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 | 69.2 | ||
Root | \(0.581861 + 1.28897i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 224.69 |
Dual form | 224.3.v.a.13.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{8}\right)\) |
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 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(4\) | −3.96863 | + | 0.500000i | −0.992157 | + | 0.125000i | ||||
\(5\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(6\) | 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 | ||||||||
\(11\) | −5.22101 | + | 12.6046i | −0.474637 | + | 1.14588i | 0.487454 | + | 0.873149i | \(0.337926\pi\) |
−0.962091 | + | 0.272727i | \(0.912074\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(14\) | 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 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 25.8137 | + | 8.84285i | 1.17335 | + | 0.401948i | ||||
\(23\) | 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 | ||||
\(29\) | 22.1916 | + | 53.5752i | 0.765227 | + | 1.84742i | 0.400295 | + | 0.916386i | \(0.368907\pi\) |
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 | ||||
\(37\) | −67.6340 | − | 28.0149i | −1.82795 | − | 0.757160i | −0.969864 | − | 0.243646i | \(-0.921656\pi\) |
−0.858082 | − | 0.513514i | \(-0.828344\pi\) | |||||||
\(38\) | 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 | ||||||||
\(43\) | 13.9560 | − | 33.6929i | 0.324559 | − | 0.783555i | −0.674419 | − | 0.738349i | \(-0.735606\pi\) |
0.998978 | − | 0.0452058i | \(-0.0143943\pi\) | |||||||
\(44\) | 14.4179 | − | 52.6336i | 0.327680 | − | 1.19622i | ||||
\(45\) | 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 | ||||||||
\(53\) | −36.5379 | + | 88.2103i | −0.689394 | + | 1.66434i | 0.0566038 | + | 0.998397i | \(0.481973\pi\) |
−0.745998 | + | 0.665948i | \(0.768027\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −31.5000 | + | 46.3006i | −0.562500 | + | 0.826797i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 104.161 | − | 51.0061i | 1.79587 | − | 0.879416i | ||||
\(59\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −63.0000 | −1.00000 | ||||||||
\(64\) | −59.5294 | + | 23.5000i | −0.930147 | + | 0.367188i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −39.7306 | − | 95.9183i | −0.592995 | − | 1.43162i | −0.880597 | − | 0.473866i | \(-0.842858\pi\) |
0.287602 | − | 0.957750i | \(-0.407142\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 59.8665 | + | 59.8665i | 0.843190 | + | 0.843190i | 0.989272 | − | 0.146082i | \(-0.0466664\pi\) |
−0.146082 | + | 0.989272i | \(0.546666\pi\) | |||||||
\(72\) | −59.5294 | − | 40.5000i | −0.826797 | − | 0.562500i | ||||
\(73\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(74\) | −47.4490 | + | 138.511i | −0.641202 | + | 1.87177i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −88.2324 | + | 36.5471i | −1.14588 | + | 0.474637i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 23.3317i | 0.295338i | 0.989037 | + | 0.147669i | \(0.0471771\pi\) | ||||
−0.989037 | + | 0.147669i | \(0.952823\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | − | 81.0000i | − | 1.00000i | ||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −69.0014 | − | 23.6374i | −0.802342 | − | 0.274854i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −106.866 | − | 22.1871i | −1.21439 | − | 0.252126i | ||||
\(89\) | 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 | ||||
\(99\) | −46.9891 | − | 113.442i | −0.474637 | − | 1.14588i | ||||
\(100\) | −78.9949 | − | 61.3172i | −0.789949 | − | 0.613172i | ||||
\(101\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(102\) | 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 | ||||||||
\(106\) | 180.651 | + | 61.8844i | 1.70425 | + | 0.583815i | ||||
\(107\) | 64.6556 | − | 156.093i | 0.604258 | − | 1.45881i | −0.264901 | − | 0.964276i | \(-0.585339\pi\) |
0.869159 | − | 0.494533i | \(-0.164661\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 23.1268 | − | 9.57945i | 0.212173 | − | 0.0878848i | −0.274066 | − | 0.961711i | \(-0.588369\pi\) |
0.486239 | + | 0.873826i | \(0.338369\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 96.3648 | + | 57.0774i | 0.860400 | + | 0.509620i | ||||
