const double catalog[][3] = { // { RA (rad), declination (rad), luminosity ((100^-1/5)^mag) }
	{0.02254,0.78940,0.00209},
	{0.02209,-0.00878,0.00305},
	{0.02328,-0.09961,0.01432},
	{0.02487,0.23381,0.00625},
	{0.02734,1.01991,0.00413},
	{0.02756,-0.85652,0.00525},
	{0.02811,1.12043,0.00581},
	{0.02886,0.50652,0.00353},
	{0.02982,-0.40330,0.00337},
	{0.03187,-0.30345,0.00334},
	{0.03375,-0.04449,0.00268},
	{0.03395,-0.39285,0.00421},
	{0.03516,-0.58520,0.00535},
	{0.03579,-0.04272,0.00373},
	{0.03660,0.50773,0.14997},
	{0.03617,-0.15401,0.00402},
	{0.03789,0.63926,0.00334},
	{0.03734,-0.30679,0.00377},
	{0.03870,0.44441,0.00322},
	{0.04074,1.39128,0.00394},
	{0.04005,1.03236,0.12359},
	{0.03944,0.31786,0.00614},
	{0.03944,-0.94251,0.00294},
	{0.04080,-0.48848,0.00679},
	{0.04107,-0.79844,0.02805},
	{0.04380,0.19453,0.00625},
	{0.04504,0.80411,0.00973},
	{0.04579,0.99773,0.00201},
	{0.04500,-0.09161,0.00461},
	{0.04379,-1.43508,0.00773},
	{0.04675,-0.21956,0.00457},
	{0.04644,-1.27801,0.00221},
	{0.04915,-0.26997,0.01107},
	{0.05050,-0.48520,0.00685},
	{0.05120,-0.61319,0.00794},
	{0.05229,0.84042,0.00344},
	{0.05309,-0.31308,0.00794},
	{0.05603,0.65787,0.00203},
	{0.05776,0.26500,0.07379},
	{0.05847,0.47102,0.00302},
	{0.05896,0.71620,0.00515},
	{0.05978,-0.45417,0.00421},
	{0.05994,-0.45875,0.00299},
	{0.06125,0.57956,0.00316},
	{0.06372,0.35267,0.01202},
	{0.06309,-0.13580,0.00895},
	{0.05813,-1.48343,0.00492},
	{0.06388,-0.33044,0.01675},
	{0.06517,0.38893,0.00319},
	{0.06536,0.15395,0.00483},
	{0.06505,-0.16702,0.00501},
	{0.06596,0.55040,0.00263},
	{0.06622,0.47618,0.00288},
	{0.06532,-0.60920,0.00340},
	{0.07083,1.34305,0.00288},
	{0.07138,0.76087,0.00347},
	{0.07046,-0.54884,0.00540},
	{0.06946,-1.32490,0.00254},
	{0.07229,0.14382,0.00360},
	{0.07397,1.07396,0.00506},
	{0.07290,-0.35274,0.00258},
	{0.07484,0.83684,0.00441},
	{0.07458,0.67512,0.01432},
	{0.07338,-1.37498,0.00196},
	{0.07730,0.89768,0.00350},
	{0.07655,-0.33250,0.00263},
	{0.07765,0.02948,0.00340},
	{0.07997,0.64202,0.01556},
	{0.07979,0.19558,0.00380},
	{0.08160,0.76430,0.00360},
	{0.08133,0.55008,0.00449},
	{0.08158,-0.14055,0.00261},
	{0.08164,-0.75460,0.00294},
	{0.08477,-0.15401,0.03767},
	{0.08593,0.71087,0.00294},
	{0.08764,0.85286,0.00247},
	{0.08758,-1.13228,0.02032},
	{0.08904,0.53993,0.00437},
	{0.09058,0.57441,0.00483},
	{0.08988,0.14295,0.00711},
	{0.09123,0.19158,0.00238},
	{0.09216,0.66268,0.00847},
	{0.09010,-1.21519,0.00625},
