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lfunc_lfunctions • Show schema
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{'Lhash': '1099232408577853470164034905923', 'a10': [282.7000566893242, 489.65086148851134], 'a2': [3.5413812651491097, -6.133852280210808], 'a3': [0.0, 0.0], 'a4': [-9.08276253029822, -15.73180617555937], 'a5': [-39.9138126514911, 69.13275143616802], 'a6': [0.0, 0.0], 'a7': [43.15867542417507, 122.24699888189774], 'a8': [97.98630072715727, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.104180648217781, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-43.15867542417507, -122.24699888189774]]]], 'bad_primes': [3, 7], 'central_character': '63.37', 'coefficient_field': 'CDF', 'conductor': 63, 'conductor_radical': 21, 'conjugate': '2684425441595147804442275406879', 'degree': 2, 'euler_factors': [[[1.0, 0], [-3.5413812651491097, 6.133852280210808], [-16.0, -27.712812921102035]], [[1.0, 0], [0, 0]], [[1.0, 0], [39.9138126514911, -69.13275143616802], [-1562.5, 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'6.53172781641714239469902512069663', '7.78351928278602256665776457930560', '8.711884023178081049163715470371251', '10.55273099568533605101876896910608', '11.89183494484657478897741506401556', '13.14834119740066171576691001842358', '13.95172127208168416479548769332736'], 'prelabel': '2-63-7.2-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.178707386378586, 'root_angle': -0.12820249520476468, 'root_number': '0.9199826859024761 - 0.3919589999472726*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0641012476024', 'prec': 54}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.867141472878998590617865335301', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '4.14113630618112886663513500779', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.94295543733906248290774680853', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10.104180648217781, 'bad_primes': [3, 7], 'central_character': '7.2', 'conductor': 63, 'conductor_radical': 21, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/63/6/e/d/37/2'], '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': '2-63-7.2-c5-0-4', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-63-7.2-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.178707386378586, 'root_angle': -0.06410124760238234, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.867141472878998590617865335301', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1099232408577853470164034905923', 'Lhash_array': ['1099232408577853470164034905923'], 'label': '2-63-7.2-c5-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/63/6/e/d/37/2'}