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lfunc_lfunctions • Show schema
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{'Lhash': '1583391688180467796762621857427', 'a10': 1, 'a2': -1, 'a3': -1, 'a4': 1, 'a5': -1, 'a6': 1, 'a7': 3, 'a8': -1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 40.484153824789175, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, 1]], [5, [1, 1]], [13, [1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '5070.1', 'coefficient_field': '1.1.1.1', 'conductor': 5070, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[1, 1], [1, 1], [1, 1], [1, -3, 7], [1, 1, 11], [1], [1, 0, 17], [1, -5, 19], [1, 4, 23], [1, 0, 29], [1, 10, 31], [1, -1, 37], [1, 6, 41], [1, 2, 43], [1, -9, 47], [1, 13, 53], [1, 4, 59], [1, 2, 61], [1, -12, 67], [1, -2, 71], [1, -16, 73], [1, 10, 79], [1, 12, 83], [1, 1, 89], [1, 12, 97], [1, -4, 101], [1, 9, 103], [1, 6, 107], [1, -10, 109], [1, -16, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [[[1, 1], 1]], [[[1, 1], 1]], [[[1, -3, 7], 1]], [[[1, 1, 11], 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-0.44672707657034866, -0.7558057060674986, -1.0599175944362913, -1.3391937971013412, -1.5740801016300803, -1.7465330344722028, -1.8411798745177932], 'positive_zeros': ['1.24907580045746988515620789018476', '2.05874485144909035505789823908903', '3.28268674688962100617480697604002', '4.18805425242667360026731729045729', '5.13202677683347561333967431902350', '5.58083830356357407411598168677331', '6.59281974936670294299730115426297', '7.38296364446977614928003210959323', '7.83964863322762188092883445742808'], 'prelabel': '2-5070-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.3627159157697095, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 2115055069503829239, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.24907580045746988515620789018', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.05874485144909035505789823909', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.28268674688962100617480697604', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 40.484153824789175, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 5070, 'conductor_radical': 390, 'degree': 2, 'dirichlet_coefficients': [1, -1, -1, 1, -1, 1, 3, -1, 1, 1, -1, -1, 0, -3, 1, 1, 0, -1, 5, -1, -3, 1, -4, 1, 1, 0, -1, 3, 0, -1, -10, -1, 1, 0, -3, 1, 1, -5, 0, 1, -6, 3, -2, -1, -1, 4, 9, -1, 2, -1, 0, 0, -13, 1, 1, -3, -5, 0, -4, 1, -2, 10, 3, 1, 0, -1, 12, 0, 4, 3, 2, -1, 16, -1, -1, 5, -3, 0, -10, -1, 1, 6, -12, -3, 0, 2, 0, 1, -1, 1, 0, -4, 10, -9, -5, 1, -12, -2, -1, 1], 'euler11': [1, 1, 11], 'euler13': [1, 0, 0], 'euler17': [1, 0, 17], 'euler19': [1, -5, 19], 'euler2': [1, 1, 0], 'euler23': [1, 4, 23], 'euler29': [1, 0, 29], 'euler3': [1, 1, 0], 'euler31': [1, 10, 31], 'euler37': [1, -1, 37], 'euler41': [1, 6, 41], 'euler43': [1, 2, 43], 'euler47': [1, -9, 47], 'euler5': [1, 1, 0], 'euler53': [1, 13, 53], 'euler59': [1, 4, 59], 'euler61': [1, 2, 61], 'euler67': [1, -12, 67], 'euler7': [1, -3, 7], 'euler71': [1, -2, 71], 'euler73': [1, -16, 73], 'euler79': [1, 10, 79], 'euler83': [1, 12, 83], 'euler89': [1, 1, 89], 'euler97': [1, 12, 97], 'euler_factors': [[1, 1, 0], [1, 1, 0], [1, 1, 0], [1, -3, 7], [1, 1, 11], [1, 0, 0], [1, 0, 17], [1, -5, 19], [1, 4, 23], [1, 0, 29], [1, 10, 31], [1, -1, 37], [1, 6, 41], [1, 2, 43], [1, -9, 47], [1, 13, 53], [1, 4, 59], [1, 2, 61], [1, -12, 67], [1, -2, 71], [1, -16, 73], [1, 10, 79], [1, 12, 83], [1, 1, 89], [1, 12, 97]], 'index': 68, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/5070/c', 'ModularForm/GL2/Q/holomorphic/5070/2/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/5070/2/a/c'], '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': '2-5070-1.1-c1-0-68', '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': '2-5070-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.3627159157697095, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2115055069503829239, 'z1': {'__RealLiteral__': 0, 'data': '1.24907580045746988515620789018', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21517595
{'Lhash': '1583391688180467796762621857427', 'Lhash_array': ['1583391688180467796762621857427'], 'factors': ['2-5070-1.1-c1-0-68'], 'label': '2-5070-1.1-c1-0-68', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5070/2/a/c'}
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id: 24568734
{'Lhash': '1583391688180467796762621857427', 'Lhash_array': ['1583391688180467796762621857427'], 'factors': ['2-5070-1.1-c1-0-68'], 'label': '2-5070-1.1-c1-0-68', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5070/2/a/c/1/1'}
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id: 27547
{'Lhash': '2115055069503829239', 'Lhash_array': ['2115055069503829239'], 'factors': ['2-5070-1.1-c1-0-68'], 'label': '2-5070-1.1-c1-0-68', 'type': 'ECQ', 'url': 'EllipticCurve/Q/5070/c'}