Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,5,Mod(17,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.17");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.g (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: | \(11.1639560131\) |
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: | \( 2^{2}\cdot 3^{10} \) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 17.3 | ||
Root | \(3.72537 - 4.42407i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 108.17 |
Dual form | 108.5.g.a.89.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 7.67992 | + | 4.43400i | 0.307197 | + | 0.177360i | 0.645671 | − | 0.763615i | \(-0.276578\pi\) |
−0.338475 | + | 0.940976i | \(0.609911\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −30.9381 | − | 53.5864i | −0.631390 | − | 1.09360i | −0.987268 | − | 0.159068i | \(-0.949151\pi\) |
0.355877 | − | 0.934533i | \(-0.384182\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 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 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 395.955i | − | 1.37009i | −0.728502 | − | 0.685044i | \(-0.759783\pi\) | ||
0.728502 | − | 0.685044i | \(-0.240217\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 140.350 | 0.388782 | 0.194391 | − | 0.980924i | \(-0.437727\pi\) | ||||
0.194391 | + | 0.980924i | \(0.437727\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 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 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −323.853 | + | 186.976i | −0.385080 | + | 0.222326i | −0.680026 | − | 0.733188i | \(-0.738032\pi\) |
0.294946 | + | 0.955514i | \(0.404698\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 521.830 | − | 903.837i | 0.543008 | − | 0.940517i | −0.455722 | − | 0.890122i | \(-0.650619\pi\) |
0.998729 | − | 0.0503946i | \(-0.0160479\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 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 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2344.14 | + | 1353.39i | 1.39449 | + | 0.805110i | 0.993808 | − | 0.111108i | \(-0.0354398\pi\) |
0.400682 | + | 0.916217i | \(0.368773\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −167.963 | − | 290.920i | −0.0908397 | − | 0.157339i | 0.817025 | − | 0.576602i | \(-0.195622\pi\) |
−0.907865 | + | 0.419263i | \(0.862288\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 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 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 2765.43i | − | 0.984490i | −0.870457 | − | 0.492245i | \(-0.836176\pi\) | ||
0.870457 | − | 0.492245i | \(-0.163824\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −970.381 | −0.320787 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 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 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 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 | \(0.444576\pi\) |
−0.939551 | + | 0.342408i | \(0.888758\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 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 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 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 | \(-0.959343\pi\) |
0.385611 | − | 0.922661i | \(-0.373991\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 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 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 1283.28i | − | 0.162010i | −0.996714 | − | 0.0810051i | \(-0.974187\pi\) | ||
0.996714 | − | 0.0810051i | \(-0.0258130\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9635.72 | −1.16359 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 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 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1034.99 | − | 597.553i | 0.101460 | − | 0.0585779i | −0.448411 | − | 0.893827i | \(-0.648010\pi\) |
0.549871 | + | 0.835249i | \(0.314677\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6767.50 | − | 11721.6i | 0.637901 | − | 1.10488i | −0.347991 | − | 0.937498i | \(-0.613136\pi\) |
0.985892 | − | 0.167380i | \(-0.0535306\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 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 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11083.8 | − | 6399.21i | −0.868021 | − | 0.501152i | −0.00133098 | − | 0.999999i | \(-0.500424\pi\) |
−0.866690 | + | 0.498847i | \(0.833757\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4110.39 | − | 7119.40i | −0.310804 | − | 0.538329i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 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 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 10387.6i | − | 0.664807i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 449.363 | 0.0278606 | 0.0139303 | − | 0.999903i | \(-0.495566\pi\) | ||||
0.0139303 | + | 0.999903i | \(0.495566\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 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 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 24400.6 | − | 14087.7i | 1.30005 | − | 0.750584i | 0.319637 | − | 0.947540i | \(-0.396439\pi\) |
0.980412 | + | 0.196956i | \(0.0631055\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4747.58 | − | 8223.05i | 0.245721 | − | 0.425602i | −0.716613 | − | 0.697471i | \(-0.754309\pi\) |
0.962334 | + | 0.271869i | \(0.0876419\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 17040.3i | 0.833305i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3316.22 | −0.157727 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1730.39 | − | 999.043i | −0.0779422 | − | 0.0449999i | 0.460522 | − | 0.887648i | \(-0.347662\pi\) |
