | + | 1.09539i | 0.987055 | + | 0.160380i | \(0.0512720\pi\) |
−0.354634 | + | 0.935005i | \(0.615395\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 931802. | 0.238838 | 0.119419 | − | 0.992844i | \(-0.461897\pi\) | ||||
0.119419 | + | 0.992844i | \(0.461897\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.43159e6 | 0.362739 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.44266e6 | − | 2.49877e6i | −0.361378 | − | 0.625925i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 741706. | − | 1.28467e6i | 0.183684 | − | 0.318149i | −0.759449 | − | 0.650567i | \(-0.774531\pi\) |
0.943132 | + | 0.332418i | \(0.107865\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.27258e6 | + | 483604.i | 0.311592 | + | 0.118411i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.26750e6 | + | 3.92743e6i | −0.548957 | + | 0.950821i | 0.449390 | + | 0.893336i | \(0.351641\pi\) |
−0.998346 | + | 0.0574849i | \(0.981692\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.03739e6 | − | 1.79681e6i | −0.248337 | − | 0.430132i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.17157e6 | −0.277331 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.80527e6 | −1.35896 | −0.679479 | − | 0.733695i | \(-0.737794\pi\) | ||||
−0.679479 | + | 0.733695i | \(0.737794\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −69889.8 | − | 121053.i | −0.0161798 | − | 0.0280242i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 739789. | − | 1.28135e6i | 0.169380 | − | 0.293375i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −111626. | − | 313549.i | −0.0252776 | − | 0.0710031i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.97166e6 | − | 3.41502e6i | 0.441613 | − | 0.764897i | −0.556196 | − | 0.831051i | \(-0.687740\pi\) |
0.997809 | + | 0.0661543i | \(0.0210730\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 50261.5 | + | 87055.5i | 0.0111353 | + | 0.0192870i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.03473e6 | −0.665070 | −0.332535 | − | 0.943091i | \(-0.607904\pi\) | ||||
−0.332535 | + | 0.943091i | \(0.607904\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.47871e6 | −0.320575 | −0.160288 | − | 0.987070i | \(-0.551242\pi\) | ||||
−0.160288 | + | 0.987070i | \(0.551242\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −698892. | − | 1.21052e6i | −0.149892 | − | 0.259620i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 511990. | − | 886792.i | 0.108635 | − | 0.188161i | −0.806583 | − | 0.591121i | \(-0.798685\pi\) |
0.915217 | + | 0.402960i | \(0.132019\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.97936e6 | − | 547024.i | −0.625447 | − | 0.114835i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −369920. | + | 640721.i | −0.0768345 | + | 0.133081i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6628.46 | − | 11480.8i | −0.00136226 | − | 0.00235950i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 561509. | 0.114189 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.52236e6 | 0.306353 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.17762e6 | + | 5.50380e6i | 0.632796 | + | 1.09603i | 0.986978 | + | 0.160858i | \(0.0514260\pi\) |
−0.354182 | + | 0.935176i | \(0.615241\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −122200. | + | 211657.i | −0.0240829 | + | 0.0417128i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.01007e6 | + | 2.36150e6i | −0.392051 | + | 0.460595i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.58321e6 | − | 4.47426e6i | 0.498662 | − | 0.863708i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.00131e6 | + | 6.93047e6i | 0.764504 | + | 1.32416i | 0.940508 | + | 0.339770i | \(0.110349\pi\) |
−0.176005 | + | 0.984389i | \(0.556317\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.90490e6 | −0.738478 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.89285e6 | −0.541530 | −0.270765 | − | 0.962646i | \(-0.587277\pi\) | ||||
−0.270765 | + | 0.962646i | \(0.587277\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 181718. | + | 314745.i | 0.0336730 | + | 0.0583233i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 18778.2 | − | 32524.8i | 0.00344462 | − | 0.00596626i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.04409e6 | + | 5.92598e6i | −0.915993 | + | 1.07614i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.83363e6 | + | 4.90799e6i | −0.509438 | + | 0.882373i | 0.490502 | + | 0.871440i | \(0.336813\pi\) |
