Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(451,900)]
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, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.451");
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.c (of order \(2\), degree \(1\), 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: | \(8\) |
Coefficient field: | 8.0.15012375625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 7x^{6} + 28x^{4} + 112x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | no (minimal twist has level 180) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 451.8 | ||
Root | \(1.46040 + 1.36646i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 900.451 |
Dual form | 900.3.c.o.451.7 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.46040 | + | 1.36646i | 0.730202 | + | 0.683231i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.265564 | + | 3.99117i | 0.0663911 | + | 0.997794i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.87135i | − | 0.267335i | −0.991026 | − | 0.133668i | \(-0.957325\pi\) | ||
0.991026 | − | 0.133668i | \(-0.0426755\pi\) | |||||||
\(8\) | −5.06596 | + | 6.19161i | −0.633245 | + | 0.773952i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 15.1162i | − | 1.37420i | −0.726565 | − | 0.687098i | \(-0.758884\pi\) | ||
0.726565 | − | 0.687098i | \(-0.241116\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −18.1245 | −1.39419 | −0.697097 | − | 0.716977i | \(-0.745525\pi\) | ||||
−0.697097 | + | 0.716977i | \(0.745525\pi\) | |||||||
\(14\) | 2.55712 | − | 2.73292i | 0.182652 | − | 0.195209i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −15.8590 | + | 2.11983i | −0.991184 | + | 0.132489i | ||||
\(17\) | −12.6890 | −0.746414 | −0.373207 | − | 0.927748i | \(-0.621742\pi\) | ||||
−0.373207 | + | 0.927748i | \(0.621742\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 28.1867i | − | 1.48351i | −0.670671 | − | 0.741755i | \(-0.733994\pi\) | ||
0.670671 | − | 0.741755i | \(-0.266006\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 20.6556 | − | 22.0757i | 0.938893 | − | 1.00344i | ||||
\(23\) | 10.9317i | 0.475291i | 0.971352 | + | 0.237646i | \(0.0763757\pi\) | ||||
−0.971352 | + | 0.237646i | \(0.923624\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −26.4691 | − | 24.7665i | −1.01804 | − | 0.952556i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 7.46887 | − | 0.496963i | 0.266745 | − | 0.0177487i | ||||
\(29\) | −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 | \(-0.128998\pi\) | |||||||
\(32\) | −26.0572 | − | 18.5748i | −0.814286 | − | 0.580464i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −18.5311 | − | 17.3391i | −0.545033 | − | 0.509973i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −17.8755 | −0.483121 | −0.241561 | − | 0.970386i | \(-0.577659\pi\) | ||||
−0.241561 | + | 0.970386i | \(0.577659\pi\) | |||||||
\(38\) | 38.5161 | − | 41.1640i | 1.01358 | − | 1.08326i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −28.8444 | −0.703522 | −0.351761 | − | 0.936090i | \(-0.614417\pi\) | ||||
−0.351761 | + | 0.936090i | \(0.614417\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 56.3734i | 1.31101i | 0.755191 | + | 0.655505i | \(0.227544\pi\) | ||||
−0.755191 | + | 0.655505i | \(0.772456\pi\) | |||||||
\(44\) | 60.3312 | − | 4.01431i | 1.37116 | − | 0.0912344i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −14.9377 | + | 15.9647i | −0.324734 | + | 0.347059i | ||||
\(47\) | − | 49.5329i | − | 1.05389i | −0.849899 | − | 0.526946i | \(-0.823337\pi\) | ||
0.849899 | − | 0.526946i | \(-0.176663\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 45.4981 | 0.928532 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.81323 | − | 72.3381i | −0.0925621 | − | 1.39112i | ||||
\(53\) | −60.1494 | −1.13489 | −0.567447 | − | 0.823410i | \(-0.692069\pi\) | ||||
−0.567447 | + | 0.823410i | \(0.692069\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 11.5867 | + | 9.48016i | 0.206905 | + | 0.169289i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −14.5311 | − | 13.5964i | −0.250537 | − | 0.234421i | ||||
\(59\) | 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 | \(0.409424\pi\) | |||||||
\(62\) | 33.4018 | − | 35.6982i | 0.538739 | − | 0.575777i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.6722 | − | 62.7329i | −0.198003 | − | 0.980201i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 131.460i | − | 1.96209i | −0.193770 | − | 0.981047i | \(-0.562072\pi\) | ||
0.193770 | − | 0.981047i | \(-0.437928\pi\) | |||||||
\(68\) | −3.36976 | − | 50.6442i | −0.0495552 | − | 0.744767i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 52.0957i | − | 0.733742i | −0.930272 | − | 0.366871i | \(-0.880429\pi\) | ||
0.930272 | − | 0.366871i | \(-0.119571\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 62.2490 | 0.852726 | 0.426363 | − | 0.904552i | \(-0.359795\pi\) | ||||
0.426363 | + | 0.904552i | \(0.359795\pi\) | |||||||
\(74\) | −26.1054 | − | 24.4262i | −0.352776 | − | 0.330083i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 112.498 | − | 7.48539i | 1.48024 | − | 0.0984919i | ||||
\(77\) | −28.2876 | −0.367371 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 103.274i | − | 1.30726i | −0.756814 | − | 0.653630i | \(-0.773245\pi\) | ||
0.756814 | − | 0.653630i | \(-0.226755\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −42.1245 | − | 39.4148i | −0.513714 | − | 0.480668i | ||||
\(83\) | 57.2212i | 0.689413i | 0.938711 | + | 0.344706i | \(0.112021\pi\) | ||||
−0.938711 | + | 0.344706i | \(0.887979\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −77.0321 | + | 82.3280i | −0.895722 | + | 0.957302i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 93.5934 | + | 76.5778i | 1.06356 | + | 0.870202i | ||||
\(89\) | −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 | ||||||||
\(92\) | −43.6303 | + | 2.90307i | −0.474242 | + | 0.0315551i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 67.6848 | − | 72.3381i | 0.720051 | − | 0.769554i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 66.7471 | 0.688114 | 0.344057 | − | 0.938949i | \(-0.388199\pi\) | ||||
0.344057 | + | 0.938949i | \(0.388199\pi\) | |||||||
\(98\) | 66.4456 | + | 62.1714i | 0.678016 | + | 0.634402i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 164.571 | 1.62942 | 0.814709 | − | 0.579871i | \(-0.196897\pi\) | ||||
0.814709 | + | 0.579871i | \(0.196897\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 43.2740i | − | 0.420136i | −0.977687 | − | 0.210068i | \(-0.932631\pi\) | ||
0.977687 | − | 0.210068i | \(-0.0673685\pi\) | |||||||
\(104\) | 91.8180 | − | 112.220i | 0.882865 | − | 1.07904i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −87.8424 | − | 82.1918i | −0.828702 | − | 0.775394i | ||||
\(107\) | 173.025i | 1.61706i | 0.588458 | + | 0.808528i | \(0.299735\pi\) | ||||
−0.588458 | + | 0.808528i | \(0.700265\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −162.498 | −1.49081 | −0.745404 | − | 0.666613i | \(-0.767743\pi\) | ||||
