Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,3,Mod(13,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 7, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("224.13");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.v (of order \(8\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.10355792167\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{8})\) |
Coefficient field: | 8.0.157351936.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + x^{4} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{8}]$ |
Embedding invariants
Embedding label | 181.1 | ||
Root | \(-0.581861 - 1.28897i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 224.181 |
Dual form | 224.3.v.a.125.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{5}{8}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.125246 | + | 1.99607i | 0.0626229 | + | 0.998037i | ||||
\(3\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(4\) | −3.96863 | + | 0.500000i | −0.992157 | + | 0.125000i | ||||
\(5\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.94975 | − | 4.94975i | −0.707107 | − | 0.707107i | ||||
\(8\) | −1.49509 | − | 7.85905i | −0.186886 | − | 0.982382i | ||||
\(9\) | 6.36396 | − | 6.36396i | 0.707107 | − | 0.707107i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −15.9450 | − | 6.60464i | −1.44955 | − | 0.600421i | −0.487454 | − | 0.873149i | \(-0.662074\pi\) |
−0.962091 | + | 0.272727i | \(0.912074\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(14\) | 9.26013 | − | 10.5000i | 0.661438 | − | 0.750000i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 15.5000 | − | 3.96863i | 0.968750 | − | 0.248039i | ||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | 13.5000 | + | 11.9059i | 0.750000 | + | 0.661438i | ||||
\(19\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 11.1863 | − | 32.6546i | 0.508468 | − | 1.48430i | ||||
\(23\) | 12.1660 | − | 12.1660i | 0.528957 | − | 0.528957i | −0.391304 | − | 0.920261i | \(-0.627976\pi\) |
0.920261 | + | 0.391304i | \(0.127976\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −17.6777 | − | 17.6777i | −0.707107 | − | 0.707107i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 22.1186 | + | 17.1688i | 0.789949 | + | 0.613172i | ||||
\(29\) | −1.02556 | + | 0.424802i | −0.0353642 | + | 0.0146483i | −0.400295 | − | 0.916386i | \(-0.631093\pi\) |
0.364931 | + | 0.931034i | \(0.381093\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | 9.86299 | + | 30.4421i | 0.308218 | + | 0.951316i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −22.0742 | + | 28.4382i | −0.613172 | + | 0.789949i | ||||
\(37\) | 4.13596 | − | 9.98508i | 0.111783 | − | 0.269867i | −0.858082 | − | 0.513514i | \(-0.828344\pi\) |
0.969864 | + | 0.243646i | \(0.0783436\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −71.9560 | − | 29.8052i | −1.67340 | − | 0.693143i | −0.674419 | − | 0.738349i | \(-0.735606\pi\) |
−0.998978 | + | 0.0452058i | \(0.985606\pi\) | |||||||
\(44\) | 66.5821 | + | 18.2388i | 1.51323 | + | 0.414519i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 25.8080 | + | 22.7605i | 0.561044 | + | 0.494794i | ||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000i | 1.00000i | ||||||||
\(50\) | 33.0719 | − | 37.5000i | 0.661438 | − | 0.750000i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 42.5379 | + | 17.6198i | 0.802602 | + | 0.332449i | 0.745998 | − | 0.665948i | \(-0.231973\pi\) |
0.0566038 | + | 0.998397i | \(0.481973\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −31.5000 | + | 46.3006i | −0.562500 | + | 0.826797i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.976384 | − | 1.99390i | −0.0168342 | − | 0.0343775i | ||||
\(59\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −63.0000 | −1.00000 | ||||||||
\(64\) | −59.5294 | + | 23.5000i | −0.930147 | + | 0.367188i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −78.2694 | + | 32.4202i | −1.16820 | + | 0.483884i | −0.880597 | − | 0.473866i | \(-0.842858\pi\) |
−0.287602 | + | 0.957750i | \(0.592858\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −59.8665 | − | 59.8665i | −0.843190 | − | 0.843190i | 0.146082 | − | 0.989272i | \(-0.453334\pi\) |
−0.989272 | + | 0.146082i | \(0.953334\pi\) | |||||||
\(72\) | −59.5294 | − | 40.5000i | −0.826797 | − | 0.562500i | ||||
\(73\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(74\) | 20.4490 | + | 7.00509i | 0.276338 | + | 0.0946634i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 46.2324 | + | 111.615i | 0.600421 | + | 1.44955i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 23.3317i | − | 0.295338i | −0.989037 | − | 0.147669i | \(-0.952823\pi\) | ||
