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lfunc_lfunctions • Show schema
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{'Lhash': '592454966235111673956970623096', 'a10': [-244.87165316257338, -75.5329017309584], 'a2': [0.7589883738944887, 1.5760555981415505], 'a3': [6.184026756402879, 9.070301357830509], 'a4': [37.99545942223263, -47.64479912675238], 'a5': [-99.63965219306074, 107.38600577842638], 'a6': [-9.601694819877451, 16.630623266798644], 'a7': [-494.10186971643066, 285.2698474878786], 'a8': [213.07657366667672, 48.633337484831024], 'a9': [222.3054269651467, -566.4249901907024], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.892325595653594, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 10}, 'bad_lfactors': [[43, [[1.0, 0], [-68072.62002629762, -41078.966050222145]]]], 'bad_primes': [43], 'central_character': '43.12', 'coefficient_field': 'CDF', 'conductor': 43, 'conductor_radical': 43, 'conjugate': '3114815419957827120904313716606', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.7589883738944887, -1.5760555981415505], [-39.90334731895894, 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3.1452067651672113, 'root_angle': -0.7761474809264941, 'root_number': '-0.7627422263642368 - 0.6467026334575477*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.388073740463', 'prec': 50}, 'spectral_label': 'c6-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.46736456096691417960652749547', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.91288442704404054699071510203', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.31962293719793786413122226038', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.892325595653594, 'bad_primes': [43], 'central_character': '43.12', 'conductor': 43, 'conductor_radical': 43, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/43/7/h/a/12/11'], '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': '2-43-43.12-c6-0-4', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'prelabel': '2-43-43.12-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.1452067651672113, 'root_angle': -0.38807374046324705, 'self_dual': False, 'spectral_label': 'c6-0', 'z1': {'__RealLiteral__': 0, 'data': '0.46736456096691417960652749547', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '592454966235111673956970623096', 'Lhash_array': ['592454966235111673956970623096'], 'label': '2-43-43.12-c6-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/43/7/h/a/12/11'}