\(113\) | 186.911i | 1.65408i | 0.562144 | + | 0.827040i | \(0.309977\pi\) | ||||
−0.562144 | + | 0.827040i | \(0.690023\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −114.858 | − | 201.524i | −0.990152 | − | 1.73728i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −46.0580 | − | 46.0580i | −0.380644 | − | 0.380644i | ||||
\(122\) | 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 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −186.484 | + | 91.3187i | −1.39167 | + | 0.681483i | ||||
\(135\) | 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 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(140\) | 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 | ||||||||
\(148\) | 282.422 | + | 77.3638i | 1.90825 | + | 0.522728i | ||||
\(149\) | −55.0774 | + | 132.969i | −0.369647 | + | 0.892407i | 0.624161 | + | 0.781296i | \(0.285441\pi\) |
−0.993808 | + | 0.111111i | \(0.964559\pi\) | |||||||
\(150\) | 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 | ||||||||
\(154\) | 84.0014 | + | 171.541i | 0.545464 | + | 1.11390i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(158\) | 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 | ||||
\(163\) | −72.6583 | − | 175.413i | −0.445756 | − | 1.07615i | −0.973896 | − | 0.226994i | \(-0.927110\pi\) |
0.528140 | − | 0.849158i | \(-0.322890\pi\) | |||||||
\(164\) | 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 | ||||||||
\(172\) | −38.5399 | + | 140.692i | −0.224069 | + | 0.817979i | ||||
\(173\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 175.000i | 1.00000i | ||||||||
\(176\) | −30.9026 | + | 216.092i | −0.175583 | + | 1.22780i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 30.5837 | − | 12.6682i | 0.170858 | − | 0.0707719i | −0.295615 | − | 0.955307i | \(-0.595524\pi\) |
0.466473 | + | 0.884535i | \(0.345524\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(182\) | 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 | \(-0.936931\pi\) | ||||
−0.980435 | + | 0.196842i | \(0.936931\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 313.240 | 1.62300 | 0.811502 | − | 0.584349i | \(-0.198650\pi\) | ||||
0.811502 | + | 0.584349i | \(0.198650\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −24.5000 | − | 194.463i | −0.125000 | − | 0.992157i | ||||
\(197\) | −334.564 | − | 138.581i | −1.69830 | − | 0.703457i | −0.698371 | − | 0.715736i | \(-0.746091\pi\) |
−0.999925 | + | 0.0122790i | \(0.996091\pi\) | |||||||
\(198\) | −220.553 | + | 108.002i | −1.11390 | + | 0.545464i | ||||
\(199\) | 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 | ||||||||
\(203\) | −155.341 | + | 375.026i | −0.765227 | + | 1.84742i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 154.848i | 0.748058i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 125.038 | − | 51.7925i | 0.592598 | − | 0.245462i | −0.0661700 | − | 0.997808i | \(-0.521078\pi\) |
0.658768 | + | 0.752346i | \(0.271078\pi\) | |||||||
\(212\) | 100.900 | − | 368.343i | 0.475944 | − | 1.73747i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −319.670 | − | 109.508i | −1.49379 | − | 0.511717i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −22.0178 | − | 44.9631i | −0.100999 | − | 0.206253i | ||||
\(219\) | 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 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −387.872 | + | 254.505i | −1.67186 | + | 1.09700i | ||||
\(233\) | 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 | \(0.5\pi\) | |||||||||
\(242\) | −86.1665 | + | 97.7037i | −0.356060 | + | 0.403734i | ||||
\(243\) | 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 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(252\) | 250.023 | − | 31.5000i | 0.992157 | − | 0.125000i | ||||
\(253\) | 89.8293 | + | 216.867i | 0.355056 | + | 0.857182i | ||||
\(254\) | −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 | ||||||||
\(259\) | −196.104 | − | 473.438i | −0.757160 | − | 1.82795i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −482.177 | − | 199.724i | −1.84742 | − | 0.765227i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 352.139 | + | 352.139i | 1.33893 | + | 1.33893i | 0.897095 | + | 0.441837i | \(0.145673\pi\) |