0.989037 | − | 0.147669i | \(-0.0471771\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | − | 81.0000i | − | 1.00000i | ||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 50.4811 | − | 147.363i | 0.586990 | − | 1.71352i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −28.0669 | + | 135.187i | −0.318943 | + | 1.53622i | ||||
\(89\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −42.1994 | + | 54.3654i | −0.458689 | + | 0.590928i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(98\) | −97.8077 | + | 6.13705i | −0.998037 | + | 0.0626229i | ||||
\(99\) | −143.505 | + | 59.4417i | −1.44955 | + | 0.600421i | ||||
\(100\) | 78.9949 | + | 61.3172i | 0.789949 | + | 0.613172i | ||||
\(101\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −29.8427 | + | 87.1156i | −0.281535 | + | 0.821845i | ||||
\(107\) | 121.344 | + | 50.2625i | 1.13406 | + | 0.469743i | 0.869159 | − | 0.494533i | \(-0.164661\pi\) |
0.264901 | + | 0.964276i | \(0.414661\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 82.8732 | + | 200.074i | 0.760304 | + | 1.83554i | 0.486239 | + | 0.873826i | \(0.338369\pi\) |
0.274066 | + | 0.961711i | \(0.411631\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −96.3648 | − | 57.0774i | −0.860400 | − | 0.509620i | ||||
\(113\) | − | 186.911i | − | 1.65408i | −0.562144 | − | 0.827040i | \(-0.690023\pi\) | ||
0.562144 | − | 0.827040i | \(-0.309977\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.85768 | − | 2.19866i | 0.0332558 | − | 0.0189540i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 125.062 | + | 125.062i | 1.03357 | + | 1.03357i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −7.89049 | − | 125.753i | −0.0626229 | − | 0.998037i | ||||
\(127\) | 253.992 | 1.99994 | 0.999969 | − | 0.00787402i | \(-0.00250640\pi\) | ||||
0.999969 | + | 0.00787402i | \(0.00250640\pi\) | |||||||
\(128\) | −54.3636 | − | 115.882i | −0.424715 | − | 0.905327i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −74.5161 | − | 152.171i | −0.556090 | − | 1.13560i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 192.830 | − | 192.830i | 1.40752 | − | 1.40752i | 0.635036 | − | 0.772482i | \(-0.280985\pi\) |
0.772482 | − | 0.635036i | \(-0.219015\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 112.000 | − | 126.996i | 0.788732 | − | 0.894338i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 73.3852 | − | 123.898i | 0.509620 | − | 0.860400i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −11.4215 | + | 41.6951i | −0.0771725 | + | 0.281723i | ||||
\(149\) | 241.077 | + | 99.8575i | 1.61797 | + | 0.670185i | 0.993808 | − | 0.111111i | \(-0.0354409\pi\) |
0.624161 | + | 0.781296i | \(0.285441\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 200.498 | − | 200.498i | 1.32780 | − | 1.32780i | 0.420517 | − | 0.907285i | \(-0.361849\pi\) |
0.907285 | − | 0.420517i | \(-0.138151\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −217.001 | + | 106.263i | −1.40910 | + | 0.690018i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(158\) | 46.5719 | − | 2.92220i | 0.294759 | − | 0.0184950i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −120.437 | −0.748058 | ||||||||
\(162\) | 161.682 | − | 10.1449i | 0.998037 | − | 0.0626229i | ||||
\(163\) | −244.832 | + | 101.413i | −1.50204 | + | 0.622164i | −0.973896 | − | 0.226994i | \(-0.927110\pi\) |
−0.528140 | + | 0.849158i | \(0.677110\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −119.501 | + | 119.501i | −0.707107 | + | 0.707107i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 300.469 | + | 82.3076i | 1.74691 | + | 0.478532i | ||||
\(173\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 175.000i | 1.00000i | ||||||||
\(176\) | −273.359 | − | 39.0921i | −1.55318 | − | 0.222114i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −136.414 | − | 329.332i | −0.762088 | − | 1.83984i | −0.466473 | − | 0.884535i | \(-0.654476\pi\) |
−0.295615 | − | 0.955307i | \(-0.595524\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −113.803 | − | 77.4240i | −0.618492 | − | 0.420783i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 374.526 | 1.96087 | 0.980435 | − | 0.196842i | \(-0.0630686\pi\) | ||||
0.980435 | + | 0.196842i | \(0.0630686\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −313.240 | −1.62300 | −0.811502 | − | 0.584349i | \(-0.801350\pi\) | ||||
−0.811502 | + | 0.584349i | \(0.801350\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −24.5000 | − | 194.463i | −0.125000 | − | 0.992157i | ||||
\(197\) | 59.4061 | − | 143.419i | 0.301554 | − | 0.728015i | −0.698371 | − | 0.715736i | \(-0.746091\pi\) |
0.999925 | − | 0.0122790i | \(-0.00390863\pi\) | |||||||
\(198\) | −136.623 | − | 279.002i | −0.690018 | − | 1.40910i | ||||