	{0.09390,-0.50583,0.00847},
	{0.09500,-0.35007,0.00895},
	{0.09785,0.23531,0.00322},
	{0.09371,-1.35136,0.00409},
	{0.09976,-0.21310,0.00278},
	{0.10127,-0.54168,0.00240},
	{0.10487,0.67330,0.00111},
	{0.10585,0.90792,0.00592},
	{0.10817,1.07916,0.00692},
	{0.10688,-0.03873,0.00373},
	{0.10955,0.92584,0.00506},
	{0.11084,0.03385,0.00492},
	{0.11236,-1.34834,0.07586},
	{0.11468,-0.73838,0.11066},
	{0.11433,-0.76236,0.02655},
	{0.11617,-0.00087,0.00334},
	{0.11888,-0.44588,0.00406},
	{0.12238,0.31229,0.00946},
	{0.12317,0.77483,0.00855},
	{0.12186,-0.57608,0.01191},
	{0.12310,0.28702,0.00377},
	{0.12363,0.17784,0.00384},
	{0.12371,-0.35491,0.00268},
	{0.12409,-0.69665,0.00673},
	{0.12629,0.64403,0.00313},
	{0.12531,-0.88196,0.00313},
	{0.13490,1.34424,0.00328},
	{0.13235,1.04680,0.00421},
	{0.13143,0.51926,0.00809},
	{0.13031,-0.25943,0.00350},
	{0.13009,-0.56054,0.00236},
	{0.13107,-0.06907,0.00515},
	{0.13255,-0.41518,0.00839},
	{0.13292,-0.71453,0.00334},
	{0.13280,-0.84151,0.00530},
	{0.13710,1.16098,0.00337},
	{0.13712,0.58611,0.00449},
	{0.13864,0.95159,0.01282},
	{0.13826,0.92222,0.00575},
	{0.13708,-0.85178,0.01236},
	{0.13764,-1.09883,0.01786},
	{0.13771,-1.09896,0.01528},
	{0.14158,0.75913,0.00209},
	{0.14539,1.23886,0.00270},
	{0.14399,1.09836,0.02168},
	{0.14221,0.35420,0.00705},
	{0.14136,0.12140,0.00540},
	{0.14214,0.48137,0.00215},
	{0.14320,0.49358,0.00302},
	{0.14475,0.95810,0.00425},
	{0.14281,-1.10010,0.00920},
	{0.15016,1.16501,0.00256},
	{0.14698,-0.51589,0.00603},
	{0.14568,-1.24383,0.00353},
	{0.15037,-0.91408,0.00592},
	{0.15237,0.23337,0.00275},
	{0.15380,-0.06271,0.00832},
	{0.15510,-0.00882,0.00425},
	{0.15768,0.94542,0.00929},
	{0.15669,0.23050,0.00273},
	{0.15906,1.05289,0.00483},
	{0.15571,-0.83777,0.00625},
	{0.15515,-0.95682,0.00377},
	{0.15853,0.47568,0.00251},
	{0.15730,-0.26134,0.00263},
	{0.15758,-0.39868,0.00377},
	{0.16047,0.77647,0.00887},
	{0.16132,0.94068,0.03436},
	{0.16093,0.58852,0.01803},
	{0.16052,0.26584,0.00441},
	{0.16197,0.41913,0.00258},
	{0.16298,0.61784,0.00643},
	{0.17361,1.43979,0.00275},
	{0.16295,-0.43227,0.00592},
	{0.15980,-1.13664,0.00270},
	{0.16366,0.05472,0.00278},
	{0.16276,-0.94936,0.00273},
	{0.16823,0.51159,0.01786},
	{0.17089,0.86140,0.00673},
	{0.17160,0.53862,0.04920},
	{0.17175,0.37089,0.00449},
	{0.17421,0.37417,0.00718},
	{0.17675,0.98676,0.12823},
	{0.16877,-1.27649,0.00182},
	{0.17438,-0.59274,0.00211},
