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lfunc_lfunctions • Show schema
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{'Lhash': '1350575078894933175696727240021', 'a10': [-0.4543170543003763, -2.576560050395996], 'a2': [-0.8936326403234123, 0.44879918020046217], 'a3': [0.6475685200403952, 1.606441723764884], 'a4': [0.5971585917027862, -0.8021231927550437], 'a5': [-0.7503654895765841, 2.506395282308296], 'a6': [-1.2996580950195202, -1.1449405382159512], 'a7': [0.3184892519150703, -0.7383410768520693], 'a8': [-0.17364817766693036, 0.984807753012208], 'a9': [-2.1613100237053846, 2.0805621791791347], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.293576512744743, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.8936326403234123, -0.44879918020046217]]], [3, [[1.0, 0], [-0.6475685200403952, -1.606441723764884]]]], 'bad_primes': [2, 3], 'central_character': '162.25', 'coefficient_field': 'CDF', 'conductor': 162, 'conductor_radical': 6, 'conjugate': '3477945567743091489041791302473', 'degree': 2, 'euler_factors': [[[1.0, 0], 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1.1373550513119213, 'root_angle': -0.6483766618900068, 'root_number': '-0.4494406007695463 - 0.8933102184459267*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.324188330945', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.06541587930599642142530118216', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.79919556725813851265055859874', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.70421315745547264587977367909', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.293576512744743, 'bad_primes': [2, 3], 'central_character': '81.25', 'conductor': 162, 'conductor_radical': 6, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/162/2/g/a/25/3'], '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': '2-162-81.25-c1-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-162-81.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1373550513119213, 'root_angle': -0.3241883309450034, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.06541587930599642142530118216', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1350575078894933175696727240021', 'Lhash_array': ['1350575078894933175696727240021'], 'label': '2-162-81.25-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/2/g/a/25/3'}