Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(199,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.199");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.f (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(24.5232237924\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 12x^{14} + 138x^{12} - 1000x^{10} + 5291x^{8} - 17800x^{6} + 39458x^{4} - 53588x^{2} + 32761 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{28} \) |
Twist minimal: | no (minimal twist has level 180) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.7 | ||
Root | \(-1.36646 - 0.842371i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 900.199 |
Dual form | 900.3.f.i.199.5 |
$q$-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 \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.36646 | + | 1.46040i | −0.683231 | + | 0.730202i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.265564 | − | 3.99117i | −0.0663911 | − | 0.997794i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.87135 | −0.267335 | −0.133668 | − | 0.991026i | \(-0.542675\pi\) | ||||
−0.133668 | + | 0.991026i | \(0.542675\pi\) | |||||||
\(8\) | 6.19161 | + | 5.06596i | 0.773952 | + | 0.633245i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 15.1162i | 1.37420i | 0.726565 | + | 0.687098i | \(0.241116\pi\) | ||||
−0.726565 | + | 0.687098i | \(0.758884\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 18.1245i | − | 1.39419i | −0.716977 | − | 0.697097i | \(-0.754475\pi\) | ||
0.716977 | − | 0.697097i | \(-0.245525\pi\) | |||||||
\(14\) | 2.55712 | − | 2.73292i | 0.182652 | − | 0.195209i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −15.8590 | + | 2.11983i | −0.991184 | + | 0.132489i | ||||
\(17\) | − | 12.6890i | − | 0.746414i | −0.927748 | − | 0.373207i | \(-0.878258\pi\) | ||
0.927748 | − | 0.373207i | \(-0.121742\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 28.1867i | 1.48351i | 0.670671 | + | 0.741755i | \(0.266006\pi\) | ||||
−0.670671 | + | 0.741755i | \(0.733994\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −22.0757 | − | 20.6556i | −1.00344 | − | 0.938893i | ||||
\(23\) | 10.9317 | 0.475291 | 0.237646 | − | 0.971352i | \(-0.423624\pi\) | ||||
0.237646 | + | 0.971352i | \(0.423624\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 26.4691 | + | 24.7665i | 1.01804 | + | 0.952556i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.496963 | + | 7.46887i | 0.0177487 | + | 0.266745i | ||||
\(29\) | −9.95007 | −0.343106 | −0.171553 | − | 0.985175i | \(-0.554878\pi\) | ||||
−0.171553 | + | 0.985175i | \(0.554878\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 24.4440i | − | 0.788516i | −0.919000 | − | 0.394258i | \(-0.871002\pi\) | ||
0.919000 | − | 0.394258i | \(-0.128998\pi\) | |||||||
\(32\) | 18.5748 | − | 26.0572i | 0.580464 | − | 0.814286i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 18.5311 | + | 17.3391i | 0.545033 | + | 0.509973i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 17.8755i | 0.483121i | 0.970386 | + | 0.241561i | \(0.0776593\pi\) | ||||
−0.970386 | + | 0.241561i | \(0.922341\pi\) | |||||||
\(38\) | −41.1640 | − | 38.5161i | −1.08326 | − | 1.01358i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 28.8444 | 0.703522 | 0.351761 | − | 0.936090i | \(-0.385583\pi\) | ||||
0.351761 | + | 0.936090i | \(0.385583\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −56.3734 | −1.31101 | −0.655505 | − | 0.755191i | \(-0.727544\pi\) | ||||
−0.655505 | + | 0.755191i | \(0.727544\pi\) | |||||||
\(44\) | 60.3312 | − | 4.01431i | 1.37116 | − | 0.0912344i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −14.9377 | + | 15.9647i | −0.324734 | + | 0.347059i | ||||
\(47\) | 49.5329 | 1.05389 | 0.526946 | − | 0.849899i | \(-0.323337\pi\) | ||||
0.526946 | + | 0.849899i | \(0.323337\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −45.4981 | −0.928532 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −72.3381 | + | 4.81323i | −1.39112 | + | 0.0925621i | ||||
\(53\) | 60.1494i | 1.13489i | 0.823410 | + | 0.567447i | \(0.192069\pi\) | ||||
−0.823410 | + | 0.567447i | \(0.807931\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −11.5867 | − | 9.48016i | −0.206905 | − | 0.169289i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 13.5964 | − | 14.5311i | 0.234421 | − | 0.250537i | ||||
\(59\) | 110.939i | 1.88032i | 0.340739 | + | 0.940158i | \(0.389323\pi\) | ||||
−0.340739 | + | 0.940158i | \(0.610677\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 34.2490 | 0.561460 | 0.280730 | − | 0.959787i | \(-0.409424\pi\) | ||||
0.280730 | + | 0.959787i | \(0.409424\pi\) | |||||||
\(62\) | 35.6982 | + | 33.4018i | 0.575777 | + | 0.538739i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 12.6722 | + | 62.7329i | 0.198003 | + | 0.980201i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −131.460 | −1.96209 | −0.981047 | − | 0.193770i | \(-0.937928\pi\) | ||||
−0.981047 | + | 0.193770i | \(0.937928\pi\) | |||||||
\(68\) | −50.6442 | + | 3.36976i | −0.744767 | + | 0.0495552i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 52.0957i | 0.733742i | 0.930272 | + | 0.366871i | \(0.119571\pi\) | ||||
−0.930272 | + | 0.366871i | \(0.880429\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 62.2490i | 0.852726i | 0.904552 | + | 0.426363i | \(0.140205\pi\) | ||||
−0.904552 | + | 0.426363i | \(0.859795\pi\) | |||||||
\(74\) | −26.1054 | − | 24.4262i | −0.352776 | − | 0.330083i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 112.498 | − | 7.48539i | 1.48024 | − | 0.0984919i | ||||
\(77\) | − | 28.2876i | − | 0.367371i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 103.274i | 1.30726i | 0.756814 | + | 0.653630i | \(0.226755\pi\) | ||||
−0.756814 | + | 0.653630i | \(0.773245\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −39.4148 | + | 42.1245i | −0.480668 | + | 0.513714i | ||||
\(83\) | 57.2212 | 0.689413 | 0.344706 | − | 0.938711i | \(-0.387979\pi\) | ||||
0.344706 | + | 0.938711i | \(0.387979\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 77.0321 | − | 82.3280i | 0.895722 | − | 0.957302i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −76.5778 | + | 93.5934i | −0.870202 | + | 1.06356i | ||||
\(89\) | −145.120 | −1.63056 | −0.815281 | − | 0.579066i | \(-0.803417\pi\) | ||||
−0.815281 | + | 0.579066i | \(0.803417\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 33.9173i | 0.372717i | ||||||||
\(92\) | −2.90307 | − | 43.6303i | −0.0315551 | − | 0.474242i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −67.6848 | + | 72.3381i | −0.720051 | + | 0.769554i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 66.7471i | − | 0.688114i | −0.938949 | − | 0.344057i | \(-0.888199\pi\) | ||
0.938949 | − | 0.344057i | \(-0.111801\pi\) | |||||||
\(98\) | 62.1714 | − | 66.4456i | 0.634402 | − | 0.678016i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −164.571 | −1.62942 | −0.814709 | − | 0.579871i | \(-0.803103\pi\) | ||||
−0.814709 | + | 0.579871i | \(0.803103\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 43.2740 | 0.420136 | 0.210068 | − | 0.977687i | \(-0.432631\pi\) | ||||
0.210068 | + | 0.977687i | \(0.432631\pi\) | |||||||
\(104\) | 91.8180 | − | 112.220i | 0.882865 | − | 1.07904i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −87.8424 | − | 82.1918i | −0.828702 | − | 0.775394i | ||||
\(107\) | −173.025 | −1.61706 | −0.808528 | − | 0.588458i | \(-0.799735\pi\) | ||||
