Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [144,5,Mod(65,144)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(144, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("144.65");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 144 = 2^{4} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 144.q (of order \(6\), 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: | \(14.8852746841\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 6x^{6} + 121x^{5} + 1104x^{4} - 1647x^{3} + 6529x^{2} + 85254x + 440076 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{6} \) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 113.2 | ||
Root | \(3.72537 + 4.42407i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 144.113 |
Dual form | 144.5.q.c.65.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −0.256692 | + | 8.99634i | −0.0285213 | + | 0.999593i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −7.67992 | − | 4.43400i | −0.307197 | − | 0.177360i | 0.338475 | − | 0.940976i | \(-0.390089\pi\) |
−0.645671 | + | 0.763615i | \(0.723422\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 30.9381 | + | 53.5864i | 0.631390 | + | 1.09360i | 0.987268 | + | 0.159068i | \(0.0508488\pi\) |
−0.355877 | + | 0.934533i | \(0.615818\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −80.8682 | − | 4.61857i | −0.998373 | − | 0.0570194i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −94.7648 | + | 54.7125i | −0.783180 | + | 0.452169i | −0.837556 | − | 0.546351i | \(-0.816016\pi\) |
0.0543761 | + | 0.998521i | \(0.482683\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 77.8628 | − | 134.862i | 0.460727 | − | 0.798002i | −0.538271 | − | 0.842772i | \(-0.680922\pi\) |
0.998997 | + | 0.0447702i | \(0.0142556\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 41.8612 | − | 67.9530i | 0.186050 | − | 0.302013i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 395.955i | 1.37009i | 0.728502 | + | 0.685044i | \(0.240217\pi\) | ||||
−0.728502 | + | 0.685044i | \(0.759783\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −140.350 | −0.388782 | −0.194391 | − | 0.980924i | \(-0.562273\pi\) | ||||
−0.194391 | + | 0.980924i | \(0.562273\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −490.023 | + | 264.575i | −1.11116 | + | 0.599943i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −802.818 | − | 463.507i | −1.51761 | − | 0.876195i | −0.999785 | − | 0.0207115i | \(-0.993407\pi\) |
−0.517829 | − | 0.855484i | \(-0.673260\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −273.179 | − | 473.160i | −0.437087 | − | 0.757056i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 62.3085 | − | 726.332i | 0.0854712 | − | 0.996341i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 323.853 | − | 186.976i | 0.385080 | − | 0.222326i | −0.294946 | − | 0.955514i | \(-0.595302\pi\) |
0.680026 | + | 0.733188i | \(0.261968\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −521.830 | + | 903.837i | −0.543008 | + | 0.940517i | 0.455722 | + | 0.890122i | \(0.349381\pi\) |
−0.998729 | + | 0.0503946i | \(0.983952\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −467.887 | − | 866.580i | −0.429648 | − | 0.795758i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 548.719i | − | 0.447934i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −194.990 | −0.142432 | −0.0712162 | − | 0.997461i | \(-0.522688\pi\) | ||||
−0.0712162 | + | 0.997461i | \(0.522688\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1193.28 | + | 735.098i | 0.784537 | + | 0.483299i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2344.14 | − | 1353.39i | −1.39449 | − | 0.805110i | −0.400682 | − | 0.916217i | \(-0.631227\pi\) |
−0.993808 | + | 0.111108i | \(0.964560\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 167.963 | + | 290.920i | 0.0908397 | + | 0.157339i | 0.907865 | − | 0.419263i | \(-0.137712\pi\) |
−0.817025 | + | 0.576602i | \(0.804378\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 600.583 | + | 394.040i | 0.296584 | + | 0.194588i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2468.76 | + | 1425.34i | −1.11759 | + | 0.645241i | −0.940785 | − | 0.339005i | \(-0.889910\pi\) |
−0.176805 | + | 0.984246i | \(0.556576\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −713.836 | + | 1236.40i | −0.297308 | + | 0.514952i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3562.15 | − | 101.638i | −1.36953 | − | 0.0390767i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2765.43i | 0.984490i | 0.870457 | + | 0.492245i | \(0.163824\pi\) | ||||
−0.870457 | + | 0.492245i | \(0.836176\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 970.381 | 0.320787 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 36.0268 | − | 1262.64i | 0.0110886 | − | 0.388624i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4354.55 | + | 2514.10i | 1.25095 | + | 0.722236i | 0.971298 | − | 0.237866i | \(-0.0764479\pi\) |
0.279651 | + | 0.960102i | \(0.409781\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3523.59 | + | 6103.03i | 0.946947 | + | 1.64016i | 0.751806 | + | 0.659384i | \(0.229183\pi\) |
0.195140 | + | 0.980775i | \(0.437484\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2254.42 | − | 4476.33i | −0.568007 | − | 1.12782i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1195.96 | + | 690.488i | −0.283067 | + | 0.163429i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3439.96 | − | 5958.19i | 0.766309 | − | 1.32729i | −0.173242 | − | 0.984879i | \(-0.555424\pi\) |
0.939551 | − | 0.342408i | \(-0.111242\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4375.95 | − | 7103.45i | 0.919123 | − | 1.49201i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 821.812i | 0.163026i | 0.996672 | + | 0.0815128i | \(0.0259752\pi\) | ||||
−0.996672 | + | 0.0815128i | \(0.974025\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4091.53 | 0.767786 | 0.383893 | − | 0.923378i | \(-0.374583\pi\) | ||||
0.383893 | + | 0.923378i | \(0.374583\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4326.83 | − | 2336.16i | 0.769215 | − | 0.415317i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5863.69 | − | 3385.40i | −0.988985 | − | 0.570991i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3783.56 | + | 6553.32i | 0.606243 | + | 1.05004i | 0.991854 | + | 0.127382i | \(0.0406573\pi\) |
−0.385611 | + | 0.922661i | \(0.626009\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6518.34 | + | 746.992i | 0.993498 | + | 0.113853i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6777.78 | + | 3913.15i | −0.983855 | + | 0.568029i | −0.903432 | − | 0.428732i | \(-0.858961\pi\) |
−0.0804236 | + | 0.996761i | \(0.525627\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1755.67 | − | 3040.90i | 0.242999 | − | 0.420886i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1598.97 | + | 2961.48i | 0.211253 | + | 0.391265i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1283.28i | 0.162010i | 0.996714 | + | 0.0810051i | \(0.0258130\pi\) | ||||
−0.996714 | + | 0.0810051i | \(0.974187\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9635.72 | 1.16359 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7997.27 | − | 4926.57i | −0.924647 | − | 0.569612i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1077.88 | + | 622.313i | 0.119432 | + | 0.0689544i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1890.33 | + | 3274.14i | 0.200906 | + | 0.347979i | 0.948821 | − | 0.315816i | \(-0.102278\pi\) |
−0.747915 | + | 0.663795i | \(0.768945\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7916.15 | − | 3986.82i | 0.807688 | − | 0.406777i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1034.99 | + | 597.553i | −0.101460 | + | 0.0585779i | −0.549871 | − | 0.835249i | \(-0.685323\pi\) |
0.448411 | + | 0.893827i | \(0.351990\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6767.50 | + | 11721.6i | −0.637901 | + | 1.10488i | 0.347991 | + | 0.937498i | \(0.386864\pi\) |
−0.985892 | + | 0.167380i | \(0.946469\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4936.46 | + | 140.852i | 0.447752 | + | 0.0127757i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 18095.0i | − | 1.58049i | −0.612792 | − | 0.790244i | \(-0.709954\pi\) | ||