−0.999940 | + | 0.0109328i | \(0.996520\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.59180e6 | + | 2.75708e6i | 0.283331 | + | 0.490744i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 458347. | 0.0807746 | 0.0403873 | − | 0.999184i | \(-0.487141\pi\) | ||||
0.0403873 | + | 0.999184i | \(0.487141\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.35741e6 | −0.760326 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.66268e6 | − | 2.87984e6i | −0.287268 | − | 0.497563i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.46450e6 | − | 7.73274e6i | 0.763798 | − | 1.32294i | −0.177082 | − | 0.984196i | \(-0.556666\pi\) |
0.940880 | − | 0.338740i | \(-0.110001\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.55772e6 | − | 469609.i | −0.433313 | − | 0.0795581i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 395694. | − | 685362.i | 0.0663844 | − | 0.114981i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.06653e6 | − | 1.84729e6i | −0.177197 | − | 0.306914i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −113466. | −0.0186698 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.62364e6 | −0.590509 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.51245e6 | − | 4.35170e6i | −0.405512 | − | 0.702367i | 0.588869 | − | 0.808229i | \(-0.299573\pi\) |
−0.994381 | + | 0.105861i | \(0.966240\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.06664e6 | − | 5.31158e6i | 0.490240 | − | 0.849121i | −0.509696 | − | 0.860354i | \(-0.670242\pi\) |
0.999937 | + | 0.0112329i | \(0.00357563\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −202409. | − | 568552.i | −0.0320502 | − | 0.0900268i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 177427. | − | 307313.i | 0.0278288 | − | 0.0482009i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −313955. | − | 543786.i | −0.0487785 | − | 0.0844868i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 644319. | 0.0991663 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 773959. | 0.118005 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.45330e6 | + | 2.51719e6i | 0.219518 | + | 0.380217i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.86080e6 | + | 3.22300e6i | −0.278461 | + | 0.482308i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 100075. | − | 81596.2i | 0.0148372 | − | 0.0120976i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.24987e6 | − | 2.16484e6i | 0.183599 | − | 0.318004i | −0.759504 | − | 0.650502i | \(-0.774558\pi\) |
0.943104 | + | 0.332499i | \(0.107892\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.48765e6 | + | 4.30873e6i | 0.362068 | + | 0.627119i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −987131. | −0.142358 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.07863e6 | −1.01153 | −0.505767 | − | 0.862670i | \(-0.668791\pi\) | ||||
−0.505767 | + | 0.862670i | \(0.668791\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.06397e6 | + | 3.57490e6i | 0.292262 | + | 0.506213i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.43061e6 | − | 2.47790e6i | 0.200744 | − | 0.347700i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.05154e6 | + | 5.76263e6i | 0.285277 | + | 0.801323i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.56031e6 | + | 2.70253e6i | −0.215019 | + | 0.372425i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.86600e6 | + | 1.01602e7i | 0.801132 | + | 1.38760i | 0.918871 | + | 0.394557i | \(0.129102\pi\) |
−0.117739 | + | 0.993045i | \(0.537565\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 73403.5 | 0.00993544 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9534.44 | 0.00127905 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.77645e6 | − | 8.27305e6i | −0.635088 | − | 1.10001i | −0.986496 | − | 0.163783i | \(-0.947630\pi\) |
0.351408 | − | 0.936222i | \(-0.385703\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.40649e6 | − | 7.63226e6i | 0.580726 | − | 1.00585i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −836596. | − | 153603.i | −0.109284 | − | 0.0200651i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.92055e6 | + | 6.79058e6i | −0.507652 | + | 0.879279i | 0.492309 | + | 0.870420i | \(0.336153\pi\) |
−0.999961 | + | 0.00885809i | \(0.997180\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.22895e6 | + | 3.86066e6i | 0.286095 | + | 0.495531i | 0.972874 | − | 0.231335i | \(-0.0743093\pi\) |