−0.808528 | + | 0.588458i | \(0.799735\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 162.498 | 1.49081 | 0.745404 | − | 0.666613i | \(-0.232257\pi\) | ||||
0.745404 | + | 0.666613i | \(0.232257\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 29.6776 | − | 3.96693i | 0.264979 | − | 0.0354190i | ||||
\(113\) | 72.3895i | 0.640615i | 0.947314 | + | 0.320307i | \(0.103786\pi\) | ||||
−0.947314 | + | 0.320307i | \(0.896214\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.64238 | + | 39.7125i | 0.0227792 | + | 0.342349i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −162.015 | − | 151.593i | −1.37301 | − | 1.28469i | ||||
\(119\) | 23.7456i | 0.199543i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −107.498 | −0.888414 | ||||||||
\(122\) | −46.8000 | + | 50.0174i | −0.383606 | + | 0.409979i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −97.5603 | + | 6.49146i | −0.786777 | + | 0.0523505i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −148.535 | −1.16957 | −0.584785 | − | 0.811188i | \(-0.698821\pi\) | ||||
−0.584785 | + | 0.811188i | \(0.698821\pi\) | |||||||
\(128\) | −108.931 | − | 67.2156i | −0.851027 | − | 0.525122i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 26.7284i | − | 0.204034i | −0.994783 | − | 0.102017i | \(-0.967470\pi\) | ||
0.994783 | − | 0.102017i | \(-0.0325296\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 52.7471i | − | 0.396595i | ||||||
\(134\) | 179.635 | − | 191.985i | 1.34056 | − | 1.43273i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 64.2821 | − | 78.5656i | 0.472662 | − | 0.577688i | ||||
\(137\) | 126.953i | 0.926664i | 0.886185 | + | 0.463332i | \(0.153346\pi\) | ||||
−0.886185 | + | 0.463332i | \(0.846654\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 20.7013i | − | 0.148930i | −0.997224 | − | 0.0744652i | \(-0.976275\pi\) | ||
0.997224 | − | 0.0744652i | \(-0.0237250\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −76.0808 | − | 71.1868i | −0.535780 | − | 0.501315i | ||||
\(143\) | 273.973 | 1.91589 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −90.9088 | − | 85.0609i | −0.622663 | − | 0.582609i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 71.3442 | − | 4.74709i | 0.482055 | − | 0.0320750i | ||||
\(149\) | −167.140 | −1.12174 | −0.560871 | − | 0.827903i | \(-0.689534\pi\) | ||||
−0.560871 | + | 0.827903i | \(0.689534\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 65.6136i | 0.434527i | 0.976113 | + | 0.217264i | \(0.0697132\pi\) | ||||
−0.976113 | + | 0.217264i | \(0.930287\pi\) | |||||||
\(152\) | −142.793 | + | 174.521i | −0.939425 | + | 1.14817i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 41.3113 | + | 38.6539i | 0.268255 | + | 0.250999i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 30.3735i | − | 0.193462i | −0.995311 | − | 0.0967310i | \(-0.969161\pi\) | ||
0.995311 | − | 0.0967310i | \(-0.0308387\pi\) | |||||||
\(158\) | −150.821 | − | 141.119i | −0.954565 | − | 0.893161i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20.4570 | −0.127062 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 45.1453 | 0.276965 | 0.138483 | − | 0.990365i | \(-0.455777\pi\) | ||||
0.138483 | + | 0.990365i | \(0.455777\pi\) | |||||||
\(164\) | −7.66005 | − | 115.123i | −0.0467076 | − | 0.701970i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −78.1906 | + | 83.5662i | −0.471028 | + | 0.503411i | ||||
\(167\) | 32.7951 | 0.196378 | 0.0981889 | − | 0.995168i | \(-0.468695\pi\) | ||||
0.0981889 | + | 0.995168i | \(0.468695\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −159.498 | −0.943776 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 14.9708 | + | 224.996i | 0.0870394 | + | 1.30812i | ||||
\(173\) | 316.067i | 1.82698i | 0.406865 | + | 0.913488i | \(0.366622\pi\) | ||||
−0.406865 | + | 0.913488i | \(0.633378\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −32.0436 | − | 239.726i | −0.182066 | − | 1.36208i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 198.301 | − | 211.934i | 1.11405 | − | 1.19064i | ||||
\(179\) | 258.857i | 1.44613i | 0.690781 | + | 0.723064i | \(0.257267\pi\) | ||||
−0.690781 | + | 0.723064i | \(0.742733\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −74.4981 | −0.411592 | −0.205796 | − | 0.978595i | \(-0.565978\pi\) | ||||
−0.205796 | + | 0.978595i | \(0.565978\pi\) | |||||||
\(182\) | −49.5329 | − | 46.3466i | −0.272159 | − | 0.254652i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 67.6848 | + | 55.3795i | 0.367852 | + | 0.300975i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 191.809 | 1.02572 | ||||||||
\(188\) | −13.1542 | − | 197.695i | −0.0699690 | − | 1.05157i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 63.7080i | − | 0.333550i | −0.985995 | − | 0.166775i | \(-0.946665\pi\) | ||
0.985995 | − | 0.166775i | \(-0.0533353\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 45.5019i | − | 0.235761i | −0.993028 | − | 0.117881i | \(-0.962390\pi\) | ||
0.993028 | − | 0.117881i | \(-0.0376100\pi\) | |||||||
\(194\) | 97.4778 | + | 91.2074i | 0.502463 | + | 0.470141i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 12.0827 | + | 181.591i | 0.0616463 | + | 0.926483i | ||||
\(197\) | − | 185.926i | − | 0.943787i | −0.881656 | − | 0.471893i | \(-0.843571\pi\) | ||
0.881656 | − | 0.471893i | \(-0.156429\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 155.904i | − | 0.783439i | −0.920085 | − | 0.391719i | \(-0.871880\pi\) | ||
0.920085 | − | 0.391719i | \(-0.128120\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 224.880 | − | 240.340i | 1.11327 | − | 1.18980i | ||||
\(203\) | 18.6200 | 0.0917243 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −59.1322 | + | 63.1975i | −0.287050 | + | 0.306784i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 38.4209 | + | 287.436i | 0.184716 | + | 1.38190i | ||||
\(209\) | −426.075 | −2.03863 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 242.219i | − | 1.14796i | −0.818870 | − | 0.573979i | \(-0.805399\pi\) | ||
0.818870 | − | 0.573979i | \(-0.194601\pi\) | |||||||
\(212\) | 240.067 | − | 15.9735i | 1.13239 | − | 0.0753468i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 236.432 | − | 252.686i | 1.10482 | − | 1.18078i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 45.7432i | 0.210798i | ||||||||
\(218\) | −222.047 | + | 237.313i | −1.01857 | + | 1.08859i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −229.983 | −1.04065 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −250.054 | −1.12132 | −0.560660 | − | 0.828046i | \(-0.689452\pi\) | ||||
−0.560660 | + | 0.828046i | \(0.689452\pi\) | |||||||
\(224\) | −34.7600 | + | 48.7620i | −0.155178 | + | 0.217687i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −105.718 | − | 98.9174i | −0.467778 | − | 0.437688i | ||||
\(227\) | 60.4646 | 0.266364 | 0.133182 | − | 0.991092i | \(-0.457481\pi\) | ||||
0.133182 | + | 0.991092i | \(0.457481\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −78.2490 | −0.341699 | −0.170849 | − | 0.985297i | \(-0.554651\pi\) | ||||
−0.170849 | + | 0.985297i | \(0.554651\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −61.6070 | − | 50.4066i | −0.265547 | − | 0.217270i | ||||
\(233\) | − | 164.742i | − | 0.707046i | −0.935426 | − | 0.353523i | \(-0.884984\pi\) | ||
