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lfunc_lfunctions • Show schema
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{'Lhash': '4693330801369853259271583528483', 'a10': [-7.00893229087635, -4.404004047916641], 'a2': [2.581685999435539, -0.2908861514553586], 'a3': [-2.1140140752765615, 1.3283230823887235], 'a4': [2.680776197845674, -0.6118696734587126], 'a5': [-2.491037431501465, -1.9865360623323927], 'a6': [-5.071329751425791, 4.044250523009685], 'a7': [1.3016093805373377, -5.7027233046427455], 'a8': [-3.065979969874161, 1.0728327918372522], 'a9': [-1.2003403527972873, 2.492532425752754], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7901927666448612, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[29, [[1.0, 0], [19.927169966983097, -21.069121887420152]]]], 'bad_primes': [29], 'central_character': '29.15', 'coefficient_field': 'CDF', 'conductor': 29, 'conductor_radical': 29, 'conjugate': '5136192757788275059366593718370', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.581685999435539, 0.2908861514553586], [3.8997116487272945, 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False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.00158451139842', 'prec': 57}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.70238518447027919563140712172', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.69523961997338967315373210074', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.64677035675330715675302602732', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7901927666448612, 'bad_primes': [29], 'central_character': '29.15', 'conductor': 29, 'conductor_radical': 29, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/29/3/f/a/15/4'], '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': '2-29-29.15-c2-0-3', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-29-29.15-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8889278748272332, 'root_angle': -0.001584511398415149, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '3.70238518447027919563140712172', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4693330801369853259271583528483', 'Lhash_array': ['4693330801369853259271583528483'], 'label': '2-29-29.15-c2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/29/3/f/a/15/4'}