0.612792 | − | 0.790244i | \(-0.290046\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10676.5 | 0.898621 | 0.449311 | − | 0.893376i | \(-0.351670\pi\) | ||||
0.449311 | + | 0.893376i | \(0.351670\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 50.0524 | − | 1754.20i | 0.00406236 | − | 0.142375i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11083.8 | + | 6399.21i | 0.868021 | + | 0.501152i | 0.866690 | − | 0.498847i | \(-0.166243\pi\) |
0.00133098 | + | 0.999999i | \(0.499576\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4110.39 | + | 7119.40i | 0.310804 | + | 0.538329i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6919.50 | + | 10546.5i | −0.505479 | + | 0.770433i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −21217.8 | + | 12250.1i | −1.49833 | + | 0.865060i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1333.59 | + | 2309.85i | −0.0910861 | + | 0.157766i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 12777.3 | − | 20741.3i | 0.844555 | − | 1.37096i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10387.6i | 0.664807i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −449.363 | −0.0278606 | −0.0139303 | − | 0.999903i | \(-0.504434\pi\) | ||||
−0.0139303 | + | 0.999903i | \(0.504434\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2660.33 | + | 1436.37i | −0.159866 | + | 0.0863152i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10075.4 | − | 5817.06i | −0.587113 | − | 0.338970i | 0.176842 | − | 0.984239i | \(-0.443412\pi\) |
−0.763955 | + | 0.645270i | \(0.776745\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4342.17 | − | 7520.86i | −0.245473 | − | 0.425172i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3699.08 | + | 5301.90i | −0.202968 | + | 0.290913i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −24400.6 | + | 14087.7i | −1.30005 | + | 0.750584i | −0.980412 | − | 0.196956i | \(-0.936894\pi\) |
−0.319637 | + | 0.947540i | \(0.603561\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4747.58 | + | 8223.05i | −0.245721 | + | 0.425602i | −0.962334 | − | 0.271869i | \(-0.912358\pi\) |
0.716613 | + | 0.697471i | \(0.245691\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12189.1 | − | 22575.6i | −0.613103 | − | 1.13554i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 17040.3i | 0.833305i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3316.22 | −0.157727 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −10939.8 | − | 6739.28i | −0.506263 | − | 0.311874i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1730.39 | + | 999.043i | 0.0779422 | + | 0.0449999i | 0.538465 | − | 0.842648i | \(-0.319005\pi\) |
−0.460522 | + | 0.887648i | \(0.652338\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1855.61 | − | 3214.02i | −0.0813830 | − | 0.140959i | 0.822461 | − | 0.568821i | \(-0.192600\pi\) |
−0.903844 | + | 0.427862i | \(0.859267\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1828.75 | − | 32020.2i | 0.0781216 | − | 1.36786i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8015.23 | − | 4627.59i | 0.333620 | − | 0.192616i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1458.43 | + | 2526.07i | −0.0591679 | + | 0.102482i | −0.894092 | − | 0.447883i | \(-0.852178\pi\) |
0.834924 | + | 0.550365i | \(0.185511\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −24878.8 | − | 709.864i | −0.984090 | − | 0.0280790i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 57360.2i | − | 2.21289i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5975.21 | 0.224894 | 0.112447 | − | 0.993658i | \(-0.464131\pi\) | ||||
0.112447 | + | 0.993658i | \(0.464131\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −249.089 | + | 8729.88i | −0.00914927 | + | 0.320657i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3610.95 | + | 2084.78i | 0.129476 | + | 0.0747529i | 0.563339 | − | 0.826226i | \(-0.309517\pi\) |
−0.433863 | + | 0.900979i | \(0.642850\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2155.27 | + | 3733.05i | 0.0754622 | + | 0.130704i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 11349.9 | + | 648.218i | 0.388149 | + | 0.0221681i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −26710.3 | + | 15421.2i | −0.892455 | + | 0.515259i | −0.874745 | − | 0.484584i | \(-0.838971\pi\) |
−0.0177101 | + | 0.999843i | \(0.505638\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 16903.3 | − | 29277.4i | 0.551945 | − | 0.955996i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −23735.5 | + | 38529.7i | −0.757621 | + | 1.22984i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5977.90i | 0.186570i | 0.995639 | + | 0.0932852i | \(0.0297368\pi\) | ||||
−0.995639 | + | 0.0932852i | \(0.970263\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6456.49 | −0.197079 | −0.0985393 | − | 0.995133i | \(-0.531417\pi\) | ||||
−0.0985393 | + | 0.995133i | \(0.531417\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −55809.4 | + | 30132.8i | −1.66650 | + | 0.899782i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1497.51 | + | 864.586i | 0.0437548 | + | 0.0252618i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −21663.7 | − | 37522.6i | −0.619511 | − | 1.07302i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 40849.3 | − | 19132.5i | 1.14356 | − | 0.535609i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20643.3 | − | 11918.4i | 0.565865 | − | 0.326703i | −0.189631 | − | 0.981855i | \(-0.560729\pi\) |
0.755496 | + | 0.655153i | \(0.227396\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −20081.7 | + | 34782.5i | −0.539121 | + | 0.933784i | 0.459831 | + | 0.888006i | \(0.347910\pi\) |
−0.998952 | + | 0.0457779i | \(0.985423\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5904.87 | − | 10936.5i | −0.155289 | − | 0.287613i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3622.11i | 0.0933318i | 0.998911 | + | 0.0466659i | \(0.0148596\pi\) | ||||
−0.998911 | + | 0.0466659i | \(0.985140\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −46416.3 | −1.17210 | −0.586049 | − | 0.810276i | \(-0.699317\pi\) | ||||
−0.586049 | + | 0.810276i | \(0.699317\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 52718.9 | + | 32476.5i | 1.30489 | + | 0.803854i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 20038.8 | + | 11569.4i | 0.486272 | + | 0.280749i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12001.9 | + | 20787.8i | 0.285589 | + | 0.494654i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 62781.7 | + | 41190.9i | 1.46519 | + | 0.961303i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 13300.3 | − | 7678.91i | 0.304486 | − | 0.175795i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −764.093 | + | 1323.45i | −0.0171625 | + | 0.0297264i | −0.874479 | − | 0.485063i | \(-0.838797\pi\) |
0.857317 | + | 0.514790i | \(0.172130\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7393.30 | − | 210.953i | −0.162959 | − | 0.00464971i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 2978.99i | − | 0.0644453i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −64577.8 | −1.37140 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1050.26 | + | 36808.8i | −0.0218983 | + | 0.767473i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 53399.4 | + | 30830.2i | 1.09333 | + | 0.631235i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13741.4 | + | 23800.8i | 0.276326 | + | 0.478610i | 0.970469 | − | 0.241227i | \(-0.0775498\pi\) |
−0.694143 | + | 0.719837i | \(0.744216\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 19906.2 | + | 39525.3i | 0.393209 | + | 0.780747i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 39178.5 | − | 22619.7i | 0.760319 | − | 0.438970i | −0.0690916 | − | 0.997610i | \(-0.522010\pi\) |
0.829410 | + | 0.558640i | \(0.188677\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 40074.3 | − | 69410.7i | 0.764178 | − | 1.32360i | −0.176502 | − | 0.984300i | \(-0.556478\pi\) |
0.940680 | − | 0.339295i | \(-0.110189\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 31961.4 | − | 51882.7i | 0.598965 | − | 0.972297i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 90756.0i | − | 1.67172i | −0.548942 | − | 0.835860i | \(-0.684969\pi\) | ||