0.935426 | − | 0.353523i | \(-0.115016\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 442.775 | − | 29.4614i | 1.87617 | − | 0.124836i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −34.6782 | − | 32.4474i | −0.145707 | − | 0.136334i | ||||
\(239\) | 243.741i | 1.01984i | 0.860223 | + | 0.509918i | \(0.170324\pi\) | ||||
−0.860223 | + | 0.509918i | \(0.829676\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 383.494 | 1.59126 | 0.795631 | − | 0.605781i | \(-0.207139\pi\) | ||||
0.795631 | + | 0.605781i | \(0.207139\pi\) | |||||||
\(242\) | 146.892 | − | 156.991i | 0.606992 | − | 0.648722i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −9.09532 | − | 136.694i | −0.0372759 | − | 0.560221i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 510.870 | 2.06830 | ||||||||
\(248\) | 123.832 | − | 151.348i | 0.499324 | − | 0.610274i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 199.753i | 0.795830i | 0.917422 | + | 0.397915i | \(0.130266\pi\) | ||||
−0.917422 | + | 0.397915i | \(0.869734\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 165.245i | 0.653143i | ||||||||
\(254\) | 202.968 | − | 216.922i | 0.799086 | − | 0.854023i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 247.013 | − | 67.2365i | 0.964893 | − | 0.262643i | ||||
\(257\) | 158.366i | 0.616209i | 0.951352 | + | 0.308105i | \(0.0996947\pi\) | ||||
−0.951352 | + | 0.308105i | \(0.900305\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 33.4512i | − | 0.129155i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 39.0343 | + | 36.5234i | 0.148986 | + | 0.139402i | ||||
\(263\) | −121.610 | −0.462395 | −0.231197 | − | 0.972907i | \(-0.574264\pi\) | ||||
−0.231197 | + | 0.972907i | \(0.574264\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 77.0321 | + | 72.0769i | 0.289594 | + | 0.270966i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 34.9112 | + | 524.681i | 0.130266 | + | 1.95776i | ||||
\(269\) | 414.670 | 1.54152 | 0.770762 | − | 0.637124i | \(-0.219876\pi\) | ||||
0.770762 | + | 0.637124i | \(0.219876\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 193.331i | 0.713399i | 0.934219 | + | 0.356700i | \(0.116098\pi\) | ||||
−0.934219 | + | 0.356700i | \(0.883902\pi\) | |||||||
\(272\) | 26.8986 | + | 201.235i | 0.0988918 | + | 0.739834i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −185.403 | − | 173.476i | −0.676652 | − | 0.633126i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 472.615i | 1.70619i | 0.521755 | + | 0.853095i | \(0.325278\pi\) | ||||
−0.521755 | + | 0.853095i | \(0.674722\pi\) | |||||||
\(278\) | 30.2323 | + | 28.2876i | 0.108749 | + | 0.101754i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 256.815 | 0.913934 | 0.456967 | − | 0.889484i | \(-0.348936\pi\) | ||||
0.456967 | + | 0.889484i | \(0.348936\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 416.837 | 1.47292 | 0.736461 | − | 0.676480i | \(-0.236495\pi\) | ||||
0.736461 | + | 0.676480i | \(0.236495\pi\) | |||||||
\(284\) | 207.923 | − | 13.8348i | 0.732123 | − | 0.0487140i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −374.374 | + | 400.111i | −1.30900 | + | 1.39899i | ||||
\(287\) | −53.9779 | −0.188076 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 127.988 | 0.442866 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 248.447 | − | 16.5311i | 0.850845 | − | 0.0566135i | ||||
\(293\) | 240.705i | 0.821520i | 0.911744 | + | 0.410760i | \(0.134737\pi\) | ||||
−0.911744 | + | 0.410760i | \(0.865263\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −90.5564 | + | 110.678i | −0.305934 | + | 0.373913i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 228.390 | − | 244.091i | 0.766409 | − | 0.819099i | ||||
\(299\) | − | 198.132i | − | 0.662648i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 105.494 | 0.350479 | ||||||||
\(302\) | −95.8225 | − | 89.6585i | −0.317293 | − | 0.296883i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −59.7510 | − | 447.012i | −0.196549 | − | 1.47043i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 206.547 | 0.672792 | 0.336396 | − | 0.941721i | \(-0.390792\pi\) | ||||
0.336396 | + | 0.941721i | \(0.390792\pi\) | |||||||
\(308\) | −112.901 | + | 7.51217i | −0.366560 | + | 0.0243902i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 458.610i | 1.47463i | 0.675549 | + | 0.737315i | \(0.263907\pi\) | ||||
−0.675549 | + | 0.737315i | \(0.736093\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 383.992i | − | 1.22681i | −0.789768 | − | 0.613406i | \(-0.789799\pi\) | ||
0.789768 | − | 0.613406i | \(-0.210201\pi\) | |||||||
\(314\) | 44.3577 | + | 41.5043i | 0.141266 | + | 0.132179i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 412.183 | − | 27.4258i | 1.30438 | − | 0.0867905i | ||||
\(317\) | − | 429.433i | − | 1.35468i | −0.735671 | − | 0.677339i | \(-0.763133\pi\) | ||
0.735671 | − | 0.677339i | \(-0.236867\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 150.407i | − | 0.471495i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 27.9537 | − | 29.8755i | 0.0868127 | − | 0.0927810i | ||||
\(323\) | 357.662 | 1.10731 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −61.6894 | + | 65.9305i | −0.189231 | + | 0.202241i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 178.593 | + | 146.125i | 0.544492 | + | 0.445502i | ||||
\(329\) | −92.6933 | −0.281742 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 58.1282i | 0.175614i | 0.996138 | + | 0.0878070i | \(0.0279859\pi\) | ||||
−0.996138 | + | 0.0878070i | \(0.972014\pi\) | |||||||
\(332\) | −15.1959 | − | 228.380i | −0.0457709 | − | 0.687892i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −44.8132 | + | 47.8941i | −0.134171 | + | 0.143395i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 405.751i | − | 1.20401i | −0.798493 | − | 0.602004i | \(-0.794369\pi\) | ||
0.798493 | − | 0.602004i | \(-0.205631\pi\) | |||||||
\(338\) | 217.948 | − | 232.932i | 0.644817 | − | 0.689147i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 369.499 | 1.08358 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 176.839 | 0.515565 | ||||||||
\(344\) | −349.042 | − | 285.585i | −1.01466 | − | 0.830190i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −461.586 | − | 431.893i | −1.33406 | − | 1.24825i | ||||
\(347\) | 324.186 | 0.934255 | 0.467127 | − | 0.884190i | \(-0.345289\pi\) | ||||
0.467127 | + | 0.884190i | \(0.345289\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −34.7471 | −0.0995619 | −0.0497809 | − | 0.998760i | \(-0.515852\pi\) | ||||
−0.0497809 | + | 0.998760i | \(0.515852\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 393.884 | + | 280.780i | 1.11899 | + | 0.797671i | ||||
\(353\) | − | 13.5869i | − | 0.0384899i | −0.999815 | − | 0.0192449i | \(-0.993874\pi\) | ||
0.999815 | − | 0.0192449i | \(-0.00612623\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 38.5387 | + | 579.199i | 0.108255 | + | 1.62696i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −378.036 | − | 353.718i | −1.05597 | − | 0.988039i | ||||
\(359\) | 139.028i | 0.387265i | 0.981074 | + | 0.193633i | \(0.0620270\pi\) | ||||
−0.981074 | + | 0.193633i | \(0.937973\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −433.490 | −1.20080 | ||||||||
\(362\) | 101.799 | − | 108.797i | 0.281212 | − | 0.300545i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 135.370 | − | 9.00722i | 0.371895 | − | 0.0247451i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.87135 | −0.00509904 | −0.00254952 | − | 0.999997i | \(-0.500812\pi\) | ||||