−0.686779 | + | 0.726866i | \(0.740976\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.11295e6 | −0.905030 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.37476e6 | 0.173404 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.72772e6 | + | 4.72456e6i | 0.341084 | + | 0.590774i | 0.984634 | − | 0.174629i | \(-0.0558728\pi\) |
−0.643551 | + | 0.765404i | \(0.722539\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.12299e6 | − | 3.67712e6i | 0.263179 | − | 0.455839i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.54666e6 | − | 4.16674e6i | 0.435893 | − | 0.512102i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 72196.8 | − | 125049.i | 0.00879725 | − | 0.0152373i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 103975. | + | 180090.i | 0.0125614 | + | 0.0217570i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.52379e6 | 0.661670 | 0.330835 | − | 0.943689i | \(-0.392670\pi\) | ||||
0.330835 | + | 0.943689i | \(0.392670\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.79367e6 | −0.331808 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 847995. | + | 1.46877e6i | 0.0998676 | + | 0.172976i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.32543e6 | − | 7.49187e6i | 0.505118 | − | 0.874890i | −0.494865 | − | 0.868970i | \(-0.664782\pi\) |
0.999982 | − | 0.00591957i | \(-0.00188427\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 699290. | − | 821550.i | 0.0809776 | − | 0.0951353i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.79867e6 | + | 8.31154e6i | −0.551042 | + | 0.954433i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.10796e6 | − | 1.05793e7i | −0.695551 | − | 1.20473i | −0.969995 | − | 0.243127i | \(-0.921827\pi\) |
0.274444 | − | 0.961603i | \(-0.411506\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.61479e7 | 1.82360 | 0.911801 | − | 0.410632i | \(-0.134692\pi\) | ||||
0.911801 | + | 0.410632i | \(0.134692\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.89262e6 | 0.211967 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.85801e6 | + | 8.41433e6i | 0.539598 | + | 0.934611i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.52286e6 | − | 9.56587e6i | 0.608404 | − | 1.05379i | −0.383100 | − | 0.923707i | \(-0.625143\pi\) |
0.991504 | − | 0.130080i | \(-0.0415233\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.02468e6 | − | 555344.i | −0.330473 | − | 0.0606763i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 314130. | − | 544090.i | 0.0340414 | − | 0.0589614i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.17071e6 | + | 8.95593e6i | 0.555775 | + | 0.962631i | 0.997843 | + | 0.0656490i | \(0.0209118\pi\) |
−0.442068 | + | 0.896982i | \(0.645755\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.88226e6 | 1.05358 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.11422e7 | −1.17831 | −0.589154 | − | 0.808021i | \(-0.700539\pi\) | ||||
−0.589154 | + | 0.808021i | \(0.700539\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −570310. | − | 987806.i | −0.0598252 | − | 0.103620i | 0.834562 | − | 0.550915i | \(-0.185721\pi\) |
−0.894387 | + | 0.447294i | \(0.852388\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 968792. | − | 1.67800e6i | 0.100810 | − | 0.174607i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.49479e6 | + | 4.19875e6i | 0.154297 | + | 0.433411i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.55723e6 | − | 9.62541e6i | 0.569061 | − | 0.985642i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −37530.9 | − | 65005.5i | −0.00381259 | − | 0.00660360i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −792230. | −0.0798407 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.26422e6 | −0.726299 | −0.363150 | − | 0.931731i | \(-0.618299\pi\) | ||||
−0.363150 | + | 0.931731i | \(0.618299\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 312290. | + | 540901.i | 0.0309776 | + | 0.0536548i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.05189e7 | − | 1.82192e7i | 1.03523 | − | 1.79306i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 114212. | + | 705774.i | 0.0111523 | + | 0.0689155i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.43110e6 | − | 4.21079e6i | 0.235533 | − | 0.407954i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.32494e6 | + | 9.22307e6i | 0.511882 | + | 0.886605i | 0.999905 | + | 0.0137746i | \(0.00438474\pi\) |
−0.488023 | + | 0.872831i | \(0.662282\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.95575e6 | −0.186546 | −0.0932730 | − | 0.995641i | \(-0.529733\pi\) | ||||
