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lfunc_lfunctions • Show schema
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{'Lhash': '697530622189220279792426437786', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.766044443118978, -0.6427876096865394], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.1133407984528387, 0.6427876096865394], 'a8': [0.0, 0.0], 'a9': [0.17364817766693036, 0.984807753012208], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.820589166085193, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.766044443118978, 0.6427876096865394]]], [19, [[1.0, 0], [0.5, 0.8660254037844386]]]], 'bad_primes': [2, 3, 19], 'central_character': '3648.2111', 'coefficient_field': 'CDF', 'conductor': 3648, 'conductor_radical': 114, 'conjugate': '1222094930955970144250492258942', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.766044443118978, 0.6427876096865394]], [[1.0, 0], [0, 0], [-0.766044443118978, 0.6427876096865394]], [[1.0, 0], [1.1133407984528387, -0.6427876096865394], 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'9.015953940434456666755799416294754'], 'prelabel': '2-3648-228.59-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3492920981333854, 'root_angle': -0.15929225866108168, 'root_number': '0.87737566105569984257905819925628 - 0.47980407395839575821773071266438*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.07964612933054084', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.55025463803956389330141263975', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.16803266547935812452378559317', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.58089608787631806614970873336', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.820589166085193, 'bad_primes': [2, 3, 19], 'central_character': '228.59', 'conductor': 3648, 'conductor_radical': 114, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3648/1/cu/a/2111/1'], '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': '2-3648-228.59-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3648-228.59-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3492920981333854, 'root_angle': -0.07964612933054084, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.55025463803956389330141263975', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '697530622189220279792426437786', 'Lhash_array': ['697530622189220279792426437786'], 'label': '2-3648-228.59-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3648/1/cu/a/2111/1'}