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lfunc_lfunctions • Show schema
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{'Lhash': '1741889640319621955593703314538', 'a10': [-10301415.798385905, 0], 'a2': [128.0, 0], 'a3': [-2187.0, 0], 'a4': [16384.0, 0], 'a5': [-80479.81092488988, 0], 'a6': [-279936.0, 0], 'a7': [425425.2702598304, 0], 'a8': [2097152.0, 0], 'a9': [4782969.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 111.300933977938, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '7.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-128.0, 0]]], [3, [[1.0, 0], [2187.0, 0]]], [13, [[1.0, 0], [62748517.0, 0]]]], 'bad_primes': [2, 3, 13], 'central_character': '78.1', 'coefficient_field': 'CDF', 'conductor': 78, 'conductor_radical': 78, 'degree': 2, 'euler_factors': [[[1.0, 0], [-128.0, 0]], [[1.0, 0], [2187.0, 0]], [[1.0, 0], [80479.81092488988, 0], [30517578125.0, 0]], [[1.0, 0], [-425425.2702598304, 0], [4747561509943.0, 0]], [[1.0, 0], [-18797164.391697362, 0], [4177248169415651.0, 0]], [[1.0, 0], [62748517.0, 0]], [[1.0, 0], [1906358920.841807, 0], [2862423051509816000, 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'prec': 10}, 'spectral_label': 'c15-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.37410863845763963938254475682', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.81368408913742127548972492668', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.19029324698499320408484023098', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 111.300933977938, 'bad_primes': [2, 3, 13], 'central_character': '1.1', 'conductor': 78, 'conductor_radical': 78, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/78/16/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': '2-78-1.1-c15-0-20', 'motivic_weight': 15, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [15], 'order_of_vanishing': 1, 'prelabel': '2-78-1.1-c15-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.549925780683862, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c15-0', 'z1': {'__RealLiteral__': 0, 'data': '1.37410863845763963938254475682', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1741889640319621955593703314538', 'Lhash_array': ['1741889640319621955593703314538'], 'label': '2-78-1.1-c15-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/78/16/a/f/1/2'}