−0.0932730 | + | 0.995641i | \(0.529733\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 937249. | 0.0887065 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 645496. | + | 1.11803e6i | 0.0606224 | + | 0.105001i | 0.894744 | − | 0.446580i | \(-0.147358\pi\) |
−0.834121 | + | 0.551581i | \(0.814025\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 30556.3 | − | 52925.0i | 0.00284766 | − | 0.00493230i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.00704e6 | + | 2.82871e6i | 0.0931312 | + | 0.261599i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.31437e6 | + | 9.20475e6i | −0.487718 | + | 0.844752i | −0.999900 | − | 0.0141249i | \(-0.995504\pi\) |
0.512183 | + | 0.858877i | \(0.328837\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.03716e6 | + | 1.56528e7i | 0.823054 | + | 1.42557i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.62477e6 | 0.146852 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.25503e6 | −0.291972 | −0.145986 | − | 0.989287i | \(-0.546635\pi\) | ||||
−0.145986 | + | 0.989287i | \(0.546635\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.40454e6 | + | 5.89684e6i | 0.303078 | + | 0.524947i | 0.976832 | − | 0.214009i | \(-0.0686522\pi\) |
−0.673753 | + | 0.738956i | \(0.735319\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −26396.1 | + | 45719.3i | −0.00233214 | + | 0.00403939i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.35395e6 | − | 1.53382e6i | −0.732551 | − | 0.134500i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.50263e6 | − | 6.06673e6i | 0.304845 | − | 0.528007i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.20361e6 | + | 9.01291e6i | 0.449510 | + | 0.778574i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 391529. | 0.0335705 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.20192e7 | 1.02291 | 0.511456 | − | 0.859310i | \(-0.329107\pi\) | ||||
0.511456 | + | 0.859310i | \(0.329107\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 188535. | + | 326552.i | 0.0159270 | + | 0.0275863i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.15506e7 | − | 2.00063e7i | 0.968576 | − | 1.67762i | 0.268892 | − | 0.963170i | \(-0.413343\pi\) |
0.699684 | − | 0.714452i | \(-0.253324\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.19352e6 | + | 8.45119e6i | −0.598779 | + | 0.703466i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.78984e6 | + | 4.83215e6i | −0.230522 | + | 0.399275i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.06846e6 | + | 1.22429e7i | 0.579793 | + | 1.00423i | 0.995503 | + | 0.0947337i | \(0.0302000\pi\) |
−0.415709 | + | 0.909497i | \(0.636467\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.95356e6 | 0.484787 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.84254e6 | 0.472291 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 399753. | + | 692393.i | 0.0320807 | + | 0.0555654i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.72809e6 | + | 9.92134e6i | −0.456367 | + | 0.790452i | −0.998766 | − | 0.0496699i | \(-0.984183\pi\) |
0.542398 | + | 0.840122i | \(0.317516\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −52291.9 | + | 61434.4i | −0.00413620 | + | 0.00485935i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.96297e6 | − | 1.55243e7i | 0.703866 | − | 1.21913i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.25440e6 | + | 2.17269e6i | 0.0978037 | + | 0.169401i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.40181e6 | 0.185929 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.39944e6 | 0.491866 | 0.245933 | − | 0.969287i | \(-0.420906\pi\) | ||||
0.245933 | + | 0.969287i | \(0.420906\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.11850e6 | + | 5.40139e6i | 0.237989 | + | 0.412209i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.01096e6 | − | 6.94719e6i | 0.303931 | − | 0.526425i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.20639e6 | + | 1.69033e6i | 0.692693 | + | 0.127182i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.57396e6 | + | 6.19028e6i | −0.267014 | + | 0.462482i | −0.968089 | − | 0.250606i | \(-0.919370\pi\) |
0.701075 | + | 0.713087i | \(0.252704\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.91092e6 | − | 3.30981e6i | −0.141765 | − | 0.245544i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.83984e6 | −0.503874 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 19723.7 | 0.00144285 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.27033e6 | + | 3.93233e6i | 0.164927 | + | 0.285661i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 641705. | − | 1.11147e6i | 0.0462928 | − | 0.0801814i | −0.841951 | − | 0.539555i | \(-0.818593\pi\) |