−0.00254952 | + | 0.999997i | \(0.500812\pi\) | |||||||
\(368\) | −173.365 | + | 23.1733i | −0.471101 | + | 0.0629710i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 112.560i | − | 0.303397i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 384.864i | 1.03181i | 0.856647 | + | 0.515903i | \(0.172544\pi\) | ||||
−0.856647 | + | 0.515903i | \(0.827456\pi\) | |||||||
\(374\) | −262.100 | + | 280.119i | −0.700803 | + | 0.748982i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 306.689 | + | 250.932i | 0.815661 | + | 0.667371i | ||||
\(377\) | 180.340i | 0.478356i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 483.150i | − | 1.27480i | −0.770533 | − | 0.637401i | \(-0.780010\pi\) | ||
0.770533 | − | 0.637401i | \(-0.219990\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 93.0394 | + | 87.0545i | 0.243559 | + | 0.227891i | ||||
\(383\) | −130.500 | −0.340730 | −0.170365 | − | 0.985381i | \(-0.554495\pi\) | ||||
−0.170365 | + | 0.985381i | \(0.554495\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 66.4512 | + | 62.1767i | 0.172153 | + | 0.161079i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −266.399 | + | 17.7257i | −0.686596 | + | 0.0456847i | ||||
\(389\) | 10.2911 | 0.0264553 | 0.0132277 | − | 0.999913i | \(-0.495789\pi\) | ||||
0.0132277 | + | 0.999913i | \(0.495789\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 138.713i | − | 0.354764i | ||||||
\(392\) | −281.706 | − | 230.491i | −0.718639 | − | 0.587988i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 271.527 | + | 254.061i | 0.689155 | + | 0.644824i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 228.864i | − | 0.576483i | −0.957558 | − | 0.288242i | \(-0.906929\pi\) | ||
0.957558 | − | 0.288242i | \(-0.0930706\pi\) | |||||||
\(398\) | 227.683 | + | 213.037i | 0.572069 | + | 0.535269i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −96.9322 | −0.241726 | −0.120863 | − | 0.992669i | \(-0.538566\pi\) | ||||
−0.120863 | + | 0.992669i | \(0.538566\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −443.036 | −1.09934 | ||||||||
\(404\) | 43.7042 | + | 656.832i | 0.108179 | + | 1.62582i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −25.4436 | + | 27.1928i | −0.0626689 | + | 0.0669773i | ||||
\(407\) | −270.209 | −0.663903 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 135.494 | 0.331282 | 0.165641 | − | 0.986186i | \(-0.447031\pi\) | ||||
0.165641 | + | 0.986186i | \(0.447031\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −11.4920 | − | 172.714i | −0.0278933 | − | 0.419209i | ||||
\(413\) | − | 207.605i | − | 0.502675i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −472.273 | − | 336.660i | −1.13527 | − | 0.809279i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 582.215 | − | 622.241i | 1.39286 | − | 1.48862i | ||||
\(419\) | − | 384.912i | − | 0.918643i | −0.888270 | − | 0.459322i | \(-0.848093\pi\) | ||
0.888270 | − | 0.459322i | \(-0.151907\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −543.230 | −1.29033 | −0.645166 | − | 0.764043i | \(-0.723212\pi\) | ||||
−0.645166 | + | 0.764043i | \(0.723212\pi\) | |||||||
\(422\) | 353.738 | + | 330.983i | 0.838242 | + | 0.784321i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −304.714 | + | 372.422i | −0.718665 | + | 0.878353i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −64.0918 | −0.150098 | ||||||||
\(428\) | 45.9493 | + | 690.573i | 0.107358 | + | 1.61349i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 778.192i | − | 1.80555i | −0.430113 | − | 0.902775i | \(-0.641526\pi\) | ||
0.430113 | − | 0.902775i | \(-0.358474\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.25291i | 0.0121314i | 0.999982 | + | 0.00606571i | \(0.00193079\pi\) | ||||
−0.999982 | + | 0.00606571i | \(0.998069\pi\) | |||||||
\(434\) | −66.8036 | − | 62.5064i | −0.153925 | − | 0.144024i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −43.1537 | − | 648.558i | −0.0989764 | − | 1.48752i | ||||
\(437\) | 308.128i | 0.705099i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 208.302i | − | 0.474492i | −0.971450 | − | 0.237246i | \(-0.923755\pi\) | ||
0.971450 | − | 0.237246i | \(-0.0762447\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 314.262 | − | 335.868i | 0.711001 | − | 0.759882i | ||||
\(443\) | −735.826 | −1.66101 | −0.830504 | − | 0.557013i | \(-0.811947\pi\) | ||||
−0.830504 | + | 0.557013i | \(0.811947\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 341.689 | − | 365.180i | 0.766120 | − | 0.818790i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −23.7140 | − | 117.395i | −0.0529331 | − | 0.262042i | ||||
\(449\) | 617.155 | 1.37451 | 0.687255 | − | 0.726416i | \(-0.258816\pi\) | ||||
0.687255 | + | 0.726416i | \(0.258816\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 436.016i | 0.966777i | ||||||||
\(452\) | 288.919 | − | 19.2241i | 0.639201 | − | 0.0425311i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −82.6226 | + | 88.3028i | −0.181988 | + | 0.194500i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 322.747i | − | 0.706230i | −0.935580 | − | 0.353115i | \(-0.885122\pi\) | ||
0.935580 | − | 0.353115i | \(-0.114878\pi\) | |||||||
\(458\) | 106.924 | − | 114.275i | 0.233459 | − | 0.249509i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −509.034 | −1.10419 | −0.552097 | − | 0.833780i | \(-0.686172\pi\) | ||||
−0.552097 | + | 0.833780i | \(0.686172\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 741.978 | 1.60254 | 0.801272 | − | 0.598300i | \(-0.204157\pi\) | ||||
0.801272 | + | 0.598300i | \(0.204157\pi\) | |||||||
\(464\) | 157.798 | − | 21.0924i | 0.340081 | − | 0.0454578i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 240.590 | + | 225.113i | 0.516287 | + | 0.483075i | ||||
\(467\) | 310.692 | 0.665293 | 0.332647 | − | 0.943052i | \(-0.392058\pi\) | ||||
0.332647 | + | 0.943052i | \(0.392058\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 246.008 | 0.524537 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −562.010 | + | 686.889i | −1.19070 | + | 1.45527i | ||||
\(473\) | − | 852.149i | − | 1.80158i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 94.7728 | − | 6.30598i | 0.199102 | − | 0.0132479i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −355.960 | − | 333.062i | −0.744686 | − | 0.696783i | ||||
\(479\) | − | 479.112i | − | 1.00023i | −0.865958 | − | 0.500117i | \(-0.833290\pi\) | ||
0.865958 | − | 0.500117i | \(-0.166710\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 323.984 | 0.673564 | ||||||||
\(482\) | −524.030 | + | 560.057i | −1.08720 | + | 1.16194i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 28.5477 | + | 429.044i | 0.0589828 | + | 0.886454i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −572.858 | −1.17630 | −0.588150 | − | 0.808752i | \(-0.700143\pi\) | ||||
−0.588150 | + | 0.808752i | \(0.700143\pi\) | |||||||
\(488\) | 212.057 | + | 173.504i | 0.434543 | + | 0.355541i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.260515i | 0.000530580i | 1.00000 | 0.000265290i | \(8.44445e-5\pi\) | |||||
−1.00000 | 0.000265290i | \(0.999916\pi\) | ||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 126.257i | 0.256099i | ||||||||
\(494\) | −698.085 | + | 746.078i | −1.41313 | + | 1.51028i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 51.8171 | + | 387.656i | 0.104470 | + | 0.781565i | ||||