−0.745404 | + | 0.666613i | \(0.767743\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.96693 | + | 29.6776i | 0.0354190 | + | 0.264979i | ||||
\(113\) | −72.3895 | −0.640615 | −0.320307 | − | 0.947314i | \(-0.603786\pi\) | ||||
−0.320307 | + | 0.947314i | \(0.603786\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.64238 | − | 39.7125i | −0.0227792 | − | 0.342349i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −151.593 | + | 162.015i | −1.28469 | + | 1.37301i | ||||
\(119\) | 23.7456i | 0.199543i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −107.498 | −0.888414 | ||||||||
\(122\) | 50.0174 | + | 46.8000i | 0.409979 | + | 0.383606i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 97.5603 | − | 6.49146i | 0.786777 | − | 0.0523505i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 148.535i | − | 1.16957i | −0.811188 | − | 0.584785i | \(-0.801179\pi\) | ||
0.811188 | − | 0.584785i | \(-0.198821\pi\) | |||||||
\(128\) | 67.2156 | − | 108.931i | 0.525122 | − | 0.851027i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 26.7284i | 0.204034i | 0.994783 | + | 0.102017i | \(0.0325296\pi\) | ||||
−0.994783 | + | 0.102017i | \(0.967470\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −52.7471 | −0.396595 | ||||||||
\(134\) | 179.635 | − | 191.985i | 1.34056 | − | 1.43273i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 64.2821 | − | 78.5656i | 0.472662 | − | 0.577688i | ||||
\(137\) | 126.953 | 0.926664 | 0.463332 | − | 0.886185i | \(-0.346654\pi\) | ||||
0.463332 | + | 0.886185i | \(0.346654\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.7013i | 0.148930i | 0.997224 | + | 0.0744652i | \(0.0237250\pi\) | ||||
−0.997224 | + | 0.0744652i | \(0.976275\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 71.1868 | − | 76.0808i | 0.501315 | − | 0.535780i | ||||
\(143\) | 273.973i | 1.91589i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 90.9088 | + | 85.0609i | 0.622663 | + | 0.582609i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.74709 | − | 71.3442i | −0.0320750 | − | 0.482055i | ||||
\(149\) | −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 | \(0.930287\pi\) | |||||||
\(152\) | 174.521 | + | 142.793i | 1.14817 | + | 0.939425i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −41.3113 | − | 38.6539i | −0.268255 | − | 0.250999i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 30.3735 | 0.193462 | 0.0967310 | − | 0.995311i | \(-0.469161\pi\) | ||||
0.0967310 | + | 0.995311i | \(0.469161\pi\) | |||||||
\(158\) | 141.119 | − | 150.821i | 0.893161 | − | 0.954565i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 20.4570 | 0.127062 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 45.1453i | − | 0.276965i | −0.990365 | − | 0.138483i | \(-0.955777\pi\) | ||
0.990365 | − | 0.138483i | \(-0.0442225\pi\) | |||||||
\(164\) | −7.66005 | − | 115.123i | −0.0467076 | − | 0.701970i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −78.1906 | + | 83.5662i | −0.471028 | + | 0.503411i | ||||
\(167\) | − | 32.7951i | − | 0.196378i | −0.995168 | − | 0.0981889i | \(-0.968695\pi\) | ||
0.995168 | − | 0.0981889i | \(-0.0313049\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 159.498 | 0.943776 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −224.996 | + | 14.9708i | −1.30812 | + | 0.0870394i | ||||
\(173\) | −316.067 | −1.82698 | −0.913488 | − | 0.406865i | \(-0.866622\pi\) | ||||
−0.913488 | + | 0.406865i | \(0.866622\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 32.0436 | + | 239.726i | 0.182066 | + | 1.36208i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −211.934 | − | 198.301i | −1.19064 | − | 1.11405i | ||||
\(179\) | 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 | \(0.565978\pi\) | |||||||
\(182\) | −46.3466 | + | 49.5329i | −0.254652 | + | 0.272159i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −67.6848 | − | 55.3795i | −0.367852 | − | 0.300975i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 191.809i | 1.02572i | ||||||||
\(188\) | 197.695 | − | 13.1542i | 1.05157 | − | 0.0699690i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 63.7080i | 0.333550i | 0.985995 | + | 0.166775i | \(0.0533353\pi\) | ||||
−0.985995 | + | 0.166775i | \(0.946665\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −45.5019 | −0.235761 | −0.117881 | − | 0.993028i | \(-0.537610\pi\) | ||||
−0.117881 | + | 0.993028i | \(0.537610\pi\) | |||||||
\(194\) | 97.4778 | + | 91.2074i | 0.502463 | + | 0.470141i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 12.0827 | + | 181.591i | 0.0616463 | + | 0.926483i | ||||
\(197\) | −185.926 | −0.943787 | −0.471893 | − | 0.881656i | \(-0.656429\pi\) | ||||
−0.471893 | + | 0.881656i | \(0.656429\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 155.904i | 0.783439i | 0.920085 | + | 0.391719i | \(0.128120\pi\) | ||||
−0.920085 | + | 0.391719i | \(0.871880\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 240.340 | + | 224.880i | 1.18980 | + | 1.11327i | ||||
\(203\) | 18.6200i | 0.0917243i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 59.1322 | − | 63.1975i | 0.287050 | − | 0.306784i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 287.436 | − | 38.4209i | 1.38190 | − | 0.184716i | ||||
\(209\) | −426.075 | −2.03863 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 242.219i | − | 1.14796i | −0.818870 | − | 0.573979i | \(-0.805399\pi\) | ||
0.818870 | − | 0.573979i | \(-0.194601\pi\) | |||||||
\(212\) | −15.9735 | − | 240.067i | −0.0753468 | − | 1.13239i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −236.432 | + | 252.686i | −1.10482 | + | 1.18078i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −45.7432 | −0.210798 | ||||||||
\(218\) | −237.313 | − | 222.047i | −1.08859 | − | 1.01857i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 229.983 | 1.04065 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 250.054i | 1.12132i | 0.828046 | + | 0.560660i | \(0.189452\pi\) | ||||
−0.828046 | + | 0.560660i | \(0.810548\pi\) | |||||||
\(224\) | −34.7600 | + | 48.7620i | −0.155178 | + | 0.217687i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −105.718 | − | 98.9174i | −0.467778 | − | 0.437688i | ||||
\(227\) | − | 60.4646i | − | 0.266364i | −0.991092 | − | 0.133182i | \(-0.957481\pi\) | ||
0.991092 | − | 0.133182i | \(-0.0425195\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 78.2490 | 0.341699 | 0.170849 | − | 0.985297i | \(-0.445349\pi\) | ||||
0.170849 | + | 0.985297i | \(0.445349\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 50.4066 | − | 61.6070i | 0.217270 | − | 0.265547i | ||||
\(233\) | 164.742 | 0.707046 | 0.353523 | − | 0.935426i | \(-0.384984\pi\) | ||||
0.353523 | + | 0.935426i | \(0.384984\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −442.775 | + | 29.4614i | −1.87617 | + | 0.124836i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −32.4474 | + | 34.6782i | −0.136334 | + | 0.145707i | ||||