0.888243 | + | 0.459373i | \(0.151926\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.53678e6 | + | 4.31670e6i | 0.110096 | + | 0.309253i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.07102e6 | − | 7.05122e6i | 0.289639 | − | 0.501670i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 681640. | + | 1.18064e6i | 0.0481626 | + | 0.0834201i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.39582e7 | −0.979477 | −0.489739 | − | 0.871869i | \(-0.662908\pi\) | ||||
−0.489739 | + | 0.871869i | \(0.662908\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 118970. | + | 206061.i | 0.00823460 | + | 0.0142627i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.71410e6 | + | 2.96891e6i | −0.117836 | + | 0.204097i | −0.918910 | − | 0.394468i | \(-0.870929\pi\) |
0.801074 | + | 0.598565i | \(0.204262\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.45831e6 | + | 9.01164e6i | 0.0995708 | + | 0.615298i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 89755.7 | − | 155461.i | 0.00608686 | − | 0.0105428i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.19542e7 | + | 2.07052e7i | 0.805208 | + | 1.39466i | 0.916150 | + | 0.400835i | \(0.131280\pi\) |
−0.110942 | + | 0.993827i | \(0.535387\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 415617. | 0.0278066 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.30858e6 | −0.286327 | −0.143163 | − | 0.989699i | \(-0.545727\pi\) | ||||
−0.143163 | + | 0.989699i | \(0.545727\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.92807e6 | − | 6.80362e6i | −0.259292 | − | 0.449107i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.70939e6 | + | 2.96074e6i | −0.112083 | + | 0.194133i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.09408e6 | − | 5.88212e6i | −0.136392 | − | 0.383115i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.97785e6 | + | 5.15779e6i | −0.192665 | + | 0.333706i | −0.946133 | − | 0.323779i | \(-0.895046\pi\) |
0.753467 | + | 0.657485i | \(0.228380\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.46864e6 | + | 1.12040e7i | 0.415743 | + | 0.720089i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.92155e6 | 0.633450 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.58463e7 | −1.00505 | −0.502526 | − | 0.864562i | \(-0.667596\pi\) | ||||
−0.502526 | + | 0.864562i | \(0.667596\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −91888.3 | − | 159155.i | −0.00578970 | − | 0.0100281i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.40913e6 | − | 5.90479e6i | 0.213394 | − | 0.369609i | −0.739381 | − | 0.673288i | \(-0.764882\pi\) |
0.952775 | + | 0.303679i | \(0.0982149\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.08562e6 | + | 382930.i | 0.129695 | + | 0.0238126i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −337037. | + | 583765.i | −0.0208221 | + | 0.0360649i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 169190. | + | 293045.i | 0.0103845 | + | 0.0179865i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.93983e7 | 1.79270 | 0.896349 | − | 0.443349i | \(-0.146210\pi\) | ||||
0.896349 | + | 0.443349i | \(0.146210\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.91144e6 | −0.600483 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.02235e7 | − | 1.77077e7i | −0.615393 | − | 1.06589i | −0.990316 | − | 0.138835i | \(-0.955664\pi\) |
0.374923 | − | 0.927056i | \(-0.377669\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 665545. | − | 1.15276e6i | 0.0398037 | − | 0.0689420i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.34501e6 | − | 5.10467e6i | 0.258189 | − | 0.303330i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.87555e6 | − | 1.71049e7i | 0.583066 | − | 1.00990i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −230586. | − | 399387.i | −0.0135271 | − | 0.0234297i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.92140e6 | 0.111999 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.96113e6 | −0.287347 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.22719e6 | + | 2.12556e6i | 0.0706279 | + | 0.122331i | 0.899177 | − | 0.437586i | \(-0.144166\pi\) |