\(497\) | − | 97.4891i | − | 0.196155i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 467.713i | 0.937300i | 0.883384 | + | 0.468650i | \(0.155260\pi\) | ||||
−0.883384 | + | 0.468650i | \(0.844740\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −291.721 | − | 272.955i | −0.581117 | − | 0.543736i | ||||
\(503\) | −728.659 | −1.44863 | −0.724313 | − | 0.689471i | \(-0.757843\pi\) | ||||
−0.724313 | + | 0.689471i | \(0.757843\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −241.325 | − | 225.801i | −0.476927 | − | 0.446247i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 39.4457 | + | 592.831i | 0.0776491 | + | 1.16699i | ||||
\(509\) | 453.697 | 0.891350 | 0.445675 | − | 0.895195i | \(-0.352964\pi\) | ||||
0.445675 | + | 0.895195i | \(0.352964\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 116.490i | − | 0.227964i | ||||||
\(512\) | −239.341 | + | 452.615i | −0.467463 | + | 0.884013i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −231.278 | − | 216.401i | −0.449958 | − | 0.421013i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 748.747i | 1.44825i | ||||||||
\(518\) | 48.8523 | + | 45.7098i | 0.0943095 | + | 0.0882429i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 624.519 | 1.19869 | 0.599346 | − | 0.800490i | \(-0.295427\pi\) | ||||
0.599346 | + | 0.800490i | \(0.295427\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −319.527 | −0.610950 | −0.305475 | − | 0.952200i | \(-0.598815\pi\) | ||||
−0.305475 | + | 0.952200i | \(0.598815\pi\) | |||||||
\(524\) | −106.678 | + | 7.09812i | −0.203584 | + | 0.0135460i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 166.175 | − | 177.600i | 0.315922 | − | 0.337642i | ||||
\(527\) | −310.171 | −0.588560 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −409.498 | −0.774098 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −210.523 | + | 14.0078i | −0.395720 | + | 0.0263304i | ||||
\(533\) | − | 522.791i | − | 0.980846i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −813.951 | − | 665.972i | −1.51857 | − | 1.24249i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −566.630 | + | 605.586i | −1.05322 | + | 1.12562i | ||||
\(539\) | − | 687.756i | − | 1.27598i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 449.984 | 0.831764 | 0.415882 | − | 0.909419i | \(-0.363473\pi\) | ||||
0.415882 | + | 0.909419i | \(0.363473\pi\) | |||||||
\(542\) | −282.342 | − | 264.180i | −0.520926 | − | 0.487416i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −330.640 | − | 235.697i | −0.607794 | − | 0.433266i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −650.049 | −1.18839 | −0.594195 | − | 0.804321i | \(-0.702529\pi\) | ||||
−0.594195 | + | 0.804321i | \(0.702529\pi\) | |||||||
\(548\) | 506.692 | − | 33.7142i | 0.924620 | − | 0.0615223i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 280.460i | − | 0.509001i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 193.261i | − | 0.349477i | ||||||
\(554\) | −690.209 | − | 645.810i | −1.24586 | − | 1.16572i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −82.6226 | + | 5.49753i | −0.148602 | + | 0.00988765i | ||||
\(557\) | 127.555i | 0.229004i | 0.993423 | + | 0.114502i | \(0.0365272\pi\) | ||||
−0.993423 | + | 0.114502i | \(0.963473\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1021.74i | 1.82780i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −350.928 | + | 375.055i | −0.624428 | + | 0.667357i | ||||
\(563\) | 474.827 | 0.843387 | 0.421694 | − | 0.906738i | \(-0.361436\pi\) | ||||
0.421694 | + | 0.906738i | \(0.361436\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −569.592 | + | 608.751i | −1.00635 | + | 1.07553i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −263.914 | + | 322.556i | −0.464638 | + | 0.567881i | ||||
\(569\) | 125.095 | 0.219850 | 0.109925 | − | 0.993940i | \(-0.464939\pi\) | ||||
0.109925 | + | 0.993940i | \(0.464939\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 190.288i | − | 0.333253i | −0.986020 | − | 0.166627i | \(-0.946713\pi\) | ||
0.986020 | − | 0.166627i | \(-0.0532874\pi\) | |||||||
\(572\) | −72.7575 | − | 1093.47i | −0.127198 | − | 1.91167i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 73.7587 | − | 78.8296i | 0.128500 | − | 0.137334i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 492.739i | − | 0.853968i | −0.904259 | − | 0.426984i | \(-0.859576\pi\) | ||
0.904259 | − | 0.426984i | \(-0.140424\pi\) | |||||||
\(578\) | −174.891 | + | 186.915i | −0.302580 | + | 0.323382i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −107.081 | −0.184304 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −909.227 | −1.55957 | ||||||||
\(584\) | −315.351 | + | 385.422i | −0.539984 | + | 0.659969i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −351.527 | − | 328.915i | −0.599876 | − | 0.561288i | ||||
\(587\) | −293.954 | −0.500774 | −0.250387 | − | 0.968146i | \(-0.580558\pi\) | ||||
−0.250387 | + | 0.968146i | \(0.580558\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 688.996 | 1.16977 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −37.8930 | − | 283.486i | −0.0640084 | − | 0.478862i | ||||
\(593\) | 434.184i | 0.732181i | 0.930579 | + | 0.366091i | \(0.119304\pi\) | ||||
−0.930579 | + | 0.366091i | \(0.880696\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 44.3863 | + | 667.083i | 0.0744737 | + | 1.11927i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 289.352 | + | 270.739i | 0.483867 | + | 0.452741i | ||||
\(599\) | − | 509.345i | − | 0.850325i | −0.905117 | − | 0.425162i | \(-0.860217\pi\) | ||
0.905117 | − | 0.425162i | \(-0.139783\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 293.502 | 0.488356 | 0.244178 | − | 0.969730i | \(-0.421482\pi\) | ||||
0.244178 | + | 0.969730i | \(0.421482\pi\) | |||||||
\(602\) | −144.154 | + | 154.064i | −0.239458 | + | 0.255921i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 261.875 | − | 17.4246i | 0.433569 | − | 0.0288488i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −35.0896 | −0.0578082 | −0.0289041 | − | 0.999582i | \(-0.509202\pi\) | ||||
−0.0289041 | + | 0.999582i | \(0.509202\pi\) | |||||||
\(608\) | 734.465 | + | 523.564i | 1.20800 | + | 0.861124i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 897.760i | − | 1.46933i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 49.6109i | − | 0.0809314i | −0.999181 | − | 0.0404657i | \(-0.987116\pi\) | ||
0.999181 | − | 0.0404657i | \(-0.0128842\pi\) | |||||||
\(614\) | −282.239 | + | 301.642i | −0.459672 | + | 0.491274i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 143.304 | − | 175.146i | 0.232636 | − | 0.284327i | ||||
\(617\) | 427.251i | 0.692465i | 0.938149 | + | 0.346232i | \(0.112539\pi\) | ||||
−0.938149 | + | 0.346232i | \(0.887461\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 903.263i | 1.45923i | 0.683858 | + | 0.729615i | \(0.260301\pi\) | ||||
−0.683858 | + | 0.729615i | \(0.739699\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −669.756 | − | 626.673i | −1.07678 | − | 1.00751i | ||||
\(623\) | 271.570 | 0.435906 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 560.784 | + | 524.711i | 0.895821 | + | 0.838196i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −121.226 | + | 8.06613i | −0.193035 | + | 0.0128442i | ||||
\(629\) | 226.823 | 0.360608 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 681.512i | − | 1.08005i | −0.841649 | − | 0.540026i | \(-0.818415\pi\) | ||
