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  • lfunc_lfunctions • Show schema
    {'Lhash': '4558939942977367281097301599348', 'a10': [-0.3594841311045039, 1.575002887004851], 'a2': [0.6234898018587335, 0.7818314824680298], 'a3': [-0.760452999006923, -3.3317622816547043], 'a4': [-0.2225209339563144, 0.9749279121818236], 'a5': [1.0072521523647233, 1.2630542490907535], 'a6': [2.1307419542234567, -2.6718659003901353], 'a7': [0.3384334231378015, 1.4827737092684516], 'a8': [-0.9009688679024191, 0.4338837391175581], 'a9': [-7.8194445340510805, 3.7656460207722624], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.46313233172342644, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.6234898018587335, -0.7818314824680298]]], [29, [[1.0, 0], [4.3170279591716065, 3.2192032554237135]]]], 'bad_primes': [2, 29], 'central_character': '58.53', 'coefficient_field': 'CDF', 'conductor': 58, 'conductor_radical': 58, 'conjugate': '3077632170218498285778086068901', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'sign_arg': {'__RealLiteral__': 0, 'data': '0.052360394611', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.59636949026535389544487755160', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.81328645179728076489521002190', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.82175864823020080384906413696', 'prec': 103}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 0.46313233172342644, 'bad_primes': [2, 29], 'central_character': '29.24', 'conductor': 58, 'conductor_radical': 58, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/58/2/d/b/53/1'], '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': '2-58-29.24-c1-0-2', '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': '2-58-29.24-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6805382661712907, 'root_angle': 0.05236039461099521, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.59636949026535389544487755160', 'prec': 103}}
  • lfunc_instances • Show schema
    {'Lhash': '4558939942977367281097301599348', 'Lhash_array': ['4558939942977367281097301599348'], 'factors': ['2-58-29.24-c1-0-2'], 'label': '2-58-29.24-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/58/2/d/b/53/1'}