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  • lfunc_lfunctions • Show schema
    {'Lhash': '1138718108367351951925318054129', 'a10': [-1.0, 2.0], 'a2': [0, 1.0], 'a3': [0, 0], 'a4': [-1.0, 0], 'a5': [2.0, 1.0], 'a6': [0, 0], 'a7': [0, -2.0], 'a8': [0, -1.0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22.27826216393724, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, -1.0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-2.0, -1.0]]], [31, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '2790.559', 'coefficient_field': 'CDF', 'conductor': 2790, 'conductor_radical': 930, 'conjugate': '1328033901018199049202104013237', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.0, -1.0]], [[1.0, 0], [0, 2.0], [-7.0, 0]], [[1.0, 0], [-4.0, 0], [11.0, 0]], [[1.0, 0], [0, 2.0], [-13.0, 0]], [[1.0, 0], [0, -6.0], [-17.0, 0]], [[1.0, 0], [4.0, 0], [19.0, 0]], [[1.0, 0], [0, 0], [-23.0, 0]], [[1.0, 0], [-2.0, 0], [29.0, 0]], 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'0.4472135954999579392818347337462552470881236719223051449 - 0.8944271909999158785636694674925104941762473438446102897*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.17620819117478337', 'prec': 57}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.898290197758227478234619723578', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.00862243358654684701717613574', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.65625198489205159502731350559', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 22.27826216393724, 'bad_primes': [2, 3, 5, 31], 'central_character': '5.4', 'conductor': 2790, 'conductor_radical': 930, 'degree': 2, 'index': 38, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2790/2/d/h/559/2'], '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': '2-2790-5.4-c1-0-38', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-2790-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.71998539869958, 'root_angle': -0.17620819117478337, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.898290197758227478234619723578', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1138718108367351951925318054129', 'Lhash_array': ['1138718108367351951925318054129'], 'factors': ['2-2790-5.4-c1-0-38'], 'label': '2-2790-5.4-c1-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2790/2/d/h/559/2'}