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lfunc_lfunctions • Show schema
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{'Lhash': '1163399017185683682530563154406', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 41.394448407831774, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '5184.1', 'coefficient_field': '1.1.1.1', 'conductor': 5184, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[1], [1], [1, 1, 5], [1, 0, 7], [1, -4, 11], [1, -5, 13], [1, -5, 17], [1, -8, 19], [1, 4, 23], [1, -3, 29], [1, -4, 31], [1, 3, 37], [1, -6, 41], [1, -4, 43], [1, 12, 47], [1, 10, 53], [1, 8, 59], [1, -5, 61], [1, -8, 67], [1, -16, 71], [1, 5, 73], [1, 4, 79], [1, 4, 83], [1, 3, 89], [1, -2, 97], [1, -6, 101], [1, 4, 103], [1, -12, 107], [1, -17, 109], [1, 15, 113]], 'euler_factors_factorization': [[1], [1], [[[1, 1, 5], 1]], [[[1, 0, 7], 1]], [[[1, -4, 11], 1]], [[[1, -5, 13], 1]], [[[1, -5, 17], 1]], [[[1, -8, 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1.5814475789204483, 1.533690652610639, 1.3525416123674314, 1.0390076193946427, 0.6021774916791325, 0.058883424199191535, -0.5671307788654346, -1.2464897669226431, -1.9458405863870094, -2.6297812154741367, -3.262945535470967, -3.8121150294200556, -4.248224107827287], 'positive_zeros': ['0.917760001830333900047231319176764', '1.63247464748590096504944450469565', '3.19685309383908598200049258005358', '3.57609226214958457591135455886023', '4.40264398239140372242061680879542', '5.38287049773346250740068267095118', '6.12586762426705713001629510265770', '6.66521602937305346450512748089807', '7.74490587824072060625187216512830', '8.014397887478194407582432414744133'], 'prelabel': '2-72e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.433851755195466, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 73464899412987111, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.917760001830333900047231319177', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.63247464748590096504944450470', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.19685309383908598200049258005', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 41.394448407831774, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 5184, 'conductor_radical': 6, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 4, 0, 5, 0, 0, 0, 5, 0, 8, 0, 0, 0, -4, 0, -4, 0, 0, 0, 3, 0, 4, 0, 0, 0, 0, 0, -3, 0, 0, 0, 6, 0, 4, 0, 0, 0, -12, 0, -7, 0, 0, 0, -10, 0, -4, 0, 0, 0, -8, 0, 5, 0, 0, 0, -5, 0, 8, 0, 0, 0, 16, 0, -5, 0, 0, 0, 0, 0, -4, 0, 0, 0, -4, 0, -5, 0, 0, 0, -3, 0, 0, 0, 0, 0, -8, 0, 2, 0, 0, 0], 'euler11': [1, -4, 11], 'euler13': [1, -5, 13], 'euler17': [1, -5, 17], 'euler19': [1, -8, 19], 'euler2': [1, 0, 0], 'euler23': [1, 4, 23], 'euler29': [1, -3, 29], 'euler3': [1, 0, 0], 'euler31': [1, -4, 31], 'euler37': [1, 3, 37], 'euler41': [1, -6, 41], 'euler43': [1, -4, 43], 'euler47': [1, 12, 47], 'euler5': [1, 1, 5], 'euler53': [1, 10, 53], 'euler59': [1, 8, 59], 'euler61': [1, -5, 61], 'euler67': [1, -8, 67], 'euler7': [1, 0, 7], 'euler71': [1, -16, 71], 'euler73': [1, 5, 73], 'euler79': [1, 4, 79], 'euler83': [1, 4, 83], 'euler89': [1, 3, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 1, 5], [1, 0, 7], [1, -4, 11], [1, -5, 13], [1, -5, 17], [1, -8, 19], [1, 4, 23], [1, -3, 29], [1, -4, 31], [1, 3, 37], [1, -6, 41], [1, -4, 43], [1, 12, 47], [1, 10, 53], [1, 8, 59], [1, -5, 61], [1, -8, 67], [1, -16, 71], [1, 5, 73], [1, 4, 79], [1, 4, 83], [1, 3, 89], [1, -2, 97]], 'index': 30, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/5184/l', 'ModularForm/GL2/Q/holomorphic/5184/2/a/l/1/1', 'ModularForm/GL2/Q/holomorphic/5184/2/a/l'], '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': '2-72e2-1.1-c1-0-30', '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': '2-72e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.433851755195466, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 73464899412987111, 'z1': {'__RealLiteral__': 0, 'data': '0.917760001830333900047231319177', 'prec': 107}}
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lfunc_instances • Show schema
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id: 21548555
{'Lhash': '1163399017185683682530563154406', 'Lhash_array': ['1163399017185683682530563154406'], 'label': '2-72e2-1.1-c1-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5184/2/a/l'}
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id: 24569256
{'Lhash': '1163399017185683682530563154406', 'Lhash_array': ['1163399017185683682530563154406'], 'label': '2-72e2-1.1-c1-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5184/2/a/l/1/1'}
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id: 34532
{'Lhash': '73464899412987111', 'Lhash_array': ['73464899412987111'], 'label': '2-72e2-1.1-c1-0-30', 'type': 'ECQ', 'url': 'EllipticCurve/Q/5184/l'}