\(239\) | 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 | \(0.207139\pi\) | |||||||
\(242\) | −156.991 | − | 146.892i | −0.648722 | − | 0.606992i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 9.09532 | + | 136.694i | 0.0372759 | + | 0.560221i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 510.870i | 2.06830i | ||||||||
\(248\) | 151.348 | + | 123.832i | 0.610274 | + | 0.499324i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 199.753i | − | 0.795830i | −0.917422 | − | 0.397915i | \(-0.869734\pi\) | ||
0.917422 | − | 0.397915i | \(-0.130266\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 165.245 | 0.653143 | ||||||||
\(254\) | 202.968 | − | 216.922i | 0.799086 | − | 0.854023i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 247.013 | − | 67.2365i | 0.964893 | − | 0.262643i | ||||
\(257\) | 158.366 | 0.616209 | 0.308105 | − | 0.951352i | \(-0.400305\pi\) | ||||
0.308105 | + | 0.951352i | \(0.400305\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 33.4512i | 0.129155i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −36.5234 | + | 39.0343i | −0.139402 | + | 0.148986i | ||||
\(263\) | − | 121.610i | − | 0.462395i | −0.972907 | − | 0.231197i | \(-0.925736\pi\) | ||
0.972907 | − | 0.231197i | \(-0.0742643\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −77.0321 | − | 72.0769i | −0.289594 | − | 0.270966i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 524.681 | − | 34.9112i | 1.95776 | − | 0.130266i | ||||
\(269\) | 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 | \(0.883902\pi\) | |||||||
\(272\) | 201.235 | − | 26.8986i | 0.739834 | − | 0.0988918i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 185.403 | + | 173.476i | 0.676652 | + | 0.633126i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −472.615 | −1.70619 | −0.853095 | − | 0.521755i | \(-0.825278\pi\) | ||||
−0.853095 | + | 0.521755i | \(0.825278\pi\) | |||||||
\(278\) | −28.2876 | + | 30.2323i | −0.101754 | + | 0.108749i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −256.815 | −0.913934 | −0.456967 | − | 0.889484i | \(-0.651064\pi\) | ||||
−0.456967 | + | 0.889484i | \(0.651064\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 416.837i | − | 1.47292i | −0.676480 | − | 0.736461i | \(-0.736495\pi\) | ||
0.676480 | − | 0.736461i | \(-0.263505\pi\) | |||||||
\(284\) | 207.923 | − | 13.8348i | 0.732123 | − | 0.0487140i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −374.374 | + | 400.111i | −1.30900 | + | 1.39899i | ||||
\(287\) | 53.9779i | 0.188076i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −127.988 | −0.442866 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 16.5311 | + | 248.447i | 0.0566135 | + | 0.850845i | ||||
\(293\) | −240.705 | −0.821520 | −0.410760 | − | 0.911744i | \(-0.634737\pi\) | ||||
−0.410760 | + | 0.911744i | \(0.634737\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 90.5564 | − | 110.678i | 0.305934 | − | 0.373913i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −244.091 | − | 228.390i | −0.819099 | − | 0.766409i | ||||
\(299\) | − | 198.132i | − | 0.662648i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 105.494 | 0.350479 | ||||||||
\(302\) | −89.6585 | + | 95.8225i | −0.296883 | + | 0.317293i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 59.7510 | + | 447.012i | 0.196549 | + | 1.47043i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 206.547i | 0.672792i | 0.941721 | + | 0.336396i | \(0.109208\pi\) | ||||
−0.941721 | + | 0.336396i | \(0.890792\pi\) | |||||||
\(308\) | −7.51217 | − | 112.901i | −0.0243902 | − | 0.366560i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 458.610i | − | 1.47463i | −0.675549 | − | 0.737315i | \(-0.736093\pi\) | ||
0.675549 | − | 0.737315i | \(-0.263907\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −383.992 | −1.22681 | −0.613406 | − | 0.789768i | \(-0.710201\pi\) | ||||
−0.613406 | + | 0.789768i | \(0.710201\pi\) | |||||||
\(314\) | 44.3577 | + | 41.5043i | 0.141266 | + | 0.132179i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 412.183 | − | 27.4258i | 1.30438 | − | 0.0867905i | ||||
\(317\) | −429.433 | −1.35468 | −0.677339 | − | 0.735671i | \(-0.736867\pi\) | ||||
−0.677339 | + | 0.735671i | \(0.736867\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 150.407i | 0.471495i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 29.8755 | + | 27.9537i | 0.0927810 | + | 0.0868127i | ||||
\(323\) | 357.662i | 1.10731i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 61.6894 | − | 65.9305i | 0.189231 | − | 0.202241i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 146.125 | − | 178.593i | 0.445502 | − | 0.544492i | ||||
\(329\) | −92.6933 | −0.281742 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 58.1282i | 0.175614i | 0.996138 | + | 0.0878070i | \(0.0279859\pi\) | ||||
−0.996138 | + | 0.0878070i | \(0.972014\pi\) | |||||||
\(332\) | −228.380 | + | 15.1959i | −0.687892 | + | 0.0457709i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 44.8132 | − | 47.8941i | 0.134171 | − | 0.143395i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 405.751 | 1.20401 | 0.602004 | − | 0.798493i | \(-0.294369\pi\) | ||||
0.602004 | + | 0.798493i | \(0.294369\pi\) | |||||||
\(338\) | 232.932 | + | 217.948i | 0.689147 | + | 0.644817i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −369.499 | −1.08358 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 176.839i | − | 0.515565i | ||||||
\(344\) | −349.042 | − | 285.585i | −1.01466 | − | 0.830190i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −461.586 | − | 431.893i | −1.33406 | − | 1.24825i | ||||
\(347\) | − | 324.186i | − | 0.934255i | −0.884190 | − | 0.467127i | \(-0.845289\pi\) | ||
0.884190 | − | 0.467127i | \(-0.154711\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 34.7471 | 0.0995619 | 0.0497809 | − | 0.998760i | \(-0.484148\pi\) | ||||
0.0497809 | + | 0.998760i | \(0.484148\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −280.780 | + | 393.884i | −0.797671 | + | 1.11899i | ||||
\(353\) | 13.5869 | 0.0384899 | 0.0192449 | − | 0.999815i | \(-0.493874\pi\) | ||||
0.0192449 | + | 0.999815i | \(0.493874\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −38.5387 | − | 579.199i | −0.108255 | − | 1.62696i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −353.718 | + | 378.036i | −0.988039 | + | 1.05597i | ||||
\(359\) | 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 | ||||||||
\(362\) | −108.797 | − | 101.799i | −0.300545 | − | 0.281212i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −135.370 | + | 9.00722i | −0.371895 | + | 0.0247451i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 1.87135i | − | 0.00509904i | −0.999997 | − | 0.00254952i | \(-0.999188\pi\) | ||
0.999997 | − | 0.00254952i | \(-0.000811538\pi\) | |||||||
