-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1935755433967301766694834455291', 'a10': [0, 0], 'a2': [0, 0], 'a3': [446.72406499988097, -576.0890640777536], 'a4': [0, 0], 'a5': [0, 11638.026026463842], 'a6': [0, 0], 'a7': [24223.09950999357, 0], 'a8': [0, 0], 'a9': [-132316.2194999643, -514705.697013582], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 43.87170322926171, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '6.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-446.72406499988097, 576.0890640777536]]]], 'bad_primes': [2, 3], 'central_character': '48.17', 'coefficient_field': 'CDF', 'conductor': 48, 'conductor_radical': 6, 'conjugate': '499141523140002933373246156822', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-446.72406499988097, 576.0890640777536]], [[1.0, 0], [0, -11638.026026463842], [-244140625.0, 0]], [[1.0, 0], [-24223.09950999357, 0], [13841287201.0, 0]], [[1.0, 0], [0, -1354677.6426163982], [-3138428376721.0, 0]], [[1.0, 0], [5790801.484358483, 0], [23298085122481.0, 0]], [[1.0, 0], [0, 46355457.384045586], [-582622237229761.0, 0]], [[1.0, 0], [-33615897.924242444, 0], [2213314919066161.0, 0]], [[1.0, 0], [0, 186090663.90411726], [-21914624432020320, 0]], [[1.0, 0], [0, -236538341.94062606], [-353814783205469060, 0]], [[1.0, 0], [-52907853.53288163, 0], [787662783788549800, 0]], [[1.0, 0], [4832403789.218003, 0], [6582952005840035000, 0]], [[1.0, 0], [0, 6239916325.105996], [-22563490300366184000, 0]], [[1.0, 0], [-6783286987.694352, 0], [39959630797262580000, 0]], [[1.0, 0], [0, 11981689956.993252], [-116191483108948570000, 0]], [[1.0, 0], [0, 7562349581.559288], [-491258904256726200000, 0]], [[1.0, 0], [0, 50606604071.413895], [-1779197418239532700000, 0]], [[1.0, 0], [51102896107.65187, 0], [2654348974297586300000, 0]], [[1.0, 0], [9111256470.659992, 0], [8182718904632857000000, 0]], [[1.0, 0], [0, -139772499584.76962], [-16409682740640810000000, 0]], [[1.0, 0], [6809462714.191648, 0], [22902048046490260000000, 0]], [[1.0, 0], [321423109799.59424, 0], [59091511031674160000000, 0]], [[1.0, 0], [0, 538395193023.4135], [-106890007738661120000000, 0]], [[1.0, 0], [0, 53885495681.58658], [-246990403565262140000000, 0]], [[1.0, 0], [-70873666262.0111, 0], [693842360995438000000000, 0]], [[1.0, 0], [0, 221868293811.6381], [-1126825030131969800000000, 0]], [[1.0, 0], [-1711651858464.5408, 0], [1425760886846179000000000, 0]], [[1.0, 0], [0, -1996360912880.8901], [-2252191588960823300000000, 0]], [[1.0, 0], [-89177187499.42021, 0], [2812664781782894700000000, 0]], [[1.0, 0], [0, -2336081805706.1885], [-4334523100191687000000000, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 19, 'label': '2-48-3.2-c12-0-19', 'leading_term': '1.61277675158413280431418359838435776218505969330247850', 'load_key': 'CMFs-workshop', 'motivic_weight': 12, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [12], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/48/13/e/d/17/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.08203125', 'prec': 34}, 'plot_values': [1.6127767515841327, 1.9010410075382997, 2.157345873030496, 2.3759195900521526, 2.5517873365791104, 2.6808876043772165, 2.760168788261774, 2.787663815433111, 2.7625410718462855, 2.685130348215001, 2.556923024306443, 2.3805462291201223, 2.1597112482081218, 1.8991369890573861, 1.6044498518680983, 1.2820618765352754, 0.9390295371430638, 0.5828960225696133, 0.22152026557280885, -0.1371036471966801, -0.4850327452807407, -0.8145629519382983, -1.118414044095542, -1.3899074061031083, -1.6231322199013916, -1.8130958647039768, -1.9558545316940783, -2.048620393955561, -2.089842107056249, -2.079255946978919, -2.0179055124238894, -1.908128618145759, -1.7535107724882943, -1.558805450573057, -1.3298222271482447, -1.073284700181762, -0.7966609963011992, -0.5079704791443215, -0.21557105770165863, 0.07206781035750921, 0.3466007293537306, 0.6000444277345137, 0.8250117829381143, 1.0149351574117889, 1.164272409434589, 1.2686891461765837, 1.3252111844508545, 1.3323417771713517, 1.2901389450684357, 1.2002492120482224, 1.0658951607679628, 0.891815478411327, 0.6841575212629036, 0.45032385509230727, 0.19877568650503813, -0.061202455457483894, -0.3197710443747605, -0.5668298690502348, -0.7923301934974767, -0.9865957033035312, -1.140642498370936, -1.2464879912460405, -1.2974384770618521, -1.2883453765176094, -1.2158207284424214, -1.078403423604892, -0.8766689151024272, -0.6132766893424475, -0.2929515996260836, 0.0776027957336509, 0.4898585451976361, 0.9336826204626287, 1.3976162719797451, 1.8692071975015996, 2.3353851807032076, 2.782869966850797, 3.1985985594112734, 3.5701579190727473, 3.886208288881524, 4.136882107356676, 4.314143741260953, 4.412096089026921, 4.427221472757023, 4.358546128396919, 4.2077199759038795, 3.979006138773146, 3.679177800163388, 3.3173233284613635, 2.9045640611777164, 2.4536925744290397, 1.978742551396843, 1.4945043611609714, 1.0160030373450315, 0.5579573819219993, 0.13424030639874526, -0.24263882592879737, -0.5620092379076362, -0.815451510951261, -0.9971302466962929, -1.1040313655297824, -1.1360921053236328, -1.0962157187953299, -0.9901672876731924, -0.8263518142660913, -0.6154806322151941, -0.37013699903720776, -0.10425628702847713, 