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  • lfunc_lfunctions • Show schema
    {'Lhash': '1276373925132429441615414881256', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 1.0], 'a4': [0, 0], 'a5': [0, -3.414213562373095], 'a6': [0, 0], 'a7': [1.4142135623730951, 0], 'a8': [0, 0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.265021750468673, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [2, 3], 'central_character': '1536.769', 'coefficient_field': 'CDF', 'conductor': 1536, 'conductor_radical': 6, 'conjugate': '1294063253647901775282645504776', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, 3.414213562373095], [-5.0, 0]], [[1.0, 0], [-1.4142135623730951, 0], [7.0, 0]], [[1.0, 0], [0, -4.82842712474619], [-11.0, 0]], [[1.0, 0], [0, 0.8284271247461901], [-13.0, 0]], [[1.0, 0], [-4.82842712474619, 0], [17.0, 0]], [[1.0, 0], [0, -2.8284271247461903], [-19.0, 0]], [[1.0, 0], 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'5.69256996572227893868721698322558', '6.23428632156070182196063512697139', '7.00525879278427592204392860888074', '7.915337892010674828851189332263719', '8.311849590901972414916399424558236', '9.574890922532682282061293267054257'], 'prelabel': '2-1536-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.5021453068752977, 'root_angle': 0.0, 'root_number': '1', 'self_dual': False, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.00688148998046423973535354506', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.58708227562947187906135834894', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.09503193862240682454721253132', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 12.265021750468673, 'bad_primes': [2, 3], 'central_character': '8.5', 'conductor': 1536, 'conductor_radical': 6, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1536/2/d/e/769/3'], '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': '2-1536-8.5-c1-0-16', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1536-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.5021453068752977, 'root_angle': 0.0, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.00688148998046423973535354506', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1276373925132429441615414881256', 'Lhash_array': ['1276373925132429441615414881256'], 'factors': ['2-1536-8.5-c1-0-16'], 'label': '2-1536-8.5-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1536/2/d/e/769/3'}