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lfunc_lfunctions • Show schema
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{'Lhash': '3337050154571569124581500962888', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.5, -0.8660254037844386], 'a4': [-1.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.5, -0.8660254037844386], 'a8': [0.0, 0.0], 'a9': [-0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.13624474844880965, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.5, 0.8660254037844386]]], [7, [[1.0, 0], [-0.5, 0.8660254037844386]]], [13, [[1.0, 0], [-0.5, -0.8660254037844386]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.23', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': '1971609908966263913256462033259', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], 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-1.1135581321320367], 'positive_zeros': ['2.63246840570324538629877096216668', '4.06639766111190915217367692288493', '4.96317471180409279700529314242258', '5.95423315817357622615728553005963', '7.906844754017836480402007131655862', '8.676571157915595226815636698646914', '9.184746018849948894942346576849703', '10.36961570628701526227411392802658', '11.06044224702581829300215777348618', '12.46799419406341853253916434073366'], 'prelabel': '2-273-273.23-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.3691134628387451, 'root_angle': 0.3172422830645206, 'root_number': '0.54312153351364132555738938383435 + 0.83965409534747734858463905761595*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.1586211415322603', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.63246840570324538629877096217', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.06639766111190915217367692288', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.96317471180409279700529314242', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.13624474844880965, 'bad_primes': [3, 7, 13], 'central_character': '273.23', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/1/bp/a/23/1'], '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': '2-273-273.23-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-273-273.23-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.3691134628387451, 'root_angle': 0.1586211415322603, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.63246840570324538629877096217', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3337050154571569124581500962888', 'Lhash_array': ['3337050154571569124581500962888'], 'label': '2-273-273.23-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/1/bp/a/23/1'}