0.441837 | + | 0.897095i | \(0.354327\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 205.635 | + | 360.798i | 0.767296 | + | 1.34626i | ||||
\(269\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(270\) | 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 | ||||
\(275\) | −315.116 | + | 130.525i | −1.14588 | + | 0.474637i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 114.018 | − | 275.264i | 0.411617 | − | 0.993731i | −0.573087 | − | 0.819495i | \(-0.694254\pi\) |
0.984704 | − | 0.174237i | \(-0.0557457\pi\) | |||||||
\(278\) | 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 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(284\) | −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 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 119.052 | − | 573.424i | 0.402202 | − | 1.93724i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 272.313 | + | 93.2848i | 0.913803 | + | 0.313036i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 235.850 | − | 97.6923i | 0.783555 | − | 0.324559i | ||||
\(302\) | −425.321 | − | 375.097i | −1.40835 | − | 1.24204i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(308\) | 331.888 | − | 189.158i | 1.07756 | − | 0.614149i | ||||
\(309\) | 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 | ||||
\(317\) | 131.860 | + | 318.339i | 0.415963 | + | 1.00422i | 0.983505 | + | 0.180879i | \(0.0578941\pi\) |
−0.567543 | + | 0.823344i | \(0.692106\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −791.158 | −2.48012 | ||||||||
\(320\) | 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 | ||||||||
\(326\) | −341.037 | + | 167.001i | −1.04612 | + | 0.512273i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −196.256 | + | 473.803i | −0.592917 | + | 1.43143i | 0.287755 | + | 0.957704i | \(0.407091\pi\) |
−0.880673 | + | 0.473725i | \(0.842909\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 608.706 | − | 252.134i | 1.82795 | − | 0.757160i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 608.805i | 1.80654i | 0.429069 | + | 0.903272i | \(0.358842\pi\) | ||||
−0.429069 | + | 0.903272i | \(0.641158\pi\) | |||||||
\(338\) | −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 | ||||
\(344\) | 285.660 | + | 59.3074i | 0.830406 | + | 0.172405i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 526.326 | + | 218.011i | 1.51679 | + | 0.628275i | 0.976945 | − | 0.213490i | \(-0.0684831\pi\) |
0.539844 | + | 0.841765i | \(0.318483\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(350\) | 349.313 | − | 21.9180i | 0.998037 | − | 0.0626229i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 435.206 | + | 34.6192i | 1.23638 | + | 0.0983500i | ||||
\(353\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −29.1171 | − | 59.4606i | −0.0813326 | − | 0.166091i | ||||
\(359\) | 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 | ||||||||
\(371\) | −617.472 | + | 255.765i | −1.66434 | + | 0.689394i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −194.921 | + | 470.580i | −0.522576 | + | 1.26161i | 0.413722 | + | 0.910403i | \(0.364228\pi\) |
−0.936298 | + | 0.351206i | \(0.885772\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 162.311 | + | 67.2314i | 0.428261 | + | 0.177392i | 0.586393 | − | 0.810026i | \(-0.300547\pi\) |
−0.158132 | + | 0.987418i | \(0.550547\pi\) | |||||||
\(380\) | 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 | ||||
\(387\) | 125.604 | + | 303.236i | 0.324559 | + | 0.783555i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 107.794 | + | 44.6495i | 0.277104 | + | 0.114780i | 0.516908 | − | 0.856041i | \(-0.327083\pi\) |
−0.239804 | + | 0.970821i | \(0.577083\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −385.094 | + | 73.2595i | −0.982382 | + | 0.186886i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −234.715 | + | 685.172i | −0.595724 | + | 1.73901i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 243.203 | + | 426.713i | 0.614149 | + | 1.07756i | ||||
\(397\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 344.160 | + | 203.848i | 0.860400 | + | 0.509620i | ||||