0.841649 | − | 0.540026i | \(-0.181585\pi\) | |||||||
\(632\) | −523.179 | + | 639.430i | −0.827816 | + | 1.01176i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 627.146 | + | 586.804i | 0.989189 | + | 0.925558i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 824.630i | 1.29455i | ||||||||
\(638\) | 219.655 | + | 205.525i | 0.344286 | + | 0.322140i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −252.576 | −0.394035 | −0.197018 | − | 0.980400i | \(-0.563126\pi\) | ||||
−0.197018 | + | 0.980400i | \(0.563126\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.2038 | −0.0236451 | −0.0118225 | − | 0.999930i | \(-0.503763\pi\) | ||||
−0.0118225 | + | 0.999930i | \(0.503763\pi\) | |||||||
\(644\) | 5.43265 | + | 81.6474i | 0.00843579 | + | 0.126782i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −488.732 | + | 522.331i | −0.756550 | + | 0.808563i | ||||
\(647\) | −463.576 | −0.716501 | −0.358250 | − | 0.933626i | \(-0.616627\pi\) | ||||
−0.358250 | + | 0.933626i | \(0.616627\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1676.97 | −2.58392 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −11.9890 | − | 180.183i | −0.0183880 | − | 0.276354i | ||||
\(653\) | − | 351.503i | − | 0.538289i | −0.963100 | − | 0.269145i | \(-0.913259\pi\) | ||
0.963100 | − | 0.269145i | \(-0.0867410\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −457.442 | + | 61.1452i | −0.697320 | + | 0.0932091i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 126.662 | − | 135.370i | 0.192495 | − | 0.205729i | ||||
\(659\) | − | 494.229i | − | 0.749967i | −0.927031 | − | 0.374984i | \(-0.877648\pi\) | ||
0.927031 | − | 0.374984i | \(-0.122352\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 165.735 | 0.250734 | 0.125367 | − | 0.992110i | \(-0.459989\pi\) | ||||
0.125367 | + | 0.992110i | \(0.459989\pi\) | |||||||
\(662\) | −84.8908 | − | 79.4300i | −0.128234 | − | 0.119985i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 354.292 | + | 289.880i | 0.533572 | + | 0.436567i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −108.771 | −0.163075 | ||||||||
\(668\) | −8.70921 | − | 130.891i | −0.0130377 | − | 0.195944i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 517.714i | 0.771555i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 3.74322i | − | 0.00556199i | −0.999996 | − | 0.00278099i | \(-0.999115\pi\) | ||
0.999996 | − | 0.00278099i | \(-0.000885219\pi\) | |||||||
\(674\) | 592.561 | + | 554.443i | 0.879170 | + | 0.822616i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 42.3570 | + | 636.585i | 0.0626583 | + | 0.941693i | ||||
\(677\) | 969.987i | 1.43277i | 0.697704 | + | 0.716386i | \(0.254205\pi\) | ||||
−0.697704 | + | 0.716386i | \(0.745795\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 124.907i | 0.183957i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −504.907 | + | 539.619i | −0.740333 | + | 0.791230i | ||||
\(683\) | −808.424 | −1.18364 | −0.591819 | − | 0.806071i | \(-0.701590\pi\) | ||||
−0.591819 | + | 0.806071i | \(0.701590\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −241.643 | + | 258.256i | −0.352250 | + | 0.376466i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 894.023 | − | 119.502i | 1.29945 | − | 0.173695i | ||||
\(689\) | 1090.18 | 1.58226 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 395.903i | 0.572942i | 0.958089 | + | 0.286471i | \(0.0924821\pi\) | ||||
−0.958089 | + | 0.286471i | \(0.907518\pi\) | |||||||
\(692\) | 1261.48 | − | 83.9361i | 1.82295 | − | 0.121295i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −442.988 | + | 473.443i | −0.638312 | + | 0.682195i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 366.008i | − | 0.525119i | ||||||
\(698\) | 47.4806 | − | 50.7448i | 0.0680237 | − | 0.0727003i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 961.043 | 1.37096 | 0.685480 | − | 0.728091i | \(-0.259592\pi\) | ||||
0.685480 | + | 0.728091i | \(0.259592\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −503.851 | −0.716716 | ||||||||
\(704\) | −948.280 | + | 191.555i | −1.34699 | + | 0.272095i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 19.8424 | + | 18.5660i | 0.0281054 | + | 0.0262975i | ||||
\(707\) | 307.970 | 0.435601 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 817.751 | 1.15339 | 0.576693 | − | 0.816961i | \(-0.304343\pi\) | ||||
0.576693 | + | 0.816961i | \(0.304343\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −898.527 | − | 735.171i | −1.26198 | − | 1.03254i | ||||
\(713\) | − | 267.214i | − | 0.374775i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1033.14 | − | 68.7432i | 1.44294 | − | 0.0960100i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −203.037 | − | 189.977i | −0.282782 | − | 0.264592i | ||||
\(719\) | − | 91.2179i | − | 0.126868i | −0.997986 | − | 0.0634339i | \(-0.979795\pi\) | ||
0.997986 | − | 0.0634339i | \(-0.0202052\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −80.9806 | −0.112317 | ||||||||
\(722\) | 592.348 | − | 633.071i | 0.820427 | − | 0.876830i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 19.7840 | + | 297.335i | 0.0273260 | + | 0.410683i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −662.682 | −0.911530 | −0.455765 | − | 0.890100i | \(-0.650634\pi\) | ||||
−0.455765 | + | 0.890100i | \(0.650634\pi\) | |||||||
\(728\) | −171.823 | + | 210.003i | −0.236021 | + | 0.288465i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 715.324i | 0.978556i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 430.623i | − | 0.587480i | −0.955885 | − | 0.293740i | \(-0.905100\pi\) | ||
0.955885 | − | 0.293740i | \(-0.0948999\pi\) | |||||||
\(734\) | 2.55712 | − | 2.73292i | 0.00348382 | − | 0.00372333i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 203.055 | − | 284.849i | 0.275889 | − | 0.387023i | ||||
\(737\) | − | 1987.17i | − | 2.69630i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 523.620i | − | 0.708552i | −0.935141 | − | 0.354276i | \(-0.884727\pi\) | ||
0.935141 | − | 0.354276i | \(-0.115273\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 164.384 | + | 153.809i | 0.221541 | + | 0.207290i | ||||
\(743\) | −880.661 | −1.18528 | −0.592638 | − | 0.805469i | \(-0.701914\pi\) | ||||
−0.592638 | + | 0.805469i | \(0.701914\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −562.057 | − | 525.902i | −0.753428 | − | 0.704962i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −50.9378 | − | 765.545i | −0.0680986 | − | 1.02346i | ||||
\(749\) | 323.790 | 0.432296 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 602.683i | − | 0.802507i | −0.915967 | − | 0.401254i | \(-0.868575\pi\) | ||
0.915967 | − | 0.401254i | \(-0.131425\pi\) | |||||||
\(752\) | −785.540 | + | 105.001i | −1.04460 | + | 0.139629i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −263.370 | − | 246.428i | −0.349297 | − | 0.326828i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 427.136i | 0.564249i | 0.959378 | + | 0.282124i | \(0.0910390\pi\) | ||||
−0.959378 | + | 0.282124i | \(0.908961\pi\) | |||||||
\(758\) | 705.594 | + | 660.206i | 0.930863 | + | 0.870984i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −239.700 | −0.314980 | −0.157490 | − | 0.987521i | \(-0.550340\pi\) | ||||
−0.157490 | + | 0.987521i | \(0.550340\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −304.090 | −0.398545 | ||||||||