\(368\) | −23.1733 | − | 173.365i | −0.0629710 | − | 0.471101i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 112.560i | 0.303397i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 384.864 | 1.03181 | 0.515903 | − | 0.856647i | \(-0.327456\pi\) | ||||
0.515903 | + | 0.856647i | \(0.327456\pi\) | |||||||
\(374\) | −262.100 | + | 280.119i | −0.700803 | + | 0.748982i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 306.689 | + | 250.932i | 0.815661 | + | 0.667371i | ||||
\(377\) | 180.340 | 0.478356 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 483.150i | 1.27480i | 0.770533 | + | 0.637401i | \(0.219990\pi\) | ||||
−0.770533 | + | 0.637401i | \(0.780010\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −87.0545 | + | 93.0394i | −0.227891 | + | 0.243559i | ||||
\(383\) | − | 130.500i | − | 0.340730i | −0.985381 | − | 0.170365i | \(-0.945505\pi\) | ||
0.985381 | − | 0.170365i | \(-0.0544947\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −66.4512 | − | 62.1767i | −0.172153 | − | 0.161079i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 17.7257 | + | 266.399i | 0.0456847 | + | 0.686596i | ||||
\(389\) | 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 | ||||||
\(392\) | −230.491 | + | 281.706i | −0.587988 | + | 0.718639i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −271.527 | − | 254.061i | −0.689155 | − | 0.644824i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 228.864 | 0.576483 | 0.288242 | − | 0.957558i | \(-0.406929\pi\) | ||||
0.288242 | + | 0.957558i | \(0.406929\pi\) | |||||||
\(398\) | −213.037 | + | 227.683i | −0.535269 | + | 0.572069i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 96.9322 | 0.241726 | 0.120863 | − | 0.992669i | \(-0.461434\pi\) | ||||
0.120863 | + | 0.992669i | \(0.461434\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 443.036i | 1.09934i | ||||||||
\(404\) | 43.7042 | + | 656.832i | 0.108179 | + | 1.62582i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −25.4436 | + | 27.1928i | −0.0626689 | + | 0.0669773i | ||||
\(407\) | 270.209i | 0.663903i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −135.494 | −0.331282 | −0.165641 | − | 0.986186i | \(-0.552969\pi\) | ||||
−0.165641 | + | 0.986186i | \(0.552969\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 172.714 | − | 11.4920i | 0.419209 | − | 0.0278933i | ||||
\(413\) | 207.605 | 0.502675 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 472.273 | + | 336.660i | 1.13527 | + | 0.809279i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −622.241 | − | 582.215i | −1.48862 | − | 1.39286i | ||||
\(419\) | − | 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 | \(0.723212\pi\) | |||||||
\(422\) | 330.983 | − | 353.738i | 0.784321 | − | 0.838242i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 304.714 | − | 372.422i | 0.718665 | − | 0.878353i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 64.0918i | − | 0.150098i | ||||||
\(428\) | −690.573 | + | 45.9493i | −1.61349 | + | 0.107358i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 778.192i | 1.80555i | 0.430113 | + | 0.902775i | \(0.358474\pi\) | ||||
−0.430113 | + | 0.902775i | \(0.641526\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.25291 | 0.0121314 | 0.00606571 | − | 0.999982i | \(-0.498069\pi\) | ||||
0.00606571 | + | 0.999982i | \(0.498069\pi\) | |||||||
\(434\) | −66.8036 | − | 62.5064i | −0.153925 | − | 0.144024i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −43.1537 | − | 648.558i | −0.0989764 | − | 1.48752i | ||||
\(437\) | 308.128 | 0.705099 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 208.302i | 0.474492i | 0.971450 | + | 0.237246i | \(0.0762447\pi\) | ||||
−0.971450 | + | 0.237246i | \(0.923755\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 335.868 | + | 314.262i | 0.759882 | + | 0.711001i | ||||
\(443\) | − | 735.826i | − | 1.66101i | −0.557013 | − | 0.830504i | \(-0.688053\pi\) | ||
0.557013 | − | 0.830504i | \(-0.311947\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −341.689 | + | 365.180i | −0.766120 | + | 0.818790i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −117.395 | + | 23.7140i | −0.262042 | + | 0.0529331i | ||||
\(449\) | 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 | ||||||||
\(452\) | −19.2241 | − | 288.919i | −0.0425311 | − | 0.639201i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 82.6226 | − | 88.3028i | 0.181988 | − | 0.194500i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 322.747 | 0.706230 | 0.353115 | − | 0.935580i | \(-0.385122\pi\) | ||||
0.353115 | + | 0.935580i | \(0.385122\pi\) | |||||||
\(458\) | 114.275 | + | 106.924i | 0.249509 | + | 0.233459i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 509.034 | 1.10419 | 0.552097 | − | 0.833780i | \(-0.313828\pi\) | ||||
0.552097 | + | 0.833780i | \(0.313828\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 741.978i | − | 1.60254i | −0.598300 | − | 0.801272i | \(-0.704157\pi\) | ||
0.598300 | − | 0.801272i | \(-0.295843\pi\) | |||||||
\(464\) | 157.798 | − | 21.0924i | 0.340081 | − | 0.0454578i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 240.590 | + | 225.113i | 0.516287 | + | 0.483075i | ||||
\(467\) | − | 310.692i | − | 0.665293i | −0.943052 | − | 0.332647i | \(-0.892058\pi\) | ||
0.943052 | − | 0.332647i | \(-0.107942\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −246.008 | −0.524537 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −686.889 | − | 562.010i | −1.45527 | − | 1.19070i | ||||
\(473\) | 852.149 | 1.80158 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −94.7728 | + | 6.30598i | −0.199102 | + | 0.0132479i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −333.062 | + | 355.960i | −0.696783 | + | 0.744686i | ||||
\(479\) | − | 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 | ||||||||
\(482\) | 560.057 | + | 524.030i | 1.16194 | + | 1.08720i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −28.5477 | − | 429.044i | −0.0589828 | − | 0.886454i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 572.858i | − | 1.17630i | −0.808752 | − | 0.588150i | \(-0.799857\pi\) | ||
0.808752 | − | 0.588150i | \(-0.200143\pi\) | |||||||
\(488\) | −173.504 | + | 212.057i | −0.355541 | + | 0.434543i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 0.260515i | − | 0.000530580i | −1.00000 | 0.000265290i | \(-0.999916\pi\) | |||
1.00000 | 0.000265290i | \(-8.44445e-5\pi\) | ||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 126.257 | 0.256099 | ||||||||
\(494\) | −698.085 | + | 746.078i | −1.41313 | + | 1.51028i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 51.8171 | + | 387.656i | 0.104470 | + | 0.781565i | ||||
\(497\) | −97.4891 | −0.196155 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 467.713i | − | 0.937300i | −0.883384 | − | 0.468650i | \(-0.844740\pi\) | ||
0.883384 | − | 0.468650i | \(-0.155260\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 272.955 | − | 291.721i | 0.543736 | − | 0.581117i | ||||
