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lfunc_lfunctions • Show schema
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{'Lhash': '1100380259344323966362988464843', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-0.6784479339461047, -0.5410441730642654], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-0.4338837391175581, 0.9009688679024191], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9262646634468525, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [29, [[1.0, 0], [-0.4338837391175581, -0.9009688679024191]]]], 'bad_primes': [2, 29], 'central_character': '1856.769', 'coefficient_field': 'CDF', 'conductor': 1856, 'conductor_radical': 58, 'conjugate': '1655675610076570325223988225790', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0.4338837391175581, -0.9009688679024191]], [[1.0, 0], [0.6784479339461047, 0.5410441730642654], [0.2225209339563144, 0.9749279121818236]], [[1.0, 0], [0, 0], [-0.9009688679024191, -0.4338837391175581]], [[1.0, 0], [0, 0], 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'7.09059352510724518759700615924098', '7.77268781838790362610809992694624', '8.446440603506879860410981755959864', '9.606992605294654343686926128015796'], 'prelabel': '2-1856-29.15-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9624264457333104, 'root_angle': -0.17287621996705888, 'root_number': '0.85610729784048958052901787464383 - 0.51679811782189693304488186730477*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.08643810998352944', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.868046967473695138475411780637', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.77050554572069811797245974033', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.32858372658675056549833515028', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9262646634468525, 'bad_primes': [2, 29], 'central_character': '29.15', 'conductor': 1856, 'conductor_radical': 58, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1856/1/ca/a/769/1'], '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': '2-1856-29.15-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': '2-1856-29.15-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9624264457333104, 'root_angle': -0.08643810998352944, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.868046967473695138475411780637', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1100380259344323966362988464843', 'Lhash_array': ['1100380259344323966362988464843'], 'label': '2-1856-29.15-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1856/1/ca/a/769/1'}