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lfunc_lfunctions • Show schema
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{'Lhash': '1482367131011458358236627779437', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.8660254037844386, 1.5], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-1.0, 1.7320508075688772], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6068630553617309, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-0.8660254037844386, -0.5]]]], 'bad_primes': [2, 19], 'central_character': '1216.1057', 'coefficient_field': 'CDF', 'conductor': 1216, 'conductor_radical': 38, 'conjugate': '2810503152835073441403292576904', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.8660254037844386, -1.5], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, -1.0], [-1.0, 0]], [[1.0, 0], [0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [1.0, 1.7320508075688772], [-0.5, 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'3.20312060153324186331548047291337', '4.34459692288072221695634179016292', '6.07511311539990027229873017073838', '6.24973198387071939405427140802475', '7.46563667873310485974817351382638', '7.989860403924489491363240210228510', '8.725386007813381043532035671217386', '9.335797461812900121233535170021180'], 'prelabel': '2-1216-152.69-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7790141560727448, 'root_angle': -0.5521732427912203, 'root_number': '-0.16317415307549660537721089504720 - 0.98659728145180615114454597699304*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.27608662139561013', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.16938147683957324175620717374', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.33145767731444444691075459073', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.20312060153324186331548047291', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6068630553617309, 'bad_primes': [2, 19], 'central_character': '152.69', 'conductor': 1216, 'conductor_radical': 38, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1216/1/p/a/1057/2'], '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': '2-1216-152.69-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1216-152.69-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7790141560727448, 'root_angle': -0.27608662139561013, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.16938147683957324175620717374', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1482367131011458358236627779437', 'Lhash_array': ['1482367131011458358236627779437'], 'label': '2-1216-152.69-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1216/1/p/a/1057/2'}