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lfunc_lfunctions • Show schema
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{'Lhash': '1188795930907803567957543156001', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [3.414213562373095, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 36.41178332170387, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 5, 19], 'central_character': '4560.1', 'coefficient_field': 'CDF', 'conductor': 4560, 'conductor_radical': 570, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-3.414213562373095, 0], [7.0, 0]], [[1.0, 0], [-1.4142135623730951, 0], [11.0, 0]], [[1.0, 0], [-4.242640687119285, 0], [13.0, 0]], [[1.0, 0], [-2.8284271247461903, 0], [17.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-4.82842712474619, 0], [23.0, 0]], 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'GL2', 'index': 33, 'label': '2-4560-1.1-c1-0-33', 'leading_term': '2.0938981914388528617099800791465', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/4560/2/a/bg/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [2.093898191438853, 2.0871424544184283, 2.0668389356385197, 2.032886216426028, 1.9851397405126068, 1.9234466957431122, 1.8476913900002025, 1.757848094277215, 1.654037983372968, 1.5365867198520307, 1.4060793554181132, 1.263409505883668, 1.1098201314573355, 0.9469336737647375, 0.776769731397049, 0.601748879411618, 0.4246816505415633, 0.24874210066141775, 0.07742578579588501, -0.08550760982694061, -0.23610633047262944, -0.3703121878674212, -0.4840582314880534, -0.5733764482980731, -0.6345130482205854, -0.6640484735245988, -0.6590188927157932, 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'6.19425871892741556483277878447157', '6.80101487378957457616175655600419', '7.73372965530860845693000267229165', '8.232734835395951866786952815297494'], 'prelabel': '2-4560-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.034217705859134, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.937794634178985329137266693806', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.58748057196747311901682976967', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.01785667320687823454346050223', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 36.41178332170387, 'bad_primes': [2, 3, 5, 19], 'central_character': '1.1', 'conductor': 4560, 'conductor_radical': 570, 'degree': 2, 'index': 33, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4560/2/a/bg/1/2'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '2-4560-1.1-c1-0-33', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-4560-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.034217705859134, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.937794634178985329137266693806', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1188795930907803567957543156001', 'Lhash_array': ['1188795930907803567957543156001'], 'label': '2-4560-1.1-c1-0-33', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4560/2/a/bg/1/2'}