\(199\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(200\) | −112.500 | + | 165.359i | −0.562500 | + | 0.826797i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.17894 | + | 2.97361i | 0.0353642 | + | 0.0146483i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 154.848i | − | 0.748058i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 152.962 | + | 369.283i | 0.724938 | + | 1.75015i | 0.658768 | + | 0.752346i | \(0.271078\pi\) |
0.0661700 | + | 0.997808i | \(0.478922\pi\) | |||||||
\(212\) | −177.627 | − | 48.6574i | −0.837863 | − | 0.229516i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −85.1298 | + | 248.508i | −0.397803 | + | 1.16125i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −388.982 | + | 190.479i | −1.78432 | + | 0.873759i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(224\) | 101.861 | − | 199.500i | 0.454739 | − | 0.890625i | ||||
\(225\) | −225.000 | −1.00000 | ||||||||
\(226\) | 373.088 | − | 23.4098i | 1.65083 | − | 0.103583i | ||||
\(227\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.87185 | + | 7.42484i | 0.0209994 | + | 0.0320036i | ||||
\(233\) | 241.826 | − | 241.826i | 1.03788 | − | 1.03788i | 0.0386266 | − | 0.999254i | \(-0.487702\pi\) |
0.999254 | − | 0.0386266i | \(-0.0122983\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 423.320i | 1.77121i | 0.464435 | + | 0.885607i | \(0.346257\pi\) | ||||
−0.464435 | + | 0.885607i | \(0.653743\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(242\) | −233.969 | + | 265.296i | −0.966816 | + | 1.09627i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(252\) | 250.023 | − | 31.5000i | 0.992157 | − | 0.125000i | ||||
\(253\) | −274.339 | + | 113.635i | −1.08434 | + | 0.449150i | ||||
\(254\) | 31.8115 | + | 506.987i | 0.125242 | + | 1.99601i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 224.500 | − | 123.027i | 0.876953 | − | 0.480576i | ||||
\(257\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −69.8956 | + | 28.9517i | −0.269867 | + | 0.111783i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.82322 | + | 9.23007i | −0.0146483 | + | 0.0353642i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −352.139 | − | 352.139i | −1.33893 | − | 1.33893i | −0.897095 | − | 0.441837i | \(-0.854327\pi\) |
−0.441837 | − | 0.897095i | \(-0.645673\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 294.412 | − | 167.798i | 1.09855 | − | 0.626114i | ||||
\(269\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 409.054 | + | 360.752i | 1.49290 | + | 1.31661i | ||||
\(275\) | 165.116 | + | 398.625i | 0.600421 | + | 1.44955i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −431.508 | − | 178.736i | −1.55779 | − | 0.645258i | −0.573087 | − | 0.819495i | \(-0.694254\pi\) |
−0.984704 | + | 0.174237i | \(0.944254\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −218.158 | − | 218.158i | −0.776363 | − | 0.776363i | 0.202847 | − | 0.979210i | \(-0.434981\pi\) |
−0.979210 | + | 0.202847i | \(0.934981\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(284\) | 267.521 | + | 207.655i | 0.941976 | + | 0.731178i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 256.500 | + | 130.965i | 0.890625 | + | 0.454739i | ||||
\(289\) | −289.000 | −1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −84.6569 | − | 17.5761i | −0.286003 | − | 0.0593787i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −169.129 | + | 493.715i | −0.567547 | + | 1.65676i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 208.636 | + | 503.692i | 0.693143 | + | 1.67340i | ||||
\(302\) | 425.321 | + | 375.097i | 1.40835 | + | 1.24204i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(308\) | −239.287 | − | 419.842i | −0.776905 | − | 1.36312i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.6659 | + | 92.5950i | 0.0369173 | + | 0.293022i | ||||
\(317\) | −491.682 | + | 203.661i | −1.55105 | + | 0.642465i | −0.983505 | − | 0.180879i | \(-0.942106\pi\) |
−0.567543 | + | 0.823344i | \(0.692106\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.1583 | 0.0600573 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −15.0843 | − | 240.402i | −0.0468456 | − | 0.746590i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 40.5000 | + | 321.459i | 0.125000 | + | 0.992157i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −233.091 | − | 476.001i | −0.715004 | − | 1.46013i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 386.750 | + | 160.197i | 1.16843 | + | 0.483979i | 0.880673 | − | 0.473725i | \(-0.157091\pi\) |
0.287755 | + | 0.957704i | \(0.407091\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −37.2236 | − | 89.8658i | −0.111783 | − | 0.269867i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 608.805i | − | 1.80654i | −0.429069 | − | 0.903272i | \(-0.641158\pi\) | ||