0.548942 | − | 0.835860i | \(-0.315031\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 25279.8 | 0.457760 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −59927.1 | + | 32356.0i | −1.06691 | + | 0.576047i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −708.324 | − | 408.951i | −0.0124004 | − | 0.00715938i | 0.493787 | − | 0.869583i | \(-0.335612\pi\) |
−0.506187 | + | 0.862424i | \(0.668946\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −37158.1 | − | 64359.7i | −0.639764 | − | 1.10810i | −0.985484 | − | 0.169766i | \(-0.945699\pi\) |
0.345721 | − | 0.938337i | \(-0.387634\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8393.39 | + | 58449.4i | −0.142143 | + | 0.989846i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 10964.4 | − | 6330.30i | 0.182664 | − | 0.105461i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10928.1 | + | 18928.0i | −0.179122 | + | 0.310249i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −33464.3 | − | 61979.7i | −0.539737 | − | 0.999656i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 16304.4i | − | 0.258796i | −0.991593 | − | 0.129398i | \(-0.958695\pi\) | ||
0.991593 | − | 0.129398i | \(-0.0413045\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 101439. | 1.58475 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 26906.3 | + | 16575.1i | 0.413784 | + | 0.254904i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 108732. | + | 62776.2i | 1.64623 | + | 0.950449i | 0.978553 | + | 0.205995i | \(0.0660430\pi\) |
0.667673 | + | 0.744454i | \(0.267290\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6032.63 | − | 10448.8i | −0.0899305 | − | 0.155764i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −27053.0 | + | 13624.7i | −0.397131 | + | 0.200008i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13971.9 | − | 8066.67i | 0.201996 | − | 0.116623i | −0.395590 | − | 0.918427i | \(-0.629460\pi\) |
0.597586 | + | 0.801805i | \(0.296127\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12261.9 | − | 21238.3i | 0.174609 | − | 0.302432i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11544.8 | − | 329.408i | −0.161944 | − | 0.00462074i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 75561.0i | 1.04422i | 0.852877 | + | 0.522112i | \(0.174856\pi\) | ||||
−0.852877 | + | 0.522112i | \(0.825144\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14842.2 | 0.202097 | 0.101049 | − | 0.994881i | \(-0.467780\pi\) | ||||
0.101049 | + | 0.994881i | \(0.467780\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2473.41 | + | 86686.2i | −0.0331872 | + | 1.16312i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 51775.5 | + | 29892.6i | 0.684635 | + | 0.395274i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −40381.1 | − | 69942.2i | −0.526283 | − | 0.911548i | −0.999531 | − | 0.0306193i | \(-0.990252\pi\) |
0.473248 | − | 0.880929i | \(-0.343081\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 46373.9 | − | 70681.6i | 0.595752 | − | 0.908025i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 57384.8 | − | 33131.1i | 0.726749 | − | 0.419589i | −0.0904828 | − | 0.995898i | \(-0.528841\pi\) |
0.817232 | + | 0.576309i | \(0.195508\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7288.93 | − | 12624.8i | 0.0910104 | − | 0.157635i | −0.816926 | − | 0.576742i | \(-0.804324\pi\) |
0.907937 | + | 0.419108i | \(0.137657\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5875.22 | + | 9537.22i | −0.0723327 | + | 0.117417i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 167485.i | − | 2.03335i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −73259.5 | −0.877139 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −29940.5 | + | 16165.6i | −0.353568 | + | 0.190899i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 65027.8 | + | 37543.8i | 0.757467 | + | 0.437324i | 0.828386 | − | 0.560158i | \(-0.189260\pi\) |
−0.0709185 | + | 0.997482i | \(0.522593\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −22295.1 | − | 38616.2i | −0.256192 | − | 0.443737i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 33834.8 | + | 72239.8i | 0.383575 | + | 0.818961i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −125019. | + | 72179.9i | −1.39841 | + | 0.807373i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10392.9 | + | 18001.0i | −0.114711 | + | 0.198685i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5110.11 | − | 9464.52i | −0.0556603 | − | 0.103089i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 62494.4i | − | 0.671802i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −146994. | −1.55963 | −0.779817 | − | 0.626007i | \(-0.784688\pi\) | ||||
−0.779817 | + | 0.626007i | \(0.784688\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −103715. | − | 63891.5i | −1.08623 | − | 0.669154i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 126237. | + | 72882.7i | 1.30516 | + | 0.753536i | 0.981285 | − | 0.192563i | \(-0.0616800\pi\) |
0.323878 | + | 0.946099i | \(0.395013\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 37866.9 | + | 65587.3i | 0.386519 | + | 0.669470i | 0.991979 | − | 0.126406i | \(-0.0403441\pi\) |
−0.605460 | + | 0.795876i | \(0.707011\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2534.30 | + | 44373.9i | −0.0255409 | + | 0.447205i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −80308.7 | + | 46366.3i | −0.799179 | + | 0.461406i | −0.843184 | − | 0.537625i | \(-0.819322\pi\) |
0.0440049 | + | 0.999031i | \(0.485988\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −20459.9 | + | 35437.6i | −0.201058 | + | 0.348243i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 162789. | + | 4644.84i | 1.57984 | + | 0.0450776i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 55572.4i | − | 0.532665i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −85082.0 | −0.805510 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2740.58 | + | 96049.6i | −0.0256299 | + | 0.898256i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −152757. | − | 88194.5i | −1.41127 | − | 0.814798i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5404.90 | + | 9361.56i | 0.0493323 | + | 0.0854461i | 0.889637 | − | 0.456668i | \(-0.150957\pi\) |
−0.840305 | + | 0.542114i | \(0.817624\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 15768.5 | + | 900.576i | 0.142201 | + | 0.00812142i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −52837.3 | + | 30505.6i | −0.470816 | + | 0.271825i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −65323.7 | + | 113144.i | −0.575190 | + | 0.996258i | 0.420831 | + | 0.907139i | \(0.361738\pi\) |
−0.996021 | + | 0.0891187i | \(0.971595\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −60414.6 | + | 98070.6i | −0.525705 | + | 0.853374i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 114203.i | − | 0.982125i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 60225.9 | 0.511912 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −65103.6 | + | 35150.9i | −0.546974 | + | 0.295324i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 141648. | + | 81780.7i | 1.17639 | + | 0.679191i | 0.955177 | − | 0.296034i | \(-0.0956641\pi\) |
0.221216 | + | 0.975225i | \(0.428997\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7232.92 | − | 12527.8i | −0.0593831 | − | 0.102855i | 0.834806 | − | 0.550545i | \(-0.185580\pi\) |
−0.894189 | + | 0.447690i | \(0.852247\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −93103.3 | − | 64957.3i | −0.755703 | − | 0.527247i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8348.17 | + | 4819.82i | −0.0669949 | + | 0.0386795i | −0.533123 | − | 0.846038i | \(-0.678982\pi\) |
0.466128 | + | 0.884717i | \(0.345648\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3643.92 | − | 6311.45i | 0.0289143 | − | 0.0500810i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −104760. | − | 194027.i | −0.821974 | − | 1.52239i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 56543.7i | − | 0.438728i | −0.975643 | − | 0.219364i | \(-0.929602\pi\) | ||
