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lfunc_lfunctions • Show schema
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{'Lhash': '2325724990732976518182310119361', 'a10': [0, 0], 'a2': [0, 0], 'a3': [242.2690669750293, 18.833459242761794], 'a4': [0, 0], 'a5': [0, -4818.412854768017], 'a6': [0, 0], 'a7': [-670.5296166515819, 0], 'a8': [0, 0], 'a9': [58339.60162590246, 9125.529197312282], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 121.98859251335509, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '5.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-242.2690669750293, -18.833459242761794]]]], 'bad_primes': [2, 3], 'central_character': '192.65', 'coefficient_field': 'CDF', 'conductor': 192, 'conductor_radical': 6, 'conjugate': '355407028570988734806796568555', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-242.2690669750293, -18.833459242761794]], [[1.0, 0], [0, 4818.412854768017], [-9765625.0, 0]], [[1.0, 0], [670.5296166515819, 0], [282475249.0, 0]], [[1.0, 0], [0, 233268.35286308153], [-25937424601.0, 0]], [[1.0, 0], 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0.07750394750107733549516350729359215513749344272053072607*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.48765248090174657', 'prec': 67}, 'spectral_label': 'c10-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.83467352148474514857011694273', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.54219500353257052941683496170', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.56908189253170827078516892934', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 121.98859251335509, 'bad_primes': [2, 3], 'central_character': '3.2', 'conductor': 192, 'conductor_radical': 6, 'degree': 2, 'index': 75, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/192/11/e/h/65/4'], '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': '2-192-3.2-c10-0-75', 'motivic_weight': 10, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [10], 'order_of_vanishing': 0, 'prelabel': '2-192-3.2-c10-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.044844612458569, 'root_angle': -0.48765248090174657, 'self_dual': False, 'spectral_label': 'c10-0', 'z1': {'__RealLiteral__': 0, 'data': '1.83467352148474514857011694273', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2325724990732976518182310119361', 'Lhash_array': ['2325724990732976518182310119361'], 'label': '2-192-3.2-c10-0-75', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/192/11/e/h/65/4'}