Generating aliased frequencies from Doodson coefficients

doodson_iter.py

import itertools

def frequency(i, j, k):
    return (365.242 * i / 27.3216 + j / 8.848 + k / 18.6) % 1.0

def main():
    indices = range(-4, 5)
    rows = []
    for i, j, k in itertools.product(indices, repeat=3):
        f = frequency(i, j, k)
        rows.append((i, j, k, f))
    # Print Markdown table
    print("| i | j | k | frequency | complement | ")
    print("| --- | --- | --- | --- | --- | ")
    for i, j, k, f in rows:
        if i > -1:
            print(f"| {i} | {j} | {k} | {f:.6f} |  {1-f:.6f}  |")

if __name__ == "__main__":
    main()
    

i	j	k	frequency	complement
0	-4	-4	0.332867	0.667133
0	-4	-3	0.386630	0.613370
0	-4	-2	0.440394	0.559606
0	-4	-1	0.494157	0.505843
0	-4	0	0.547920	0.452080
0	-4	1	0.601684	0.398316
0	-4	2	0.655447	0.344553
0	-4	3	0.709211	0.290789
0	-4	4	0.762974	0.237026
0	-3	-4	0.445887	0.554113
0	-3	-3	0.499650	0.500350
0	-3	-2	0.553413	0.446587
0	-3	-1	0.607177	0.392823
0	-3	0	0.660940	0.339060
0	-3	1	0.714704	0.285296
0	-3	2	0.768467	0.231533
0	-3	3	0.822231	0.177769
0	-3	4	0.875994	0.124006
0	-2	-4	0.558906	0.441094
0	-2	-3	0.612670	0.387330
0	-2	-2	0.666433	0.333567
0	-2	-1	0.720197	0.279803
0	-2	0	0.773960	0.226040
0	-2	1	0.827724	0.172276
0	-2	2	0.881487	0.118513
0	-2	3	0.935251	0.064749
0	-2	4	0.989014	0.010986
0	-1	-4	0.671926	0.328074
0	-1	-3	0.725690	0.274310
0	-1	-2	0.779453	0.220547
0	-1	-1	0.833217	0.166783
0	-1	0	0.886980	0.113020
0	-1	1	0.940744	0.059256
0	-1	2	0.994507	0.005493
0	-1	3	0.048270	0.951730
0	-1	4	0.102034	0.897966
0	0	-4	0.784946	0.215054
0	0	-3	0.838710	0.161290
0	0	-2	0.892473	0.107527
0	0	-1	0.946237	0.053763
0	0	0	0.000000	1.000000
0	0	1	0.053763	0.946237
0	0	2	0.107527	0.892473
0	0	3	0.161290	0.838710
0	0	4	0.215054	0.784946
0	1	-4	0.897966	0.102034
0	1	-3	0.951730	0.048270
0	1	-2	0.005493	0.994507
0	1	-1	0.059256	0.940744
0	1	0	0.113020	0.886980
0	1	1	0.166783	0.833217
0	1	2	0.220547	0.779453
0	1	3	0.274310	0.725690
0	1	4	0.328074	0.671926
0	2	-4	0.010986	0.989014
0	2	-3	0.064749	0.935251
0	2	-2	0.118513	0.881487
0	2	-1	0.172276	0.827724
0	2	0	0.226040	0.773960
0	2	1	0.279803	0.720197
0	2	2	0.333567	0.666433
0	2	3	0.387330	0.612670
0	2	4	0.441094	0.558906
0	3	-4	0.124006	0.875994
0	3	-3	0.177769	0.822231
0	3	-2	0.231533	0.768467
0	3	-1	0.285296	0.714704
0	3	0	0.339060	0.660940
0	3	1	0.392823	0.607177
0	3	2	0.446587	0.553413
0	3	3	0.500350	0.499650
0	3	4	0.554113	0.445887
0	4	-4	0.237026	0.762974
0	4	-3	0.290789	0.709211
0	4	-2	0.344553	0.655447
0	4	-1	0.398316	0.601684
0	4	0	0.452080	0.547920
0	4	1	0.505843	0.494157
0	4	2	0.559606	0.440394
0	4	3	0.613370	0.386630
0	4	4	0.667133	0.332867