\(764\) | −254.270 | + | 16.9186i | −0.332814 | + | 0.0221447i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 178.323 | − | 190.582i | 0.232798 | − | 0.248802i | ||||
\(767\) | 2010.71 | 2.62152 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −937.486 | −1.21910 | −0.609549 | − | 0.792748i | \(-0.708649\pi\) | ||||
−0.609549 | + | 0.792748i | \(0.708649\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −181.606 | + | 12.0837i | −0.235241 | + | 0.0156525i | ||||
\(773\) | − | 1468.30i | − | 1.89948i | −0.313040 | − | 0.949740i | \(-0.601347\pi\) | ||
0.313040 | − | 0.949740i | \(-0.398653\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 338.138 | − | 413.272i | 0.435745 | − | 0.532567i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −14.0624 | + | 15.0292i | −0.0180751 | + | 0.0193177i | ||||
\(779\) | 813.029i | 1.04368i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −787.486 | −1.00831 | ||||||||
\(782\) | 202.577 | + | 189.546i | 0.259049 | + | 0.242386i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 721.552 | − | 96.4481i | 0.920346 | − | 0.123020i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 408.886 | 0.519550 | 0.259775 | − | 0.965669i | \(-0.416352\pi\) | ||||
0.259775 | + | 0.965669i | \(0.416352\pi\) | |||||||
\(788\) | −742.063 | + | 49.3753i | −0.941705 | + | 0.0626591i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 135.466i | − | 0.171259i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 620.747i | − | 0.782783i | ||||||
\(794\) | 334.234 | + | 312.734i | 0.420949 | + | 0.393871i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −622.241 | + | 41.4026i | −0.781710 | + | 0.0520134i | ||||
\(797\) | − | 400.122i | − | 0.502035i | −0.967982 | − | 0.251018i | \(-0.919235\pi\) | ||
0.967982 | − | 0.251018i | \(-0.0807652\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 628.525i | − | 0.786639i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 132.454 | − | 141.560i | 0.165155 | − | 0.176509i | ||||
\(803\) | −940.966 | −1.17181 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 605.392 | − | 647.012i | 0.751106 | − | 0.802744i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1018.96 | − | 833.710i | −1.26109 | − | 1.03182i | ||||
\(809\) | 255.486 | 0.315805 | 0.157902 | − | 0.987455i | \(-0.449527\pi\) | ||||
0.157902 | + | 0.987455i | \(0.449527\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 295.549i | − | 0.364425i | −0.983259 | − | 0.182213i | \(-0.941674\pi\) | ||
0.983259 | − | 0.182213i | \(-0.0583259\pi\) | |||||||
\(812\) | −4.94482 | − | 74.3158i | −0.00608968 | − | 0.0915219i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 369.230 | − | 394.614i | 0.453599 | − | 0.484784i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1588.98i | − | 1.94490i | ||||||
\(818\) | −185.148 | + | 197.876i | −0.226342 | + | 0.241903i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1227.23 | 1.49480 | 0.747402 | − | 0.664372i | \(-0.231301\pi\) | ||||
0.747402 | + | 0.664372i | \(0.231301\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 881.623 | 1.07123 | 0.535615 | − | 0.844462i | \(-0.320080\pi\) | ||||
0.535615 | + | 0.844462i | \(0.320080\pi\) | |||||||
\(824\) | 267.936 | + | 219.224i | 0.325165 | + | 0.266049i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 303.187 | + | 283.684i | 0.367054 | + | 0.343443i | ||||
\(827\) | −850.269 | −1.02814 | −0.514068 | − | 0.857749i | \(-0.671862\pi\) | ||||
−0.514068 | + | 0.857749i | \(0.671862\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1328.47 | 1.60250 | 0.801251 | − | 0.598328i | \(-0.204168\pi\) | ||||
0.801251 | + | 0.598328i | \(0.204168\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1137.00 | − | 229.677i | 1.36659 | − | 0.276054i | ||||
\(833\) | 577.327i | 0.693069i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 113.150 | + | 1700.54i | 0.135347 | + | 2.03414i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 562.127 | + | 525.967i | 0.670796 | + | 0.627646i | ||||
\(839\) | − | 55.3391i | − | 0.0659583i | −0.999456 | − | 0.0329792i | \(-0.989500\pi\) | ||
0.999456 | − | 0.0329792i | \(-0.0104995\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −741.996 | −0.882278 | ||||||||
\(842\) | 742.303 | − | 793.335i | 0.881594 | − | 0.942203i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −966.739 | + | 64.3248i | −1.14543 | + | 0.0762142i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 201.166 | 0.237504 | ||||||||
\(848\) | −127.506 | − | 953.906i | −0.150361 | − | 1.12489i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 195.409i | 0.229623i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 742.887i | 0.870911i | 0.900210 | + | 0.435456i | \(0.143413\pi\) | ||||
−0.900210 | + | 0.435456i | \(0.856587\pi\) | |||||||
\(854\) | 87.5790 | − | 93.6000i | 0.102552 | − | 0.109602i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1071.30 | − | 876.537i | −1.25152 | − | 1.02399i | ||||
\(857\) | 679.145i | 0.792468i | 0.918150 | + | 0.396234i | \(0.129683\pi\) | ||||
−0.918150 | + | 0.396234i | \(0.870317\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 756.133i | 0.880248i | 0.897937 | + | 0.440124i | \(0.145066\pi\) | ||||
−0.897937 | + | 0.440124i | \(0.854934\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1136.48 | + | 1063.37i | 1.31842 | + | 1.23361i | ||||
\(863\) | 1130.05 | 1.30944 | 0.654721 | − | 0.755871i | \(-0.272786\pi\) | ||||
0.654721 | + | 0.755871i | \(0.272786\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −7.67137 | − | 7.17790i | −0.00885840 | − | 0.00828856i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 182.569 | − | 12.1478i | 0.210333 | − | 0.0139951i | ||||
\(869\) | −1561.10 | −1.79643 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2382.65i | 2.73554i | ||||||||
\(872\) | 1006.13 | + | 823.208i | 1.15381 | + | 0.944046i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −449.992 | − | 421.046i | −0.514865 | − | 0.481746i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 910.607i | 1.03832i | 0.854677 | + | 0.519160i | \(0.173755\pi\) | ||||
−0.854677 | + | 0.519160i | \(0.826245\pi\) | |||||||
\(878\) | 304.205 | + | 284.637i | 0.346475 | + | 0.324188i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −405.402 | −0.460161 | −0.230080 | − | 0.973172i | \(-0.573899\pi\) | ||||
−0.230080 | + | 0.973172i | \(0.573899\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 819.868 | 0.928503 | 0.464252 | − | 0.885703i | \(-0.346323\pi\) | ||||
0.464252 | + | 0.885703i | \(0.346323\pi\) | |||||||
\(884\) | 61.0752 | + | 917.901i | 0.0690896 | + | 1.03835i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1005.48 | − | 1074.60i | 1.13485 | − | 1.21287i | ||||
\(887\) | 1003.99 | 1.13190 | 0.565949 | − | 0.824440i | \(-0.308510\pi\) | ||||
0.565949 | + | 0.824440i | \(0.308510\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 277.961 | 0.312667 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 66.4055 | + | 998.010i | 0.0744456 | + | 1.11885i | ||||
\(893\) | 1396.17i | 1.56346i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 203.849 | + | 125.784i | 0.227510 | + | 0.140384i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −843.318 | + | 901.296i | −0.939107 | + | 1.00367i | ||||
\(899\) | 243.220i | 0.270545i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 763.237 | 0.847100 | ||||||||