0.16745972919956564, 0.4301715760618011, 0.6695482919285436, 0.8724040828569761, 1.027297883904146, 1.1250689821722895, 1.159283745291694, 1.1265715473163889, 1.0268321083687009, 0.8633015280756238, 0.6424701105155839, 0.3738514219492179, 0.06960862946717114, -0.2559492479258574, -0.5869822833596744, -0.9068212484268037, -1.1987266121518045, -1.446672084151421, -1.6361176448968708, -1.7547363255394144, -1.7930599412195383, -1.745011567003002, -1.6082967200356435, -1.384630843167249, -1.0797875672693096, -0.7034600863555045, -0.2689364775128251, 0.20740144242391573, 0.7067375173726074, 1.2086126533181243, 1.691814886095563, 2.13532905389701, 2.5193029640944133, 2.8259848335962183, 3.040586784860861, 3.1520313738341126, 3.1535424841870174, 3.043048308530917, 2.823372309569725, 2.5021976713650083, 2.0918013861247373, 1.6085652803996804, 1.0722824259422388, 0.5052879445421536, -0.06854734928106451, -0.6249142341880726, -1.1402013687384474, -1.5926154118727132, -1.9632292721391578, -2.2369050594810456, -2.403043382512097, -2.456118320730845, -2.3959673891547055, -2.2278176545216195, -1.962042296269893, -1.6136556828254447, -1.2015687485427504, -0.7476393822428988, -0.27556396527553245, 0.1903345277295898, 0.6263598881447494, 1.0106720941376768, 1.3244273918800573, 1.55276715119857, 1.6856005528261084, 1.7181362551806552, 1.6511309645223053, 1.4908376678592214, 1.2486524233889078, 0.9404751823122934, 0.5858162302221293, 0.206694574728465, -0.17361289432427807, -0.5319031488134452, -0.8463854715915694, -1.0979505903175526, -1.2712969226438995, -1.3558470550593549, -1.346398256104854, -1.2434649839523744, -1.0532882703817532, -0.7875056481192414, -0.46249490070794375, -0.098424237980054, 0.2819405972908195, 0.6546063896488684, 0.9958218572026681, 1.2835609377071544, 1.4989316858333093, 1.6274248533769746, 1.659923712115928, 1.5934090136856311, 1.4313095637560893, 1.1834688489748912, 0.8657203964207887, 0.49908779894511496, 0.1086482393826272, -0.27788049345519916, -0.6317514054452852, -0.9249061608785557, -1.1316987831086986, -1.2305217482945607, -1.2052343936926289, -1.0463030705321472, -0.7515777069175096, -0.32664962927112906, 0.21524048337426896, 0.8537491416621174, 1.5624083100997133, 2.309985968167088, 3.0621553070536662, 3.783378633519476, 4.4388971040031535, 4.996708836358738, 5.429416426647445, 5.715830693143871, 5.842230385446267, 5.803196986567913, 5.601968528749302, 5.250285099839684, 4.767729710249174, 4.180599510409305, 3.520372018490363, 2.8218571194215807, 2.1211463942441022, 1.4534853990865106, 0.8512008022349502, 0.34181225101042334, -0.05355155051539758, -0.3213313023639559, -0.45623389119057467, -0.4614016108249873, -0.34804168557077975, -0.13453897515504254, 0.15489125951397298, 0.4919229257639111, 0.8460980430365682, 1.1869338923252224, 1.486017483911265, 1.7189460293545125, 1.866981163679919, 1.9183027713012908, 1.8687743652361033, 1.7221644311388005, 1.4898048864678746, 1.1897063958169813, 0.8451881228146799, 0.48311397913794607, 0.13185611825371632, -0.18087277283732342], 'positive_zeros': ['1.52704178392593821537966344922867', '3.17840489616138815479489636266455', '4.49248424043352922792303746201882', '5.64378025292469873144710820413046', '7.73888531989805003660794583343889', '8.726750491806532863798388282522479', '9.779582374289739856884442042616547', '10.95715163799240930907632092671275', '12.37685600300538789554826835372413', '13.58327058775724209958350749113637'], 'prelabel': '2-48-3.2-c12-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.623571787884669, 'root_angle': 0.7099529338891762, 'root_number': '-0.61279021261986412565703582004887365099180333438222043 + 0.79024562973628757529547172811396043030271445792395207*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3549764669445881', 'prec': 60}, 'spectral_label': 'c12-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.52704178392593821537966344923', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.17840489616138815479489636266', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.49248424043352922792303746202', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 43.87170322926171, 'bad_primes': [2, 3], 'central_character': '3.2', 'conductor': 48, 'conductor_radical': 6, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/48/13/e/d/17/3'], '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': '2-48-3.2-c12-0-19', 'motivic_weight': 12, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [12], 'order_of_vanishing': 0, 'prelabel': '2-48-3.2-c12-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.623571787884669, 'root_angle': 0.3549764669445881, 'self_dual': False, 'spectral_label': 'c12-0', 'z1': {'__RealLiteral__': 0, 'data': '1.52704178392593821537966344923', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1935755433967301766694834455291', 'Lhash_array': ['1935755433967301766694834455291'], 'label': '2-48-3.2-c12-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/48/13/e/d/17/3'}