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lfunc_lfunctions • Show schema
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{'Lhash': '2949924611861648451651801438667', 'a10': [0.0, 0.0], 'a2': [1.618033988749895, 0.0], 'a3': [-2.23606797749979, 0.0], 'a4': [0.6180339887498949, 0.0], 'a5': [0.0, 0.0], 'a6': [-3.618033988749895, 0.0], 'a7': [1.2360679774997898, 0.0], 'a8': [-2.23606797749979, 0.0], 'a9': [2.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.591398116223624, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [5, 23], 'central_character': '575.1', 'coefficient_field': 'CDF', 'conductor': 575, 'conductor_radical': 115, 'conjugate': '2949924611861648451651801438667', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.618033988749895, 0], [2.0, 0]], [[1.0, 0], [2.23606797749979, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.2360679774997898, 0], [7.0, 0]], [[1.0, 0], [0.7639320225002103, 0], [11.0, 0]], [[1.0, 0], [3.0, 0], [13.0, 0]], [[1.0, 0], [5.23606797749979, 0], 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'8.526534161097957062624098187443184', '9.547864028753442484523812998477762', '10.76009312718436085231162643313412'], 'prelabel': '2-575-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.142754796103284, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.32708019964692189665792439050', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.93241212986199430247095182147', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.85469906029089226711569754979', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.591398116223624, 'bad_primes': [5, 23], 'central_character': '1.1', 'conductor': 575, 'conductor_radical': 115, 'degree': 2, 'index': 29, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/575/2/a/f/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': '2-575-1.1-c1-0-29', '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': '2-575-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.142754796103284, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.32708019964692189665792439050', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2949924611861648451651801438667', 'Lhash_array': ['2949924611861648451651801438667'], 'label': '2-575-1.1-c1-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/575/2/a/f/1/2'}