\(401\) | − | 258.550i | − | 0.644762i | −0.946610 | − | 0.322381i | \(-0.895517\pi\) | ||
0.946610 | − | 0.322381i | \(-0.104483\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 768.036 | + | 263.102i | 1.89172 | + | 0.648034i | ||||
\(407\) | 706.236 | − | 706.236i | 1.73522 | − | 1.73522i | ||||
\(408\) | 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 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −150.159 | − | 62.1981i | −0.356673 | − | 0.147739i | 0.197150 | − | 0.980373i | \(-0.436832\pi\) |
−0.553823 | + | 0.832635i | \(0.686832\pi\) | |||||||
\(422\) | −119.042 | − | 243.099i | −0.282090 | − | 0.576063i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −747.877 | − | 155.271i | −1.76386 | − | 0.366205i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −178.548 | + | 651.801i | −0.417168 | + | 1.52290i | ||||
\(429\) | 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 | ||||||||
\(436\) | −86.9920 | + | 49.5807i | −0.199523 | + | 0.113717i | ||||
\(437\) | 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 | ||||||||
\(443\) | 804.148 | + | 333.089i | 1.81523 | + | 0.751894i | 0.979104 | + | 0.203361i | \(0.0651866\pi\) |
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 | −0.875754 | − | 0.482757i | \(-0.839635\pi\) |
0.482757 | + | 0.875754i | \(0.339635\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 925.589i | − | 1.99911i | −0.0297960 | − | 0.999556i | \(-0.509486\pi\) | ||
0.0297960 | − | 0.999556i | \(-0.490514\pi\) | |||||||
\(464\) | 556.589 | + | 742.345i | 1.19955 | + | 1.59988i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −512.991 | − | 452.415i | −1.10084 | − | 0.970848i | ||||
\(467\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 278.115 | − | 671.428i | 0.592995 | − | 1.43162i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 351.822 | + | 351.822i | 0.743809 | + | 0.743809i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −328.841 | − | 793.893i | −0.689394 | − | 1.66434i | ||||
\(478\) | 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 | ||||||||
\(484\) | 205.816 | + | 159.758i | 0.425239 | + | 0.330078i | ||||
\(485\) | 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 | ||||||||
\(491\) | 57.3936 | − | 138.560i | 0.116891 | − | 0.282200i | −0.854596 | − | 0.519294i | \(-0.826195\pi\) |
0.971487 | + | 0.237094i | \(0.0761949\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 592.648i | 1.19245i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 918.343 | − | 380.390i | 1.84037 | − | 0.762305i | 0.885988 | − | 0.463708i | \(-0.153481\pi\) |
0.954379 | − | 0.298597i | \(-0.0965187\pi\) | |||||||
\(500\) | 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 | ||||||||
\(506\) | 421.632 | − | 206.468i | 0.833265 | − | 0.408039i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1008.00 | + | 126.996i | −1.98425 | + | 0.249992i | ||||
\(509\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(510\) | 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 | ||||||||
\(518\) | −920.456 | + | 450.735i | −1.77694 | + | 0.870145i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(522\) | −338.274 | + | 987.475i | −0.648034 | + | 1.89172i | ||||
\(523\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(524\) | 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 | ||||||||
\(536\) | 694.426 | − | 455.652i | 1.29557 | − | 0.850097i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −617.627 | − | 255.830i | −1.14588 | − | 0.474637i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 370.812 | + | 895.219i | 0.685420 | + | 1.65475i | 0.753811 | + | 0.657091i | \(0.228213\pi\) |
−0.0683919 | + | 0.997659i | \(0.521787\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −195.402 | − | 471.743i | −0.357225 | − | 0.862418i | −0.995688 | − | 0.0927652i | \(-0.970429\pi\) |
0.638463 | − | 0.769653i | \(-0.279571\pi\) | |||||||
\(548\) | −668.856 | + | 861.686i | −1.22054 | + | 1.57242i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 300.005 | + | 612.647i | 0.545464 | + | 1.11390i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −115.486 | + | 115.486i | −0.208836 | + | 0.208836i | ||||
