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  • lfunc_lfunctions • Show schema
    {'Lhash': '200217918947557860365268769764', 'a10': [1.6663000721192656, 5.663336401809757], 'a2': [-0.7437946008821793, -2.533131780579161], 'a3': [-1.3460119720745434, 1.1663260130646074], 'a4': [-4.181019143816307, 2.6869778485244873], 'a5': [-2.236067637185942, 0.001233665140103969], 'a6': [3.9556139277619624, 2.542118712116163], 'a7': [1.872765944824589, 0.8552635497562837], 'a8': [5.925819902629273, 5.134752174990118], 'a9': [0.02448734539696351, -0.17031322821106518], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9182796232447249, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[5, [[1.0, 0], [2.236067637185942, -0.001233665140103969]]], [23, [[1.0, 0], [1.214557322335877, 4.639488173361401]]]], 'bad_primes': [5, 23], 'central_character': '115.9', 'coefficient_field': 'CDF', 'conductor': 115, 'conductor_radical': 115, 'conjugate': '3268534263063213448445162881570', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'0.19364580763719977 - 0.9810715066622497*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.218984371401', 'prec': 40}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.15794408878243766500998845186', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '4.68915387490177524824104342953', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '5.55721676861352435705218101184', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 0.9182796232447249, 'bad_primes': [5, 23], 'central_character': '115.9', 'conductor': 115, 'conductor_radical': 115, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/115/2/j/a/9/1'], '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': '2-115-115.9-c1-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-115-115.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9582690766401287, 'root_angle': -0.2189843714013617, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.15794408878243766500998845186', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '200217918947557860365268769764', 'Lhash_array': ['200217918947557860365268769764'], 'factors': ['2-115-115.9-c1-0-0'], 'label': '2-115-115.9-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/115/2/j/a/9/1'}