	{0.17395,-0.78185,0.00394},
	{0.17661,-0.28828,0.00254},
	{0.17693,-0.41547,0.00350},
	{0.17762,-0.07596,0.00433},
	{0.17942,0.68868,0.00738},
	{0.17645,-1.03768,0.00441},
	{0.18351,1.15449,0.00466},
	{0.18151,0.42986,0.00384},
	{0.18354,0.88161,0.01202},
	{0.18032,-0.80433,0.01459},
	{0.18552,1.02544,0.00340},
	{0.18227,-0.98614,0.00525},
	{0.18967,0.82074,0.01057},
	{0.18638,-0.67131,0.00377},
	{0.18630,-1.05178,0.00406},
	{0.18532,-1.14263,0.00698},
	{0.19020,-0.31393,0.15276},
	{0.19391,0.83539,0.00540},
	{0.19127,-0.20964,0.00391},
	{0.18916,-1.00292,0.01803},
	{0.19919,1.30879,0.00545},
	{0.19515,0.84272,0.01528},
	{0.19282,-0.18517,0.01247},
	{0.19287,-0.67058,0.00437},
	{0.19760,0.96380,0.00679},
	{0.19522,-0.38408,0.00802},
	{0.19614,-0.74485,0.00421},
	{0.19434,-1.09079,0.00373},
	{0.20355,1.20995,0.00294},
	{0.19810,-0.08079,0.00347},
	{0.19635,-0.93750,0.00347},
	{0.19844,-0.22481,0.00347},
	{0.20181,0.96526,0.00247},
	{0.20151,0.78298,0.00380},
	{0.19938,-0.28666,0.00258},
	{0.20380,1.03977,0.00278},
	{0.20843,1.30634,0.00685},
	{0.19967,-0.82993,0.00479},
	{0.20157,-0.39308,0.00631},
	{0.20311,0.27010,0.00705},
	{0.21010,1.26842,0.00449},
	{0.20519,0.20898,0.00631},
	{0.20607,0.34172,0.00353},
	{0.20655,0.42354,0.02377},
	{0.20679,0.11765,0.00402},
	{0.20906,0.36521,0.00242},
	{0.20823,-0.31523,0.00525},
	{0.21424,1.00908,0.04207},
	{0.20952,-0.37913,0.00592},
	{0.21070,0.12741,0.00425},
	{0.21111,0.09216,0.00501},
	{0.21308,0.88957,0.01107},
	{0.21242,0.13238,0.01690},
	{0.21371,0.29567,0.00938},
	{0.21735,0.71696,0.01542},
	{0.21566,-0.23669,0.00581},
	{0.21481,-0.42126,0.00437},
	{0.21356,-0.81503,0.00310},
	{0.21764,0.48365,0.00158},
	{0.21767,0.48364,0.00145},
	{0.21623,-0.40774,0.00308},
	{0.22134,1.12133,0.00698},
	{0.21950,0.78544,0.00347},
	{0.21872,-0.18578,0.00839},
	{0.21201,-1.30766,0.00938},
	{0.22372,1.07872,0.00373},
	{0.22234,0.89899,0.00278},
	{0.21844,-0.75738,0.00256},
	{0.23948,1.46097,0.00565},
	{0.22498,0.90009,0.00328},
	{0.22116,-0.88989,0.00817},
	{0.22386,0.05908,0.00283},
	{0.23155,1.06682,0.01180},
	{0.22632,-0.76287,0.00174},
	{0.23078,0.67280,0.00211},
	{0.22985,-0.41898,0.00655},
	{0.23129,-0.01997,0.01236},
	{0.23331,0.65307,0.00377},
	{0.23472,0.91960,0.00310},
	{0.23216,-0.43244,0.00261},
	{0.22866,-1.21308,0.00325},
	{0.23999,1.02927,0.01169},
	{0.23818,0.33490,0.00506},
	{0.23690,-0.15256,0.00344},
	{0.24036,0.84960,0.00310},
	{0.23401,-1.09731,0.00525},