\(554\) | −563.727 | − | 193.113i | −1.01756 | − | 0.348579i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1027.38 | − | 425.553i | 1.84448 | − | 0.764010i | 0.899461 | − | 0.437000i | \(-0.143959\pi\) |
0.945021 | − | 0.327009i | \(-0.106041\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −408.137 | + | 462.783i | −0.726222 | + | 0.823458i | ||||
\(563\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(564\) | 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 | \(-0.944878\pi\) |
−0.172306 | − | 0.985044i | \(-0.555122\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1028.45 | − | 425.998i | −1.80114 | − | 0.746057i | −0.985989 | − | 0.166807i | \(-0.946654\pi\) |
−0.815151 | − | 0.579249i | \(-0.803346\pi\) | |||||||
\(572\) | 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 | ||||||||
\(583\) | −921.094 | − | 921.094i | −1.57992 | − | 1.57992i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1159.51 | − | 165.817i | −1.95863 | − | 0.280096i | ||||
\(593\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 152.097 | − | 555.241i | 0.255197 | − | 0.931613i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 123.037 | − | 123.037i | 0.205403 | − | 0.205403i | −0.596907 | − | 0.802310i | \(-0.703604\pi\) |
0.802310 | + | 0.596907i | \(0.203604\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(602\) | −224.540 | − | 458.539i | −0.372991 | − | 0.761692i | ||||
\(603\) | 863.264 | + | 357.576i | 1.43162 | + | 0.592995i | ||||
\(604\) | −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 | ||||||||
\(613\) | 240.474 | + | 99.6077i | 0.392291 | + | 0.162492i | 0.570105 | − | 0.821572i | \(-0.306903\pi\) |
−0.177814 | + | 0.984064i | \(0.556903\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −419.141 | − | 638.782i | −0.680424 | − | 1.03698i | ||||
\(617\) | −778.265 | + | 778.265i | −1.26137 | + | 1.26137i | −0.310939 | + | 0.950430i | \(0.600644\pi\) |
−0.950430 | + | 0.310939i | \(0.899356\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(620\) | 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 | −0.136728 | − | 0.990609i | \(-0.543659\pi\) |
0.990609 | + | 0.136728i | \(0.0436586\pi\) | |||||||
\(632\) | −183.365 | + | 34.8831i | −0.290135 | + | 0.0551947i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 618.912 | − | 303.073i | 0.976203 | − | 0.478033i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 99.0893 | + | 1579.21i | 0.155312 | + | 2.47525i | ||||
\(639\) | −761.976 | −1.19245 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1278.19 | −1.99406 | −0.997030 | − | 0.0770186i | \(-0.975460\pi\) | ||||
−0.997030 | + | 0.0770186i | \(0.975460\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(644\) | −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 | ||||||||
\(652\) | 376.060 | + | 659.818i | 0.576779 | + | 1.01199i | ||||
\(653\) | −832.060 | + | 344.650i | −1.27421 | + | 0.527796i | −0.914242 | − | 0.405169i | \(-0.867213\pi\) |
−0.359969 | + | 0.932964i | \(0.617213\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 939.078 | − | 388.979i | 1.42501 | − | 0.590256i | 0.468892 | − | 0.883255i | \(-0.344653\pi\) |
0.956113 | + | 0.292999i | \(0.0946533\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(662\) | 970.326 | + | 332.399i | 1.46575 | + | 0.502113i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −579.517 | − | 1183.44i | −0.870145 | − | 1.77694i | ||||
\(667\) | 921.779 | + | 381.814i | 1.38198 | + | 0.572434i | ||||
\(668\) | 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 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −293.229 | + | 707.917i | −0.429325 | + | 1.03648i | 0.550178 | + | 0.835048i | \(0.314560\pi\) |
−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 | ||||||||
\(688\) | 82.6042 | − | 577.626i | 0.120064 | − | 0.839572i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 328.924 | − | 794.092i | 0.474637 | − | 1.14588i | ||||
\(694\) | 369.247 | − | 1077.89i | 0.532056 | − | 1.55316i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −87.5000 | − | 694.510i | −0.125000 | − | 0.992157i | ||||
\(701\) | 167.316 | + | 403.936i | 0.238682 | + | 0.576228i | 0.997147 | − | 0.0754851i | \(-0.0240505\pi\) |
