-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2708317540011803295708822260423', 'a10': [3.1463654890329087, 0.0], 'a2': [2.3429230827771703, 0.0], 'a3': [1.1463654890329085, 0.0], 'a4': [3.4892885718100786, 0.0], 'a5': [1.3429230827771703, 0.0], 'a6': [2.6858461655543406, 0.0], 'a7': [0.0, 0.0], 'a8': [3.4892885718100786, 0.0], 'a9': [-1.6858461655543404, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.086470608755563, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [7, 13], 'central_character': '637.1', 'coefficient_field': 'CDF', 'conductor': 637, 'conductor_radical': 91, 'conjugate': '2708317540011803295708822260423', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.3429230827771703, 0], [2.0, 0]], [[1.0, 0], [-1.1463654890329085, 0], [3.0, 0]], [[1.0, 0], [-1.3429230827771703, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.1463654890329085, 0], [11.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [5.832211654587249, 0], [17.0, 0]], [[1.0, 0], [-3.3429230827771703, 0], [19.0, 0]], [[1.0, 0], [3.175134737364419, 0], [23.0, 0]], [[1.0, 0], [-10.489288571810079, 0], [29.0, 0]], [[1.0, 0], [1.6356540608429873, 0], [31.0, 0]], [[1.0, 0], [-8.518057820141589, 0], [37.0, 0]], [[1.0, 0], [-0.2927309780658171, 0], [41.0, 0]], [[1.0, 0], [8.153711880984577, 0], [43.0, 0]], [[1.0, 0], [-10.614231204463145, 0], [47.0, 0]], [[1.0, 0], [0.7820195498758958, 0], [53.0, 0]], [[1.0, 0], [12.643000452794656, 0], [59.0, 0]], [[1.0, 0], [-2.0, 0], [61.0, 0]], [[1.0, 0], [6.100384209422706, 0], [67.0, 0]], [[1.0, 0], [-1.539480676521432, 0], [71.0, 0]], [[1.0, 0], [-15.300077370017485, 0], [73.0, 0]], [[1.0, 0], [-0.882403759298602, 0], [79.0, 0]], [[1.0, 0], [-12.129153457754217, 0], [83.0, 0]], [[1.0, 0], [5.736038270265693, 0], [89.0, 0]], [[1.0, 0], [-5.34292308277717, 0], [97.0, 0]], [[1.0, 0], [11.146365489032908, 0], [101.0, 0]], [[1.0, 0], [-3.4145380438683657, 0], [103.0, 0]], [[1.0, 0], [-4.978577143620157, 0], [107.0, 0]], [[1.0, 0], [13.496634963761746, 0], [109.0, 0]], [[1.0, 0], [-16.446442859050393, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 31, 'label': '2-637-1.1-c1-0-31', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/637/2/a/j/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [4.517336931641711, 4.5273154111038325, 4.553472579863194, 4.585154822888985, 4.606639047499764, 4.599519709989199, 4.545158015120887, 4.426894785232914, 4.231930090212902, 3.9528576900041847, 3.588832847352901, 3.146307702868523, 2.6392337158217596, 2.0886262124413983, 1.5214164007390654, 0.9685776563965889, 0.46259745787867773, 0.034463023689583164, -0.28957600419137836, -0.49112570063646965, -0.5622577364112447, -0.50722029775085, -0.34291241057793587, -0.09789460306086863, 0.19012858590026882, 0.478218885925235, 0.7231583288014853, 0.8869007280706065, 0.9418267279006022, 0.875042214835595, 0.6909989386420586, 0.41187191228648795, 0.07539465986462544, -0.2697946103450703, -0.5708491586464475, -0.778628322558235, -0.8557111793019382, -0.7832376282916931, -0.5653433180793792, -0.23020467791388213, 0.17284015323135354, 0.5800284850358618, 0.9230345125824255, 1.1405935267917986, 1.190056336365958, 1.0568324288261217, 0.7598070471314361, 0.35130246034551865, -0.08904218441425596, -0.46607859853799344, -0.685173964605567, -0.6700376711176423, -0.3793156003144197, 0.18122177452272725, 0.9536428806818923, 1.8317283599926388, 2.6740818987546153, 3.3251464814159877, 3.641189342486085, 3.517078114319697, 2.909069993572995, 1.849061284741279, 0.4468452393421895, -1.1212125786754248, -2.6363239736883544, -3.8710580684853095, -4.627487182366131, -4.773164750121531, -4.268251113916369, -3.178203176048299, -1.668692608866353, 0.01752266320317105, 1.5987048351084725, 2.801151640608156, 3.407007913346083, 3.294141487494134, 2.4603777336677415, 1.0269633746181088, -0.7801573550283633, -2.6684947388661784, -4.33000333940601, -5.4956213024815375, -5.983106850814831, -5.72896381943304, -4.798172298672739, -3.3697170617552112, -1.7006992373189505, -0.07614416976920184, 1.2454412980688512, 2.0798147470067723, 2.348491812208285, 2.087859803546414, 1.4345427585226356, 0.5907210516392718, -0.2226221567453072, -0.8140498629632869, -1.0609778516910082, -0.9315429879727448, -0.4847815081925685, 0.15004019022819126, 0.8092495252569885, 1.3366027753098664, 1.6207724100340677, 1.6194537145373944, 1.3646081234303342, 0.9482597330950964, 0.49327772685075016, 