	{0.23984,0.41239,0.00649},
	{0.24105,0.42860,0.00331},
	{0.24528,1.01223,0.00328},
	{0.24839,1.20037,0.00283},
	{0.24424,0.47489,0.00366},
	{0.24307,-0.12823,0.00457},
	{0.24744,1.05971,0.10280},
	{0.24724,1.03291,0.01406},
	{0.24777,1.05353,0.00603},
	{0.24446,-0.19664,0.00752},
	{0.24402,-0.48477,0.00363},
	{0.24763,0.67194,0.02831},
	{0.24000,-1.21347,0.00661},
	{0.24961,0.40871,0.01706},
	{0.25160,0.80005,0.00356},
	{0.25533,1.15806,0.00409},
	{0.25236,0.50601,0.00679},
	{0.25411,0.59255,0.00406},
	{0.25267,0.23904,0.00296},
	{0.25445,0.37358,0.00283},
	{0.26405,1.23889,0.00278},
	{0.25627,-0.19862,0.00570},
	{0.25572,-0.51239,0.01888},
	{0.25470,-1.05935,0.00322},
	{0.26205,0.78036,0.00184},
	{0.26206,0.78039,0.00384},
	{0.26105,0.11315,0.00360},
	{0.29996,1.50547,0.01995},
	{0.40945,1.55361,0.00261},
	{0.27186,0.89073,0.00258},
	{0.26749,-0.67922,0.00581},
	{0.27500,0.82687,0.00263},
	{0.27447,0.72161,0.00406},
	{0.27410,0.55509,0.00631},
	{0.27758,1.06596,0.00429},
	{0.27245,-0.55069,0.00631},
	{0.27464,0.13771,0.01941},
	{0.27066,-0.99488,0.00360},
	{0.27508,-0.08442,0.00673},
	{0.28068,1.07478,0.00461},
	{0.27943,0.91634,0.00402},
	{0.27410,-0.80979,0.00718},
	{0.27617,-0.51532,0.00305},
	{0.27845,0.02385,0.00384},
	{0.28266,0.89029,0.00242},
	{0.28126,0.51764,0.00334},
	{0.27365,-1.14242,0.00328},
	{0.28190,0.69798,0.00205},
	{0.33259,1.52097,0.00316},
	{0.28308,0.09872,0.00398},
	{0.28401,0.26086,0.00535},
	{0.28964,1.09540,0.00242},
	{0.28659,0.37478,0.00731},
	{0.28665,0.37464,0.00597},
	{0.30196,1.39647,0.00305},
	{0.28719,0.08567,0.00288},
	{0.28735,0.08569,0.00126},
	{0.28629,-0.17417,0.00356},
	{0.29236,0.99370,0.00268},
	{0.28835,-0.17173,0.00586},
	{0.29303,0.93372,0.00281},
	{0.29042,0.22613,0.00356},
	{0.28854,-0.41875,0.00350},
	{0.29790,0.95854,0.00855},
	{0.28834,-0.81539,0.04742},
	{0.28991,-0.62240,0.00227},
	{0.29677,0.76693,0.00973},
	{0.29330,-0.41882,0.00283},
	{0.29913,1.01689,0.00483},
	{0.29680,0.55872,0.00316},
	{0.29650,0.36197,0.00603},
	{0.29570,-0.17079,0.00470},
	{0.29832,0.09861,0.00619},
	{0.29583,-0.72408,0.00824},
	{0.29370,-1.07818,0.00711},
	{0.31537,1.39057,0.00555},
	{0.29928,-0.17771,0.04169},
	{0.30327,0.82453,0.01995},
	{0.30829,1.20041,0.00766},
	{0.30426,0.62170,0.14997},
	{0.29839,-0.96422,0.02704},
	{0.30465,0.34311,0.00603},
	{0.30680,0.73446,0.00550},
	{0.30684,0.44432,0.00479},
	{0.31166,1.12055,0.00603},
	{0.31025,0.96254,0.01854},
	{0.30627,0.27357,0.00377},