−0.758465 | + | 0.651713i | \(0.774051\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 14.5947 | − | 873.040i | 0.0207312 | − | 1.24011i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1067.36 | + | 442.115i | 1.50545 | + | 0.623576i | 0.974612 | − | 0.223900i | \(-0.0718789\pi\) |
0.530834 | + | 0.847476i | \(0.321879\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −148.482 | − | 148.482i | −0.208836 | − | 0.208836i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −115.041 | + | 65.5671i | −0.160672 | + | 0.0915741i | ||||
\(717\) | 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 | ||||||||
\(725\) | −554.789 | + | 1339.38i | −0.765227 | + | 1.84742i | ||||
\(726\) | 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 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −490.352 | − | 250.366i | −0.666239 | − | 0.340171i | ||||
\(737\) | 1416.45 | 1.92191 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 554.344 | + | 1338.31i | 0.750128 | + | 1.81097i | 0.558508 | + | 0.829499i | \(0.311374\pi\) |
0.191620 | + | 0.981469i | \(0.438626\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 587.862 | + | 1200.49i | 0.792267 | + | 1.61791i | ||||
\(743\) | 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 | ||||||||
\(746\) | 963.727 | + | 330.138i | 1.29186 | + | 0.442544i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1092.65 | − | 452.590i | 1.45881 | − | 0.604258i | ||||
\(750\) | 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 | ||||||||
\(757\) | −3.26865 | + | 7.89121i | −0.00431790 | + | 0.0104243i | −0.926024 | − | 0.377465i | \(-0.876796\pi\) |
0.921706 | + | 0.387890i | \(0.126796\pi\) | |||||||
\(758\) | 113.870 | − | 332.405i | 0.150224 | − | 0.438529i | ||||
\(759\) | 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 | ||||||||
\(763\) | 161.888 | + | 67.0561i | 0.212173 | + | 0.0878848i | ||||
\(764\) | 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 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(774\) | 589.550 | − | 288.695i | 0.761692 | − | 0.372991i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 75.6231 | − | 220.756i | 0.0972020 | − | 0.283748i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1067.16 | + | 442.032i | −1.36640 | + | 0.565982i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 194.463 | + | 759.500i | 0.248039 | + | 0.968750i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(788\) | 1397.05 | + | 382.694i | 1.77291 | + | 0.485653i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −925.162 | + | 925.162i | −1.16961 | + | 1.16961i | ||||
\(792\) | 821.291 | − | 538.895i | 1.03698 | − | 0.680424i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(798\) | 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 | \(-0.284297\pi\) |
0.779048 | − | 0.626964i | \(-0.215703\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(812\) | 428.977 | − | 1566.01i | 0.528297 | − | 1.92858i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1498.15 | − | 1321.25i | −1.84048 | − | 1.62315i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 238.932 | − | 576.833i | 0.291025 | − | 0.702597i | −0.708971 | − | 0.705238i | \(-0.750840\pi\) |
0.999997 | + | 0.00264006i | \(0.000840357\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −439.820 | + | 439.820i | −0.534411 | + | 0.534411i | −0.921882 | − | 0.387471i | \(-0.873349\pi\) |
0.387471 | + | 0.921882i | \(0.373349\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1490.81 | − | 617.513i | −1.80267 | − | 0.746691i | −0.985358 | − | 0.170496i | \(-0.945463\pi\) |
−0.817312 | − | 0.576195i | \(-0.804537\pi\) | |||||||
\(828\) | −77.4240 | − | 614.534i | −0.0935073 | − | 0.742191i | ||||
\(829\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(830\) | 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 | ||||||||
\(841\) | −1783.16 | + | 1783.16i | −2.12028 | + | 2.12028i | ||||
\(842\) | −105.345 | + | 307.519i | −0.125113 | + | 0.365225i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −470.333 | + | 268.064i | −0.557267 | + | 0.317612i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 455.950i | − | 0.538312i | ||||||
