-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2548918339748919018649187789488', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': -2, 'a6': 0, 'a7': 2, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.965330172255797, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [13, [1, 1]]], 'bad_primes': [2, 3, 13], 'central_character': '1248.1', 'coefficient_field': '1.1.1.1', 'conductor': 1248, 'conductor_radical': 78, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, 2, 5], [1, -2, 7], [1, 6, 11], [1, 1], [1, 2, 17], [1, 6, 19], [1, 0, 23], [1, 6, 29], [1, -6, 31], [1, -2, 37], [1, 10, 41], [1, -8, 43], [1, -6, 47], [1, -6, 53], [1, 6, 59], [1, 10, 61], [1, -2, 67], [1, 14, 71], [1, 14, 73], [1, -4, 79], [1, -6, 83], [1, -6, 89], [1, 14, 97], [1, -6, 101], [1, 0, 103], [1, 4, 107], [1, 14, 109], [1, -14, 113]], 'euler_factors_factorization': [[1], [[[1, -1], 1]], [[[1, 2, 5], 1]], [[[1, -2, 7], 1]], [[[1, 6, 11], 1]], [[[1, 1], 1]], [[[1, 2, 17], 1]], [[[1, 6, 19], 1]], [[[1, 0, 23], 1]], [[[1, 6, 29], 1]], [[[1, -6, 31], 1]], [[[1, -2, 37], 1]], [[[1, 10, 41], 1]], [[[1, -8, 43], 1]], [[[1, -6, 47], 1]], [[[1, -6, 53], 1]], [[[1, 6, 59], 1]], [[[1, 10, 61], 1]], [[[1, -2, 67], 1]], [[[1, 14, 71], 1]], [[[1, 14, 73], 1]], [[[1, -4, 79], 1]], [[[1, -6, 83], 1]], [[[1, -6, 89], 1]], [[[1, 14, 97], 1]], [[[1, -6, 101], 1]], [[[1, 0, 103], 1]], [[[1, 4, 107], 1]], [[[1, 14, 109], 1]], [[[1, -14, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 21, 'label': '2-1248-1.1-c1-0-21', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/1248/2/a/g', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [-1.3849855291255412e-60, 0.16434819507483653, 0.3290221112142305, 0.49427766065384826, 0.6602353675592694, 0.8268227869555127, 0.9937278726936122, 1.1603652431045701, 1.3258562908354241, 1.4890232273581823, 1.6483965220579644, 1.802234801543255, 1.9485560773605572, 2.085179105062191, 2.209773677528406, 2.3199186657344586, 2.4131666043655167, 2.487113559849273, 2.539472911601911, 2.5681515312889625, 2.5713266738836076, 2.5475217156847227, 2.4956787066163617, 2.415225564935474, 2.3061356483628126, 2.1689774010577296, 2.0049518128199066, 1.8159155447536202, 1.6043877807235893, 1.3735391593733801, 1.1271615268957043, 0.8696177220925627, 0.6057711546941185, 0.3408955537332009, 0.08056592955525915, -0.16946750820176823, -0.40342002575515024, -0.6156244889786857, -0.8006911395892408, -0.953670645351378, -1.0702155616209097, -1.1467349822089845, -1.1805369483080548, -1.1699531469515005, -1.1144405826093284, -1.0146552589098072, -0.8724934673846908, -0.6910970443797492, -0.47481991558508696, -0.22915438130266724, 0.03938312264389811, 0.3234056589827, 0.61484622452678, 0.9051809093448246, 1.1856792519479027, 1.447674905595868, 1.6828485254194006, 1.883513790877881, 2.0428967480474696, 2.1553982402828766, 2.2168291343297106, 2.224608371488309, 2.177914596412242, 2.0777832412253745, 1.927142455421788, 1.7307831412200574, 1.495260531552973, 1.228727169351052, 0.9406997330900848, 0.6417648129536712, 0.3432313728994815, 0.05674012869638334, -0.20615767920984948, -0.43443774377449984, -0.6180405644798901, -0.748293019967578, -0.8182966387134154, -0.8232659448936931, -0.7608013259715115, -0.6310826274810205, -0.4369720985024916, -0.18401832790816922, 0.11964366328171049, 0.46349709151946505, 0.8349495940302653, 1.2197334223262668, 1.6023879732311557, 1.9668090829730118, 