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lfunc_lfunctions • Show schema
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{'Lhash': '1051209075240158132664745708436', 'a10': [-0.646335396156159, 0.0], 'a2': [0.1729759339829194, 0.0], 'a3': [0.0, 0.0], 'a4': [-1.9700793262627367, 0.0], 'a5': [-3.7365625452843725, 0.0], 'a6': [0.0, 0.0], 'a7': [3.031497725063497, 0.0], 'a8': [-0.6867281794465764, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.1', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '1051209075240158132664745708436', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.1729759339829194, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.7365625452843725, 0], [5.0, 0]], [[1.0, 0], [-3.031497725063497, 0], [7.0, 0]], [[1.0, 0], [2.4916961029475386, 0], [11.0, 0]], [[1.0, 0], [0.7651387316536139, 0], [13.0, 0]], [[1.0, 0], [-4.622782970928876, 0], [17.0, 0]], 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'5.58476695851257777719103905831276', '7.35368398273338432605387539774928', '7.86624929305702151148931412360595', '8.441906588099580354933921432222121', '9.399411302239532608072998550108171', '10.57484870106314574914296963722031'], 'prelabel': '2-3e6-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, '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': '0.829257742670493852461042322898', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '3.01302537208609964447957061125', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.10284203300566520078979411695', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '1.1', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/a/b/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': '2-3e6-1.1-c1-0-2', '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': '2-3e6-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.829257742670493852461042322898', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1051209075240158132664745708436', 'Lhash_array': ['1051209075240158132664745708436'], 'label': '2-3e6-1.1-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/a/b/1/4'}