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lfunc_lfunctions • Show schema
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{'Lhash': '735971608910883444126065892120', 'a10': [-0.13650867803002387, 0.7741791839317218], 'a2': [1.2905593002988025, -0.848814204778941], 'a3': [0.0, 0.0], 'a4': [0.15289822127491512, -0.35445791864584114], 'a5': [-0.3492442382830814, 0.3701772661118565], 'a6': [0.0, 0.0], 'a7': [-3.961484491117239, -0.46303112968900606], 'a8': [0.4329162028320922, 2.455189790539577], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.28', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '2547476552501976909652522277762', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.2905593002988025, 0.848814204778941], [0.7921595320783137, -1.836432213760548]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.3492442382830814, -0.3701772661118565], [-0.29072414455237916, 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0, 'data': '-0.196805018105', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.58057922962240399209997424250', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.09968287009453208064166035050', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.56487943771476065912798403413', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '81.67', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/g/b/28/7'], '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': '2-3e6-81.67-c1-0-7', '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': '2-3e6-81.67-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': -0.19680501810494685, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.58057922962240399209997424250', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '735971608910883444126065892120', 'Lhash_array': ['735971608910883444126065892120'], 'label': '2-3e6-81.67-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/g/b/28/7'}