0.429069 | − | 0.903272i | \(-0.358842\pi\) | |||||||
\(338\) | −253.500 | − | 223.566i | −0.750000 | − | 0.661438i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 242.538 | − | 242.538i | 0.707107 | − | 0.707107i | ||||
\(344\) | −126.660 | + | 610.068i | −0.368196 | + | 1.77345i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 151.674 | − | 366.173i | 0.437101 | − | 1.05525i | −0.539844 | − | 0.841765i | \(-0.681517\pi\) |
0.976945 | − | 0.213490i | \(-0.0684831\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(350\) | −349.313 | + | 21.9180i | −0.998037 | + | 0.0626229i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 43.7937 | − | 550.541i | 0.124414 | − | 1.56404i | ||||
\(353\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 640.286 | − | 313.539i | 1.78851 | − | 0.875808i | ||||
\(359\) | 178.838 | + | 178.838i | 0.498156 | + | 0.498156i | 0.910864 | − | 0.412708i | \(-0.135417\pi\) |
−0.412708 | + | 0.910864i | \(0.635417\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −255.266 | + | 255.266i | −0.707107 | + | 0.707107i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(368\) | 140.291 | − | 236.856i | 0.381225 | − | 0.643629i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −123.338 | − | 297.765i | −0.332449 | − | 0.802602i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −503.558 | − | 208.580i | −1.35002 | − | 0.559197i | −0.413722 | − | 0.910403i | \(-0.635772\pi\) |
−0.936298 | + | 0.351206i | \(0.885772\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 282.175 | − | 681.231i | 0.744526 | − | 1.79744i | 0.158132 | − | 0.987418i | \(-0.449453\pi\) |
0.586393 | − | 0.810026i | \(-0.300547\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 46.9078 | + | 747.582i | 0.122795 | + | 1.95702i | ||||
\(383\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −39.2320 | − | 625.250i | −0.101637 | − | 1.61982i | ||||
\(387\) | −647.604 | + | 268.247i | −1.67340 | + | 0.693143i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 294.361 | − | 710.650i | 0.756711 | − | 1.82686i | 0.239804 | − | 0.970821i | \(-0.422917\pi\) |
0.516908 | − | 0.856041i | \(-0.327083\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 385.094 | − | 73.2595i | 0.982382 | − | 0.186886i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 293.715 | + | 100.616i | 0.745470 | + | 0.255371i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 539.797 | − | 307.654i | 1.36312 | − | 0.776905i | ||||
\(397\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −344.160 | − | 203.848i | −0.860400 | − | 0.509620i | ||||
\(401\) | 258.550i | 0.644762i | 0.946610 | + | 0.322381i | \(0.104483\pi\) | ||||
−0.946610 | + | 0.322381i | \(0.895517\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.03642 | + | 14.7021i | −0.0124050 | + | 0.0362122i | ||||
\(407\) | −131.896 | + | 131.896i | −0.324068 | + | 0.324068i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 309.088 | − | 19.3941i | 0.746590 | − | 0.0468456i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 316.159 | − | 763.276i | 0.750972 | − | 1.81301i | 0.197150 | − | 0.980373i | \(-0.436832\pi\) |
0.553823 | − | 0.832635i | \(-0.313168\pi\) | |||||||
\(422\) | −717.958 | + | 351.574i | −1.70132 | + | 0.833115i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 74.8767 | − | 360.651i | 0.176596 | − | 0.850591i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −506.702 | − | 138.801i | −1.18388 | − | 0.324301i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 162.000i | 0.375870i | 0.982181 | + | 0.187935i | \(0.0601794\pi\) | ||||
−0.982181 | + | 0.187935i | \(0.939821\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −428.929 | − | 752.581i | −0.983783 | − | 1.72610i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 311.834 | + | 311.834i | 0.707107 | + | 0.707107i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −63.3378 | + | 152.911i | −0.142975 | + | 0.345171i | −0.979104 | − | 0.203361i | \(-0.934813\pi\) |
0.836129 | + | 0.548533i | \(0.184813\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 410.975 | + | 178.336i | 0.917354 | + | 0.398072i | ||||
\(449\) | −84.6640 | −0.188561 | −0.0942807 | − | 0.995546i | \(-0.530055\pi\) | ||||
−0.0942807 | + | 0.995546i | \(0.530055\pi\) | |||||||
\(450\) | −28.1803 | − | 449.117i | −0.0626229 | − | 0.998037i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 93.4555 | + | 741.780i | 0.206760 | + | 1.64111i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 179.600 | − | 179.600i | 0.392997 | − | 0.392997i | −0.482757 | − | 0.875754i | \(-0.660365\pi\) |
0.875754 | + | 0.482757i | \(0.160365\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 925.589i | 1.99911i | 0.0297960 | + | 0.999556i | \(0.490514\pi\) | ||||
