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lfunc_lfunctions • Show schema
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{'Lhash': '2145826501119264057297900193391', 'a10': [1.0, 0.0], 'a2': [1.0, 0.0], 'a3': [1.8216637715491628, 0.0], 'a4': [1.0, 0.0], 'a5': [1.0, 0.0], 'a6': [1.8216637715491628, 0.0], 'a7': [-3.0, 0.0], 'a8': [1.0, 0.0], 'a9': [0.31845889657472076, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.11987282308817, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [11, [[1.0, 0], [1.0, 0]]], [73, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 5, 11, 73], 'central_character': '8030.1', 'coefficient_field': 'CDF', 'conductor': 8030, 'conductor_radical': 8030, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.8216637715491628, 0], [3.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [3.0, 0], [7.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.4585815646986044, 0], [13.0, 0]], [[1.0, 0], [2.7001203016300765, 0], [17.0, 0]], [[1.0, 0], [8.401788806166854, 0], [19.0, 0]], 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'5.32584035231292581580031468271603', '6.28676583600724803227376334865980', '6.64055042180571680814519653490208', '7.33603137542634248140442201975611'], 'prelabel': '2-8030-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.007488546547425, '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': '1.69275863612017914628669453738', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.72935851969472907526536802035', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.81869688111315920307314155906', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 64.11987282308817, 'bad_primes': [2, 5, 11, 73], 'central_character': '1.1', 'conductor': 8030, 'conductor_radical': 8030, 'degree': 2, 'index': 229, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8030/2/a/u/1/4'], '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': '2-8030-1.1-c1-0-229', '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': '2-8030-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.007488546547425, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.69275863612017914628669453738', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2145826501119264057297900193391', 'Lhash_array': ['2145826501119264057297900193391'], 'label': '2-8030-1.1-c1-0-229', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8030/2/a/u/1/4'}