−0.538465 | + | 0.842648i | \(0.680995\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1855.61 | + | 3214.02i | 0.0813830 | + | 0.140959i | 0.903844 | − | 0.427862i | \(-0.140733\pi\) |
−0.822461 | + | 0.568821i | \(0.807400\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 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 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 57360.2i | 2.21289i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5975.21 | −0.224894 | −0.112447 | − | 0.993658i | \(-0.535869\pi\) | ||||
−0.112447 | + | 0.993658i | \(0.535869\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 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 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 26710.3 | − | 15421.2i | 0.892455 | − | 0.515259i | 0.0177101 | − | 0.999843i | \(-0.494362\pi\) |
0.874745 | + | 0.484584i | \(0.161029\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −16903.3 | + | 29277.4i | −0.551945 | + | 0.955996i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 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 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 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 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 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 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 3622.11i | − | 0.0933318i | −0.998911 | − | 0.0466659i | \(-0.985140\pi\) | ||
0.998911 | − | 0.0466659i | \(-0.0148596\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 46416.3 | 1.17210 | 0.586049 | − | 0.810276i | \(-0.300683\pi\) | ||||
0.586049 | + | 0.810276i | \(0.300683\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 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 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −13300.3 | + | 7678.91i | −0.304486 | + | 0.175795i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 764.093 | − | 1323.45i | 0.0171625 | − | 0.0297264i | −0.857317 | − | 0.514790i | \(-0.827870\pi\) |
0.874479 | + | 0.485063i | \(0.161203\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 2978.99i | − | 0.0644453i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −64577.8 | −1.37140 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −53399.4 | − | 30830.2i | −1.09333 | − | 0.631235i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13741.4 | − | 23800.8i | −0.276326 | − | 0.478610i | 0.694143 | − | 0.719837i | \(-0.255784\pi\) |
−0.970469 | + | 0.241227i | \(0.922450\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 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 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 90756.0i | 1.67172i | 0.548942 | + | 0.835860i | \(0.315031\pi\) | ||||
−0.548942 | + | 0.835860i | \(0.684969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −25279.8 | −0.457760 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 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 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 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 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 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 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −108732. | − | 62776.2i | −1.64623 | − | 0.950449i | −0.978553 | − | 0.205995i | \(-0.933957\pi\) |
−0.667673 | − | 0.744454i | \(-0.732710\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6032.63 | + | 10448.8i | 0.0899305 | + | 0.155764i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 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 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 75561.0i | − | 1.04422i | −0.852877 | − | 0.522112i | \(-0.825144\pi\) | ||
0.852877 | − | 0.522112i | \(-0.174856\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14842.2 | −0.202097 | −0.101049 | − | 0.994881i | \(-0.532220\pi\) | ||||
−0.101049 | + | 0.994881i | \(0.532220\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 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 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −57384.8 | + | 33131.1i | −0.726749 | + | 0.419589i | −0.817232 | − | 0.576309i | \(-0.804492\pi\) |
0.0904828 | + | 0.995898i | \(0.471159\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7288.93 | + | 12624.8i | −0.0910104 | + | 0.157635i | −0.907937 | − | 0.419108i | \(-0.862343\pi\) |
0.816926 | + | 0.576742i | \(0.195676\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 167485.i | − | 2.03335i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −73259.5 | −0.877139 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −65027.8 | − | 37543.8i | −0.757467 | − | 0.437324i | 0.0709185 | − | 0.997482i | \(-0.477407\pi\) |
−0.828386 | + | 0.560158i | \(0.810740\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 22295.1 | + | 38616.2i | 0.256192 | + | 0.443737i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 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 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 62494.4i | 0.671802i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 146994. | 1.55963 | 0.779817 | − | 0.626007i | \(-0.215312\pi\) | ||||
0.779817 | + | 0.626007i | \(0.215312\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 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 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 80308.7 | − | 46366.3i | 0.799179 | − | 0.461406i | −0.0440049 | − | 0.999031i | \(-0.514012\pi\) |
