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lfunc_lfunctions • Show schema
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{'Lhash': '1793772571437938597193710715416', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.7071067811865476, 0.7071067811865476], 'a4': [0.0, 0.0], 'a5': [1.798173770234973, -1.3291241823241884], 'a6': [0.0, 0.0], 'a7': [0.0, 2.809987867315458], 'a8': [0.0, 0.0], 'a9': [0.0, 1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.228331357659873, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-0.7071067811865476, -0.7071067811865476]]], [5, [[1.0, 0], [-1.798173770234973, 1.3291241823241884]]], [13, [[1.0, 0], [-1.402050546479965, 3.3217848011445943]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '780.73', 'coefficient_field': 'CDF', 'conductor': 780, 'conductor_radical': 390, 'conjugate': '1738576662499091285724020669589', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [-1.798173770234973, 1.3291241823241884]], 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'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.41503705446515430762819875740', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.42389659532418458386005146653', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.87860890194723581511716050722', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.228331357659873, 'bad_primes': [2, 3, 5, 13], 'central_character': '65.8', 'conductor': 780, 'conductor_radical': 390, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/780/2/r/a/73/12'], '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': '2-780-65.8-c1-0-9', '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': '2-780-65.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4956625087659337, 'root_angle': -0.027844504616891846, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.41503705446515430762819875740', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1793772571437938597193710715416', 'Lhash_array': ['1793772571437938597193710715416'], 'label': '2-780-65.8-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/780/2/r/a/73/12'}