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lfunc_lfunctions • Show schema
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{'Lhash': '1541496794988653932068464894736', 'a10': [0.0, 0.0], 'a2': [-0.7889966758171688, 0.0], 'a3': [1.0, 0.0], 'a4': [-1.3774842455494574, 0.0], 'a5': [0.0, 0.0], 'a6': [-0.7889966758171688, 0.0], 'a7': [-1.0, 0.0], 'a8': [2.66482384236338, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 46.113607167289445, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [11, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 5, 7, 11], 'central_character': '5775.1', 'coefficient_field': 'CDF', 'conductor': 5775, 'conductor_radical': 1155, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7889966758171688, 0], [2.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [4.934558490213747, 0], [13.0, 0]], [[1.0, 0], [2.3063604173544143, 0], [17.0, 0]], [[1.0, 0], [-6.4975444776703215, 0], [19.0, 0]], 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'6.60508582064244152528399466973410', '7.40412648564070109598724407621289', '7.62407697754335412653310735796466'], 'prelabel': '2-5775-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.790700049868898, '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': '1.21602655709003799528017336266', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.29058400490187993712726742467', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.25940445872498645512227128484', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 46.113607167289445, 'bad_primes': [3, 5, 7, 11], 'central_character': '1.1', 'conductor': 5775, 'conductor_radical': 1155, 'degree': 2, 'index': 134, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5775/2/a/ce/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': '2-5775-1.1-c1-0-134', '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': '2-5775-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.790700049868898, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.21602655709003799528017336266', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1541496794988653932068464894736', 'Lhash_array': ['1541496794988653932068464894736'], 'label': '2-5775-1.1-c1-0-134', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5775/2/a/ce/1/3'}