0.975643 | − | 0.219364i | \(-0.0703982\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −110623. | −0.848849 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −20437.8 | − | 12590.4i | −0.155104 | − | 0.0955487i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −31422.6 | − | 18141.9i | −0.235861 | − | 0.136175i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −79981.5 | − | 138532.i | −0.593824 | − | 1.02853i | −0.993712 | − | 0.111969i | \(-0.964284\pi\) |
0.399888 | − | 0.916564i | \(-0.369049\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 183316. | + | 120273.i | 1.34631 | + | 0.883313i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −148190. | + | 85557.3i | −1.07664 | + | 0.621598i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 52486.5 | − | 90909.4i | 0.377251 | − | 0.653418i | −0.613410 | − | 0.789764i | \(-0.710203\pi\) |
0.990661 | + | 0.136347i | \(0.0435361\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −93450.5 | − | 2666.42i | −0.664537 | − | 0.0189612i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 58234.0i | − | 0.409727i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25050.7 | −0.174398 | −0.0871989 | − | 0.996191i | \(-0.527792\pi\) | ||||
−0.0871989 | + | 0.996191i | \(0.527792\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 115.348 | − | 4042.62i | 0.000794620 | − | 0.0278492i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −45503.9 | − | 26271.7i | −0.310207 | − | 0.179098i | 0.336812 | − | 0.941572i | \(-0.390651\pi\) |
−0.647019 | + | 0.762474i | \(0.723985\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 30021.8 | + | 51999.2i | 0.202542 | + | 0.350813i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −12239.2 | − | 24301.9i | −0.0817205 | − | 0.162263i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −175082. | + | 101084.i | −1.15702 | + | 0.668008i | −0.950589 | − | 0.310452i | \(-0.899520\pi\) |
−0.206435 | + | 0.978460i | \(0.566186\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 183528. | − | 317880.i | 1.20046 | − | 2.07926i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 54918.5 | − | 89148.9i | 0.355577 | − | 0.577206i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 67105.3i | − | 0.430093i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 303603. | 1.92631 | 0.963154 | − | 0.268951i | \(-0.0866770\pi\) | ||||
0.963154 | + | 0.268951i | \(0.0866770\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 68774.8 | − | 37133.1i | 0.432000 | − | 0.233247i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −102431. | − | 59138.8i | −0.637007 | − | 0.367776i | 0.146453 | − | 0.989218i | \(-0.453214\pi\) |
−0.783461 | + | 0.621441i | \(0.786547\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 81262.3 | + | 140750.i | 0.500356 | + | 0.866642i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −46748.1 | − | 34639.2i | −0.285006 | − | 0.211182i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 18478.2 | − | 10668.4i | 0.111550 | − | 0.0644036i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20533.2 | + | 35564.6i | −0.122747 | + | 0.212604i | −0.920850 | − | 0.389917i | \(-0.872504\pi\) |
0.798103 | + | 0.602521i | \(0.205837\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −120474. | − | 223133.i | −0.713200 | − | 1.32093i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 311127.i | 1.82405i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 69403.7 | 0.402983 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −72758.7 | − | 44821.6i | −0.418420 | − | 0.257760i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −86655.8 | − | 50030.8i | −0.493594 | − | 0.284976i | 0.232470 | − | 0.972603i | \(-0.425319\pi\) |
−0.726064 | + | 0.687627i | \(0.758652\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 110257. | + | 190971.i | 0.622074 | + | 1.07746i | 0.989099 | + | 0.147253i | \(0.0470432\pi\) |
−0.367024 | + | 0.930211i | \(0.619623\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 206227. | − | 103862.i | 1.15256 | − | 0.580467i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 187350. | − | 108167.i | 1.03723 | − | 0.598847i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −218026. | + | 377633.i | −1.19579 | + | 2.07116i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −153300. | − | 4374.10i | −0.832966 | − | 0.0237670i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 211457.i | 1.13833i | 0.822224 | + | 0.569163i | \(0.192733\pi\) | ||||
−0.822224 | + | 0.569163i | \(0.807267\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −106655. | −0.568859 | −0.284430 | − | 0.958697i | \(-0.591804\pi\) | ||||
−0.284430 | + | 0.958697i | \(0.591804\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 851.246 | − | 29833.8i | 0.00449859 | − | 0.157663i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 112676. | + | 65053.4i | 0.590021 | + | 0.340649i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 107195. | + | 185667.i | 0.556218 | + | 0.963397i | 0.997808 | + | 0.0661804i | \(0.0210813\pi\) |
−0.441590 | + | 0.897217i | \(0.645585\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 63437.0 | − | 96688.5i | 0.326186 | − | 0.497162i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −174614. | + | 100814.i | −0.889759 | + | 0.513703i | −0.873864 | − | 0.486171i | \(-0.838393\pi\) |
−0.0158954 | + | 0.999874i | \(0.505060\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5690.08 | − | 9855.50i | 0.0287341 | − | 0.0497690i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9431.91 | + | 15310.8i | −0.0472046 | + | 0.0766270i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 136895.i | 0.679039i | 0.940599 | + | 0.339519i | \(0.110264\pi\) | ||||
−0.940599 | + | 0.339519i | \(0.889736\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 296189. | 1.45618 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 29390.7 | − | 15868.7i | 0.143223 | − | 0.0773295i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −74001.5 | − | 42724.8i | −0.357452 | − | 0.206375i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −183338. | − | 317551.i | −0.877850 | − | 1.52048i | −0.853696 | − | 0.520772i | \(-0.825644\pi\) |
−0.0241542 | − | 0.999708i | \(-0.507689\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 287595. | + | 24671.4i | 1.36507 | + | 0.117103i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −42379.8 | + | 24468.0i | −0.199415 | + | 0.115132i | −0.596382 | − | 0.802700i | \(-0.703396\pi\) |
0.396968 | + | 0.917833i | \(0.370062\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −143514. | + | 248574.i | −0.669472 | + | 1.15956i | 0.308580 | + | 0.951198i | \(0.400146\pi\) |
−0.978052 | + | 0.208361i | \(0.933187\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 39574.0 | + | 73295.6i | 0.183022 | + | 0.338978i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 43613.3i | − | 0.199979i | −0.994988 | − | 0.0999896i | \(-0.968119\pi\) | ||
0.994988 | − | 0.0999896i | \(-0.0318809\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 425704. | 1.93536 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −22351.1 | − | 13768.9i | −0.100753 | − | 0.0620667i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −31833.9 | − | 18379.3i | −0.142288 | − | 0.0821498i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 38340.8 | + | 66408.2i | 0.169931 | + | 0.294330i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12772.4 | − | 223636.i | 0.0561351 | − | 0.982889i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 199073. | − | 114935.i | 0.867642 | − | 0.500933i | 0.00107799 | − | 0.999999i | \(-0.499657\pi\) |
0.866564 | + | 0.499066i | \(0.166324\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15182.5 | + | 26296.8i | −0.0656224 | + | 0.113661i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 516032. | + | 14723.9i | 2.21199 | + | 0.0631144i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 33526.8i | − | 0.142531i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15921.9 | 0.0671330 | 0.0335665 | − | 0.999436i | \(-0.489313\pi\) | ||||
0.0335665 | + | 0.999436i | \(0.489313\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1533.79 | + | 53755.0i | −0.00641427 | + | 0.224802i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −145540. | − | 84027.8i | −0.603699 | − | 0.348546i | 0.166796 | − | 0.985991i | \(-0.446658\pi\) |