0.843184 | + | 0.537625i | \(0.180678\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 20459.9 | − | 35437.6i | 0.201058 | − | 0.348243i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 55572.4i | − | 0.532665i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −85082.0 | −0.805510 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 152757. | + | 88194.5i | 1.41127 | + | 0.814798i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5404.90 | − | 9361.56i | −0.0493323 | − | 0.0854461i | 0.840305 | − | 0.542114i | \(-0.182376\pi\) |
−0.889637 | + | 0.456668i | \(0.849043\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 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 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 114203.i | 0.982125i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −60225.9 | −0.511912 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 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 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8348.17 | − | 4819.82i | 0.0669949 | − | 0.0386795i | −0.466128 | − | 0.884717i | \(-0.654352\pi\) |
0.533123 | + | 0.846038i | \(0.321018\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3643.92 | + | 6311.45i | −0.0289143 | + | 0.0500810i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 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 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 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 | \(0.0357157\pi\) |
−0.399888 | + | 0.916564i | \(0.630951\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 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 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 58234.0i | 0.409727i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25050.7 | 0.174398 | 0.0871989 | − | 0.996191i | \(-0.472208\pi\) | ||||
0.0871989 | + | 0.996191i | \(0.472208\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 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 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 175082. | − | 101084.i | 1.15702 | − | 0.668008i | 0.206435 | − | 0.978460i | \(-0.433814\pi\) |
0.950589 | + | 0.310452i | \(0.100480\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −183528. | + | 317880.i | −1.20046 | + | 2.07926i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 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 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 102431. | + | 59138.8i | 0.637007 | + | 0.367776i | 0.783461 | − | 0.621441i | \(-0.213453\pi\) |
−0.146453 | + | 0.989218i | \(0.546786\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −81262.3 | − | 140750.i | −0.500356 | − | 0.866642i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 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 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 311127.i | − | 1.82405i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −69403.7 | −0.402983 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 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 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −187350. | + | 108167.i | −1.03723 | + | 0.598847i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 218026. | − | 377633.i | 1.19579 | − | 2.07116i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 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 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 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 | \(-0.978919\pi\) |
0.441590 | − | 0.897217i | \(-0.354415\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 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 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 136895.i | − | 0.679039i | −0.940599 | − | 0.339519i | \(-0.889736\pi\) | ||
0.940599 | − | 0.339519i | \(-0.110264\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −296189. | −1.45618 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 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 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 42379.8 | − | 24468.0i | 0.199415 | − | 0.115132i | −0.396968 | − | 0.917833i | \(-0.629938\pi\) |
0.596382 | + | 0.802700i | \(0.296604\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 143514. | − | 248574.i | 0.669472 | − | 1.15956i | −0.308580 | − | 0.951198i | \(-0.599854\pi\) |
0.978052 | − | 0.208361i | \(-0.0668128\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 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 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 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 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 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 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 33526.8i | 0.142531i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15921.9 | −0.0671330 | −0.0335665 | − | 0.999436i | \(-0.510687\pi\) | ||||
−0.0335665 | + | 0.999436i | \(0.510687\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 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 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 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 | \(0.420227\pi\) |
−0.962971 | + | 0.269607i | \(0.913106\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 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 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −345324. | − | 199373.i | −1.33288 | − | 0.769540i | −0.347142 | − | 0.937813i | \(-0.612848\pi\) |