\(902\) | −636.761 | − | 595.800i | −0.705943 | − | 0.660532i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −366.722 | + | 448.208i | −0.405666 | + | 0.495805i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −361.629 | −0.398709 | −0.199354 | − | 0.979927i | \(-0.563884\pi\) | ||||
−0.199354 | + | 0.979927i | \(0.563884\pi\) | |||||||
\(908\) | −16.0572 | − | 241.325i | −0.0176842 | − | 0.265776i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 294.475i | 0.323244i | 0.986853 | + | 0.161622i | \(0.0516725\pi\) | ||||
−0.986853 | + | 0.161622i | \(0.948327\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 864.965i | 0.947388i | ||||||||
\(914\) | 471.341 | + | 441.022i | 0.515691 | + | 0.482518i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 20.7802 | + | 312.306i | 0.0226858 | + | 0.340945i | ||||
\(917\) | 50.0182i | 0.0545454i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.4246i | 0.0189604i | 0.999955 | + | 0.00948022i | \(0.00301769\pi\) | ||||
−0.999955 | + | 0.00948022i | \(0.996982\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 695.575 | − | 743.395i | 0.754420 | − | 0.806285i | ||||
\(923\) | 944.209 | 1.02298 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1013.88 | + | 1083.59i | −1.09491 | + | 1.17018i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −184.821 | + | 259.270i | −0.199161 | + | 0.279386i | ||||
\(929\) | 743.488 | 0.800310 | 0.400155 | − | 0.916447i | \(-0.368956\pi\) | ||||
0.400155 | + | 0.916447i | \(0.368956\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 1282.44i | − | 1.37749i | ||||||
\(932\) | −657.513 | + | 43.7495i | −0.705486 | + | 0.0469416i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −424.549 | + | 453.736i | −0.454549 | + | 0.485799i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 802.514i | − | 0.856471i | −0.903667 | − | 0.428236i | \(-0.859135\pi\) | ||
0.903667 | − | 0.428236i | \(-0.140865\pi\) | |||||||
\(938\) | −336.160 | + | 359.271i | −0.358380 | + | 0.383018i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −730.288 | −0.776076 | −0.388038 | − | 0.921643i | \(-0.626847\pi\) | ||||
−0.388038 | + | 0.921643i | \(0.626847\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 315.318 | 0.334378 | ||||||||
\(944\) | −235.171 | − | 1759.37i | −0.249122 | − | 1.86374i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1244.48 | + | 1164.43i | 1.31552 | + | 1.23090i | ||||
\(947\) | −882.383 | −0.931767 | −0.465884 | − | 0.884846i | \(-0.654263\pi\) | ||||
−0.465884 | + | 0.884846i | \(0.654263\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1128.23 | 1.18887 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −120.294 | + | 147.023i | −0.126359 | + | 0.154436i | ||||
\(953\) | 1047.62i | 1.09929i | 0.835399 | + | 0.549644i | \(0.185237\pi\) | ||||
−0.835399 | + | 0.549644i | \(0.814763\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 972.811 | − | 64.7288i | 1.01759 | − | 0.0677080i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 699.698 | + | 654.689i | 0.730374 | + | 0.683391i | ||||
\(959\) | − | 237.573i | − | 0.247730i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 363.490 | 0.378242 | ||||||||
\(962\) | −442.712 | + | 473.149i | −0.460200 | + | 0.491838i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −101.842 | − | 1530.59i | −0.105646 | − | 1.58775i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 519.528 | 0.537258 | 0.268629 | − | 0.963244i | \(-0.413430\pi\) | ||||
0.268629 | + | 0.963244i | \(0.413430\pi\) | |||||||
\(968\) | −665.587 | − | 544.580i | −0.687589 | − | 0.562583i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 398.406i | − | 0.410305i | −0.978730 | − | 0.205152i | \(-0.934231\pi\) | ||
0.978730 | − | 0.205152i | \(-0.0657690\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 38.7393i | 0.0398143i | ||||||||
\(974\) | 782.788 | − | 836.604i | 0.803684 | − | 0.858937i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −543.154 | + | 72.6021i | −0.556510 | + | 0.0743874i | ||||
\(977\) | 367.857i | 0.376517i | 0.982120 | + | 0.188258i | \(0.0602842\pi\) | ||||
−0.982120 | + | 0.188258i | \(0.939716\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 2193.66i | − | 2.24071i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.380457 | − | 0.355984i | −0.000387431 | − | 0.000362509i | ||||
\(983\) | 1473.69 | 1.49918 | 0.749590 | − | 0.661902i | \(-0.230251\pi\) | ||||
0.749590 | + | 0.661902i | \(0.230251\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −184.386 | − | 172.525i | −0.187004 | − | 0.174975i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −135.669 | − | 2038.97i | −0.137317 | − | 2.06374i | ||||
\(989\) | −616.257 | −0.623111 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 753.090i | 0.759929i | 0.925001 | + | 0.379964i | \(0.124064\pi\) | ||||
−0.925001 | + | 0.379964i | \(0.875936\pi\) | |||||||
\(992\) | −636.941 | − | 454.044i | −0.642078 | − | 0.457705i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 142.374 | + | 133.215i | 0.143233 | + | 0.134019i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 767.370i | 0.769679i | 0.922984 | + | 0.384839i | \(0.125743\pi\) | ||||
−0.922984 | + | 0.384839i | \(0.874257\pi\) | |||||||
\(998\) | −683.050 | − | 639.112i | −0.684419 | − | 0.640393i | ||||
\(999\) | 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 | 900.3.f.i.199.7 | 16 | ||
3.2 | odd | 2 | inner | 900.3.f.i.199.9 | 16 | ||
4.3 | odd | 2 | inner | 900.3.f.i.199.12 | 16 | ||
5.2 | odd | 4 | 900.3.c.o.451.1 | 8 | |||
5.3 | odd | 4 | 180.3.c.c.91.8 | yes | 8 | ||
5.4 | even | 2 | inner | 900.3.f.i.199.10 | 16 | ||
12.11 | even | 2 | inner | 900.3.f.i.199.6 | 16 | ||
15.2 | even | 4 | 900.3.c.o.451.8 | 8 | |||
15.8 | even | 4 | 180.3.c.c.91.1 | ✓ | 8 | ||
15.14 | odd | 2 | inner | 900.3.f.i.199.8 | 16 | ||
20.3 | even | 4 | 180.3.c.c.91.7 | yes | 8 | ||
20.7 | even | 4 | 900.3.c.o.451.2 | 8 | |||
20.19 | odd | 2 | inner | 900.3.f.i.199.5 | 16 | ||
40.3 | even | 4 | 2880.3.e.i.2431.2 | 8 | |||
40.13 | odd | 4 | 2880.3.e.i.2431.3 | 8 | |||
60.23 | odd | 4 | 180.3.c.c.91.2 | yes | 8 | ||
60.47 | odd | 4 | 900.3.c.o.451.7 | 8 | |||
60.59 | even | 2 | inner | 900.3.f.i.199.11 | 16 | ||
120.53 | even | 4 | 2880.3.e.i.2431.7 | 8 | |||
120.83 | odd | 4 | 2880.3.e.i.2431.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
180.3.c.c.91.1 | ✓ | 8 | 15.8 | even | 4 | ||
180.3.c.c.91.2 | yes | 8 | 60.23 | odd | 4 | ||
180.3.c.c.91.7 | yes | 8 | 20.3 | even | 4 | ||
180.3.c.c.91.8 | yes | 8 | 5.3 | odd | 4 | ||
900.3.c.o.451.1 | 8 | 5.2 | odd | 4 | |||
900.3.c.o.451.2 | 8 | 20.7 | even | 4 | |||
900.3.c.o.451.7 | 8 | 60.47 | odd | 4 | |||
900.3.c.o.451.8 | 8 | 15.2 | even | 4 | |||
900.3.f.i.199.5 | 16 | 20.19 | odd | 2 | inner | ||
900.3.f.i.199.6 | 16 | 12.11 | even | 2 | inner | ||
900.3.f.i.199.7 | 16 | 1.1 | even | 1 | trivial | ||
900.3.f.i.199.8 | 16 | 15.14 | odd | 2 | inner | ||
900.3.f.i.199.9 | 16 | 3.2 | odd | 2 | inner | ||
900.3.f.i.199.10 | 16 | 5.4 | even | 2 | inner | ||
900.3.f.i.199.11 | 16 | 60.59 | even | 2 | inner | ||
900.3.f.i.199.12 | 16 | 4.3 | odd | 2 | inner | ||
2880.3.e.i.2431.2 | 8 | 40.3 | even | 4 | |||
2880.3.e.i.2431.3 | 8 | 40.13 | odd | 4 | |||
2880.3.e.i.2431.6 | 8 | 120.83 | odd | 4 | |||
2880.3.e.i.2431.7 | 8 | 120.53 | even | 4 |