\(848\) | −216.264 | + | 1512.26i | −0.255028 | + | 1.78333i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1163.67 | + | 482.006i | −1.36741 | + | 0.566400i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1323.41 | + | 274.760i | 1.54603 | + | 0.320981i | ||||
\(857\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 323.364 | − | 20.2898i | 0.375132 | − | 0.0235381i | ||||
\(863\) | 845.946 | 0.980238 | 0.490119 | − | 0.871655i | \(-0.336953\pi\) | ||||
0.490119 | + | 0.871655i | \(0.336953\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −294.088 | − | 121.815i | −0.338421 | − | 0.140179i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 109.862 | + | 167.433i | 0.125989 | + | 0.192010i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1091.22 | + | 451.999i | −1.24427 | + | 0.515393i | −0.905046 | − | 0.425314i | \(-0.860164\pi\) |
−0.339222 | + | 0.940706i | \(0.610164\pi\) | |||||||
\(878\) | 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 | ||||
\(883\) | −1631.41 | + | 675.753i | −1.84758 | + | 0.765293i | −0.918460 | + | 0.395514i | \(0.870566\pi\) |
−0.929120 | + | 0.369778i | \(0.879434\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 564.154 | − | 1646.86i | 0.636743 | − | 1.85876i | ||||
\(887\) | 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 | ||||||||
\(891\) | 1020.98 | + | 422.902i | 1.14588 | + | 0.474637i | ||||
\(892\) | 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 | ||||||||
\(907\) | 677.942 | − | 1636.70i | 0.747455 | − | 1.80452i | 0.175022 | − | 0.984564i | \(-0.444000\pi\) |
0.572433 | − | 0.819952i | \(-0.306000\pi\) | |||||||
\(908\) | 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 | \(0.668406\pi\) |
−0.863280 | + | 0.504725i | \(0.831594\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −700.373 | − | 1690.85i | −0.757160 | − | 1.82795i | ||||
\(926\) | −1847.54 | + | 115.926i | −1.99519 | + | 0.125190i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1412.07 | − | 1203.97i | 1.52162 | − | 1.29738i | ||||
\(929\) | 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 | \(0.750000\pi\) | |||||||
\(938\) | −1375.05 | − | 471.044i | −1.46594 | − | 0.502179i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 658.198 | − | 746.326i | 0.695770 | − | 0.788928i | ||||
\(947\) | 863.626 | − | 357.726i | 0.911960 | − | 0.377746i | 0.123154 | − | 0.992388i | \(-0.460699\pi\) |
0.788807 | + | 0.614641i | \(0.210699\pi\) | |||||||
\(948\) | 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 | \(0.777238\pi\) | |||||||
\(954\) | −1543.48 | + | 755.823i | −1.61791 | + | 0.792267i | ||||
\(955\) | 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 | ||||||||
\(963\) | 581.901 | + | 1404.83i | 0.604258 | + | 1.45881i | ||||
\(964\) | 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 | \(0.444751\pi\) | |||||||
\(968\) | 293.111 | − | 430.833i | 0.302801 | − | 0.445075i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(972\) | 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 | ||||||||
\(981\) | −86.2150 | + | 208.141i | −0.0878848 | + | 0.212173i | ||||
\(982\) | −283.765 | − | 97.2078i | −0.288967 | − | 0.0989896i | ||||
\(983\) | 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 | ||||||||
\(989\) | −240.118 | − | 579.697i | −0.242789 | − | 0.586145i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1981.99 | −1.99999 | −0.999995 | − | 0.00322633i | \(-0.998973\pi\) | ||||
−0.999995 | + | 0.00322633i | \(0.998973\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1182.97 | − | 74.2267i | 1.19011 | − | 0.0746748i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(998\) | −874.306 | − | 1785.44i | −0.876058 | − | 1.78902i | ||||
\(999\) | 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.69.2 | yes | 8 | |
7.6 | odd | 2 | CM | 224.3.v.a.69.2 | yes | 8 | |
32.13 | even | 8 | inner | 224.3.v.a.13.2 | ✓ | 8 | |
224.13 | odd | 8 | inner | 224.3.v.a.13.2 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.3.v.a.13.2 | ✓ | 8 | 32.13 | even | 8 | inner | |
224.3.v.a.13.2 | ✓ | 8 | 224.13 | odd | 8 | inner | |
224.3.v.a.69.2 | yes | 8 | 1.1 | even | 1 | trivial | |
224.3.v.a.69.2 | yes | 8 | 7.6 | odd | 2 | CM |