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lfunc_lfunctions • Show schema
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{'Lhash': '1484165862651727912213758692927', 'a10': 1, 'a2': -1, 'a3': -2, 'a4': -1, 'a5': -1, 'a6': 2, 'a7': -2, 'a8': 3, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.344367011223804, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [1, 1]], [11, [1, 1]], [19, [1, 1]]], 'bad_primes': [5, 11, 19], 'central_character': '1045.1', 'coefficient_field': '1.1.1.1', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 2, 'euler_factors': [[1, 1, 2], [1, 2, 3], [1, 1], [1, 2, 7], [1, 1], [1, -6, 13], [1, 0, 17], [1, 1], [1, 0, 23], [1, -6, 29], [1, -4, 31], [1, 0, 37], [1, 6, 41], [1, 6, 43], [1, 4, 47], [1, -12, 53], [1, 8, 59], [1, 14, 61], [1, -6, 67], [1, 8, 71], [1, -16, 73], [1, 8, 79], [1, -6, 83], [1, 2, 89], [1, -4, 97], [1, 18, 101], [1, 10, 103], [1, 20, 107], [1, 2, 109], [1, -4, 113]], 'euler_factors_factorization': [[[[1, 1, 2], 1]], [[[1, 2, 3], 1]], [[[1, 1], 1]], [[[1, 2, 7], 1]], [[[1, 1], 1]], [[[1, 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-9.1670245856378, -8.60910290735929, -7.830290111672508, -6.863157228249737, -5.748752277632519, -4.534398164522049, -3.2711615389228794, -2.0111393013542807], 'positive_zeros': ['1.17080042590956595747782018947254', '3.23559981947008472823955378050375', '4.30702204859644929662120519965778', '5.22519121956999151938912253709563', '6.22130311336718161147659456809023', '6.83006102631047061488008161721512', '8.144528575687806914758667967843355', '8.572381866452314942168735585082764', '9.581897899326145556759519845408590'], 'prelabel': '2-1045-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.888661802846398, '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': 2084829519259382411, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.17080042590956595747782018947', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.23559981947008472823955378050', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.30702204859644929662120519966', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.344367011223804, 'bad_primes': [5, 11, 19], 'central_character': '1.1', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 2, 'dirichlet_coefficients': [1, -1, -2, -1, -1, 2, -2, 3, 1, 1, -1, 2, 6, 2, 2, -1, 0, -1, -1, 1, 4, 1, 0, -6, 1, -6, 4, 2, 6, -2, 4, -5, 2, 0, 2, -1, 0, 1, -12, -3, -6, -4, -6, 1, -1, 0, -4, 2, -3, -1, 0, -6, 12, -4, 1, -6, 2, -6, -8, -2, -14, -4, -2, 7, -6, -2, 6, 0, 0, -2, -8, 3, 16, 0, -2, 1, 2, 12, -8, 1, -11, 6, 6, -4, 0, 6, -12, -3, -2, 1, -12, 0, -8, 4, 1, 10, 4, 3, -1, -1], 'euler11': [1, 1, 0], 'euler13': [1, -6, 13], 'euler17': [1, 0, 17], 'euler19': [1, 1, 0], 'euler2': [1, 1, 2], 'euler23': [1, 0, 23], 'euler29': [1, -6, 29], 'euler3': [1, 2, 3], 'euler31': [1, -4, 31], 'euler37': [1, 0, 37], 'euler41': [1, 6, 41], 'euler43': [1, 6, 43], 'euler47': [1, 4, 47], 'euler5': [1, 1, 0], 'euler53': [1, -12, 53], 'euler59': [1, 8, 59], 'euler61': [1, 14, 61], 'euler67': [1, -6, 67], 'euler7': [1, 2, 7], 'euler71': [1, 8, 71], 'euler73': [1, -16, 73], 'euler79': [1, 8, 79], 'euler83': [1, -6, 83], 'euler89': [1, 2, 89], 'euler97': [1, -4, 97], 'euler_factors': [[1, 1, 2], [1, 2, 3], [1, 1, 0], [1, 2, 7], [1, 1, 0], [1, -6, 13], [1, 0, 17], [1, 1, 0], [1, 0, 23], [1, -6, 29], [1, -4, 31], [1, 0, 37], [1, 6, 41], [1, 6, 43], [1, 4, 47], [1, -12, 53], [1, 8, 59], [1, 14, 61], [1, -6, 67], [1, 8, 71], [1, -16, 73], [1, 8, 79], [1, -6, 83], [1, 2, 89], [1, -4, 97]], 'index': 20, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1045/a', 'ModularForm/GL2/Q/holomorphic/1045/2/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/1045/2/a/a'], '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': '2-1045-1.1-c1-0-20', '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': '2-1045-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.888661802846398, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2084829519259382411, 'z1': {'__RealLiteral__': 0, 'data': '1.17080042590956595747782018947', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20695497
{'Lhash': '1484165862651727912213758692927', 'Lhash_array': ['1484165862651727912213758692927'], 'label': '2-1045-1.1-c1-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1045/2/a/a'}
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id: 24551543
{'Lhash': '1484165862651727912213758692927', 'Lhash_array': ['1484165862651727912213758692927'], 'label': '2-1045-1.1-c1-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1045/2/a/a/1/1'}
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id: 40569
{'Lhash': '2084829519259382411', 'Lhash_array': ['2084829519259382411'], 'label': '2-1045-1.1-c1-0-20', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1045/a'}