−0.0297960 | + | 0.999556i | \(0.509486\pi\) | |||||||
\(464\) | −14.2103 | + | 10.6545i | −0.0306257 | + | 0.0229623i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 512.991 | + | 452.415i | 1.10084 | + | 0.970848i | ||||
\(467\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 547.885 | + | 226.942i | 1.16820 | + | 0.483884i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 950.487 | + | 950.487i | 2.00949 | + | 2.00949i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 382.841 | − | 158.578i | 0.802602 | − | 0.332449i | ||||
\(478\) | −844.979 | + | 53.0191i | −1.76774 | + | 0.110919i | ||||
\(479\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −558.855 | − | 433.793i | −1.15466 | − | 0.896267i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −643.486 | − | 643.486i | −1.32133 | − | 1.32133i | −0.912703 | − | 0.408624i | \(-0.866009\pi\) |
−0.408624 | − | 0.912703i | \(-0.633991\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 896.606 | + | 371.387i | 1.82608 | + | 0.756388i | 0.971487 | + | 0.237094i | \(0.0761949\pi\) |
0.854596 | + | 0.519294i | \(0.173805\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 592.648i | 1.19245i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 34.1272 | + | 82.3903i | 0.0683911 | + | 0.165111i | 0.954379 | − | 0.298597i | \(-0.0965187\pi\) |
−0.885988 | + | 0.463708i | \(0.846519\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(504\) | 94.1907 | + | 495.120i | 0.186886 | + | 0.982382i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −261.184 | − | 533.369i | −0.516173 | − | 1.05409i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1008.00 | + | 126.996i | −1.98425 | + | 0.249992i | ||||
\(509\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 273.690 | + | 432.710i | 0.534550 | + | 0.845137i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −66.5439 | − | 135.891i | −0.128463 | − | 0.262337i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(522\) | −18.9027 | − | 6.47540i | −0.0362122 | − | 0.0124050i | ||||
\(523\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 658.792 | − | 747.000i | 1.25246 | − | 1.42015i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 232.976i | 0.440409i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 371.812 | + | 566.652i | 0.693679 | + | 1.05719i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 323.627 | − | 781.305i | 0.600421 | − | 1.44955i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −444.812 | + | 184.247i | −0.822203 | + | 0.340568i | −0.753811 | − | 0.657091i | \(-0.771787\pi\) |
−0.0683919 | + | 0.997659i | \(0.521787\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 893.881 | − | 370.257i | 1.63415 | − | 0.676887i | 0.638463 | − | 0.769653i | \(-0.279571\pi\) |
0.995688 | + | 0.0927652i | \(0.0295706\pi\) | |||||||
\(548\) | −668.856 | + | 861.686i | −1.22054 | + | 1.57242i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −775.005 | + | 379.510i | −1.40910 | + | 0.690018i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −115.486 | + | 115.486i | −0.208836 | + | 0.208836i | ||||
\(554\) | 302.727 | − | 883.708i | 0.546438 | − | 1.59514i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −25.3767 | − | 61.2649i | −0.0455597 | − | 0.109991i | 0.899461 | − | 0.437000i | \(-0.143959\pi\) |
−0.945021 | + | 0.327009i | \(0.893959\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 408.137 | − | 462.783i | 0.726222 | − | 0.823458i | ||||
\(563\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −400.930 | + | 400.930i | −0.707107 | + | 0.707107i | ||||
\(568\) | −380.988 | + | 560.000i | −0.670754 | + | 0.985915i | ||||
\(569\) | 658.532 | + | 658.532i | 1.15735 | + | 1.15735i | 0.985044 | + | 0.172306i | \(0.0551217\pi\) |
0.172306 | + | 0.985044i | \(0.444878\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −97.5490 | + | 235.504i | −0.170839 | + | 0.412442i | −0.985989 | − | 0.166807i | \(-0.946654\pi\) |
0.815151 | + | 0.579249i | \(0.196654\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −430.133 | −0.748058 | ||||||||
\(576\) | −229.290 | + | 528.396i | −0.398072 | + | 0.917354i | ||||
\(577\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(578\) | −36.1960 | − | 576.866i | −0.0626229 | − | 0.998037i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −561.895 | − | 561.895i | −0.963799 | − | 0.963799i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 24.4803 | − | 171.183i | 0.0413518 | − | 0.289160i | ||||
\(593\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1006.68 | − | 275.759i | −1.68905 | − | 0.462682i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −123.037 | + | 123.037i | −0.205403 | + | 0.205403i | −0.802310 | − | 0.596907i | \(-0.796396\pi\) |
