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lfunc_lfunctions • Show schema
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{'Lhash': '1292150787822312276263179154931', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-3.0, 0], 'a6': [0, 0], 'a7': [-2.0, -1.7320508075688772], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 24.1467615712352, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [2.0, 1.7320508075688772]]]], 'bad_primes': [2, 3, 7], 'central_character': '3024.1889', 'coefficient_field': 'CDF', 'conductor': 3024, 'conductor_radical': 42, 'conjugate': '138136875646468894244134192062', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.0, 0], [5.0, 0]], [[1.0, 0], [2.0, 1.7320508075688772]], [[1.0, 0], [0, -5.196152422706632], [-11.0, 0]], [[1.0, 0], [0, -3.4641016151377544], [-13.0, 0]], [[1.0, 0], [-6.0, 0], [17.0, 0]], [[1.0, 0], [0, 1.7320508075688772], [-19.0, 0]], [[1.0, 0], [0, 5.196152422706632], 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'7.81643054515517726610614443296388', '8.091557451854792137476252105068188', '8.782123655175865638387133269303999'], 'prelabel': '2-3024-21.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.9139354463846185, 'root_angle': 0.7271855258285052, 'root_number': '-0.6546536707079771437982924562468583555692080823954245575 + 0.7559289460184544544290330724683601216315026237378429087*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3635927629142526', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.01932724016355281992637817179', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.88869269192788205398542592838', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.35688742724583589401919427414', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 24.1467615712352, 'bad_primes': [2, 3, 7], 'central_character': '21.20', 'conductor': 3024, 'conductor_radical': 42, 'degree': 2, 'index': 39, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3024/2/k/a/1889/1'], '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': '2-3024-21.20-c1-0-39', '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': '2-3024-21.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.9139354463846185, 'root_angle': 0.3635927629142526, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.01932724016355281992637817179', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1292150787822312276263179154931', 'Lhash_array': ['1292150787822312276263179154931'], 'label': '2-3024-21.20-c1-0-39', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3024/2/k/a/1889/1'}