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lfunc_lfunctions • Show schema
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{'Lhash': '3147952989284707540072382287789', 'a10': [0.0, 0.0], 'a2': [-0.5, 0.36327126400268045], 'a3': [0.0, 0.0], 'a4': [-0.19098300562505258, 0.5877852522924731], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.30901699437494745, -0.9510565162951535], 'a8': [-0.30901699437494745, -0.9510565162951535], 'a9': [-0.8090169943749475, 0.5877852522924731], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.03842800597274119, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [-0.30901699437494745, 0.9510565162951535]]], [11, [[1.0, 0], [0.8090169943749475, 0.5877852522924731]]]], 'bad_primes': [7, 11], 'central_character': '77.69', 'coefficient_field': 'CDF', 'conductor': 77, 'conductor_radical': 77, 'conjugate': '4251769227450584662969413472589', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, -0.36327126400268045], [0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [0, 0], [0.8090169943749475, -0.5877852522924731]], 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'13.64000830322253703856461079701630', '14.91028726419622096218462723069965'], 'prelabel': '2-77-77.69-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.1960306250888906, 'root_angle': -0.19243252579565653, 'root_number': '0.82276102126875003317897573342151 - 0.56838745753297851562149393210771*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.09621626289782827', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.48329704472032446623488429724', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.02305203641943809312723389715', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.14991031457579889100996880776', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.03842800597274119, 'bad_primes': [7, 11], 'central_character': '77.69', 'conductor': 77, 'conductor_radical': 77, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/77/1/j/a/69/1'], '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': '2-77-77.69-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': '2-77-77.69-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.1960306250888906, 'root_angle': -0.09621626289782827, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.48329704472032446623488429724', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3147952989284707540072382287789', 'Lhash_array': ['3147952989284707540072382287789'], 'label': '2-77-77.69-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/77/1/j/a/69/1'}