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lfunc_lfunctions • Show schema
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{'Lhash': '2998598152195355680195684107349', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.0662554376171682, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]]], 'bad_primes': [2, 3], 'central_character': '384.1', 'coefficient_field': '1.1.1.1', 'conductor': 384, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[1], [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], 1]], [[[1, 0, 5], 1]], [[[1, 2, 7], 1]], [[[1, 4, 11], 1]], [[[1, 6, 13], 1]], [[[1, -6, 17], 1]], 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-3.8958465900466477, -3.845262638641828, -3.0425794096601297, -1.7793361259761968, -0.45524851281010853, 0.5443441885966589, 0.965125214823801, 0.7583222700601836, 0.08993576801796428], 'positive_zeros': ['2.36547685273488160999702672857751', '3.77490371552045331982722842815488', '5.25073137830748218691985779847416', '5.81271121311664380914911812155612', '7.29744951786402483785793531451250', '7.73185283482156320096864018539249', '9.355375973689939441990781827381898', '10.03012842475637444340101123739259', '10.72157176858504266602545238224283'], 'prelabel': '2-384-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.7510726534376488, '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': 6150820184308250, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.36547685273488160999702672858', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.77490371552045331982722842815', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.25073137830748218691985779847', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.0662554376171682, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 384, 'conductor_radical': 6, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, -2, 0, 1, 0, -4, 0, -6, 0, 0, 0, 6, 0, 0, 0, 2, 0, -4, 0, -5, 0, -1, 0, -4, 0, -10, 0, 4, 0, 0, 0, -2, 0, 6, 0, -2, 0, 8, 0, 0, 0, 12, 0, -3, 0, -6, 0, 12, 0, 0, 0, 0, 0, -4, 0, -2, 0, -2, 0, 0, 0, 4, 0, 4, 0, 4, 0, -10, 0, 5, 0, 8, 0, 6, 0, 1, 0, 12, 0, 0, 0, 4, 0, 2, 0, 12, 0, 10, 0, 0, 0, -6, 0, -4, 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, 1, 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, 1, 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': 6, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/384/b', 'ModularForm/GL2/Q/holomorphic/384/2/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/384/2/a/b'], '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': '2-384-1.1-c1-0-6', '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': '2-384-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.7510726534376488, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 6150820184308250, 'z1': {'__RealLiteral__': 0, 'data': '2.36547685273488160999702672858', 'prec': 103}}
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lfunc_instances • Show schema
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id: 10502970
{'Lhash': '2998598152195355680195684107349', 'Lhash_array': ['2998598152195355680195684107349'], 'label': '2-384-1.1-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/384/2/a/b'}
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id: 24549177
{'Lhash': '2998598152195355680195684107349', 'Lhash_array': ['2998598152195355680195684107349'], 'label': '2-384-1.1-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/384/2/a/b/1/1'}
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id: 89350
{'Lhash': '6150820184308250', 'Lhash_array': ['6150820184308250'], 'label': '2-384-1.1-c1-0-6', 'type': 'ECQ', 'url': 'EllipticCurve/Q/384/b'}