−0.985740 | + | 0.168273i | \(0.946181\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −126584. | − | 219250.i | −0.484772 | − | 0.839651i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 103948. | − | 60014.2i | 0.391922 | − | 0.226277i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 155967. | − | 270143.i | 0.583516 | − | 1.01068i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 485387.i | 1.78819i | 0.447880 | + | 0.894094i | \(0.352179\pi\) | ||||
−0.447880 | + | 0.894094i | \(0.647821\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 80589.4 | 0.294628 | 0.147314 | − | 0.989090i | \(-0.452937\pi\) | ||||
0.147314 | + | 0.989090i | \(0.452937\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −357879. | − | 206621.i | −1.28859 | − | 0.743968i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 289758. | + | 501875.i | 1.03544 | + | 1.79343i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 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 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 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 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 81994.8 | + | 47339.7i | 0.276053 | + | 0.159380i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 126958. | + | 219898.i | 0.424312 | + | 0.734931i | 0.996356 | − | 0.0852925i | \(-0.0271825\pi\) |
−0.572043 | + | 0.820223i | \(0.693849\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 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 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 49265.2i | − | 0.158792i | −0.996843 | − | 0.0793962i | \(-0.974701\pi\) | ||
0.996843 | − | 0.0793962i | \(-0.0252992\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −52312.1 | −0.167409 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 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 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 224474. | − | 129600.i | 0.693332 | − | 0.400296i | −0.111527 | − | 0.993761i | \(-0.535574\pi\) |
0.804859 | + | 0.593466i | \(0.202241\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −226228. | + | 391839.i | −0.693864 | + | 1.20181i | 0.276697 | + | 0.960957i | \(0.410760\pi\) |
−0.970562 | + | 0.240851i | \(0.922573\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 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 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 419384. | + | 242131.i | 1.24239 | + | 0.717296i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 151304. | + | 262066.i | 0.445156 | + | 0.771033i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 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 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 10939.7i | − | 0.0311096i | −0.999879 | − | 0.0155548i | \(-0.995049\pi\) | ||
0.999879 | − | 0.0155548i | \(-0.00495145\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −217268. | −0.613708 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 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 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −20483.7 | + | 11826.3i | −0.0559627 | + | 0.0323101i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37897.7 | − | 65640.8i | 0.102858 | − | 0.178154i | −0.810003 | − | 0.586425i | \(-0.800535\pi\) |
0.912861 | + | 0.408271i | \(0.133868\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 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 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1881.09 | − | 1086.05i | −0.00494128 | − | 0.00285285i | 0.497527 | − | 0.867448i | \(-0.334241\pi\) |
−0.502469 | + | 0.864595i | \(0.667575\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3964.87 | − | 6867.36i | −0.0103478 | − | 0.0179229i | 0.860805 | − | 0.508935i | \(-0.169961\pi\) |
−0.871153 | + | 0.491012i | \(0.836627\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 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 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 77207.3i | 0.195145i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 546257. | 1.37195 | 0.685975 | − | 0.727625i | \(-0.259376\pi\) | ||||
0.685975 | + | 0.727625i | \(0.259376\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 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 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −181888. | + | 105013.i | −0.442677 | + | 0.255580i | −0.704733 | − | 0.709473i | \(-0.748933\pi\) |
0.262055 | + | 0.965053i | \(0.415600\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 39984.7 | − | 69255.6i | 0.0967101 | − | 0.167507i | −0.813611 | − | 0.581410i | \(-0.802501\pi\) |
0.910321 | + | 0.413903i | \(0.135835\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 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 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −35706.7 | − | 20615.3i | −0.0837382 | − | 0.0483463i | 0.457546 | − | 0.889186i | \(-0.348728\pi\) |
−0.541284 | + | 0.840840i | \(0.682062\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −51585.7 | − | 89349.1i | −0.120239 | − | 0.208261i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 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 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 77012.8i | − | 0.174149i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 346660. | 0.779205 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 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 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −295368. | + | 170531.i | −0.644446 | + | 0.372071i | −0.786325 | − | 0.617813i | \(-0.788019\pi\) |