0.596907 | + | 0.802310i | \(0.296396\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(602\) | −979.277 | + | 479.539i | −1.62671 | + | 0.796576i | ||||
\(603\) | −291.782 | + | 704.424i | −0.483884 | + | 1.16820i | ||||
\(604\) | −695.453 | + | 895.951i | −1.15141 | + | 1.48336i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −458.474 | + | 1106.85i | −0.747919 | + | 1.80564i | −0.177814 | + | 0.984064i | \(0.556903\pi\) |
−0.570105 | + | 0.821572i | \(0.693097\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 808.066 | − | 530.218i | 1.31180 | − | 0.860743i | ||||
\(617\) | 778.265 | − | 778.265i | 1.26137 | − | 1.26137i | 0.310939 | − | 0.950430i | \(-0.399356\pi\) |
0.950430 | − | 0.310939i | \(-0.100644\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000i | 1.00000i | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −538.799 | + | 538.799i | −0.853881 | + | 0.853881i | −0.990609 | − | 0.136728i | \(-0.956341\pi\) |
0.136728 | + | 0.990609i | \(0.456341\pi\) | |||||||
\(632\) | −183.365 | + | 34.8831i | −0.290135 | + | 0.0551947i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −468.105 | − | 955.927i | −0.738335 | − | 1.50777i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.39949 | + | 38.2413i | 0.00376096 | + | 0.0599394i | ||||
\(639\) | −761.976 | −1.19245 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1278.19 | 1.99406 | 0.997030 | − | 0.0770186i | \(-0.0245401\pi\) | ||||
0.997030 | + | 0.0770186i | \(0.0245401\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(644\) | 477.971 | − | 60.2187i | 0.742191 | − | 0.0935073i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(648\) | −636.583 | + | 121.102i | −0.982382 | + | 0.186886i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 920.940 | − | 524.885i | 1.41248 | − | 0.805038i | ||||
\(653\) | −361.940 | − | 873.801i | −0.554273 | − | 1.33813i | −0.914242 | − | 0.405169i | \(-0.867213\pi\) |
0.359969 | − | 0.932964i | \(-0.382787\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −321.078 | − | 775.152i | −0.487220 | − | 1.17625i | −0.956113 | − | 0.292999i | \(-0.905347\pi\) |
0.468892 | − | 0.883255i | \(-0.344653\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(662\) | −271.326 | + | 792.045i | −0.409859 | + | 1.19644i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 174.717 | − | 85.5564i | 0.262337 | − | 0.128463i | ||||
\(667\) | −7.30886 | + | 17.6452i | −0.0109578 | + | 0.0264545i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1269.96 | −1.88701 | −0.943507 | − | 0.331352i | \(-0.892495\pi\) | ||||
−0.943507 | + | 0.331352i | \(0.892495\pi\) | |||||||
\(674\) | 1215.22 | − | 76.2503i | 1.80300 | − | 0.113131i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 414.505 | − | 534.006i | 0.613172 | − | 0.789949i | ||||
\(677\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1044.77 | − | 432.758i | −1.52968 | − | 0.633614i | −0.550178 | − | 0.835048i | \(-0.685440\pi\) |
−0.979502 | + | 0.201433i | \(0.935440\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 514.500 | + | 453.746i | 0.750000 | + | 0.661438i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1233.60 | − | 176.413i | −1.79303 | − | 0.256415i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1004.53 | + | 416.092i | 1.44955 | + | 0.600421i | ||||
\(694\) | 749.906 | + | 256.891i | 1.08056 | + | 0.370160i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −87.5000 | − | 694.510i | −0.125000 | − | 0.992157i | ||||
\(701\) | 1230.68 | − | 509.766i | 1.75561 | − | 0.727198i | 0.758465 | − | 0.651713i | \(-0.225949\pi\) |
0.997147 | − | 0.0754851i | \(-0.0240505\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 1104.41 | + | 18.4625i | 1.56876 | + | 0.0262251i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 314.639 | − | 759.606i | 0.443778 | − | 1.07138i | −0.530834 | − | 0.847476i | \(-0.678121\pi\) |
0.974612 | − | 0.223900i | \(-0.0718789\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −148.482 | − | 148.482i | −0.208836 | − | 0.208836i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 706.041 | + | 1238.79i | 0.986091 | + | 1.73015i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −334.575 | + | 379.373i | −0.465982 | + | 0.528374i | ||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −541.500 | − | 477.558i | −0.750000 | − | 0.661438i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 25.6391 | + | 10.6201i | 0.0353642 | + | 0.0146483i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −515.481 | − | 515.481i | −0.707107 | − | 0.707107i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 490.352 | + | 250.366i | 0.666239 | + | 0.340171i | ||||
