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lfunc_lfunctions • Show schema
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{'Lhash': '2492312733870197247612343761722', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': 3, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.060796103745787, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [19, [1]]], 'bad_primes': [2, 19], 'central_character': '2888.1', 'coefficient_field': '1.1.1.1', 'conductor': 2888, 'conductor_radical': 38, 'degree': 2, 'euler_factors': [[1], [1, -1, 3], [1, -3, 5], [1, 0, 7], [1, 4, 11], [1, 5, 13], [1, 5, 17], [1], [1, 1, 23], [1, -3, 29], [1, -4, 31], [1, -2, 37], [1, 5, 41], [1, 11, 43], [1, 5, 47], [1, 9, 53], [1, -13, 59], [1, 1, 61], [1, 5, 67], [1, -1, 71], [1, 9, 73], [1, -17, 79], [1, -16, 83], [1, -3, 89], [1, 13, 97], [1, -19, 101], [1, 0, 103], [1, 12, 107], [1, -7, 109], [1, -6, 113]], 'euler_factors_factorization': [[1], [[[1, -1, 3], 1]], [[[1, -3, 5], 1]], [[[1, 0, 7], 1]], [[[1, 4, 11], 1]], [[[1, 5, 13], 1]], [[[1, 5, 17], 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1.5700973314826674, 0.9947820008483769, 0.447252683944307, -0.04825655629965438, -0.4716333011419988, -0.8078681752618714, -1.0477291542204141], 'positive_zeros': ['1.96608807933469849024327586459635', '2.46551642118250277972715745043904', '3.22988420229286706395847196636120', '4.79353993362731304488189317477590', '5.14495572480637871894779014613843', '6.15282968489620782570080930624593', '6.77264020904176126088701325164547', '7.83573047658080855481603432296294', '8.385568550588585893315563521680982'], 'prelabel': '2-2888-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.80216577220589, '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': 1203216878882511574, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.96608807933469849024327586460', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.46551642118250277972715745044', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.22988420229286706395847196636', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 23.060796103745787, 'bad_primes': [2, 19], 'central_character': '1.1', 'conductor': 2888, 'conductor_radical': 38, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 3, 0, 0, 0, -2, 0, -4, 0, -5, 0, 3, 0, -5, 0, 0, 0, 0, 0, -1, 0, 4, 0, -5, 0, 3, 0, 4, 0, -4, 0, 0, 0, 2, 0, -5, 0, -5, 0, -11, 0, -6, 0, -5, 0, -7, 0, -5, 0, -9, 0, -12, 0, 0, 0, 13, 0, -1, 0, 0, 0, -15, 0, -5, 0, -1, 0, 1, 0, -9, 0, 4, 0, 0, 0, 17, 0, 1, 0, 16, 0, -15, 0, 3, 0, 3, 0, 0, 0, 4, 0, 0, 0, -13, 0, 8, 0], 'euler11': [1, 4, 11], 'euler13': [1, 5, 13], 'euler17': [1, 5, 17], 'euler19': [1, 0, 0], 'euler2': [1, 0, 0], 'euler23': [1, 1, 23], 'euler29': [1, -3, 29], 'euler3': [1, -1, 3], 'euler31': [1, -4, 31], 'euler37': [1, -2, 37], 'euler41': [1, 5, 41], 'euler43': [1, 11, 43], 'euler47': [1, 5, 47], 'euler5': [1, -3, 5], 'euler53': [1, 9, 53], 'euler59': [1, -13, 59], 'euler61': [1, 1, 61], 'euler67': [1, 5, 67], 'euler7': [1, 0, 7], 'euler71': [1, -1, 71], 'euler73': [1, 9, 73], 'euler79': [1, -17, 79], 'euler83': [1, -16, 83], 'euler89': [1, -3, 89], 'euler97': [1, 13, 97], 'euler_factors': [[1, 0, 0], [1, -1, 3], [1, -3, 5], [1, 0, 7], [1, 4, 11], [1, 5, 13], [1, 5, 17], [1, 0, 0], [1, 1, 23], [1, -3, 29], [1, -4, 31], [1, -2, 37], [1, 5, 41], [1, 11, 43], [1, 5, 47], [1, 9, 53], [1, -13, 59], [1, 1, 61], [1, 5, 67], [1, -1, 71], [1, 9, 73], [1, -17, 79], [1, -16, 83], [1, -3, 89], [1, 13, 97]], 'index': 82, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/2888/e', 'ModularForm/GL2/Q/holomorphic/2888/2/a/e/1/1', 'ModularForm/GL2/Q/holomorphic/2888/2/a/e'], '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': '2-2888-1.1-c1-0-82', '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': '2-2888-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.80216577220589, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1203216878882511574, 'z1': {'__RealLiteral__': 0, 'data': '1.96608807933469849024327586460', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20571694
{'Lhash': '2492312733870197247612343761722', 'Lhash_array': ['2492312733870197247612343761722'], 'label': '2-2888-1.1-c1-0-82', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2888/2/a/e'}
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id: 24559201
{'Lhash': '2492312733870197247612343761722', 'Lhash_array': ['2492312733870197247612343761722'], 'label': '2-2888-1.1-c1-0-82', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2888/2/a/e/1/1'}
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id: 96397
{'Lhash': '1203216878882511574', 'Lhash_array': ['1203216878882511574'], 'label': '2-2888-1.1-c1-0-82', 'type': 'ECQ', 'url': 'EllipticCurve/Q/2888/e'}