	{0.31281,1.13479,0.00592},
	{0.30631,-0.15544,0.00275},
	{0.30788,0.04268,0.00417},
	{0.31054,0.65841,0.00474},
	{0.31029,0.54846,0.00863},
	{0.30597,-1.00696,0.00273},
	{0.31177,0.36713,0.01368},
	{0.31268,0.52516,0.01570},
	{0.31296,-0.03929,0.00421},
	{0.31924,1.07697,0.00273},
	{0.31663,0.79129,0.00360},
	{0.31849,0.52472,0.00334},
	{0.33385,1.39469,0.00313},
	{0.31586,-0.53760,0.00247},
	{0.31746,-0.66072,0.00429},
	{0.32179,0.42906,0.01380},
	{0.32172,0.13221,0.00802},
	{0.32182,0.13227,0.00302},
	{0.32325,0.49794,0.00268},
	{0.32344,0.28158,0.00406},
	{0.33249,1.25217,0.00074},
	{0.32463,-0.13828,0.00887},
	{0.32597,0.12209,0.00387},
	{0.32646,-0.01700,0.00525},
	{0.33339,0.83919,0.00227},
	{0.32806,-0.79467,0.01038},
	{0.33298,0.57796,0.00391},
	{0.33635,0.78369,0.00291},
	{0.33425,-0.04364,0.00685},
	{0.33773,0.55405,0.00203},
	{0.35048,1.35386,0.00299},
	{0.34108,0.82763,0.00316},
	{0.33060,-1.20211,0.01138},
	{0.33947,0.06308,0.00863},
	{0.34376,0.65251,0.00261},
	{0.33624,-1.15886,0.00319},
	{0.35773,1.33062,0.00281},
	{0.34942,1.01633,0.01019},
	{0.34674,0.47585,0.01247},
	{0.35381,1.12850,0.00291},
	{0.34822,-0.00888,0.00449},
	{0.36556,1.37402,0.00373},
	{0.35157,-0.05667,0.00322},
	{0.35109,-0.19616,0.00347},
	{0.35397,0.50157,0.00809},
	{0.35928,0.79463,0.01117},
	{0.36373,1.01479,0.00263},
	{0.36048,0.03013,0.00331},
	{0.36032,-0.00785,0.00254},
	{0.36001,-0.33303,0.00288},
	{0.36511,0.65825,0.00586},
	{0.36488,0.59770,0.00305},
	{0.36397,0.35725,0.00409},
	{0.37426,1.23883,0.00254},
	{0.37495,1.18909,0.01271},
	{0.36441,-0.54010,0.00461},
	{0.36670,-0.13976,0.00328},
	{0.36662,-0.14283,0.03631},
	{0.37445,1.05130,0.08472},
	{0.36802,-0.12068,0.00433},
	{0.36941,-0.27332,0.00350},
	{0.37006,-0.04972,0.00347},
	{0.37348,0.41036,0.00337},
	{0.36949,-0.72418,0.00679},
	{0.37660,0.75848,0.00413},
	{0.37588,0.60353,0.00299},
	{0.36957,-0.77717,0.00313},
	{0.37359,-0.25480,0.01096},
	{0.37636,0.33462,0.00705},
	{0.37828,0.33581,0.00631},
	{0.38006,0.60000,0.00310},
	{0.37723,-0.00696,0.00273},
	{0.38247,0.79250,0.01169},
	{0.38154,0.71734,0.00261},
	{0.37914,0.06170,0.00233},
	{0.37127,-1.12346,0.00425},
	{0.37900,-0.22788,0.00545},
	{0.38303,0.70399,0.00229},
	{0.37947,-0.56798,0.00483},
	{0.66240,1.55795,0.15560},
	{0.38300,-0.19027,0.00353},
	{0.38564,0.13895,0.00331},
	{0.39807,1.22635,0.00474},
	{0.39650,1.15363,0.00350},
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