\(503\) | − | 728.659i | − | 1.44863i | −0.689471 | − | 0.724313i | \(-0.742157\pi\) | ||
0.689471 | − | 0.724313i | \(-0.257843\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 241.325 | + | 225.801i | 0.476927 | + | 0.446247i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 592.831 | − | 39.4457i | 1.16699 | − | 0.0776491i | ||||
\(509\) | 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 | ||||||
\(512\) | 452.615 | + | 239.341i | 0.884013 | + | 0.467463i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 231.278 | + | 216.401i | 0.449958 | + | 0.421013i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −748.747 | −1.44825 | ||||||||
\(518\) | −45.7098 | + | 48.8523i | −0.0882429 | + | 0.0943095i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −624.519 | −1.19869 | −0.599346 | − | 0.800490i | \(-0.704573\pi\) | ||||
−0.599346 | + | 0.800490i | \(0.704573\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 319.527i | 0.610950i | 0.952200 | + | 0.305475i | \(0.0988153\pi\) | ||||
−0.952200 | + | 0.305475i | \(0.901185\pi\) | |||||||
\(524\) | −106.678 | + | 7.09812i | −0.203584 | + | 0.0135460i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 166.175 | − | 177.600i | 0.315922 | − | 0.337642i | ||||
\(527\) | 310.171i | 0.588560i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 409.498 | 0.774098 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −14.0078 | − | 210.523i | −0.0263304 | − | 0.395720i | ||||
\(533\) | 522.791 | 0.980846 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 813.951 | + | 665.972i | 1.51857 | + | 1.24249i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 605.586 | + | 566.630i | 1.12562 | + | 1.05322i | ||||
\(539\) | − | 687.756i | − | 1.27598i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 449.984 | 0.831764 | 0.415882 | − | 0.909419i | \(-0.363473\pi\) | ||||
0.415882 | + | 0.909419i | \(0.363473\pi\) | |||||||
\(542\) | −264.180 | + | 282.342i | −0.487416 | + | 0.520926i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 330.640 | + | 235.697i | 0.607794 | + | 0.433266i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 650.049i | − | 1.18839i | −0.804321 | − | 0.594195i | \(-0.797471\pi\) | ||
0.804321 | − | 0.594195i | \(-0.202529\pi\) | |||||||
\(548\) | 33.7142 | + | 506.692i | 0.0615223 | + | 0.924620i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 280.460i | 0.509001i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −193.261 | −0.349477 | ||||||||
\(554\) | −690.209 | − | 645.810i | −1.24586 | − | 1.16572i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −82.6226 | + | 5.49753i | −0.148602 | + | 0.00988765i | ||||
\(557\) | 127.555 | 0.229004 | 0.114502 | − | 0.993423i | \(-0.463473\pi\) | ||||
0.114502 | + | 0.993423i | \(0.463473\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1021.74i | − | 1.82780i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −375.055 | − | 350.928i | −0.667357 | − | 0.624428i | ||||
\(563\) | 474.827i | 0.843387i | 0.906738 | + | 0.421694i | \(0.138564\pi\) | ||||
−0.906738 | + | 0.421694i | \(0.861436\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 569.592 | − | 608.751i | 1.00635 | − | 1.07553i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 322.556 | + | 263.914i | 0.567881 | + | 0.464638i | ||||
\(569\) | 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 | \(-0.0532874\pi\) | |||||||
\(572\) | −1093.47 | + | 72.7575i | −1.91167 | + | 0.127198i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −73.7587 | + | 78.8296i | −0.128500 | + | 0.137334i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 492.739 | 0.853968 | 0.426984 | − | 0.904259i | \(-0.359576\pi\) | ||||
0.426984 | + | 0.904259i | \(0.359576\pi\) | |||||||
\(578\) | −186.915 | − | 174.891i | −0.323382 | − | 0.302580i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 107.081 | 0.184304 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 909.227i | 1.55957i | ||||||||
\(584\) | −315.351 | + | 385.422i | −0.539984 | + | 0.659969i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −351.527 | − | 328.915i | −0.599876 | − | 0.561288i | ||||
\(587\) | 293.954i | 0.500774i | 0.968146 | + | 0.250387i | \(0.0805578\pi\) | ||||
−0.968146 | + | 0.250387i | \(0.919442\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −688.996 | −1.16977 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 283.486 | − | 37.8930i | 0.478862 | − | 0.0640084i | ||||
\(593\) | −434.184 | −0.732181 | −0.366091 | − | 0.930579i | \(-0.619304\pi\) | ||||
−0.366091 | + | 0.930579i | \(0.619304\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −44.3863 | − | 667.083i | −0.0744737 | − | 1.11927i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 270.739 | − | 289.352i | 0.452741 | − | 0.483867i | ||||
\(599\) | − | 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 | \(0.421482\pi\) | |||||||
\(602\) | 154.064 | + | 144.154i | 0.255921 | + | 0.239458i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −261.875 | + | 17.4246i | −0.433569 | + | 0.0288488i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 35.0896i | − | 0.0578082i | −0.999582 | − | 0.0289041i | \(-0.990798\pi\) | ||
0.999582 | − | 0.0289041i | \(-0.00920174\pi\) | |||||||
\(608\) | −523.564 | + | 734.465i | −0.861124 | + | 1.20800i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 897.760i | 1.46933i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −49.6109 | −0.0809314 | −0.0404657 | − | 0.999181i | \(-0.512884\pi\) | ||||
−0.0404657 | + | 0.999181i | \(0.512884\pi\) | |||||||
\(614\) | −282.239 | + | 301.642i | −0.459672 | + | 0.491274i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 143.304 | − | 175.146i | 0.232636 | − | 0.284327i | ||||
\(617\) | 427.251 | 0.692465 | 0.346232 | − | 0.938149i | \(-0.387461\pi\) | ||||
0.346232 | + | 0.938149i | \(0.387461\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 903.263i | − | 1.45923i | −0.683858 | − | 0.729615i | \(-0.739699\pi\) | ||
0.683858 | − | 0.729615i | \(-0.260301\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 626.673 | − | 669.756i | 1.00751 | − | 1.07678i | ||||
\(623\) | 271.570i | 0.435906i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −560.784 | − | 524.711i | −0.895821 | − | 0.838196i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.06613 | + | 121.226i | 0.0128442 | + | 0.193035i | ||||
\(629\) | 226.823 | 0.360608 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 681.512i | − | 1.08005i | −0.841649 | − | 0.540026i | \(-0.818415\pi\) | ||
0.841649 | − | 0.540026i | \(-0.181585\pi\) | |||||||
\(632\) | 639.430 | + | 523.179i | 1.01176 | + | 0.827816i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −627.146 | − | 586.804i | −0.989189 | − | 0.925558i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −824.630 | −1.29455 | ||||||||
\(638\) | −205.525 | + | 219.655i | −0.322140 | + | 0.344286i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 252.576 | 0.394035 | 0.197018 | − | 0.980400i | \(-0.436874\pi\) | ||||
