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lfunc_lfunctions • Show schema
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{'Lhash': '2165536510793600956168110635182', 'a10': 0, 'a2': -1, 'a3': 1, 'a4': 1, 'a5': 0, 'a6': -1, 'a7': -2, 'a8': -1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.570828394149682, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, -1]], [5, [1]], [13, [1, -1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '1950.1', 'coefficient_field': '1.1.1.1', 'conductor': 1950, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[1, 1], [1, -1], [1], [1, 2, 7], [1, -4, 11], [1, -1], [1, 8, 17], [1, 6, 19], [1, 6, 23], [1, 4, 29], [1, 0, 31], [1, -2, 37], [1, 2, 41], [1, -4, 43], [1, 0, 47], [1, -10, 53], [1, -4, 59], [1, 10, 61], [1, 12, 67], [1, 8, 71], [1, -8, 73], [1, -8, 79], [1, 12, 83], [1, 14, 89], [1, -16, 97], [1, 16, 101], [1, -12, 103], [1, 12, 107], [1, -12, 109], [1, 20, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [[[1, -1], 1]], [1], [[[1, 2, 7], 1]], [[[1, -4, 11], 1]], 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1.6989928354696247, 2.1581529346366475, 2.507202444413777, 2.731333062371135, 2.821810312207346, 2.7764390590236427, 2.5997103200547045, 2.302618417023082, 1.9021539633497202], 'positive_zeros': ['1.70830709219379145242715005823878', '2.54833875126849207240384424642412', '3.80974243367827903050974784654063', '4.34999282857824787062750680048645', '6.04011696824586895486685368245047', '6.51341800580325524726586052919722', '7.21926473255081566972637327842706', '8.275106945738770193737766007203347', '8.907841935382063111565042358126358'], 'prelabel': '2-1950-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.9459888993951417, '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': 1559165868268307906, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.70830709219379145242715005824', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.54833875126849207240384424642', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.80974243367827903050974784654', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.570828394149682, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 1950, 'conductor_radical': 390, 'degree': 2, 'dirichlet_coefficients': [1, -1, 1, 1, 0, -1, -2, -1, 1, 0, 4, 1, 1, 2, 0, 1, -8, -1, -6, 0, -2, -4, -6, -1, 0, -1, 1, -2, -4, 0, 0, -1, 4, 8, 0, 1, 2, 6, 1, 0, -2, 2, 4, 4, 0, 6, 0, 1, -3, 0, -8, 1, 10, -1, 0, 2, -6, 4, 4, 0, -10, 0, -2, 1, 0, -4, -12, -8, -6, 0, -8, -1, 8, -2, 0, -6, -8, -1, 8, 0, 1, 2, -12, -2, 0, -4, -4, -4, -14, 0, -2, -6, 0, 0, 0, -1, 16, 3, 4, 0], 'euler11': [1, -4, 11], 'euler13': [1, -1, 0], 'euler17': [1, 8, 17], 'euler19': [1, 6, 19], 'euler2': [1, 1, 0], 'euler23': [1, 6, 23], 'euler29': [1, 4, 29], 'euler3': [1, -1, 0], 'euler31': [1, 0, 31], 'euler37': [1, -2, 37], 'euler41': [1, 2, 41], 'euler43': [1, -4, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, -10, 53], 'euler59': [1, -4, 59], 'euler61': [1, 10, 61], 'euler67': [1, 12, 67], 'euler7': [1, 2, 7], 'euler71': [1, 8, 71], 'euler73': [1, -8, 73], 'euler79': [1, -8, 79], 'euler83': [1, 12, 83], 'euler89': [1, 14, 89], 'euler97': [1, -16, 97], 'euler_factors': [[1, 1, 0], [1, -1, 0], [1, 0, 0], [1, 2, 7], [1, -4, 11], [1, -1, 0], [1, 8, 17], [1, 6, 19], [1, 6, 23], [1, 4, 29], [1, 0, 31], [1, -2, 37], [1, 2, 41], [1, -4, 43], [1, 0, 47], [1, -10, 53], [1, -4, 59], [1, 10, 61], [1, 12, 67], [1, 8, 71], [1, -8, 73], [1, -8, 79], [1, 12, 83], [1, 14, 89], [1, -16, 97]], 'index': 29, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1950/h', 'ModularForm/GL2/Q/holomorphic/1950/2/a/h/1/1', 'ModularForm/GL2/Q/holomorphic/1950/2/a/h'], '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': '2-1950-1.1-c1-0-29', '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': '2-1950-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.9459888993951417, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1559165868268307906, 'z1': {'__RealLiteral__': 0, 'data': '1.70830709219379145242715005824', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20607905
{'Lhash': '2165536510793600956168110635182', 'Lhash_array': ['2165536510793600956168110635182'], 'label': '2-1950-1.1-c1-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1950/2/a/h'}
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id: 24555208
{'Lhash': '2165536510793600956168110635182', 'Lhash_array': ['2165536510793600956168110635182'], 'label': '2-1950-1.1-c1-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1950/2/a/h/1/1'}
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id: 93701
{'Lhash': '1559165868268307906', 'Lhash_array': ['1559165868268307906'], 'label': '2-1950-1.1-c1-0-29', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1950/h'}