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lfunc_lfunctions • Show schema
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{'Lhash': '2059114679112069876351479262021', 'a10': -1, 'a2': 1, 'a3': 1, 'a4': 1, 'a5': -1, 'a6': 1, 'a7': 0, 'a8': 1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 53.994841846789825, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, -1]], [7, [1]], [23, [1, -1]]], 'bad_primes': [2, 3, 7, 23], 'central_character': '6762.1', 'coefficient_field': '1.1.1.1', 'conductor': 6762, 'conductor_radical': 966, 'degree': 2, 'euler_factors': [[1, -1], [1, -1], [1, 1, 5], [1], [1, 3, 11], [1, 2, 13], [1, -2, 17], [1, -2, 19], [1, -1], [1, 7, 29], [1, 7, 31], [1, 2, 37], [1, -2, 41], [1, 6, 43], [1, 6, 47], [1, 9, 53], [1, -9, 59], [1, 6, 61], [1, -10, 67], [1, 8, 71], [1, -10, 73], [1, 15, 79], [1, 1, 83], [1, 0, 89], [1, 5, 97], [1, -10, 101], [1, -8, 103], [1, -3, 107], [1, -10, 109], [1, -10, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [[[1, -1], 1]], [[[1, 1, 5], 1]], [1], [[[1, 3, 11], 1]], [[[1, 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-1.4187146135727835, -1.8698115037303888, -2.2871678166688776, -2.6470667782995347, -2.929273265909997, -3.118082935217247, -3.20311064764427, -3.1797764162861566, -3.0494640748854756], 'positive_zeros': ['1.62435506971822069186221672196872', '2.45029171979846019904856915719334', '3.35147961504264492296698201906941', '3.78997615771395228444527853046599', '4.82751614525428780249962178035155', '5.32708612752837430175687490946549', '6.10713988924064581993303601635740', '7.16217378049248910897621172940144', '7.53850829679288581690779032209360'], 'prelabel': '2-6762-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.348118252096235, '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': 2292621296758125434, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.62435506971822069186221672197', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.45029171979846019904856915719', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.35147961504264492296698201907', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 53.994841846789825, 'bad_primes': [2, 3, 7, 23], 'central_character': '1.1', 'conductor': 6762, 'conductor_radical': 966, 'degree': 2, 'dirichlet_coefficients': [1, 1, 1, 1, -1, 1, 0, 1, 1, -1, -3, 1, -2, 0, -1, 1, 2, 1, 2, -1, 0, -3, 1, 1, -4, -2, 1, 0, -7, -1, -7, 1, -3, 2, 0, 1, -2, 2, -2, -1, 2, 0, -6, -3, -1, 1, -6, 1, 0, -4, 2, -2, -9, 1, 3, 0, 2, -7, 9, -1, -6, -7, 0, 1, 2, -3, 10, 2, 1, 0, -8, 1, 10, -2, -4, 2, 0, -2, -15, -1, 1, 2, -1, 0, -2, -6, -7, -3, 0, -1, 0, 1, -7, -6, -2, 1, -5, 0, -3, -4], 'euler11': [1, 3, 11], 'euler13': [1, 2, 13], 'euler17': [1, -2, 17], 'euler19': [1, -2, 19], 'euler2': [1, -1, 0], 'euler23': [1, -1, 0], 'euler29': [1, 7, 29], 'euler3': [1, -1, 0], 'euler31': [1, 7, 31], 'euler37': [1, 2, 37], 'euler41': [1, -2, 41], 'euler43': [1, 6, 43], 'euler47': [1, 6, 47], 'euler5': [1, 1, 5], 'euler53': [1, 9, 53], 'euler59': [1, -9, 59], 'euler61': [1, 6, 61], 'euler67': [1, -10, 67], 'euler7': [1, 0, 0], 'euler71': [1, 8, 71], 'euler73': [1, -10, 73], 'euler79': [1, 15, 79], 'euler83': [1, 1, 83], 'euler89': [1, 0, 89], 'euler97': [1, 5, 97], 'euler_factors': [[1, -1, 0], [1, -1, 0], [1, 1, 5], [1, 0, 0], [1, 3, 11], [1, 2, 13], [1, -2, 17], [1, -2, 19], [1, -1, 0], [1, 7, 29], [1, 7, 31], [1, 2, 37], [1, -2, 41], [1, 6, 43], [1, 6, 47], [1, 9, 53], [1, -9, 59], [1, 6, 61], [1, -10, 67], [1, 8, 71], [1, -10, 73], [1, 15, 79], [1, 1, 83], [1, 0, 89], [1, 5, 97]], 'index': 141, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/6762/bh', 'ModularForm/GL2/Q/holomorphic/6762/2/a/bh/1/1', 'ModularForm/GL2/Q/holomorphic/6762/2/a/bh'], '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': '2-6762-1.1-c1-0-141', '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': '2-6762-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.348118252096235, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2292621296758125434, 'z1': {'__RealLiteral__': 0, 'data': '1.62435506971822069186221672197', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21877327
{'Lhash': '2059114679112069876351479262021', 'Lhash_array': ['2059114679112069876351479262021'], 'label': '2-6762-1.1-c1-0-141', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6762/2/a/bh'}
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id: 24576536
{'Lhash': '2059114679112069876351479262021', 'Lhash_array': ['2059114679112069876351479262021'], 'label': '2-6762-1.1-c1-0-141', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6762/2/a/bh/1/1'}
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id: 34592
{'Lhash': '2292621296758125434', 'Lhash_array': ['2292621296758125434'], 'label': '2-6762-1.1-c1-0-141', 'type': 'ECQ', 'url': 'EllipticCurve/Q/6762/bh'}