1	-4	-4	0.701117	0.298883
1	-4	-3	0.754881	0.245119
1	-4	-2	0.808644	0.191356
1	-4	-1	0.862408	0.137592
1	-4	0	0.916171	0.083829
1	-4	1	0.969935	0.030065
1	-4	2	0.023698	0.976302
1	-4	3	0.077462	0.922538
1	-4	4	0.131225	0.868775
1	-3	-4	0.814137	0.185863
1	-3	-3	0.867901	0.132099
1	-3	-2	0.921664	0.078336
1	-3	-1	0.975428	0.024572
1	-3	0	0.029191	0.970809
1	-3	1	0.082955	0.917045
1	-3	2	0.136718	0.863282
1	-3	3	0.190481	0.809519
1	-3	4	0.244245	0.755755
1	-2	-4	0.927157	0.072843
1	-2	-3	0.980921	0.019079
1	-2	-2	0.034684	0.965316
1	-2	-1	0.088448	0.911552
1	-2	0	0.142211	0.857789
1	-2	1	0.195974	0.804026
1	-2	2	0.249738	0.750262
1	-2	3	0.303501	0.696499
1	-2	4	0.357265	0.642735
1	-1	-4	0.040177	0.959823
1	-1	-3	0.093941	0.906059
1	-1	-2	0.147704	0.852296
1	-1	-1	0.201467	0.798533
1	-1	0	0.255231	0.744769
1	-1	1	0.308994	0.691006
1	-1	2	0.362758	0.637242
1	-1	3	0.416521	0.583479
1	-1	4	0.470285	0.529715
1	0	-4	0.153197	0.846803
1	0	-3	0.206960	0.793040
1	0	-2	0.260724	0.739276
1	0	-1	0.314487	0.685513
1	0	0	0.368251	0.631749
1	0	1	0.422014	0.577986
1	0	2	0.475778	0.524222
1	0	3	0.529541	0.470459
1	0	4	0.583305	0.416695
1	1	-4	0.266217	0.733783
1	1	-3	0.319980	0.680020
1	1	-2	0.373744	0.626256
1	1	-1	0.427507	0.572493
1	1	0	0.481271	0.518729
1	1	1	0.535034	0.464966
1	1	2	0.588798	0.411202
1	1	3	0.642561	0.357439
1	1	4	0.696324	0.303676
1	2	-4	0.379237	0.620763
1	2	-3	0.433000	0.567000
1	2	-2	0.486764	0.513236
1	2	-1	0.540527	0.459473
1	2	0	0.594291	0.405709
1	2	1	0.648054	0.351946
1	2	2	0.701817	0.298183
1	2	3	0.755581	0.244419
1	2	4	0.809344	0.190656
1	3	-4	0.492257	0.507743
1	3	-3	0.546020	0.453980
1	3	-2	0.599784	0.400216
1	3	-1	0.653547	0.346453
1	3	0	0.707310	0.292690
1	3	1	0.761074	0.238926
1	3	2	0.814837	0.185163
1	3	3	0.868601	0.131399
1	3	4	0.922364	0.077636
1	4	-4	0.605277	0.394723
1	4	-3	0.659040	0.340960
1	4	-2	0.712803	0.287197
1	4	-1	0.766567	0.233433
1	4	0	0.820330	0.179670
1	4	1	0.874094	0.125906
1	4	2	0.927857	0.072143
1	4	3	0.981621	0.018379
1	4	4	0.035384	0.964616
2	-4	-4	0.069368	0.930632
2	-4	-3	0.123132	0.876868
2	-4	-2	0.176895	0.823105
2	-4	-1	0.230659	0.769341
2	-4	0	0.284422	0.715578
2	-4	1	0.338185	0.661815
2	-4	2	0.391949	0.608051
2	-4	3	0.445712	0.554288
2	-4	4	0.499476	0.500524
2	-3	-4	0.182388	0.817612
2	-3	-3	0.236152	0.763848
2	-3	-2	0.289915	0.710085
2	-3	-1	0.343678	0.656322
2	-3	0	0.397442	0.602558
2	-3	1	0.451205	0.548795
2	-3	2	0.504969	0.495031
2	-3	3	0.558732	0.441268
2	-3	4	0.612496	0.387504
2	-2	-4	0.295408	0.704592
2	-2	-3	0.349171	0.650829
2	-2	-2	0.402935	0.597065
2	-2	-1	0.456698	0.543302
2	-2	0	0.510462	0.489538
2	-2	1	0.564225	0.435775
2	-2	2	0.617989	0.382011
2	-2	3	0.671752	0.328248
