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lfunc_lfunctions • Show schema
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{'Lhash': '1973047276496615441329236185494', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [7.685998649774449, 0.0], 'a4': [0.0, 0.0], 'a5': [15.709301030121772, 0.0], 'a6': [0.0, 0.0], 'a7': [19.871658351897615, 0.0], 'a8': [0.0, 0.0], 'a9': [32.07457524433465, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 33.74909252328365, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-11.0, 0]]], [13, [[1.0, 0], [13.0, 0]]]], 'bad_primes': [2, 11, 13], 'central_character': '572.1', 'coefficient_field': 'CDF', 'conductor': 572, 'conductor_radical': 286, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-7.685998649774449, 0], [27.0, 0]], [[1.0, 0], [-15.709301030121772, 0], [125.0, 0]], [[1.0, 0], [-19.871658351897615, 0], [343.0, 0]], [[1.0, 0], [-11.0, 0]], [[1.0, 0], [13.0, 0]], [[1.0, 0], [-7.579742865499848, 0], [4913.0, 0]], [[1.0, 0], [1.7824252972490695, 0], [6859.0, 0]], 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'2.18742202928476696523509778943582', '3.33981906219135146903986113952713', '4.66402147626118778785467521925125', '5.65764296844575329293227230806288', '6.87519404329366735230874457463229', '7.88040182372089375475037719681325', '8.661370498009900731120759316535020', '9.339298744594617627154938090803718', '10.06232573638346338379634477098077'], 'prelabel': '2-572-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.809396915625894, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.55645986058097202722516663971', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.18742202928476696523509778944', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.33981906219135146903986113953', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 33.74909252328365, 'bad_primes': [2, 11, 13], 'central_character': '1.1', 'conductor': 572, 'conductor_radical': 286, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/572/4/a/d/1/7'], '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': '2-572-1.1-c3-0-20', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-572-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.809396915625894, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.55645986058097202722516663971', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1973047276496615441329236185494', 'Lhash_array': ['1973047276496615441329236185494'], 'label': '2-572-1.1-c3-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/572/4/a/d/1/7'}