0.141879 | + | 0.989884i | \(0.454686\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 116966. | − | 202591.i | 0.253700 | − | 0.439422i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 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 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −372953. | − | 215324.i | −0.785625 | − | 0.453581i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 202444. | + | 350643.i | 0.423983 | + | 0.734361i | 0.996325 | − | 0.0856546i | \(-0.0272981\pi\) |
−0.572341 | + | 0.820015i | \(0.693965\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 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 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 62736.6i | − | 0.127669i | −0.997961 | − | 0.0638344i | \(-0.979667\pi\) | ||
0.997961 | − | 0.0638344i | \(-0.0203329\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −27366.9 | −0.0553751 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 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 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 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 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 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 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 176940. | + | 102156.i | 0.336627 | + | 0.194352i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −112227. | − | 194383.i | −0.212339 | − | 0.367781i | 0.740107 | − | 0.672489i | \(-0.234775\pi\) |
−0.952446 | + | 0.304707i | \(0.901441\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 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 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 752836.i | − | 1.38601i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 639035. | 1.17013 | 0.585067 | − | 0.810985i | \(-0.301068\pi\) | ||||
0.585067 | + | 0.810985i | \(0.301068\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 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 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −969646. | + | 559826.i | −1.72842 | + | 0.997905i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 177786. | − | 307935.i | 0.315223 | − | 0.545983i | −0.664262 | − | 0.747500i | \(-0.731254\pi\) |
0.979485 | + | 0.201518i | \(0.0645873\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 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 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 173520. | + | 100182.i | 0.299626 | + | 0.172989i | 0.642275 | − | 0.766475i | \(-0.277991\pi\) |
−0.342649 | + | 0.939463i | \(0.611324\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −330311. | − | 572116.i | −0.567381 | − | 0.982732i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 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 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 817430.i | − | 1.36802i | −0.729474 | − | 0.684009i | \(-0.760235\pi\) | ||
0.729474 | − | 0.684009i | \(-0.239765\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −570213. | −0.949366 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 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 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −22401.2 | + | 12933.4i | −0.0363524 | + | 0.0209881i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −49202.8 | + | 85221.7i | −0.0794402 | + | 0.137594i | −0.903009 | − | 0.429623i | \(-0.858647\pi\) |
0.823568 | + | 0.567217i | \(0.191980\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 791919.i | 1.26569i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.09743e6 | 1.74513 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 287305. | + | 165876.i | 0.452300 | + | 0.261136i | 0.708801 | − | 0.705408i | \(-0.249236\pi\) |
−0.256501 | + | 0.966544i | \(0.582570\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 564370. | + | 977517.i | 0.884036 | + | 1.53120i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −387733. | + | 223858.i | −0.601314 | + | 0.347169i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −254335. | + | 440522.i | −0.392478 | + | 0.679791i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 317676.i | − | 0.485387i | −0.970103 | − | 0.242693i | \(-0.921969\pi\) | ||
0.970103 | − | 0.242693i | \(-0.0780309\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.02772e6 | −1.56255 | −0.781274 | − | 0.624188i | \(-0.785430\pi\) | ||||
−0.781274 | + | 0.624188i | \(0.785430\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 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 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.00344e6 | + | 579339.i | −1.48870 | + | 0.859501i | −0.999917 | − | 0.0129047i | \(-0.995892\pi\) |
−0.488783 | + | 0.872406i | \(0.662559\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −442071. | + | 765690.i | −0.652669 | + | 1.13046i | 0.329804 | + | 0.944049i | \(0.393017\pi\) |
−0.982473 | + | 0.186406i | \(0.940316\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 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 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 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 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 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 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 38226.0i | 0.0535359i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 165035. | 0.230043 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 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 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.01655e6 | − | 586903.i | 1.38409 | − | 0.799106i | 0.391452 | − | 0.920199i | \(-0.371973\pi\) |