0.197018 | + | 0.980400i | \(0.436874\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.2038i | 0.0236451i | 0.999930 | + | 0.0118225i | \(0.00376332\pi\) | ||||
−0.999930 | + | 0.0118225i | \(0.996237\pi\) | |||||||
\(644\) | 5.43265 | + | 81.6474i | 0.00843579 | + | 0.126782i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −488.732 | + | 522.331i | −0.756550 | + | 0.808563i | ||||
\(647\) | 463.576i | 0.716501i | 0.933626 | + | 0.358250i | \(0.116627\pi\) | ||||
−0.933626 | + | 0.358250i | \(0.883373\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1676.97 | 2.58392 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 180.183 | − | 11.9890i | 0.276354 | − | 0.0183880i | ||||
\(653\) | 351.503 | 0.538289 | 0.269145 | − | 0.963100i | \(-0.413259\pi\) | ||||
0.269145 | + | 0.963100i | \(0.413259\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 457.442 | − | 61.1452i | 0.697320 | − | 0.0932091i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −135.370 | − | 126.662i | −0.205729 | − | 0.192495i | ||||
\(659\) | − | 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 | \(0.459989\pi\) | |||||||
\(662\) | −79.4300 | + | 84.8908i | −0.119985 | + | 0.128234i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −354.292 | − | 289.880i | −0.533572 | − | 0.436567i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 108.771i | − | 0.163075i | ||||||
\(668\) | 130.891 | − | 8.70921i | 0.195944 | − | 0.0130377i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 517.714i | − | 0.771555i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.74322 | −0.00556199 | −0.00278099 | − | 0.999996i | \(-0.500885\pi\) | ||||
−0.00278099 | + | 0.999996i | \(0.500885\pi\) | |||||||
\(674\) | 592.561 | + | 554.443i | 0.879170 | + | 0.822616i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 42.3570 | + | 636.585i | 0.0626583 | + | 0.941693i | ||||
\(677\) | 969.987 | 1.43277 | 0.716386 | − | 0.697704i | \(-0.245795\pi\) | ||||
0.716386 | + | 0.697704i | \(0.245795\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 124.907i | − | 0.183957i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −539.619 | − | 504.907i | −0.791230 | − | 0.740333i | ||||
\(683\) | − | 808.424i | − | 1.18364i | −0.806071 | − | 0.591819i | \(-0.798410\pi\) | ||
0.806071 | − | 0.591819i | \(-0.201590\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 241.643 | − | 258.256i | 0.352250 | − | 0.376466i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −119.502 | − | 894.023i | −0.173695 | − | 1.29945i | ||||
\(689\) | 1090.18 | 1.58226 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 395.903i | 0.572942i | 0.958089 | + | 0.286471i | \(0.0924821\pi\) | ||||
−0.958089 | + | 0.286471i | \(0.907518\pi\) | |||||||
\(692\) | −83.9361 | − | 1261.48i | −0.121295 | − | 1.82295i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 442.988 | − | 473.443i | 0.638312 | − | 0.682195i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 366.008 | 0.525119 | ||||||||
\(698\) | 50.7448 | + | 47.4806i | 0.0727003 | + | 0.0680237i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −961.043 | −1.37096 | −0.685480 | − | 0.728091i | \(-0.740408\pi\) | ||||
−0.685480 | + | 0.728091i | \(0.740408\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 503.851i | 0.716716i | ||||||||
\(704\) | −948.280 | + | 191.555i | −1.34699 | + | 0.272095i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 19.8424 | + | 18.5660i | 0.0281054 | + | 0.0262975i | ||||
\(707\) | − | 307.970i | − | 0.435601i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −817.751 | −1.15339 | −0.576693 | − | 0.816961i | \(-0.695657\pi\) | ||||
−0.576693 | + | 0.816961i | \(0.695657\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 735.171 | − | 898.527i | 1.03254 | − | 1.26198i | ||||
\(713\) | 267.214 | 0.374775 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1033.14 | + | 68.7432i | −1.44294 | + | 0.0960100i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −189.977 | + | 203.037i | −0.264592 | + | 0.282782i | ||||
\(719\) | − | 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 | ||||||||
\(722\) | −633.071 | − | 592.348i | −0.876830 | − | 0.820427i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −19.7840 | − | 297.335i | −0.0273260 | − | 0.410683i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 662.682i | − | 0.911530i | −0.890100 | − | 0.455765i | \(-0.849366\pi\) | ||
0.890100 | − | 0.455765i | \(-0.150634\pi\) | |||||||
\(728\) | −210.003 | − | 171.823i | −0.288465 | − | 0.236021i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 715.324i | − | 0.978556i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −430.623 | −0.587480 | −0.293740 | − | 0.955885i | \(-0.594900\pi\) | ||||
−0.293740 | + | 0.955885i | \(0.594900\pi\) | |||||||
\(734\) | 2.55712 | − | 2.73292i | 0.00348382 | − | 0.00372333i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 203.055 | − | 284.849i | 0.275889 | − | 0.387023i | ||||
\(737\) | −1987.17 | −2.69630 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 523.620i | 0.708552i | 0.935141 | + | 0.354276i | \(0.115273\pi\) | ||||
−0.935141 | + | 0.354276i | \(0.884727\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −153.809 | + | 164.384i | −0.207290 | + | 0.221541i | ||||
\(743\) | − | 880.661i | − | 1.18528i | −0.805469 | − | 0.592638i | \(-0.798086\pi\) | ||
0.805469 | − | 0.592638i | \(-0.201914\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 562.057 | + | 525.902i | 0.753428 | + | 0.704962i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −765.545 | + | 50.9378i | −1.02346 | + | 0.0680986i | ||||
\(749\) | 323.790 | 0.432296 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 602.683i | − | 0.802507i | −0.915967 | − | 0.401254i | \(-0.868575\pi\) | ||
0.915967 | − | 0.401254i | \(-0.131425\pi\) | |||||||
\(752\) | 105.001 | + | 785.540i | 0.139629 | + | 1.04460i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 263.370 | + | 246.428i | 0.349297 | + | 0.326828i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −427.136 | −0.564249 | −0.282124 | − | 0.959378i | \(-0.591039\pi\) | ||||
−0.282124 | + | 0.959378i | \(0.591039\pi\) | |||||||
\(758\) | −660.206 | + | 705.594i | −0.870984 | + | 0.930863i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 239.700 | 0.314980 | 0.157490 | − | 0.987521i | \(-0.449660\pi\) | ||||
0.157490 | + | 0.987521i | \(0.449660\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 304.090i | 0.398545i | ||||||||
\(764\) | −254.270 | + | 16.9186i | −0.332814 | + | 0.0221447i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 178.323 | − | 190.582i | 0.232798 | − | 0.248802i | ||||
\(767\) | − | 2010.71i | − | 2.62152i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 937.486 | 1.21910 | 0.609549 | − | 0.792748i | \(-0.291351\pi\) | ||||