2.2968460564640143, 2.5769245706865624, 2.7926715330024647, 2.931516821978286, 2.9832466873291823, 2.9404844954065785, 2.7990764921397036, 2.5583632843475974, 2.2213217324584233, 1.794566775110954, 1.2882081968280432, 0.7155632930564656, 0.09273254016975131, -0.5619485225071068, -1.2285622208112652, -1.886342337506446, -2.514459913932739, -3.092829594011514, -3.60290291556473, -4.028414454883891, -4.356047742375187, -4.575990405619032, -4.682352006225116, -4.673423391697266, -4.5517628873328135, -4.3241020471676705, -4.001071654830435, -3.596756861660059, -3.128098391675362, -2.6141642436772896, -2.0753229028055262, -1.5323543892943197, -1.0055392206060274, -0.5137673087494511, -0.07370880069438068, 0.30091316999724976, 0.5999118866921069, 0.8170585725310094, 0.9503135286784634, 1.0018532304687877, 0.9778894872993471, 0.8882869938697437, 0.745995781838621, 0.5663247072723329, 0.36609067505082427, 0.1626853373082755, -0.026893898673912155, -0.18699887936390291, -0.3042216955911761, -0.3681738316670551, -0.37211040042165416, -0.31336351263626994, -0.1935580224630156, -0.018593737828778184, 0.20160983295435395, 0.4535976075265309, 0.7210709273387574, 0.9857547867863328, 1.2283974303671243, 1.4298512374819112, 1.5721781054697903, 1.639719724592517, 1.620073454644749, 1.504918040740794, 1.2906400529064568, 0.9787214348042116, 0.5758604711576452, 0.0938122544110782, -0.4510503480905367, -1.0384389374419936, -1.6450839219232238, -2.2458563010706243, -2.815020786049053, -3.327555459079965, -3.7604678199088797, -4.094035440725102, -4.312901751557324, -4.4069636914131785, -4.371997851941326, -4.209984861941223, -3.9291074688682164, -3.5434152584110556, -3.0721672812971743, -2.5388820181307366, -1.970141078290741, -1.3942078055480005, -0.8395336548236967, -0.3332330654867404, 0.10038896120447866, 0.44117358180906613, 0.6742320803213162, 0.7907905142079582, 0.7887029719757923, 0.6725991866760165, 0.45365241433893977, 0.1489748985971227, -0.21933030702000378, -0.6254121432607644, -1.0411421271823766, -1.4377315379398241, -1.7874041317717362, -2.0650285168196407, -2.249615025900587, -2.3255882164151975, -2.283757753779767, -2.1219268278847685, -1.8450975435474541, -1.465255794986148, -1.000742667691724, -0.4752439768636511, 0.08354731729221251, 0.6455207952655312, 1.1798991854179786, 1.6570477350129855, 2.050235153558623, 2.3372402683660454, 2.5017062723949857, 2.5341582470973094, 2.432618784085305, 2.2027799428190353, 1.8577161162703413, 1.4171500739158116, 0.9063118363656775, 0.35445541823626037, -0.20687974517761207, -0.7457591057784317, -1.2317808362732081, -1.6379232584013914, -1.9421974671202304, -2.129001442002506, -2.1900892365044142, -2.1250917708116535, -1.9415529774467002, -1.6544749175447673, -1.2853961586483669, -0.8610572561463125, -0.41173372039490236, 0.03066135190825724, 0.4345872105722252, 0.7708718772396859, 1.0145686245738093, 1.146553778939844, 1.1547625235149996, 1.0349816052803515, 0.7911455587466727, 0.43511453669118827, -0.014054905286323633, -0.5313018262881573, -1.0871410882092565, -1.6495312273790557, -2.185909957163525, -2.665265346374855, -3.0601073689716114, -3.3482100635825516, -3.5140087322135445, -3.5495586228805656, -3.454990023032904, -3.238427827699328, -2.915379285265549, -2.50762940835955, -2.041717062420718, -1.5470937173890413, -1.0540892449158246, -0.5918233519262202, -0.18620617665148967, 0.14183323754219745, 0.37776624954684207, 