−0.828549 | + | 0.559917i | \(0.810833\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.67449e6 | + | 9.82851e6i | −0.324515 | + | 0.562076i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.22708e7 | + | 1.44162e7i | −0.697320 | + | 0.819235i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.08395e6 | + | 1.87745e6i | −0.0612103 | + | 0.106019i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.10423e6 | + | 8.84079e6i | 0.286426 | + | 0.496104i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.18924e6 | 0.345137 | 0.172569 | − | 0.984998i | \(-0.444793\pi\) | ||||
0.172569 | + | 0.984998i | \(0.444793\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.03652e6 | 0.112855 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.39233e6 | − | 2.41158e6i | −0.0766762 | − | 0.132807i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 77053.6 | − | 133461.i | 0.00421700 | − | 0.00730406i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.04533e7 | − | 3.75532e6i | −1.11243 | − | 0.204248i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.17369e6 | − | 3.76494e6i | 0.117494 | − | 0.203505i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.24448e7 | − | 2.15550e7i | −0.668524 | − | 1.15792i | −0.978317 | − | 0.207113i | \(-0.933593\pi\) |
0.309794 | − | 0.950804i | \(-0.399740\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.04458e7 | −1.62546 | −0.812728 | − | 0.582643i | \(-0.802019\pi\) | ||||
−0.812728 | + | 0.582643i | \(0.802019\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.67263e6 | −0.247933 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.30925e7 | − | 2.26768e7i | −0.690443 | − | 1.19588i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 936612. | − | 1.62226e6i | 0.0490913 | − | 0.0850287i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −149819. | − | 420830.i | −0.00780470 | − | 0.0219228i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.66575e6 | − | 1.50095e7i | 0.448692 | − | 0.777157i | −0.549609 | − | 0.835422i | \(-0.685223\pi\) |
0.998301 | + | 0.0582649i | \(0.0185568\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.06372e7 | + | 1.84242e7i | 0.547430 | + | 0.948177i | 0.998450 | + | 0.0556628i | \(0.0177272\pi\) |
−0.451019 | + | 0.892514i | \(0.648939\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 35764.5 | 0.00182944 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.30833e7 | −0.665202 | −0.332601 | − | 0.943068i | \(-0.607926\pi\) | ||||
−0.332601 | + | 0.943068i | \(0.607926\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.07609e7 | − | 1.86385e7i | −0.543830 | − | 0.941941i | −0.998680 | − | 0.0513730i | \(-0.983640\pi\) |
0.454849 | − | 0.890568i | \(-0.349693\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.06968e7 | + | 1.85274e7i | −0.537342 | + | 0.930704i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.79617e6 | + | 1.46451e6i | −0.0896880 | + | 0.0731275i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.06741e7 | + | 1.84881e7i | −0.529803 | + | 0.917646i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −938016. | − | 1.62469e6i | −0.0462804 | − | 0.0801599i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.15427e7 | −0.566112 | −0.283056 | − | 0.959103i | \(-0.591348\pi\) | ||||
−0.283056 | + | 0.959103i | \(0.591348\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.35644e7 | −0.661319 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.23237e6 | + | 7.33069e6i | 0.205123 | + | 0.355284i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.11493e7 | − | 1.93112e7i | 0.537165 | − | 0.930397i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.99997e6 | − | 1.96624e7i | −0.335265 | − | 0.941735i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.92272e6 | − | 5.06229e6i | 0.139161 | − | 0.241034i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.63513e6 | + | 1.32244e7i | 0.361404 | + | 0.625969i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.91491e7 | 1.37168 | 0.685840 | − | 0.727752i | \(-0.259435\pi\) | ||||
0.685840 | + | 0.727752i | \(0.259435\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.30678e6 | 0.248265 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.51794e6 | − | 7.82531e6i | −0.210130 | − | 0.363956i | 0.741625 | − | 0.670815i | \(-0.234055\pi\) |
−0.951755 | + | 0.306859i | \(0.900722\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.05181e6 | − | 3.55383e6i | 0.0948754 | − | 0.164329i | −0.814681 | − | 0.579909i | \(-0.803088\pi\) |
0.909557 | + | 0.415580i | \(0.136421\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.08794e7 | − | 3.83355e6i | −0.959863 | − | 0.176235i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.02861e6 | − | 1.21739e7i | 0.321249 | − | 0.556420i | −0.659497 | − | 0.751707i | \(-0.729231\pi\) |