2	-2	4	0.725516	0.274484
2	-1	-4	0.408428	0.591572
2	-1	-3	0.462191	0.537809
2	-1	-2	0.515955	0.484045
2	-1	-1	0.569718	0.430282
2	-1	0	0.623482	0.376518
2	-1	1	0.677245	0.322755
2	-1	2	0.731009	0.268991
2	-1	3	0.784772	0.215228
2	-1	4	0.838535	0.161465
2	0	-4	0.521448	0.478552
2	0	-3	0.575211	0.424789
2	0	-2	0.628975	0.371025
2	0	-1	0.682738	0.317262
2	0	0	0.736502	0.263498
2	0	1	0.790265	0.209735
2	0	2	0.844028	0.155972
2	0	3	0.897792	0.102208
2	0	4	0.951555	0.048445
2	1	-4	0.634468	0.365532
2	1	-3	0.688231	0.311769
2	1	-2	0.741995	0.258005
2	1	-1	0.795758	0.204242
2	1	0	0.849521	0.150479
2	1	1	0.903285	0.096715
2	1	2	0.957048	0.042952
2	1	3	0.010812	0.989188
2	1	4	0.064575	0.935425
2	2	-4	0.747488	0.252512
2	2	-3	0.801251	0.198749
2	2	-2	0.855014	0.144986
2	2	-1	0.908778	0.091222
2	2	0	0.962541	0.037459
2	2	1	0.016305	0.983695
2	2	2	0.070068	0.929932
2	2	3	0.123832	0.876168
2	2	4	0.177595	0.822405
2	3	-4	0.860507	0.139493
2	3	-3	0.914271	0.085729
2	3	-2	0.968034	0.031966
2	3	-1	0.021798	0.978202
2	3	0	0.075561	0.924439
2	3	1	0.129325	0.870675
2	3	2	0.183088	0.816912
2	3	3	0.236852	0.763148
2	3	4	0.290615	0.709385
2	4	-4	0.973527	0.026473
2	4	-3	0.027291	0.972709
2	4	-2	0.081054	0.918946
2	4	-1	0.134818	0.865182
2	4	0	0.188581	0.811419
2	4	1	0.242345	0.757655
2	4	2	0.296108	0.703892
2	4	3	0.349871	0.650129
2	4	4	0.403635	0.596365
3	-4	-4	0.437619	0.562381
3	-4	-3	0.491382	0.508618
3	-4	-2	0.545146	0.454854
3	-4	-1	0.598909	0.401091
3	-4	0	0.652673	0.347327
3	-4	1	0.706436	0.293564
3	-4	2	0.760200	0.239800
3	-4	3	0.813963	0.186037
3	-4	4	0.867726	0.132274
3	-3	-4	0.550639	0.449361
3	-3	-3	0.604402	0.395598
3	-3	-2	0.658166	0.341834
3	-3	-1	0.711929	0.288071
3	-3	0	0.765693	0.234307
3	-3	1	0.819456	0.180544
3	-3	2	0.873219	0.126781
3	-3	3	0.926983	0.073017
3	-3	4	0.980746	0.019254
3	-2	-4	0.663659	0.336341
3	-2	-3	0.717422	0.282578
3	-2	-2	0.771186	0.228814
3	-2	-1	0.824949	0.175051
3	-2	0	0.878713	0.121287
3	-2	1	0.932476	0.067524
3	-2	2	0.986239	0.013761
3	-2	3	0.040003	0.959997
3	-2	4	0.093766	0.906234
3	-1	-4	0.776679	0.223321
3	-1	-3	0.830442	0.169558
3	-1	-2	0.884206	0.115794
3	-1	-1	0.937969	0.062031
3	-1	0	0.991732	0.008268
3	-1	1	0.045496	0.954504
3	-1	2	0.099259	0.900741
3	-1	3	0.153023	0.846977
3	-1	4	0.206786	0.793214
3	0	-4	0.889699	0.110301
3	0	-3	0.943462	0.056538
3	0	-2	0.997225	0.002775
3	0	-1	0.050989	0.949011
3	0	0	0.104752	0.895248
3	0	1	0.158516	0.841484
3	0	2	0.212279	0.787721
3	0	3	0.266043	0.733957
3	0	4	0.319806	0.680194
3	1	-4	0.002718	0.997282
3	1	-3	0.056482	0.943518
3	1	-2	0.110245	0.889755
3	1	-1	0.164009	0.835991
3	1	0	0.217772	0.782228
3	1	1	0.271536	0.728464
3	1	2	0.325299	0.674701
3	1	3	0.379062	0.620938
3	1	4	0.432826	0.567174