0.992641 | + | 0.121092i | \(0.0386397\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 260195. | − | 450672.i | 0.352625 | − | 0.610765i | −0.634083 | − | 0.773265i | \(-0.718622\pi\) |
0.986709 | + | 0.162500i | \(0.0519558\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 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 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 717096. | + | 414016.i | 0.949594 | + | 0.548248i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 535690. | + | 927843.i | 0.706118 | + | 1.22303i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 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 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 563606.i | 0.726146i | 0.931761 | + | 0.363073i | \(0.118272\pi\) | ||||
−0.931761 | + | 0.363073i | \(0.881728\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 886399. | 1.13686 | 0.568431 | − | 0.822731i | \(-0.307551\pi\) | ||||
0.568431 | + | 0.822731i | \(0.307551\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 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 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 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 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 390280.i | 0.482900i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.09499e6 | −1.34884 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −49585.4 | − | 28628.1i | −0.0605419 | − | 0.0349539i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 142861. | + | 247443.i | 0.173660 | + | 0.300788i | 0.939697 | − | 0.342009i | \(-0.111107\pi\) |
−0.766037 | + | 0.642797i | \(0.777774\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 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 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 719876.i | 0.856089i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −185850. | −0.220055 | −0.110028 | − | 0.993929i | \(-0.535094\pi\) | ||||
−0.110028 | + | 0.993929i | \(0.535094\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 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 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 346728. | − | 200183.i | 0.401751 | − | 0.231951i | −0.285488 | − | 0.958382i | \(-0.592156\pi\) |
0.687239 | + | 0.726431i | \(0.258822\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −100187. | + | 173529.i | −0.115588 | + | 0.200204i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 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 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 902928. | + | 521306.i | 1.01970 | + | 0.588726i | 0.914018 | − | 0.405673i | \(-0.132963\pi\) |
0.105686 | + | 0.994400i | \(0.466296\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.25461e6 | − | 2.17305e6i | −1.41087 | − | 2.44369i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 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 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1.20759e6i | − | 1.32964i | −0.747005 | − | 0.664819i | \(-0.768509\pi\) | ||
0.747005 | − | 0.664819i | \(-0.231491\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 211385. | 0.231776 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 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 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −308452. | + | 178085.i | −0.331232 | + | 0.191237i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −226893. | + | 392990.i | −0.242643 | + | 0.420270i | −0.961466 | − | 0.274923i | \(-0.911348\pi\) |
0.718823 | + | 0.695193i | \(0.244681\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 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 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −572069. | − | 330284.i | −0.599321 | − | 0.346018i | 0.169453 | − | 0.985538i | \(-0.445800\pi\) |
−0.768774 | + | 0.639520i | \(0.779133\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 70211.6 | + | 121610.i | 0.0732560 | + | 0.126883i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 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 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 311407.i | 0.318373i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 910142. | 0.926748 | 0.463374 | − | 0.886163i | \(-0.346639\pi\) | ||||
0.463374 | + | 0.886163i | \(0.346639\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 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 | ||||||||
\(999\) | 0 | 0 |
(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 | 108.5.g.a.17.3 | 8 | ||
3.2 | odd | 2 | 36.5.g.a.5.3 | ✓ | 8 | ||
4.3 | odd | 2 | 432.5.q.c.17.3 | 8 | |||
9.2 | odd | 6 | inner | 108.5.g.a.89.3 | 8 | ||
9.4 | even | 3 | 324.5.c.a.161.4 | 8 | |||
9.5 | odd | 6 | 324.5.c.a.161.5 | 8 | |||
9.7 | even | 3 | 36.5.g.a.29.3 | yes | 8 | ||
12.11 | even | 2 | 144.5.q.c.113.2 | 8 | |||
36.7 | odd | 6 | 144.5.q.c.65.2 | 8 | |||
36.11 | even | 6 | 432.5.q.c.305.3 | 8 | |||
36.23 | even | 6 | 1296.5.e.g.161.5 | 8 | |||
36.31 | odd | 6 | 1296.5.e.g.161.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.5.g.a.5.3 | ✓ | 8 | 3.2 | odd | 2 | ||
36.5.g.a.29.3 | yes | 8 | 9.7 | even | 3 | ||
108.5.g.a.17.3 | 8 | 1.1 | even | 1 | trivial | ||
108.5.g.a.89.3 | 8 | 9.2 | odd | 6 | inner | ||
144.5.q.c.65.2 | 8 | 36.7 | odd | 6 | |||
144.5.q.c.113.2 | 8 | 12.11 | even | 2 | |||
324.5.c.a.161.4 | 8 | 9.4 | even | 3 | |||
324.5.c.a.161.5 | 8 | 9.5 | odd | 6 | |||
432.5.q.c.17.3 | 8 | 4.3 | odd | 2 | |||
432.5.q.c.305.3 | 8 | 36.11 | even | 6 | |||
1296.5.e.g.161.4 | 8 | 36.31 | odd | 6 | |||
1296.5.e.g.161.5 | 8 | 36.23 | even | 6 |