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lfunc_lfunctions • Show schema
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{'Lhash': '1332012633611551987759395897645', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-3.1622776601683795, 0], 'a4': [0, 0], 'a5': [0, 2.23606797749979], 'a6': [0, 0], 'a7': [0, -4.242640687119285], 'a8': [0, 0], 'a9': [7.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.692473971915598, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, -2.23606797749979]]], [23, [[1.0, 0], [-4.743416490252569, -0.7071067811865476]]]], 'bad_primes': [2, 5, 23], 'central_character': '1840.1839', 'coefficient_field': 'CDF', 'conductor': 1840, 'conductor_radical': 230, 'conjugate': '401932737712013735056501099271', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [3.1622776601683795, 0], [3.0, 0]], [[1.0, 0], [0, -2.23606797749979]], [[1.0, 0], [0, 4.242640687119285], [-7.0, 0]], [[1.0, 0], [0, 0], [11.0, 0]], [[1.0, 0], [0, 0], [-13.0, 0]], [[1.0, 0], [0, 0], [17.0, 0]], [[1.0, 0], [0, 0], 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'8.934018647053878880677392408365390', '9.352822479559527115912665098617923'], 'prelabel': '2-1840-460.459-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.833076306560515, 'root_angle': 0.2735519809641282, 'root_number': '-0.1474419561548971334579251375353471544607771374765932225 + 0.9890707100936805070769772308194006375499533225457559461*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.27355198096412825', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.05077269191663283650414639431', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.26038205265691797041900241180', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.97095303718592121737034638264', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.692473971915598, 'bad_primes': [2, 5, 23], 'central_character': '460.459', 'conductor': 1840, 'conductor_radical': 230, 'degree': 2, 'index': 43, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1840/2/m/c/1839/2'], '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': '2-1840-460.459-c1-0-43', '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': '2-1840-460.459-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.833076306560515, 'root_angle': 0.2735519809641282, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.05077269191663283650414639431', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1332012633611551987759395897645', 'Lhash_array': ['1332012633611551987759395897645'], 'factors': ['2-1840-460.459-c1-0-43'], 'label': '2-1840-460.459-c1-0-43', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1840/2/m/c/1839/2'}