0.980746 | + | 0.195287i | \(0.0625639\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.21495e7 | − | 2.10435e7i | −0.552098 | − | 0.956262i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.26076e7 | 0.569619 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −362495. | −0.0162837 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 496976. | + | 860788.i | 0.0221968 | + | 0.0384460i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.46706e6 | − | 6.00512e6i | 0.153966 | − | 0.266677i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.32247e7 | + | 1.55369e7i | −0.583938 | + | 0.686030i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.81039e7 | + | 3.13569e7i | −0.794828 | + | 1.37668i | 0.128121 | + | 0.991759i | \(0.459106\pi\) |
−0.922948 | + | 0.384924i | \(0.874228\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.57028e6 | − | 6.18391e6i | −0.155858 | − | 0.269955i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.92414e7 | 0.835213 | 0.417607 | − | 0.908628i | \(-0.362869\pi\) | ||||
0.417607 | + | 0.908628i | \(0.362869\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.97804e7 | 0.853756 | 0.426878 | − | 0.904309i | \(-0.359613\pi\) | ||||
0.426878 | + | 0.904309i | \(0.359613\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.16029e6 | + | 3.74174e6i | 0.0927159 | + | 0.160589i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.90057e7 | − | 3.29189e7i | 0.811101 | − | 1.40487i | −0.100993 | − | 0.994887i | \(-0.532202\pi\) |
0.912094 | − | 0.409981i | \(-0.134465\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.92921e7 | + | 3.44133e7i | −1.24307 | + | 1.46040i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 25203.1 | − | 43653.1i | 0.00106356 | − | 0.00184213i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.01647e6 | − | 1.38849e7i | −0.336399 | − | 0.582660i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.49558e7 | −1.04139 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.01757e6 | 0.0422263 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.39136e6 | − | 5.87400e6i | −0.139950 | − | 0.242401i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.29581e6 | + | 2.24441e6i | −0.0531777 | + | 0.0921064i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.98023e6 | − | 363579.i | −0.0808159 | − | 0.0148382i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.66813e7 | + | 2.88929e7i | −0.677033 | + | 1.17266i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.32603e7 | + | 2.29675e7i | 0.535222 | + | 0.927032i | 0.999153 | + | 0.0411606i | \(0.0131055\pi\) |
−0.463930 | + | 0.885872i | \(0.653561\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.84829e6 | −0.234757 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.66343e7 | −1.46249 | −0.731244 | − | 0.682116i | \(-0.761060\pi\) | ||||
−0.731244 | + | 0.682116i | \(0.761060\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 162132. | + | 280821.i | 0.00643714 | + | 0.0111494i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.38403e7 | + | 2.39721e7i | −0.546504 | + | 0.946572i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.30218e7 | − | 3.65772e7i | −0.511383 | − | 1.43644i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.77545e7 | − | 3.07516e7i | 0.693456 | − | 1.20110i | −0.277243 | − | 0.960800i | \(-0.589421\pi\) |
0.970699 | − | 0.240300i | \(-0.0772460\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.37269e6 | + | 1.62340e7i | 0.364095 | + | 0.630632i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.55350e6 | 0.0986580 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.97172e6 | −0.114197 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.43144e6 | − | 2.47933e6i | −0.0547110 | − | 0.0947623i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.17173e7 | + | 2.02950e7i | −0.445441 | + | 0.771526i | −0.998083 | − | 0.0618929i | \(-0.980286\pi\) |
0.552642 | + | 0.833419i | \(0.313620\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.70553e7 | + | 6.48136e6i | 0.644891 | + | 0.245071i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.38671e6 | + | 9.33005e6i | −0.202591 | + | 0.350897i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 31967.4 | + | 55369.1i | 0.00119585 | + | 0.00207128i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.37868e6 | 0.125718 | 0.0628592 | − | 0.998022i | \(-0.479978\pi\) | ||||