\(737\) | 1462.13 | 1.98389 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 271.130 | − | 112.306i | 0.366888 | − | 0.151970i | −0.191620 | − | 0.981469i | \(-0.561374\pi\) |
0.558508 | + | 0.829499i | \(0.311374\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 578.914 | − | 283.487i | 0.780208 | − | 0.382057i | ||||
\(743\) | 797.810 | + | 797.810i | 1.07377 | + | 1.07377i | 0.997053 | + | 0.0767160i | \(0.0244435\pi\) |
0.0767160 | + | 0.997053i | \(0.475557\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 353.273 | − | 1031.26i | 0.473557 | − | 1.38239i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −351.837 | − | 849.410i | −0.469743 | − | 1.13406i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1269.96i | − | 1.69103i | −0.533955 | − | 0.845513i | \(-0.679295\pi\) | ||
0.533955 | − | 0.845513i | \(-0.320705\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1398.73 | − | 579.373i | −1.84773 | − | 0.765355i | −0.926024 | − | 0.377465i | \(-0.876796\pi\) |
−0.921706 | − | 0.387890i | \(-0.873204\pi\) | |||||||
\(758\) | 1395.13 | + | 477.922i | 1.84054 | + | 0.630503i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 580.112 | − | 1400.51i | 0.760304 | − | 1.83554i | ||||
\(764\) | −1486.35 | + | 187.263i | −1.94549 | + | 0.245109i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1243.13 | − | 156.620i | 1.61028 | − | 0.202876i | ||||
\(773\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(774\) | −616.550 | − | 1259.07i | −0.796576 | − | 1.62671i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1455.38 | + | 498.560i | 1.87066 | + | 0.640823i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 559.175 | + | 1349.97i | 0.715973 | + | 1.72851i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 194.463 | + | 759.500i | 0.248039 | + | 0.968750i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(788\) | −164.051 | + | 598.879i | −0.208187 | + | 0.759999i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −925.162 | + | 925.162i | −1.16961 | + | 1.16961i | ||||
\(792\) | 681.709 | + | 1038.94i | 0.860743 | + | 1.31180i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 363.791 | − | 712.500i | 0.454739 | − | 0.890625i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −516.084 | + | 32.3823i | −0.643497 | + | 0.0403769i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1137.46 | + | 1137.46i | −1.40601 | + | 1.40601i | −0.626964 | + | 0.779048i | \(0.715703\pi\) |
−0.779048 | + | 0.626964i | \(0.784297\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(812\) | −29.9773 | − | 8.21170i | −0.0369179 | − | 0.0101129i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −279.793 | − | 246.754i | −0.343726 | − | 0.303138i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1403.06 | − | 581.167i | −1.70897 | − | 0.707878i | −0.999997 | − | 0.00264006i | \(-0.999160\pi\) |
−0.708971 | − | 0.705238i | \(-0.750840\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 439.820 | − | 439.820i | 0.534411 | − | 0.534411i | −0.387471 | − | 0.921882i | \(-0.626651\pi\) |
0.921882 | + | 0.387471i | \(0.126651\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −138.974 | + | 335.513i | −0.168046 | + | 0.405699i | −0.985358 | − | 0.170496i | \(-0.945463\pi\) |
0.817312 | + | 0.576195i | \(0.195463\pi\) | |||||||
\(828\) | 77.4240 | + | 614.534i | 0.0935073 | + | 0.742191i | ||||
\(829\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −593.805 | + | 593.805i | −0.706071 | + | 0.706071i | ||||
\(842\) | 1563.15 | + | 535.481i | 1.85648 | + | 0.635963i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −791.690 | − | 1389.06i | −0.938021 | − | 1.64581i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1238.05i | − | 1.46169i | ||||||
\(848\) | 729.264 | + | 104.289i | 0.859981 | + | 0.122983i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −71.1605 | − | 171.797i | −0.0836199 | − | 0.201876i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 213.595 | − | 1028.80i | 0.249526 | − | 1.20187i | ||||
\(857\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −323.364 | + | 20.2898i | −0.375132 | + | 0.0235381i | ||||
\(863\) | −845.946 | −0.980238 | −0.490119 | − | 0.871655i | \(-0.663047\pi\) | ||||
−0.490119 | + | 0.871655i | \(0.663047\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −154.098 | + | 372.025i | −0.177328 | + | 0.428107i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 1448.49 | − | 950.433i | 1.66111 | − | 1.08995i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −496.228 | − | 1198.00i | −0.565824 | − | 1.36602i | −0.905046 | − | 0.425314i | \(-0.860164\pi\) |