−0.770496 | + | 0.637445i | \(0.779991\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 74034.3 | + | 128231.i | 0.304606 | + | 0.527594i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −78473.0 | − | 4481.78i | −0.320265 | − | 0.0182911i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −44038.0 | + | 25425.3i | −0.178285 | + | 0.102933i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 178029. | − | 308355.i | 0.714971 | − | 1.23837i | −0.247999 | − | 0.968760i | \(-0.579773\pi\) |
0.962971 | − | 0.269607i | \(-0.0868937\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −19682.3 | + | 31950.2i | −0.0784153 | + | 0.127291i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 180472.i | 0.713301i | 0.934238 | + | 0.356651i | \(0.116081\pi\) | ||||
−0.934238 | + | 0.356651i | \(0.883919\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10598.2 | 0.0415575 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −34137.0 | + | 18431.3i | −0.132803 | + | 0.0717036i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 345324. | + | 199373.i | 1.33288 | + | 0.769540i | 0.985740 | − | 0.168273i | \(-0.0538190\pi\) |
0.347142 | + | 0.937813i | \(0.387152\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 126584. | + | 219250.i | 0.484772 | + | 0.839651i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8745.01 | + | 101941.i | −0.0332296 | + | 0.387359i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 103948. | − | 60014.2i | 0.391922 | − | 0.226277i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 155967. | − | 270143.i | 0.583516 | − | 1.01068i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −131878. | − | 244253.i | −0.489595 | − | 0.906788i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 485387.i | − | 1.78819i | −0.447880 | − | 0.894094i | \(-0.647821\pi\) | ||
0.447880 | − | 0.894094i | \(-0.352179\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −80589.4 | −0.294628 | −0.147314 | − | 0.989090i | \(-0.547063\pi\) | ||||
−0.147314 | + | 0.989090i | \(0.547063\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 259050. | + | 159583.i | 0.939865 | + | 0.578987i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −357879. | − | 206621.i | −1.28859 | − | 0.743968i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 289758. | + | 501875.i | 1.03544 | + | 1.79343i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −340533. | − | 223423.i | −1.20773 | − | 0.792389i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −365042. | + | 210757.i | −1.28496 | + | 0.741871i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −80233.3 | + | 138968.i | −0.280316 | + | 0.485521i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −53779.2 | − | 1534.48i | −0.186494 | − | 0.00532123i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 156223.i | − | 0.537734i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −446700. | −1.52623 | −0.763117 | − | 0.646260i | \(-0.776332\pi\) | ||||
−0.763117 | + | 0.646260i | \(0.776332\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1657.33 | − | 58084.8i | 0.00562094 | − | 0.196999i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −81994.8 | − | 47339.7i | −0.276053 | − | 0.159380i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −126958. | − | 219898.i | −0.424312 | − | 0.734931i | 0.572043 | − | 0.820223i | \(-0.306151\pi\) |
−0.996356 | + | 0.0852925i | \(0.972818\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −256759. | − | 509815.i | −0.851885 | − | 1.69149i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −45452.8 | + | 26242.2i | −0.149712 | + | 0.0864364i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −234113. | + | 405495.i | −0.765552 | + | 1.32597i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8162.51 | + | 13250.2i | −0.0264995 | + | 0.0430165i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 49265.2i | 0.158792i | 0.996843 | + | 0.0793962i | \(0.0252992\pi\) | ||||
−0.996843 | + | 0.0793962i | \(0.974701\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 52312.1 | 0.167409 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 343127. | − | 185262.i | 1.09026 | − | 0.588655i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 342365. | + | 197665.i | 1.08012 | + | 0.623608i | 0.930929 | − | 0.365200i | \(-0.118999\pi\) |
0.149192 | + | 0.988808i | \(0.452333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −56748.3 | − | 98290.9i | −0.177769 | − | 0.307905i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 161637. | + | 372405.i | 0.502775 | + | 1.15838i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −224474. | + | 129600.i | −0.693332 | + | 0.400296i | −0.804859 | − | 0.593466i | \(-0.797759\pi\) |
0.111527 | + | 0.993761i | \(0.464426\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 226228. | − | 391839.i | 0.693864 | − | 1.20181i | −0.276697 | − | 0.960957i | \(-0.589240\pi\) |
0.970562 | − | 0.240851i | \(-0.0774267\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 101923. | + | 188774.i | 0.310430 | + | 0.574953i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 506482.i | 1.53189i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 499076. | 1.49905 | 0.749523 | − | 0.661978i | \(-0.230283\pi\) | ||||
0.749523 | + | 0.661978i | \(0.230283\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −307761. | − | 189590.i | −0.918028 | − | 0.565534i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −419384. | − | 242131.i | −1.24239 | − | 0.717296i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −151304. | − | 262066.i | −0.445156 | − | 0.771033i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 99904.2 | − | 50314.9i | 0.291925 | − | 0.147023i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −238.906 | + | 137.932i | −0.000693347 | + | 0.000400304i | −0.500347 | − | 0.865825i | \(-0.666794\pi\) |
0.499653 | + | 0.866225i | \(0.333461\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 73239.0 | − | 126854.i | 0.211111 | − | 0.365656i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −32585.8 | − | 929.767i | −0.0932938 | − | 0.00266195i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10939.7i | 0.0311096i | 0.999879 | + | 0.0155548i | \(0.00495145\pi\) | ||||
−0.999879 | + | 0.0155548i | \(0.995049\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 217268. | 0.613708 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11914.7 | − | 417576.i | 0.0334298 | − | 1.17162i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13902.7 | + | 8026.70i | 0.0387475 | + | 0.0223709i | 0.519249 | − | 0.854623i | \(-0.326212\pi\) |
−0.480501 | + | 0.876994i | \(0.659545\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −267567. | − | 463439.i | −0.740769 | − | 1.28305i | −0.952145 | − | 0.305645i | \(-0.901128\pi\) |
0.211376 | − | 0.977405i | \(-0.432205\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −305702. | + | 465941.i | −0.840744 | + | 1.28143i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 20483.7 | − | 11826.3i | 0.0559627 | − | 0.0323101i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −37897.7 | + | 65640.8i | −0.102858 | + | 0.178154i | −0.912861 | − | 0.408271i | \(-0.866132\pi\) |
0.810003 | + | 0.586425i | \(0.199465\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −109226. | + | 177306.i | −0.294504 | + | 0.478067i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 443923.i | 1.18912i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −279865. | −0.744778 | −0.372389 | − | 0.928077i | \(-0.621461\pi\) | ||||
−0.372389 | + | 0.928077i | \(0.621461\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −190095. | + | 102637.i | −0.502598 | + | 0.271364i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1881.09 | + | 1086.05i | 0.00494128 | + | 0.00285285i | 0.502469 | − | 0.864595i | \(-0.332425\pi\) |
−0.497527 | + | 0.867448i | \(0.665759\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3964.87 | + | 6867.36i | 0.0103478 | + | 0.0179229i | 0.871153 | − | 0.491012i | \(-0.163373\pi\) |
