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lfunc_lfunctions • Show schema
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{'Lhash': '1467682205965645015978953566423', 'a10': 0, 'a2': -1, 'a3': 0, 'a4': 1, 'a5': 0, 'a6': 0, 'a7': 3, 'a8': -1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.318036774617276, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [37, [1, 1]]], 'bad_primes': [2, 3, 37], 'central_character': '666.1', 'coefficient_field': '1.1.1.1', 'conductor': 666, 'conductor_radical': 222, 'degree': 2, 'euler_factors': [[1, 1], [1], [1, 0, 5], [1, -3, 7], [1, 1, 11], [1, -1, 13], [1, -3, 17], [1, -3, 19], [1, -1, 23], [1, -4, 29], [1, 6, 31], [1, 1], [1, -10, 41], [1, -12, 43], [1, -6, 47], [1, -1, 53], [1, 0, 59], [1, -2, 61], [1, -2, 67], [1, 0, 71], [1, 3, 73], [1, -14, 79], [1, 9, 83], [1, -3, 89], [1, 10, 97], [1, -6, 101], [1, 2, 103], [1, -13, 107], [1, -11, 109], [1, 18, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [1], [[[1, 0, 5], 1]], [[[1, -3, 7], 1]], [[[1, 1, 11], 1]], [[[1, -1, 13], 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-1.7325947068699774, -2.9071025599041067, -3.493381435089505, -3.0885086313939842, -1.5810500560072633, 0.7924013506970029, 3.5048814063206324, 5.894621563988376], 'positive_zeros': ['1.15779711357483022032503243328550', '2.46404015546282379837947782123145', '3.90575639700327756731471854422084', '5.18717331204885286486593982486657', '6.01497418650790910506005868954373', '7.43313124434508075165402720463878', '7.80630444762192273011758362778454', '8.792199929808722838659257912611837', '9.590711301042029947842936857344872', '10.56855320922795157861129741430423'], 'prelabel': '2-666-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.3060868965885213, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 866017728865347443, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.15779711357483022032503243329', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.46404015546282379837947782123', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.90575639700327756731471854422', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.318036774617276, 'bad_primes': [2, 3, 37], 'central_character': '1.1', 'conductor': 666, 'conductor_radical': 222, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, 0, 0, 3, -1, 0, 0, -1, 0, 1, -3, 0, 1, 3, 0, 3, 0, 0, 1, 1, 0, -5, -1, 0, 3, 4, 0, -6, -1, 0, -3, 0, 0, -1, -3, 0, 0, 10, 0, 12, -1, 0, -1, 6, 0, 2, 5, 0, 1, 1, 0, 0, -3, 0, -4, 0, 0, 2, 6, 0, 1, 0, 0, 2, 3, 0, 0, 0, 0, -3, 1, 0, 3, -3, 0, 14, 0, 0, -10, -9, 0, 0, -12, 0, 1, 3, 0, 3, 1, 0, -6, 0, 0, -10, -2, 0, -5], 'euler11': [1, 1, 11], 'euler13': [1, -1, 13], 'euler17': [1, -3, 17], 'euler19': [1, -3, 19], 'euler2': [1, 1, 0], 'euler23': [1, -1, 23], 'euler29': [1, -4, 29], 'euler3': [1, 0, 0], 'euler31': [1, 6, 31], 'euler37': [1, 1, 0], 'euler41': [1, -10, 41], 'euler43': [1, -12, 43], 'euler47': [1, -6, 47], 'euler5': [1, 0, 5], 'euler53': [1, -1, 53], 'euler59': [1, 0, 59], 'euler61': [1, -2, 61], 'euler67': [1, -2, 67], 'euler7': [1, -3, 7], 'euler71': [1, 0, 71], 'euler73': [1, 3, 73], 'euler79': [1, -14, 79], 'euler83': [1, 9, 83], 'euler89': [1, -3, 89], 'euler97': [1, 10, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, 0, 5], [1, -3, 7], [1, 1, 11], [1, -1, 13], [1, -3, 17], [1, -3, 19], [1, -1, 23], [1, -4, 29], [1, 6, 31], [1, 1, 0], [1, -10, 41], [1, -12, 43], [1, -6, 47], [1, -1, 53], [1, 0, 59], [1, -2, 61], [1, -2, 67], [1, 0, 71], [1, 3, 73], [1, -14, 79], [1, 9, 83], [1, -3, 89], [1, 10, 97]], 'index': 2, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/666/b', 'ModularForm/GL2/Q/holomorphic/666/2/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/666/2/a/b'], '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': '2-666-1.1-c1-0-2', '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': '2-666-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.3060868965885213, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 866017728865347443, 'z1': {'__RealLiteral__': 0, 'data': '1.15779711357483022032503243329', 'prec': 103}}
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lfunc_instances • Show schema
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id: 12843894
{'Lhash': '1467682205965645015978953566423', 'Lhash_array': ['1467682205965645015978953566423'], 'label': '2-666-1.1-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/666/2/a/b'}
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id: 24550118
{'Lhash': '1467682205965645015978953566423', 'Lhash_array': ['1467682205965645015978953566423'], 'label': '2-666-1.1-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/666/2/a/b/1/1'}
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id: 94492
{'Lhash': '866017728865347443', 'Lhash_array': ['866017728865347443'], 'label': '2-666-1.1-c1-0-2', 'type': 'ECQ', 'url': 'EllipticCurve/Q/666/b'}