3	2	-4	0.115738	0.884262
3	2	-3	0.169502	0.830498
3	2	-2	0.223265	0.776735
3	2	-1	0.277029	0.722971
3	2	0	0.330792	0.669208
3	2	1	0.384556	0.615444
3	2	2	0.438319	0.561681
3	2	3	0.492082	0.507918
3	2	4	0.545846	0.454154
3	3	-4	0.228758	0.771242
3	3	-3	0.282522	0.717478
3	3	-2	0.336285	0.663715
3	3	-1	0.390049	0.609951
3	3	0	0.443812	0.556188
3	3	1	0.497575	0.502425
3	3	2	0.551339	0.448661
3	3	3	0.605102	0.394898
3	3	4	0.658866	0.341134
3	4	-4	0.341778	0.658222
3	4	-3	0.395542	0.604458
3	4	-2	0.449305	0.550695
3	4	-1	0.503068	0.496932
3	4	0	0.556832	0.443168
3	4	1	0.610595	0.389405
3	4	2	0.664359	0.335641
3	4	3	0.718122	0.281878
3	4	4	0.771886	0.228114
4	-4	-4	0.805870	0.194130
4	-4	-3	0.859633	0.140367
4	-4	-2	0.913397	0.086603
4	-4	-1	0.967160	0.032840
4	-4	0	0.020923	0.979077
4	-4	1	0.074687	0.925313
4	-4	2	0.128450	0.871550
4	-4	3	0.182214	0.817786
4	-4	4	0.235977	0.764023
4	-3	-4	0.918890	0.081110
4	-3	-3	0.972653	0.027347
4	-3	-2	0.026416	0.973584
4	-3	-1	0.080180	0.919820
4	-3	0	0.133943	0.866057
4	-3	1	0.187707	0.812293
4	-3	2	0.241470	0.758530
4	-3	3	0.295234	0.704766
4	-3	4	0.348997	0.651003
4	-2	-4	0.031909	0.968091
4	-2	-3	0.085673	0.914327
4	-2	-2	0.139436	0.860564
4	-2	-1	0.193200	0.806800
4	-2	0	0.246963	0.753037
4	-2	1	0.300727	0.699273
4	-2	2	0.354490	0.645510
4	-2	3	0.408254	0.591746
4	-2	4	0.462017	0.537983
4	-1	-4	0.144929	0.855071
4	-1	-3	0.198693	0.801307
4	-1	-2	0.252456	0.747544
4	-1	-1	0.306220	0.693780
4	-1	0	0.359983	0.640017
4	-1	1	0.413747	0.586253
4	-1	2	0.467510	0.532490
4	-1	3	0.521273	0.478727
4	-1	4	0.575037	0.424963
4	0	-4	0.257949	0.742051
4	0	-3	0.311713	0.688287
4	0	-2	0.365476	0.634524
4	0	-1	0.419240	0.580760
4	0	0	0.473003	0.526997
4	0	1	0.526766	0.473234
4	0	2	0.580530	0.419470
4	0	3	0.634293	0.365707
4	0	4	0.688057	0.311943
4	1	-4	0.370969	0.629031
4	1	-3	0.424733	0.575267
4	1	-2	0.478496	0.521504
4	1	-1	0.532259	0.467741
4	1	0	0.586023	0.413977
4	1	1	0.639786	0.360214
4	1	2	0.693550	0.306450
4	1	3	0.747313	0.252687
4	1	4	0.801077	0.198923
4	2	-4	0.483989	0.516011
4	2	-3	0.537753	0.462247
4	2	-2	0.591516	0.408484
4	2	-1	0.645279	0.354721
4	2	0	0.699043	0.300957
4	2	1	0.752806	0.247194
4	2	2	0.806570	0.193430
4	2	3	0.860333	0.139667
4	2	4	0.914097	0.085903
4	3	-4	0.597009	0.402991
4	3	-3	0.650772	0.349228
4	3	-2	0.704536	0.295464
4	3	-1	0.758299	0.241701
4	3	0	0.812063	0.187937
4	3	1	0.865826	0.134174
4	3	2	0.919590	0.080410
4	3	3	0.973353	0.026647
4	3	4	0.027116	0.972884
4	4	-4	0.710029	0.289971
4	4	-3	0.763792	0.236208
4	4	-2	0.817556	0.182444
4	4	-1	0.871319	0.128681
4	4	0	0.925083	0.074917
4	4	1	0.978846	0.021154
4	4	2	0.032609	0.967391
4	4	3	0.086373	0.913627
4	4	4	0.140136	0.859864