−0.860805 | + | 0.508935i | \(0.830039\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −386683. | + | 554232.i | −1.00270 | + | 1.43717i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −68766.5 | + | 39702.4i | −0.177174 | + | 0.102292i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −124678. | + | 215949.i | −0.319176 | + | 0.552830i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 65668.0 | + | 121625.i | 0.167039 | + | 0.309376i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 77207.3i | − | 0.195145i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −546257. | −1.37195 | −0.685975 | − | 0.727625i | \(-0.740624\pi\) | ||||
−0.685975 | + | 0.727625i | \(0.740624\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −11710.0 | − | 7213.76i | −0.0292248 | − | 0.0180034i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3451.07 | + | 1992.48i | 0.00855868 | + | 0.00494135i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 111162. | + | 192539.i | 0.273955 | + | 0.474504i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3795.60 | − | 66458.5i | 0.00929563 | − | 0.162760i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 181888. | − | 105013.i | 0.442677 | − | 0.255580i | −0.262055 | − | 0.965053i | \(-0.584400\pi\) |
0.704733 | + | 0.709473i | \(0.251067\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −39984.7 | + | 69255.6i | −0.0967101 | + | 0.167507i | −0.910321 | − | 0.413903i | \(-0.864165\pi\) |
0.813611 | + | 0.581410i | \(0.197499\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 26800.0 | + | 764.681i | 0.0644191 | + | 0.00183807i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 247483.i | − | 0.591203i | −0.955311 | − | 0.295601i | \(-0.904480\pi\) | ||
0.955311 | − | 0.295601i | \(-0.0955200\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −550211. | −1.30629 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16576.6 | − | 580964.i | 0.0391141 | − | 1.37084i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 35706.7 | + | 20615.3i | 0.0837382 | + | 0.0483463i | 0.541284 | − | 0.840840i | \(-0.317938\pi\) |
−0.457546 | + | 0.889186i | \(0.651272\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 51585.7 | + | 89349.1i | 0.120239 | + | 0.208261i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −330875. | − | 18897.0i | −0.766537 | − | 0.0437787i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 709817. | − | 409813.i | 1.63446 | − | 0.943659i | 0.651772 | − | 0.758415i | \(-0.274026\pi\) |
0.982693 | − | 0.185244i | \(-0.0593074\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −120074. | + | 207974.i | −0.274818 | + | 0.475999i | −0.970089 | − | 0.242749i | \(-0.921951\pi\) |
0.695271 | + | 0.718747i | \(0.255284\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −291066. | + | 472485.i | −0.662162 | + | 1.07488i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 77012.8i | 0.174149i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −346660. | −0.779205 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −217647. | + | 117513.i | −0.486297 | + | 0.262563i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −667824. | − | 385568.i | −1.48326 | − | 0.856360i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 101639. | + | 176044.i | 0.224404 | + | 0.388679i | 0.956140 | − | 0.292909i | \(-0.0946233\pi\) |
−0.731737 | + | 0.681587i | \(0.761290\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −360693. | + | 168937.i | −0.791644 | + | 0.370781i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 295368. | − | 170531.i | 0.644446 | − | 0.372071i | −0.141879 | − | 0.989884i | \(-0.545314\pi\) |
0.786325 | + | 0.617813i | \(0.211981\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −116966. | + | 202591.i | −0.253700 | + | 0.439422i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 193438. | + | 358269.i | 0.417106 | + | 0.772529i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 753067.i | − | 1.61433i | −0.590326 | − | 0.807165i | \(-0.701001\pi\) | ||
0.590326 | − | 0.807165i | \(-0.298999\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 249860. | 0.532495 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 614155. | + | 378339.i | 1.30126 | + | 0.801618i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 372953. | + | 215324.i | 0.785625 | + | 0.453581i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −202444. | − | 350643.i | −0.423983 | − | 0.734361i | 0.572341 | − | 0.820015i | \(-0.306035\pi\) |
−0.996325 | + | 0.0856546i | \(0.972702\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 458550. | + | 300853.i | 0.954818 | + | 0.626453i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 72922.0 | − | 42101.6i | 0.150970 | − | 0.0871623i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 535881. | − | 928174.i | 1.10307 | − | 1.91057i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 816472. | + | 23296.3i | 1.67104 | + | 0.0476797i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 62736.6i | 0.127669i | 0.997961 | + | 0.0638344i | \(0.0203329\pi\) | ||||
−0.997961 | + | 0.0638344i | \(0.979667\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 27366.9 | 0.0553751 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6489.12 | + | 227426.i | −0.0130559 | + | 0.457574i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −64041.4 | − | 36974.3i | −0.128122 | − | 0.0739710i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −478518. | − | 828817.i | −0.951931 | − | 1.64879i | −0.741240 | − | 0.671241i | \(-0.765762\pi\) |
−0.210692 | − | 0.977553i | \(-0.567572\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −275703. | − | 547430.i | −0.545383 | − | 1.08290i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 837870. | − | 483744.i | 1.64815 | − | 0.951562i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 75556.6 | − | 130868.i | 0.147795 | − | 0.255989i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3860.88 | − | 6267.35i | 0.00751015 | − | 0.0121912i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 109853.i | 0.212498i | 0.994340 | + | 0.106249i | \(0.0338841\pi\) | ||||
−0.994340 | + | 0.106249i | \(0.966116\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −837495. | −1.61106 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 588540. | − | 317766.i | 1.12590 | − | 0.607899i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −176940. | − | 102156.i | −0.336627 | − | 0.194352i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 112227. | + | 194383.i | 0.212339 | + | 0.367781i | 0.952446 | − | 0.304707i | \(-0.0985587\pi\) |
−0.740107 | + | 0.672489i | \(0.765225\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −523676. | − | 90513.3i | −0.985389 | − | 0.170317i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −115191. | + | 66505.6i | −0.215568 | + | 0.124458i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26396.8 | + | 45720.6i | −0.0491296 | + | 0.0850950i | −0.889544 | − | 0.456849i | \(-0.848978\pi\) |
0.840415 | + | 0.541944i | \(0.182311\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 54135.1 | + | 100264.i | 0.100208 | + | 0.185597i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 752836.i | 1.38601i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −639035. | −1.17013 | −0.585067 | − | 0.810985i | \(-0.698932\pi\) | ||||
−0.585067 | + | 0.810985i | \(0.698932\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −167477. | − | 103171.i | −0.305014 | − | 0.187898i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 647838. | + | 374029.i | 1.17351 | + | 0.677529i | 0.954505 | − | 0.298194i | \(-0.0963842\pi\) |
0.219009 | + | 0.975723i | \(0.429718\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8859.52 | − | 15345.1i | −0.0159624 | − | 0.0276477i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 566180. | − | 285146.i | 1.01464 | − | 0.511006i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 969646. | − | 559826.i | 1.72842 | − | 0.997905i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −177786. | + | 307935.i | −0.315223 | + | 0.545983i | −0.979485 | − | 0.201518i | \(-0.935413\pi\) |
