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lfunc_lfunctions • Show schema
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{'Lhash': '1330512945189692017174713060507', 'a10': [0.0, 0.0], 'a2': [0.6104249647797777, 1.8786948647835056], 'a3': [0.0, 0.0], 'a4': [-2.347858762962574, 1.705819241042368], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.5877852522924731, 0.8090169943749475], 'a8': [-3.0397921457095998, -2.208538270154693], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.3458520537546707, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-0.5877852522924731, -0.8090169943749475]]], [11, [[1.0, 0], [0.8910065241883679, -0.4539904997395468]]]], 'bad_primes': [3, 7, 11], 'central_character': '693.314', 'coefficient_field': 'CDF', 'conductor': 693, 'conductor_radical': 231, 'conjugate': '3582521065186103858426952764017', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.6104249647797777, -1.8786948647835056], [-0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], 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'10.48091789185026035367920581138135'], 'prelabel': '2-693-231.83-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5880918752666718, 'root_angle': 0.9389150103588607, 'root_number': '-0.98164283850439478323780161927000 + 0.19072843944476319959780821695850*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.4694575051794303', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.04958964635061490947976977415', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.46170051947185904185253277059', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.41433405185479067865796405359', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.3458520537546707, 'bad_primes': [3, 7, 11], 'central_character': '231.83', 'conductor': 693, 'conductor_radical': 231, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/693/1/bp/a/314/4'], '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': '2-693-231.83-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': '2-693-231.83-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5880918752666718, 'root_angle': 0.46945750517943036, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.04958964635061490947976977415', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1330512945189692017174713060507', 'Lhash_array': ['1330512945189692017174713060507'], 'label': '2-693-231.83-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/693/1/bp/a/314/4'}