0.5144304679876583, 0.5524712740358363], 'positive_zeros': ['2.01074202882877077393828448728874', '2.92133996435419900993581940697288', '4.17228712390106732432301137169297', '4.78263033612980466766564281150302', '5.86780953840629681522673799949633', '7.15914697119095734461341250765306', '7.84278157109124886213393953191628', '8.267121982133789942052976540935791', '9.092559319520639094989226590241115'], 'prelabel': '2-1248-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.1567911195161136, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 1256218849839652146, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.01074202882877077393828448729', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.92133996435419900993581940697', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.17228712390106732432301137169', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 9.965330172255797, 'bad_primes': [2, 3, 13], 'central_character': '1.1', 'conductor': 1248, 'conductor_radical': 78, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, -2, 0, 2, 0, 1, 0, -6, 0, -1, 0, -2, 0, -2, 0, -6, 0, 2, 0, 0, 0, -1, 0, 1, 0, -6, 0, 6, 0, -6, 0, -4, 0, 2, 0, -1, 0, -10, 0, 8, 0, -2, 0, 6, 0, -3, 0, -2, 0, 6, 0, 12, 0, -6, 0, -6, 0, -10, 0, 2, 0, 2, 0, 2, 0, 0, 0, -14, 0, -14, 0, -1, 0, -12, 0, 4, 0, 1, 0, 6, 0, 4, 0, -6, 0, 6, 0, -2, 0, 6, 0, 12, 0, -14, 0, -6, 0], 'euler11': [1, 6, 11], 'euler13': [1, 1, 0], 'euler17': [1, 2, 17], 'euler19': [1, 6, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, 6, 29], 'euler3': [1, -1, 0], 'euler31': [1, -6, 31], 'euler37': [1, -2, 37], 'euler41': [1, 10, 41], 'euler43': [1, -8, 43], 'euler47': [1, -6, 47], 'euler5': [1, 2, 5], 'euler53': [1, -6, 53], 'euler59': [1, 6, 59], 'euler61': [1, 10, 61], 'euler67': [1, -2, 67], 'euler7': [1, -2, 7], 'euler71': [1, 14, 71], 'euler73': [1, 14, 73], 'euler79': [1, -4, 79], 'euler83': [1, -6, 83], 'euler89': [1, -6, 89], 'euler97': [1, 14, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 2, 5], [1, -2, 7], [1, 6, 11], [1, 1, 0], [1, 2, 17], [1, 6, 19], [1, 0, 23], [1, 6, 29], [1, -6, 31], [1, -2, 37], [1, 10, 41], [1, -8, 43], [1, -6, 47], [1, -6, 53], [1, 6, 59], [1, 10, 61], [1, -2, 67], [1, 14, 71], [1, 14, 73], [1, -4, 79], [1, -6, 83], [1, -6, 89], [1, 14, 97]], 'index': 21, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1248/g', 'ModularForm/GL2/Q/holomorphic/1248/2/a/g/1/1', 'ModularForm/GL2/Q/holomorphic/1248/2/a/g'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-1248-1.1-c1-0-21', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-1248-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.1567911195161136, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1256218849839652146, 'z1': {'__RealLiteral__': 0, 'data': '2.01074202882877077393828448729', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 20639793
{'Lhash': '2548918339748919018649187789488', 'Lhash_array': ['2548918339748919018649187789488'], 'label': '2-1248-1.1-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1248/2/a/g'}
-
id: 24552370
{'Lhash': '2548918339748919018649187789488', 'Lhash_array': ['2548918339748919018649187789488'], 'label': '2-1248-1.1-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1248/2/a/g/1/1'}
-
id: 36062
{'Lhash': '1256218849839652146', 'Lhash_array': ['1256218849839652146'], 'label': '2-1248-1.1-c1-0-21', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1248/g'}