0.339222 | − | 0.940706i | \(-0.389836\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | −583.388 | + | 661.500i | −0.661438 | + | 0.750000i | ||||
\(883\) | 9.41299 | + | 22.7250i | 0.0106602 | + | 0.0257361i | 0.929120 | − | 0.369778i | \(-0.120566\pi\) |
−0.918460 | + | 0.395514i | \(0.870566\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −313.154 | − | 107.275i | −0.353447 | − | 0.121078i | ||||
\(887\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1257.20 | − | 1257.20i | −1.41417 | − | 1.41417i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −534.975 | + | 1291.54i | −0.600421 | + | 1.44955i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −304.500 | + | 842.672i | −0.339844 | + | 0.940482i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −10.6038 | − | 168.996i | −0.0118083 | − | 0.188191i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 892.941 | − | 112.500i | 0.992157 | − | 0.125000i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1468.94 | + | 279.449i | −1.62494 | + | 0.309125i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −360.452 | − | 149.304i | −0.397411 | − | 0.164613i | 0.175022 | − | 0.984564i | \(-0.444000\pi\) |
−0.572433 | + | 0.819952i | \(0.694000\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 931.304i | 1.02229i | 0.859495 | + | 0.511144i | \(0.170778\pi\) | ||||
−0.859495 | + | 0.511144i | \(0.829222\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 380.988 | + | 336.000i | 0.416836 | + | 0.367615i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1257.20 | − | 1257.20i | 1.36801 | − | 1.36801i | 0.504725 | − | 0.863280i | \(-0.331594\pi\) |
0.863280 | − | 0.504725i | \(-0.168406\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −249.627 | + | 103.399i | −0.269867 | + | 0.111783i | ||||
\(926\) | −1847.54 | + | 115.926i | −1.99519 | + | 0.125190i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −23.0470 | − | 27.0305i | −0.0248351 | − | 0.0291277i | ||||
\(929\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −838.805 | + | 1080.63i | −0.900005 | + | 1.15948i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(938\) | −384.372 | + | 1122.04i | −0.409778 | + | 1.19621i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1778.20 | + | 2016.29i | −1.87970 | + | 2.13138i | ||||
\(947\) | 630.374 | + | 1521.86i | 0.665653 | + | 1.60703i | 0.788807 | + | 0.614641i | \(0.210699\pi\) |
−0.123154 | + | 0.992388i | \(0.539301\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −115.186 | − | 115.186i | −0.120866 | − | 0.120866i | 0.644086 | − | 0.764953i | \(-0.277238\pi\) |
−0.764953 | + | 0.644086i | \(0.777238\pi\) | |||||||
\(954\) | 364.483 | + | 744.318i | 0.382057 | + | 0.780208i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −211.660 | − | 1680.00i | −0.221402 | − | 1.75732i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1908.92 | −1.99053 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 961.000 | 1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1092.10 | − | 452.362i | 1.13406 | − | 0.469743i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1119.47 | + | 1119.47i | 1.15767 | + | 1.15767i | 0.984975 | + | 0.172699i | \(0.0552488\pi\) |
0.172699 | + | 0.984975i | \(0.444751\pi\) | |||||||
\(968\) | 795.889 | − | 1169.85i | 0.822199 | − | 1.20852i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1203.85 | − | 1365.04i | 1.23599 | − | 1.40148i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1947.27i | − | 1.99311i | −0.0829069 | − | 0.996557i | \(-0.526420\pi\) | ||
0.0829069 | − | 0.996557i | \(-0.473580\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1800.66 | + | 745.859i | 1.83554 | + | 0.760304i | ||||
\(982\) | −629.019 | + | 1836.21i | −0.640549 | + | 1.86987i | ||||
\(983\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1238.03 | + | 512.808i | −1.25180 | + | 0.518512i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1981.99 | 1.99999 | 0.999995 | − | 0.00322633i | \(-0.00102697\pi\) | ||||
0.999995 | + | 0.00322633i | \(0.00102697\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1182.97 | + | 74.2267i | −1.19011 | + | 0.0746748i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(998\) | −160.183 | + | 78.4394i | −0.160504 | + | 0.0785966i | ||||
\(999\) | 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 | 224.3.v.a.181.1 | yes | 8 | |
7.6 | odd | 2 | CM | 224.3.v.a.181.1 | yes | 8 | |
32.29 | even | 8 | inner | 224.3.v.a.125.1 | ✓ | 8 | |
224.125 | odd | 8 | inner | 224.3.v.a.125.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.3.v.a.125.1 | ✓ | 8 | 32.29 | even | 8 | inner | |
224.3.v.a.125.1 | ✓ | 8 | 224.125 | odd | 8 | inner | |
224.3.v.a.181.1 | yes | 8 | 1.1 | even | 1 | trivial | |
224.3.v.a.181.1 | yes | 8 | 7.6 | odd | 2 | CM |