0.609549 | + | 0.792748i | \(0.291351\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −12.0837 | − | 181.606i | −0.0156525 | − | 0.235241i | ||||
\(773\) | 1468.30 | 1.89948 | 0.949740 | − | 0.313040i | \(-0.101347\pi\) | ||||
0.949740 | + | 0.313040i | \(0.101347\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −338.138 | + | 413.272i | −0.435745 | + | 0.532567i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 15.0292 | + | 14.0624i | 0.0193177 | + | 0.0180751i | ||||
\(779\) | 813.029i | 1.04368i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −787.486 | −1.00831 | ||||||||
\(782\) | 189.546 | − | 202.577i | 0.242386 | − | 0.259049i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −721.552 | + | 96.4481i | −0.920346 | + | 0.123020i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 408.886i | 0.519550i | 0.965669 | + | 0.259775i | \(0.0836483\pi\) | ||||
−0.965669 | + | 0.259775i | \(0.916352\pi\) | |||||||
\(788\) | −49.3753 | − | 742.063i | −0.0626591 | − | 0.941705i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 135.466i | 0.171259i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −620.747 | −0.782783 | ||||||||
\(794\) | 334.234 | + | 312.734i | 0.420949 | + | 0.393871i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −622.241 | + | 41.4026i | −0.781710 | + | 0.0520134i | ||||
\(797\) | −400.122 | −0.502035 | −0.251018 | − | 0.967982i | \(-0.580765\pi\) | ||||
−0.251018 | + | 0.967982i | \(0.580765\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 628.525i | 0.786639i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 141.560 | + | 132.454i | 0.176509 | + | 0.165155i | ||||
\(803\) | − | 940.966i | − | 1.17181i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −605.392 | + | 647.012i | −0.751106 | + | 0.802744i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −833.710 | + | 1018.96i | −1.03182 | + | 1.26109i | ||||
\(809\) | 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 | \(-0.0583259\pi\) | |||||||
\(812\) | −74.3158 | + | 4.94482i | −0.0915219 | + | 0.00608968i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −369.230 | + | 394.614i | −0.453599 | + | 0.484784i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1588.98 | 1.94490 | ||||||||
\(818\) | −197.876 | − | 185.148i | −0.241903 | − | 0.226342i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1227.23 | −1.49480 | −0.747402 | − | 0.664372i | \(-0.768699\pi\) | ||||
−0.747402 | + | 0.664372i | \(0.768699\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 881.623i | − | 1.07123i | −0.844462 | − | 0.535615i | \(-0.820080\pi\) | ||
0.844462 | − | 0.535615i | \(-0.179920\pi\) | |||||||
\(824\) | 267.936 | + | 219.224i | 0.325165 | + | 0.266049i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 303.187 | + | 283.684i | 0.367054 | + | 0.343443i | ||||
\(827\) | 850.269i | 1.02814i | 0.857749 | + | 0.514068i | \(0.171862\pi\) | ||||
−0.857749 | + | 0.514068i | \(0.828138\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1328.47 | −1.60250 | −0.801251 | − | 0.598328i | \(-0.795832\pi\) | ||||
−0.801251 | + | 0.598328i | \(0.795832\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 229.677 | + | 1137.00i | 0.276054 | + | 1.36659i | ||||
\(833\) | −577.327 | −0.693069 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −113.150 | − | 1700.54i | −0.135347 | − | 2.03414i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 525.967 | − | 562.127i | 0.627646 | − | 0.670796i | ||||
\(839\) | − | 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 | ||||||||
\(842\) | −793.335 | − | 742.303i | −0.942203 | − | 0.881594i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 966.739 | − | 64.3248i | 1.14543 | − | 0.0762142i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 201.166i | 0.237504i | ||||||||
\(848\) | 953.906 | − | 127.506i | 1.12489 | − | 0.150361i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 195.409i | − | 0.229623i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 742.887 | 0.870911 | 0.435456 | − | 0.900210i | \(-0.356587\pi\) | ||||
0.435456 | + | 0.900210i | \(0.356587\pi\) | |||||||
\(854\) | 87.5790 | − | 93.6000i | 0.102552 | − | 0.109602i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1071.30 | − | 876.537i | −1.25152 | − | 1.02399i | ||||
\(857\) | 679.145 | 0.792468 | 0.396234 | − | 0.918150i | \(-0.370317\pi\) | ||||
0.396234 | + | 0.918150i | \(0.370317\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 756.133i | − | 0.880248i | −0.897937 | − | 0.440124i | \(-0.854934\pi\) | ||
0.897937 | − | 0.440124i | \(-0.145066\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1063.37 | + | 1136.48i | −1.23361 | + | 1.31842i | ||||
\(863\) | 1130.05i | 1.30944i | 0.755871 | + | 0.654721i | \(0.227214\pi\) | ||||
−0.755871 | + | 0.654721i | \(0.772786\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 7.67137 | + | 7.17790i | 0.00885840 | + | 0.00828856i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −12.1478 | − | 182.569i | −0.0139951 | − | 0.210333i | ||||
\(869\) | −1561.10 | −1.79643 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2382.65i | 2.73554i | ||||||||
\(872\) | 823.208 | − | 1006.13i | 0.944046 | − | 1.15381i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 449.992 | + | 421.046i | 0.514865 | + | 0.481746i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −910.607 | −1.03832 | −0.519160 | − | 0.854677i | \(-0.673755\pi\) | ||||
−0.519160 | + | 0.854677i | \(0.673755\pi\) | |||||||
\(878\) | −284.637 | + | 304.205i | −0.324188 | + | 0.346475i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 405.402 | 0.460161 | 0.230080 | − | 0.973172i | \(-0.426101\pi\) | ||||
0.230080 | + | 0.973172i | \(0.426101\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 819.868i | − | 0.928503i | −0.885703 | − | 0.464252i | \(-0.846323\pi\) | ||
0.885703 | − | 0.464252i | \(-0.153677\pi\) | |||||||
\(884\) | 61.0752 | + | 917.901i | 0.0690896 | + | 1.03835i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1005.48 | − | 1074.60i | 1.13485 | − | 1.21287i | ||||
\(887\) | − | 1003.99i | − | 1.13190i | −0.824440 | − | 0.565949i | \(-0.808510\pi\) | ||
0.824440 | − | 0.565949i | \(-0.191490\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −277.961 | −0.312667 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −998.010 | + | 66.4055i | −1.11885 | + | 0.0744456i | ||||
\(893\) | −1396.17 | −1.56346 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −203.849 | − | 125.784i | −0.227510 | − | 0.140384i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 901.296 | + | 843.318i | 1.00367 | + | 0.939107i | ||||
\(899\) | 243.220i | 0.270545i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 763.237 | 0.847100 | ||||||||
\(902\) | −595.800 | + | 636.761i | −0.660532 | + | 0.705943i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 366.722 | − | 448.208i | 0.405666 | − | 0.495805i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 361.629i | − | 0.398709i | −0.979927 | − | 0.199354i | \(-0.936116\pi\) | ||
