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lfunc_lfunctions • Show schema
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{'Lhash': '2399543349365963185351417057674', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.198766312851504, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '1152.1', 'coefficient_field': '1.1.1.1', 'conductor': 1152, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[1], [1], [1, 0, 5], [1, 2, 7], [1, -4, 11], [1, 6, 13], [1, 6, 17], [1, 0, 19], [1, -4, 23], [1, -4, 29], [1, 10, 31], [1, 2, 37], [1, -2, 41], [1, -8, 43], [1, 12, 47], [1, 12, 53], [1, -4, 59], [1, 2, 61], [1, -4, 67], [1, 4, 71], [1, 10, 73], [1, -6, 79], [1, 12, 83], [1, 2, 89], [1, 6, 97], [1, -4, 101], [1, -10, 103], [1, -12, 107], [1, -2, 109], [1, -14, 113]], 'euler_factors_factorization': [[1], [1], [[[1, 0, 5], 1]], [[[1, 2, 7], 1]], [[[1, -4, 11], 1]], [[[1, 6, 13], 1]], [[[1, 6, 17], 1]], [[[1, 0, 19], 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0.9645862326342182, 1.394803485979123, 1.77503988374714, 2.0762910366926763, 2.274724527604974, 2.3532955010239722], 'positive_zeros': ['1.89290593869789230240007927287551', '3.04605515966584879794132221617625', '4.14300745369301184814326433788647', '4.99207876302239290655432150673757', '6.19174829158795733764599049329239', '6.86617713649335228477722027286356', '7.56237844869816331895572212868657', '8.825925610400178898897528083053705', '9.392805556443339877432708764972153'], 'prelabel': '2-1152-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.032946803498456, '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': 1620517197723338625, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.89290593869789230240007927288', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.04605515966584879794132221618', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.14300745369301184814326433789', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.198766312851504, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 1152, 'conductor_radical': 6, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 4, 0, -6, 0, 0, 0, -6, 0, 0, 0, 0, 0, 4, 0, -5, 0, 0, 0, 4, 0, -10, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 8, 0, 0, 0, -12, 0, -3, 0, 0, 0, -12, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, 0, 4, 0, 0, 0, -4, 0, -10, 0, 0, 0, -8, 0, 6, 0, 0, 0, -12, 0, 0, 0, 0, 0, -2, 0, 12, 0, 0, 0, 0, 0, -6, 0, 0, 0], 'euler11': [1, -4, 11], 'euler13': [1, 6, 13], 'euler17': [1, 6, 17], 'euler19': [1, 0, 19], 'euler2': [1, 0, 0], 'euler23': [1, -4, 23], 'euler29': [1, -4, 29], 'euler3': [1, 0, 0], 'euler31': [1, 10, 31], 'euler37': [1, 2, 37], 'euler41': [1, -2, 41], 'euler43': [1, -8, 43], 'euler47': [1, 12, 47], 'euler5': [1, 0, 5], 'euler53': [1, 12, 53], 'euler59': [1, -4, 59], 'euler61': [1, 2, 61], 'euler67': [1, -4, 67], 'euler7': [1, 2, 7], 'euler71': [1, 4, 71], 'euler73': [1, 10, 73], 'euler79': [1, -6, 79], 'euler83': [1, 12, 83], 'euler89': [1, 2, 89], 'euler97': [1, 6, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 0, 5], [1, 2, 7], [1, -4, 11], [1, 6, 13], [1, 6, 17], [1, 0, 19], [1, -4, 23], [1, -4, 29], [1, 10, 31], [1, 2, 37], [1, -2, 41], [1, -8, 43], [1, 12, 47], [1, 12, 53], [1, -4, 59], [1, 2, 61], [1, -4, 67], [1, 4, 71], [1, 10, 73], [1, -6, 79], [1, 12, 83], [1, 2, 89], [1, 6, 97]], 'index': 16, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1152/j', 'ModularForm/GL2/Q/holomorphic/1152/2/a/j/1/1', 'ModularForm/GL2/Q/holomorphic/1152/2/a/j'], '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': '2-1152-1.1-c1-0-16', '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': '2-1152-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.032946803498456, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1620517197723338625, 'z1': {'__RealLiteral__': 0, 'data': '1.89290593869789230240007927288', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20719791
{'Lhash': '2399543349365963185351417057674', 'Lhash_array': ['2399543349365963185351417057674'], 'label': '2-1152-1.1-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1152/2/a/j'}
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id: 24551982
{'Lhash': '2399543349365963185351417057674', 'Lhash_array': ['2399543349365963185351417057674'], 'label': '2-1152-1.1-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1152/2/a/j/1/1'}
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id: 41376
{'Lhash': '1620517197723338625', 'Lhash_array': ['1620517197723338625'], 'label': '2-1152-1.1-c1-0-16', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1152/j'}