0.664262 | + | 0.747500i | \(0.268746\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 146680. | + | 4185.21i | 0.258691 | + | 0.00738121i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 32911.2i | 0.0577364i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 173106. | 0.302079 | 0.151040 | − | 0.988528i | \(-0.451738\pi\) | ||||
0.151040 | + | 0.988528i | \(0.451738\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −26038.4 | + | 912575.i | −0.0451993 | + | 1.58411i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −173520. | − | 100182.i | −0.299626 | − | 0.172989i | 0.342649 | − | 0.939463i | \(-0.388676\pi\) |
−0.642275 | + | 0.766475i | \(0.722009\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 330311. | + | 572116.i | 0.567381 | + | 0.982732i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −156022. | + | 237804.i | −0.266602 | + | 0.406346i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 678115. | − | 391510.i | 1.15269 | − | 0.665506i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 200920. | − | 348003.i | 0.339758 | − | 0.588478i | −0.644629 | − | 0.764495i | \(-0.722988\pi\) |
0.984387 | + | 0.176018i | \(0.0563216\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −592667. | + | 962072.i | −0.997015 | + | 1.61845i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 817430.i | 1.36802i | 0.729474 | + | 0.684009i | \(0.239765\pi\) | ||||
−0.729474 | + | 0.684009i | \(0.760235\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 570213. | 0.949366 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 95549.6 | − | 51589.4i | 0.158266 | − | 0.0854513i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 329000. | + | 189948.i | 0.542153 | + | 0.313012i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −44963.4 | − | 77878.9i | −0.0737152 | − | 0.127678i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −115628. | − | 246875.i | −0.188599 | − | 0.402674i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 22401.2 | − | 12933.4i | 0.0363524 | − | 0.0209881i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 49202.8 | − | 85221.7i | 0.0794402 | − | 0.137594i | −0.823568 | − | 0.567217i | \(-0.808020\pi\) |
0.903009 | + | 0.429623i | \(0.141353\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 68984.0 | + | 127766.i | 0.110814 | + | 0.205240i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 791919.i | 1.26569i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.09743e6 | 1.74513 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 187919. | + | 115764.i | 0.297329 | + | 0.183164i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −287305. | − | 165876.i | −0.452300 | − | 0.261136i | 0.256501 | − | 0.966544i | \(-0.417430\pi\) |
−0.708801 | + | 0.705408i | \(0.750764\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −564370. | − | 977517.i | −0.884036 | − | 1.53120i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5926.93 | − | 103777.i | 0.00923773 | − | 0.161747i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −387733. | + | 223858.i | −0.601314 | + | 0.347169i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −254335. | + | 440522.i | −0.392478 | + | 0.679791i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −679773. | − | 19395.9i | −1.04380 | − | 0.0297826i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 317676.i | 0.485387i | 0.970103 | + | 0.242693i | \(0.0780309\pi\) | ||||
−0.970103 | + | 0.242693i | \(0.921969\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.02772e6 | 1.56255 | 0.781274 | − | 0.624188i | \(-0.214570\pi\) | ||||
0.781274 | + | 0.624188i | \(0.214570\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3809.88 | + | 133526.i | −0.00576408 | + | 0.202015i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −45889.1 | − | 26494.1i | −0.0690867 | − | 0.0398872i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −23573.6 | − | 40830.6i | −0.0353168 | − | 0.0611705i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −779223. | − | 44503.3i | −1.16170 | − | 0.0663474i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.00344e6 | − | 579339.i | 1.48870 | − | 0.859501i | 0.488783 | − | 0.872406i | \(-0.337441\pi\) |
0.999917 | + | 0.0129047i | \(0.00410780\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 442071. | − | 765690.i | 0.652669 | − | 1.13046i | −0.329804 | − | 0.944049i | \(-0.606983\pi\) |
0.982473 | − | 0.186406i | \(-0.0596839\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −282215. | + | 458117.i | −0.414640 | + | 0.673083i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 772574.i | − | 1.12961i | −0.825224 | − | 0.564806i | \(-0.808951\pi\) | ||
0.825224 | − | 0.564806i | \(-0.191049\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −83501.8 | −0.121503 | −0.0607515 | − | 0.998153i | \(-0.519350\pi\) | ||||
−0.0607515 | + | 0.998153i | \(0.519350\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 639589. | − | 345329.i | 0.926188 | − | 0.500070i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −489559. | − | 282647.i | −0.705529 | − | 0.407337i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18487.9 | − | 32021.9i | −0.0265164 | − | 0.0459277i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 623971. | + | 435339.i | 0.890664 | + | 0.621408i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 652813. | − | 376902.i | 0.927395 | − | 0.535432i | 0.0414082 | − | 0.999142i | \(-0.486816\pi\) |
0.885987 | + | 0.463711i | \(0.153482\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −283720. | + | 491418.i | −0.401142 | + | 0.694798i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 283329. | + | 524758.i | 0.398690 | + | 0.738420i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 38226.0i | − | 0.0535359i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −165035. | −0.230043 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 111706. | + | 68814.4i | 0.154975 | + | 0.0954693i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 156542. | + | 90379.3i | 0.216158 | + | 0.124799i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 194125. | + | 336234.i | 0.266798 | + | 0.462108i | 0.968033 | − | 0.250822i | \(-0.0807010\pi\) |
−0.701235 | + | 0.712930i | \(0.747368\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −84291.9 | − | 55303.6i | −0.115306 | − | 0.0756522i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.01655e6 | + | 586903.i | −1.38409 | + | 0.799106i | −0.992641 | − | 0.121092i | \(-0.961360\pi\) |
−0.391452 | + | 0.920199i | \(0.628027\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −260195. | + | 450672.i | −0.352625 | + | 0.610765i | −0.986709 | − | 0.162500i | \(-0.948044\pi\) |
0.634083 | + | 0.773265i | \(0.281378\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.50675e6 | + | 42992.1i | 2.03253 | + | 0.0579939i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 387934.i | 0.520878i | 0.965490 | + | 0.260439i | \(0.0838673\pi\) | ||||
−0.965490 | + | 0.260439i | \(0.916133\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 273510. | 0.365546 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 18805.1 | − | 659067.i | 0.0250172 | − | 0.876782i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −717096. | − | 414016.i | −0.949594 | − | 0.548248i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −535690. | − | 927843.i | −0.706118 | − | 1.22303i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −137745. | − | 273504.i | −0.180738 | − | 0.358869i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −556635. | + | 321373.i | −0.727033 | + | 0.419753i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −596348. | + | 1.03290e6i | −0.775355 | + | 1.34295i | 0.159240 | + | 0.987240i | \(0.449096\pi\) |
−0.934595 | + | 0.355714i | \(0.884238\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −354449. | + | 575375.i | −0.458750 | + | 0.744686i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 563606.i | − | 0.726146i | −0.931761 | − | 0.363073i | \(-0.881728\pi\) | ||
0.931761 | − | 0.363073i | \(-0.118272\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −886399. | −1.13686 | −0.568431 | − | 0.822731i | \(-0.692449\pi\) | ||||
