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lfunc_lfunctions • Show schema
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{'Lhash': '532132372843167292856975777491', 'a10': [0, 0], 'a2': [0, 0.6180339887498949], 'a3': [0, 1.0], 'a4': [1.618033988749895, 0], 'a5': [0, 0], 'a6': [-0.6180339887498949, 0], 'a7': [0, 2.0], 'a8': [0, 2.23606797749979], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.97195037899008, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, -1.0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '1875.1249', 'coefficient_field': 'CDF', 'conductor': 1875, 'conductor_radical': 15, 'conjugate': '2432831929719387726082595895793', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -0.6180339887498949], [-2.0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -2.0], [-7.0, 0]], [[1.0, 0], [3.0, 0], [11.0, 0]], [[1.0, 0], [0, 1.0], [-13.0, 0]], [[1.0, 0], [0, 0.2360679774997897], [-17.0, 0]], [[1.0, 0], [6.708203932499369, 0], [19.0, 0]], [[1.0, 0], [0, -7.618033988749895], 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'5.78678932456484747606989159405536', '6.75517523272380675154696923869811', '7.00607146701682031854145591106577', '8.088592876974064850635118439010633', '8.606037261840449960165868714752649'], 'prelabel': '2-1875-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8693604612377586, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.41977842533846591014964943112', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.83194035763247316576318712521', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.55312829957554503856751277856', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.97195037899008, 'bad_primes': [3, 5], 'central_character': '5.4', 'conductor': 1875, 'conductor_radical': 15, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1875/2/b/a/1249/3'], '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': '2-1875-5.4-c1-0-13', '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': '2-1875-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8693604612377586, 'root_angle': 0.5, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.41977842533846591014964943112', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '532132372843167292856975777491', 'Lhash_array': ['532132372843167292856975777491'], 'label': '2-1875-5.4-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1875/2/b/a/1249/3'}