0.1174260147245819, -0.09936878436216423, -0.13555600603581758, -0.030736601383551852, 0.12992712263795533, 0.2450559555270381, 0.2315038945851837, 0.053565189196167005, -0.26220881013659414, -0.6318385030188838, -0.938035472637592, -1.0674321117221568, -0.9503532672848313, -0.590961369986266, -0.07744592946935151, 0.43306635376892144, 0.7532208667612592, 0.7189763207483063, 0.24393598882747394, -0.6413053740036715, -1.7779891820346716, -2.90283239138354, -3.704074409266884, -3.898289602153588, -3.3094216135147043, -1.929023408127039, 0.06030918681009801, 2.3082080949125086, 4.3649613697958785, 5.7815930828349185, 6.218766829690642, 5.537664888287543, 3.848697428064741, 1.503038201252505, -0.9744482438895321, -2.9976297780605266, -4.051580786746021, -3.8136799678221687, -2.233541283816762, 0.4487323780619606, 3.7517022994852707, 7.058270433421192, 9.752817733471895, 11.356737091468043, 11.629650143745913, 10.612327152586042, 8.60221374006347, 6.069616502720278, 3.5374792749656403, 1.4563485293459684, 0.10631139553950827, -0.4505612699220433, -0.35806154999248796, 0.09884423422044307, 0.5901912868379217, 0.8400718339563729, 0.7006930991637002, 0.1821627415316929, -0.5674752005570757, -1.3225809347713002, -1.8597484459272413, -2.0313877289223616, -1.810429820074637, -1.2934567665684984, -0.663124367658194, -0.12367367625674817, 0.16841403562095672, 0.15551677653467208, -0.10495537007972316, -0.46422018559141875, -0.737217927573037, -0.7702374258993592, -0.4979110907990753, 0.030153244483813565, 0.6627691927025321, 1.1968090600014945, 1.4468734890584394, 1.311567432521927, 0.8134742838388915, 0.09819648366016226, -0.6086996245959682, -1.0737123373939772, -1.1329735813010662, -0.7492044121936093, -0.027963223349745214, 0.8137876523861366, 1.5177629549407328, 1.8704690300379767, 1.7763085321072127, 1.2918644498531102, 0.6077982601761016, -0.01768287367688813, -0.35275787968531214, -0.2815217231094432, 0.1431080805111238, 0.7046496819395807, 1.0892076021006476, 0.9941943555830688, 0.24502695722512693, -1.1204622305020042, -2.832578361908651, -4.4487587172937495, -5.479273875545263, -5.544626458381438, -4.516112468894382, -2.592317420087542, -0.28100297948352926, 1.7165220767568765, 2.691067673561807, 2.1301771429513736, -0.11840148700368935, -3.775339048380754, -8.176168401744778, -12.427176585180376, -15.629667102892695, -17.110323336772552, -16.59252056642907, -14.26007320967994, -10.69621209844459, -6.717078211832466, -3.1495216320950647, -0.6181727639102087, 0.5979201518186145, 0.6015937395337179, -0.197161182170536, -1.23738614052939, -1.9921432498627372, -2.1239863735490476, -1.5655206064456324, -0.5063059549245609, 0.7014446358629202, 1.680557835592755, 2.1607187321212167, 2.0607688461811655, 1.4978061710725818, 0.7262408961083168, 0.03408915591464988, -0.36305254154632405, -0.3918370429457404, -0.13193483626865696, 0.23197596401079632, 0.49479719620834506, 0.517312317516944, 0.2803350172769846, -0.11327931306314862, -0.48756152274776776, -0.6718794281493408, -0.5760434346399832, -0.23090533765612323, 0.22255095622332038], 'positive_zeros': ['2.13648582623965500768110420761025', '2.91868243165336358882903193606621', '4.02691821596254686839092015711278', '4.94775821718714729055606283018232', '5.97417129810271293235761021519506', '6.59010937519673736239124424301734', '7.78625288877059975270319363518016', '8.873697915208596104311527575212451', '9.697945126639058778520668004482669', '10.88133094215117859094217182785044'], 'prelabel': '2-637-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.13648582623965500768110420761', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.91868243165336358882903193607', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.02691821596254686839092015711', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 5.086470608755563, 'bad_primes': [7, 13], 'central_character': '1.1', 'conductor': 637, 'conductor_radical': 91, 'degree': 2, 'index': 31, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/637/2/a/j/1/3'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-637-1.1-c1-0-31', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-637-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.13648582623965500768110420761', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2708317540011803295708822260423', 'Lhash_array': ['2708317540011803295708822260423'], 'label': '2-637-1.1-c1-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/a/j/1/3'}