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lfunc_lfunctions • Show schema
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{'Lhash': '1170632750855417543656455735540,2142684720012302901814312290909', 'a10': 0, 'a2': 0, 'a3': 3, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 53.0327185866685, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -3, 3]], [19, [1, -8, 19]]], 'bad_primes': [2, 3, 19], 'central_character': '912.1', 'coefficient_field': '1.1.1.1', 'conductor': 831744, 'conductor_radical': 114, 'degree': 4, 'euler_factors': [[1], [1, -3, 3], [1, 0, 2, 0, 25], [1, 2, 15, 14, 49], [1, 0, -10, 0, 121], [1, 0, -23, 0, 169], [1, 0, -31, 0, 289], [1, -8, 19], [1, 0, -19, 0, 529], [1, -18, 139, -522, 841], [1, 0, 46, 0, 961], [1, 0, -26, 0, 1369], [1, 0, 82, 0, 1681], [1, 4, 90, 172, 1849], [1, 0, -82, 0, 2209], [1, 18, 187, 954, 2809], [1, -6, 127, -354, 3481], [1, 16, 186, 976, 3721], [1, 0, -59, 0, 4489], [1, -24, 286, -1704, 5041], [1, -22, 267, -1606, 5329], [1, 0, -110, 0, 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['0.923466411521167865382362748965447', '1.69028020783213549665740772791983', '2.48557632430000821629214565507408', '3.02482974477889927597006412686325', '3.31130025298000745540489865114873', '3.68828982477715838594221815009418', '4.56078980769246016118577449844868', '4.84615344726309464006343551243338', '5.36289130826234626919889280487080', '6.35130228305099953158678794438888', '6.47517911242109154942842088452726', '6.88067588100079673853203211155239', '7.54907452133010029137486358438014', '7.919638778770828429176326313829517', '8.302578397461485617962229000043634', '8.386583985166649078361424791657155', '9.294512334634324008400509642943564', '9.515191572864907516077214823731079', '9.602994139561981452123843556916461', '10.03442972649494056335382487408194'], 'prelabel': '4-912e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.698584196266771, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 287298652293280435, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.923466411521167865382362748965', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.69028020783213549665740772792', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.48557632430000821629214565507', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 53.0327185866685, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 831744, 'conductor_radical': 114, 'degree': 4, 'dirichlet_coefficients': [1, 0, 3, 0, 0, 0, -2, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, -6, 0, 0, 0, -2, 0, 9, 0, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -11, 0, 0, 0, -18, 0, 0, 0, 24, 0, 6, 0, -16, 0, -12, 0, 0, 0, 0, 0, 0, 0, 24, 0, 22, 0, -6, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 54, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, -10, 0, 121], 'euler13': [1, 0, -23, 0, 169], 'euler17': [1, 0, -31, 0, 289], 'euler19': [1, -8, 19, 0, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -19, 0, 529], 'euler29': [1, -18, 139, -522, 841], 'euler3': [1, -3, 3, 0, 0], 'euler31': [1, 0, 46, 0, 961], 'euler37': [1, 0, -26, 0, 1369], 'euler41': [1, 0, 82, 0, 1681], 'euler43': [1, 4, 90, 172, 1849], 'euler47': [1, 0, -82, 0, 2209], 'euler5': [1, 0, 2, 0, 25], 'euler53': [1, 18, 187, 954, 2809], 'euler59': [1, -6, 127, -354, 3481], 'euler61': [1, 16, 186, 976, 3721], 'euler67': [1, 0, -59, 0, 4489], 'euler7': [1, 2, 15, 14, 49], 'euler71': [1, -24, 286, -1704, 5041], 'euler73': [1, -22, 267, -1606, 5329], 'euler79': [1, 0, -110, 0, 6241], 'euler83': [1, 0, -58, 0, 6889], 'euler89': [1, -12, 214, -1068, 7921], 'euler97': [1, 0, -2, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, -3, 3, 0, 0], [1, 0, 2, 0, 25], [1, 2, 15, 14, 49], [1, 0, -10, 0, 121], [1, 0, -23, 0, 169], [1, 0, -31, 0, 289], [1, -8, 19, 0, 0], [1, 0, -19, 0, 529], [1, -18, 139, -522, 841], [1, 0, 46, 0, 961], [1, 0, -26, 0, 1369], [1, 0, 82, 0, 1681], [1, 4, 90, 172, 1849], [1, 0, -82, 0, 2209], [1, 18, 187, 954, 2809], [1, -6, 127, -354, 3481], [1, 16, 186, 976, 3721], [1, 0, -59, 0, 4489], [1, -24, 286, -1704, 5041], [1, -22, 267, -1606, 5329], [1, 0, -110, 0, 6241], [1, 0, -58, 0, 6889], [1, -12, 214, -1068, 7921], [1, 0, -2, 0, 9409]], 'index': 47, 'instance_types': ['ECNF', 'HMF', 'CMF'], 'instance_urls': ['EllipticCurve/2.2.57.1/256.1/a', 'ModularForm/GL2/TotallyReal/2.2.57.1/holomorphic/2.2.57.1-256.1-a', 'ModularForm/GL2/Q/holomorphic/912/2/f/e'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-912e2-1.1-c1e2-0-47', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-912e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.698584196266771, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 287298652293280435, 'z1': {'__RealLiteral__': 0, 'data': '0.923466411521167865382362748965', 'prec': 107}}
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lfunc_instances • Show schema
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id: 17410756
{'Lhash': '1170632750855417543656455735540,2142684720012302901814312290909', 'Lhash_array': ['1170632750855417543656455735540', '2142684720012302901814312290909'], 'label': '4-912e2-1.1-c1e2-0-47', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/912/2/f/e'}
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id: 9488228
{'Lhash': '_1170632750855417543656455735540', 'Lhash_array': ['_1170632750855417543656455735540'], 'label': '4-912e2-1.1-c1e2-0-47', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.57.1/holomorphic/2.2.57.1-256.1-a'}
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id: 9488039
{'Lhash': '_1170632750855417543656455735540', 'Lhash_array': ['_1170632750855417543656455735540'], 'label': '4-912e2-1.1-c1e2-0-47', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.57.1/256.1/a'}