0.0628592 | + | 0.998022i | \(0.479978\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.32572e7 | −0.860783 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.38835e7 | + | 2.40470e7i | 0.511123 | + | 0.885292i | 0.999917 | + | 0.0128922i | \(0.00410382\pi\) |
−0.488793 | + | 0.872400i | \(0.662563\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.41787e7 | − | 4.18787e7i | 0.885428 | − | 1.53361i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.91295e6 | − | 5.37335e6i | −0.0696826 | − | 0.195734i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.08752e7 | − | 1.88363e7i | 0.394058 | − | 0.682529i | −0.598922 | − | 0.800807i | \(-0.704404\pi\) |
0.992981 | + | 0.118278i | \(0.0377374\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 426645. | + | 738971.i | 0.0153780 | + | 0.0266355i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.16236e7 | −0.416764 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.00654e7 | −0.715676 | −0.357838 | − | 0.933784i | \(-0.616486\pi\) | ||||
−0.357838 | + | 0.933784i | \(0.616486\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.38485e7 | − | 4.13069e7i | −0.846161 | − | 1.46559i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 91120.9 | − | 157826.i | 0.00321616 | − | 0.00557056i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.25788e7 | − | 2.30952e6i | −0.441664 | − | 0.0810914i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.10033e7 | − | 1.90583e7i | 0.384339 | − | 0.665695i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.95054e6 | + | 3.37844e6i | 0.0677782 | + | 0.117395i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.84721e7 | 0.984241 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.68366e7 | 1.26681 | 0.633407 | − | 0.773819i | \(-0.281656\pi\) | ||||
0.633407 | + | 0.773819i | \(0.281656\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 673616. | + | 1.16674e6i | 0.0230464 | + | 0.0399175i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.34625e7 | + | 4.06383e7i | −0.798595 | + | 1.38321i | 0.121937 | + | 0.992538i | \(0.461090\pi\) |
−0.920531 | + | 0.390669i | \(0.872244\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.49593e7 | + | 2.93230e7i | −0.845182 | + | 0.992949i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −99013.8 | + | 171497.i | −0.00333568 | + | 0.00577756i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.18284e7 | + | 2.04873e7i | 0.396449 | + | 0.686671i | 0.993285 | − | 0.115693i | \(-0.0369089\pi\) |
−0.596836 | + | 0.802364i | \(0.703576\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −264120. | −0.00880734 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.32488e6 | −0.0439544 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.17046e7 | − | 2.02729e7i | −0.386342 | − | 0.669165i | 0.605612 | − | 0.795760i | \(-0.292928\pi\) |
−0.991954 | + | 0.126595i | \(0.959595\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.68637e6 | + | 9.84908e6i | −0.186743 | + | 0.323449i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.11694e7 | + | 1.31222e7i | −0.364952 | + | 0.428759i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.29314e6 | − | 3.97184e6i | 0.0745487 | − | 0.129122i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.03205e6 | − | 3.51961e6i | −0.0657280 | − | 0.113844i | 0.831289 | − | 0.555841i | \(-0.187604\pi\) |
−0.897017 | + | 0.441997i | \(0.854270\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.79732e7 | 0.900263 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.43565e7 | −2.06080 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.48780e6 | − | 1.12372e7i | −0.206709 | − | 0.358031i | 0.743967 | − | 0.668217i | \(-0.232942\pi\) |
−0.950676 | + | 0.310186i | \(0.899609\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.09416e6 | + | 3.62720e6i | −0.0663891 | + | 0.114989i |
(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 | 336.6.q.k.289.1 | 8 | ||
4.3 | odd | 2 | 168.6.q.a.121.1 | yes | 8 | ||
7.4 | even | 3 | inner | 336.6.q.k.193.1 | 8 | ||
12.11 | even | 2 | 504.6.s.a.289.4 | 8 | |||
28.11 | odd | 6 | 168.6.q.a.25.1 | ✓ | 8 | ||
84.11 | even | 6 | 504.6.s.a.361.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.6.q.a.25.1 | ✓ | 8 | 28.11 | odd | 6 | ||
168.6.q.a.121.1 | yes | 8 | 4.3 | odd | 2 | ||
336.6.q.k.193.1 | 8 | 7.4 | even | 3 | inner | ||
336.6.q.k.289.1 | 8 | 1.1 | even | 1 | trivial | ||
504.6.s.a.289.4 | 8 | 12.11 | even | 2 | |||
504.6.s.a.361.4 | 8 | 84.11 | even | 6 |