−0.568431 | + | 0.822731i | \(0.692449\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 353127. | − | 190662.i | 0.450863 | − | 0.243431i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −191045. | − | 110300.i | −0.242822 | − | 0.140193i | 0.373651 | − | 0.927569i | \(-0.378106\pi\) |
−0.616473 | + | 0.787376i | \(0.711439\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13902.5 | − | 24079.8i | −0.0175909 | − | 0.0304683i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −658579. | + | 285846.i | −0.829568 | + | 0.360061i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 346490. | − | 200046.i | 0.434499 | − | 0.250858i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 26506.0 | − | 45909.8i | 0.0330901 | − | 0.0573138i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −617264. | − | 1.14324e6i | −0.767160 | − | 1.42087i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 390280.i | 0.482900i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.09499e6 | −1.34884 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −159276. | − | 98118.7i | −0.195332 | − | 0.120331i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 49585.4 | + | 28628.1i | 0.0605419 | + | 0.0349539i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −142861. | − | 247443.i | −0.173660 | − | 0.300788i | 0.766037 | − | 0.642797i | \(-0.222226\pi\) |
−0.939697 | + | 0.342009i | \(0.888893\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 86457.8 | − | 43542.8i | 0.104635 | − | 0.0526974i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.17520e6 | − | 678500.i | 1.41603 | − | 0.817547i | 0.420086 | − | 0.907484i | \(-0.362000\pi\) |
0.995947 | + | 0.0899368i | \(0.0286665\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 428197. | − | 741658.i | 0.513691 | − | 0.889738i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 562221. | + | 16041.8i | 0.671529 | + | 0.0191607i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 719876.i | − | 0.856089i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 185850. | 0.220055 | 0.110028 | − | 0.993929i | \(-0.464906\pi\) | ||||
0.110028 | + | 0.993929i | \(0.464906\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 37732.2 | − | 1.32241e6i | 0.0444828 | − | 1.55900i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 110832. | + | 63988.6i | 0.130095 | + | 0.0751103i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 53267.2 | + | 92261.6i | 0.0622553 | + | 0.107829i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 601413. | − | 916653.i | 0.699863 | − | 1.06671i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −346728. | + | 200183.i | −0.401751 | + | 0.231951i | −0.687239 | − | 0.726431i | \(-0.741178\pi\) |
0.285488 | + | 0.958382i | \(0.407844\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 100187. | − | 173529.i | 0.115588 | − | 0.200204i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −688082. | + | 1.11696e6i | −0.790454 | + | 1.28314i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 384227.i | 0.439506i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −351423. | −0.400268 | −0.200134 | − | 0.979769i | \(-0.564138\pi\) | ||||
−0.200134 | + | 0.979769i | \(0.564138\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −599766. | + | 323827.i | −0.680222 | + | 0.367267i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −902928. | − | 521306.i | −1.01970 | − | 0.588726i | −0.105686 | − | 0.994400i | \(-0.533704\pi\) |
−0.914018 | + | 0.405673i | \(0.867037\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.25461e6 | + | 2.17305e6i | 1.41087 | + | 2.44369i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −398552. | − | 34189.8i | −0.446295 | − | 0.0382854i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −972731. | + | 561606.i | −1.08466 | + | 0.626227i | −0.932149 | − | 0.362075i | \(-0.882069\pi\) |
−0.152509 | + | 0.988302i | \(0.548735\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 318578. | − | 551793.i | 0.353739 | − | 0.612694i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −396512. | − | 734386.i | −0.438425 | − | 0.812014i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.20759e6i | 1.32964i | 0.747005 | + | 0.664819i | \(0.231491\pi\) | ||||
−0.747005 | + | 0.664819i | \(0.768509\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −211385. | −0.231776 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −313556. | − | 193161.i | −0.342367 | − | 0.210909i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.50982e6 | − | 871695.i | −1.64168 | − | 0.947823i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −82853.4 | − | 143506.i | −0.0897146 | − | 0.155390i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −83573.1 | + | 1.46331e6i | −0.0901185 | + | 1.57792i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 308452. | − | 178085.i | 0.331232 | − | 0.191237i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 226893. | − | 392990.i | 0.242643 | − | 0.420270i | −0.718823 | − | 0.695193i | \(-0.755319\pi\) |
0.961466 | + | 0.274923i | \(0.0886523\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 499948. | + | 14265.0i | 0.532448 | + | 0.0151923i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35561.3i | 0.0377171i | 0.999822 | + | 0.0188586i | \(0.00600322\pi\) | ||||
−0.999822 | + | 0.0188586i | \(0.993997\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −587525. | −0.620584 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 21839.9 | − | 765426.i | 0.0229742 | − | 0.805182i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 572069. | + | 330284.i | 0.599321 | + | 0.346018i | 0.768774 | − | 0.639520i | \(-0.220867\pi\) |
−0.169453 | + | 0.985538i | \(0.554200\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −70211.6 | − | 121610.i | −0.0732560 | − | 0.126883i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −863391. | − | 49310.3i | −0.897159 | − | 0.0512389i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −344484. | + | 198888.i | −0.356502 | + | 0.205826i | −0.667545 | − | 0.744569i | \(-0.732655\pi\) |
0.311043 | + | 0.950396i | \(0.399322\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16060.5 | − | 27817.5i | 0.0165533 | − | 0.0286712i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 832639. | − | 1.35162e6i | 0.854718 | − | 1.38746i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 311407.i | − | 0.318373i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −910142. | −0.926748 | −0.463374 | − | 0.886163i | \(-0.653361\pi\) | ||||
−0.463374 | + | 0.886163i | \(0.653361\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −85607.2 | + | 46221.3i | −0.0868184 | + | 0.0468752i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 356473. | + | 205810.i | 0.360065 | + | 0.207884i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 478202. | + | 828270.i | 0.481084 | + | 0.833262i | 0.999764 | − | 0.0217063i | \(-0.00690988\pi\) |
−0.518680 | + | 0.854968i | \(0.673577\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −12149.5 | + | 141628.i | −0.0121739 | + | 0.141911i |
(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 | 144.5.q.c.113.2 | 8 | ||
3.2 | odd | 2 | 432.5.q.c.17.3 | 8 | |||
4.3 | odd | 2 | 36.5.g.a.5.3 | ✓ | 8 | ||
9.2 | odd | 6 | inner | 144.5.q.c.65.2 | 8 | ||
9.4 | even | 3 | 1296.5.e.g.161.5 | 8 | |||
9.5 | odd | 6 | 1296.5.e.g.161.4 | 8 | |||
9.7 | even | 3 | 432.5.q.c.305.3 | 8 | |||
12.11 | even | 2 | 108.5.g.a.17.3 | 8 | |||
36.7 | odd | 6 | 108.5.g.a.89.3 | 8 | |||
36.11 | even | 6 | 36.5.g.a.29.3 | yes | 8 | ||
36.23 | even | 6 | 324.5.c.a.161.4 | 8 | |||
36.31 | odd | 6 | 324.5.c.a.161.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.5.g.a.5.3 | ✓ | 8 | 4.3 | odd | 2 | ||
36.5.g.a.29.3 | yes | 8 | 36.11 | even | 6 | ||
108.5.g.a.17.3 | 8 | 12.11 | even | 2 | |||
108.5.g.a.89.3 | 8 | 36.7 | odd | 6 | |||
144.5.q.c.65.2 | 8 | 9.2 | odd | 6 | inner | ||
144.5.q.c.113.2 | 8 | 1.1 | even | 1 | trivial | ||
324.5.c.a.161.4 | 8 | 36.23 | even | 6 | |||
324.5.c.a.161.5 | 8 | 36.31 | odd | 6 | |||
432.5.q.c.17.3 | 8 | 3.2 | odd | 2 | |||
432.5.q.c.305.3 | 8 | 9.7 | even | 3 | |||
1296.5.e.g.161.4 | 8 | 9.5 | odd | 6 | |||
1296.5.e.g.161.5 | 8 | 9.4 | even | 3 |