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lfunc_lfunctions • Show schema
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{'Lhash': '1936029559438648749801096696833', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [2.6690790882822886, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [3.6690790882822886, 0.0], 'a8': [0.0, 0.0], 'a9': [4.123983179505812, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.346236985957799, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [23, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 5, 23], 'central_character': '920.1', 'coefficient_field': 'CDF', 'conductor': 920, 'conductor_radical': 230, 'conjugate': '1936029559438648749801096696833', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-2.6690790882822886, 0], [3.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-3.6690790882822886, 0], [7.0, 0]], [[1.0, 0], [1.214174997058765, 0], [11.0, 0]], [[1.0, 0], [-2.2141749970587647, 0], [13.0, 0]], [[1.0, 0], [-1.214174997058765, 0], [17.0, 0]], 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'7.78037878588799609529744487741569', '8.476557987426808450293619736966415', '8.845705517746448356968639695938126', '9.990020666548238193387097792698514'], 'prelabel': '2-920-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.710394249174426, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.52725803079340913300722093006', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.58051813204220411644192487717', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.69275157339682111977888467977', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.346236985957799, 'bad_primes': [2, 5, 23], 'central_character': '1.1', 'conductor': 920, 'conductor_radical': 230, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/920/2/a/g/1/3'], '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': '2-920-1.1-c1-0-12', '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': '2-920-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.710394249174426, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.52725803079340913300722093006', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1936029559438648749801096696833', 'Lhash_array': ['1936029559438648749801096696833'], 'label': '2-920-1.1-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/920/2/a/g/1/3'}