0.979927 | − | 0.199354i | \(-0.0638845\pi\) | |||||||
\(908\) | 241.325 | − | 16.0572i | 0.265776 | − | 0.0176842i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 294.475i | − | 0.323244i | −0.986853 | − | 0.161622i | \(-0.948327\pi\) | ||
0.986853 | − | 0.161622i | \(-0.0516725\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 864.965 | 0.947388 | ||||||||
\(914\) | 471.341 | + | 441.022i | 0.515691 | + | 0.482518i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 20.7802 | + | 312.306i | 0.0226858 | + | 0.340945i | ||||
\(917\) | 50.0182 | 0.0545454 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 17.4246i | − | 0.0189604i | −0.999955 | − | 0.00948022i | \(-0.996982\pi\) | ||
0.999955 | − | 0.00948022i | \(-0.00301769\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 743.395 | + | 695.575i | 0.806285 | + | 0.754420i | ||||
\(923\) | 944.209i | 1.02298i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1013.88 | − | 1083.59i | 1.09491 | − | 1.17018i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 259.270 | + | 184.821i | 0.279386 | + | 0.199161i | ||||
\(929\) | 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 | ||||||
\(932\) | 43.7495 | + | 657.513i | 0.0469416 | + | 0.705486i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 424.549 | − | 453.736i | 0.454549 | − | 0.485799i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 802.514 | 0.856471 | 0.428236 | − | 0.903667i | \(-0.359135\pi\) | ||||
0.428236 | + | 0.903667i | \(0.359135\pi\) | |||||||
\(938\) | −359.271 | − | 336.160i | −0.383018 | − | 0.358380i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 730.288 | 0.776076 | 0.388038 | − | 0.921643i | \(-0.373153\pi\) | ||||
0.388038 | + | 0.921643i | \(0.373153\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 315.318i | − | 0.334378i | ||||||
\(944\) | −235.171 | − | 1759.37i | −0.249122 | − | 1.86374i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1244.48 | + | 1164.43i | 1.31552 | + | 1.23090i | ||||
\(947\) | 882.383i | 0.931767i | 0.884846 | + | 0.465884i | \(0.154263\pi\) | ||||
−0.884846 | + | 0.465884i | \(0.845737\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1128.23 | −1.18887 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −147.023 | − | 120.294i | −0.154436 | − | 0.126359i | ||||
\(953\) | −1047.62 | −1.09929 | −0.549644 | − | 0.835399i | \(-0.685237\pi\) | ||||
−0.549644 | + | 0.835399i | \(0.685237\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −972.811 | + | 64.7288i | −1.01759 | + | 0.0677080i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 654.689 | − | 699.698i | 0.683391 | − | 0.730374i | ||||
\(959\) | − | 237.573i | − | 0.247730i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 363.490 | 0.378242 | ||||||||
\(962\) | 473.149 | + | 442.712i | 0.491838 | + | 0.460200i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 101.842 | + | 1530.59i | 0.105646 | + | 1.58775i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 519.528i | 0.537258i | 0.963244 | + | 0.268629i | \(0.0865705\pi\) | ||||
−0.963244 | + | 0.268629i | \(0.913430\pi\) | |||||||
\(968\) | 544.580 | − | 665.587i | 0.562583 | − | 0.687589i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 398.406i | 0.410305i | 0.978730 | + | 0.205152i | \(0.0657690\pi\) | ||||
−0.978730 | + | 0.205152i | \(0.934231\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 38.7393 | 0.0398143 | ||||||||
\(974\) | 782.788 | − | 836.604i | 0.803684 | − | 0.858937i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −543.154 | + | 72.6021i | −0.556510 | + | 0.0743874i | ||||
\(977\) | 367.857 | 0.376517 | 0.188258 | − | 0.982120i | \(-0.439716\pi\) | ||||
0.188258 | + | 0.982120i | \(0.439716\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2193.66i | 2.24071i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0.355984 | − | 0.380457i | 0.000362509 | − | 0.000387431i | ||||
\(983\) | 1473.69i | 1.49918i | 0.661902 | + | 0.749590i | \(0.269749\pi\) | ||||
−0.661902 | + | 0.749590i | \(0.730251\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 184.386 | + | 172.525i | 0.187004 | + | 0.174975i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2038.97 | + | 135.669i | −2.06374 | + | 0.137317i | ||||
\(989\) | −616.257 | −0.623111 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 753.090i | 0.759929i | 0.925001 | + | 0.379964i | \(0.124064\pi\) | ||||
−0.925001 | + | 0.379964i | \(0.875936\pi\) | |||||||
\(992\) | −454.044 | + | 636.941i | −0.457705 | + | 0.642078i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −142.374 | − | 133.215i | −0.143233 | − | 0.134019i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −767.370 | −0.769679 | −0.384839 | − | 0.922984i | \(-0.625743\pi\) | ||||
−0.384839 | + | 0.922984i | \(0.625743\pi\) | |||||||
\(998\) | 639.112 | − | 683.050i | 0.640393 | − | 0.684419i | ||||
\(999\) | 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.c.o.451.8 | 8 | ||
3.2 | odd | 2 | inner | 900.3.c.o.451.1 | 8 | ||
4.3 | odd | 2 | inner | 900.3.c.o.451.7 | 8 | ||
5.2 | odd | 4 | 900.3.f.i.199.8 | 16 | |||
5.3 | odd | 4 | 900.3.f.i.199.9 | 16 | |||
5.4 | even | 2 | 180.3.c.c.91.1 | ✓ | 8 | ||
12.11 | even | 2 | inner | 900.3.c.o.451.2 | 8 | ||
15.2 | even | 4 | 900.3.f.i.199.10 | 16 | |||
15.8 | even | 4 | 900.3.f.i.199.7 | 16 | |||
15.14 | odd | 2 | 180.3.c.c.91.8 | yes | 8 | ||
20.3 | even | 4 | 900.3.f.i.199.6 | 16 | |||
20.7 | even | 4 | 900.3.f.i.199.11 | 16 | |||
20.19 | odd | 2 | 180.3.c.c.91.2 | yes | 8 | ||
40.19 | odd | 2 | 2880.3.e.i.2431.6 | 8 | |||
40.29 | even | 2 | 2880.3.e.i.2431.7 | 8 | |||
60.23 | odd | 4 | 900.3.f.i.199.12 | 16 | |||
60.47 | odd | 4 | 900.3.f.i.199.5 | 16 | |||
60.59 | even | 2 | 180.3.c.c.91.7 | yes | 8 | ||
120.29 | odd | 2 | 2880.3.e.i.2431.3 | 8 | |||
120.59 | even | 2 | 2880.3.e.i.2431.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
180.3.c.c.91.1 | ✓ | 8 | 5.4 | even | 2 | ||
180.3.c.c.91.2 | yes | 8 | 20.19 | odd | 2 | ||
180.3.c.c.91.7 | yes | 8 | 60.59 | even | 2 | ||
180.3.c.c.91.8 | yes | 8 | 15.14 | odd | 2 | ||
900.3.c.o.451.1 | 8 | 3.2 | odd | 2 | inner | ||
900.3.c.o.451.2 | 8 | 12.11 | even | 2 | inner | ||
900.3.c.o.451.7 | 8 | 4.3 | odd | 2 | inner | ||
900.3.c.o.451.8 | 8 | 1.1 | even | 1 | trivial | ||
900.3.f.i.199.5 | 16 | 60.47 | odd | 4 | |||
900.3.f.i.199.6 | 16 | 20.3 | even | 4 | |||
900.3.f.i.199.7 | 16 | 15.8 | even | 4 | |||
900.3.f.i.199.8 | 16 | 5.2 | odd | 4 | |||
900.3.f.i.199.9 | 16 | 5.3 | odd | 4 | |||
900.3.f.i.199.10 | 16 | 15.2 | even | 4 | |||
900.3.f.i.199.11 | 16 | 20.7 | even | 4 | |||
900.3.f.i.199.12 | 16 | 60.23 | odd | 4 | |||
2880.3.e.i.2431.2 | 8 | 120.59 | even | 2 | |||
2880.3.e.i.2431.3 | 8 | 120.29 | odd | 2 | |||
2880.3.e.i.2431.6 | 8 | 40.19 | odd | 2 | |||
2880.3.e.i.2431.7 | 8 | 40.29 | even | 2 |