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  • lfunc_lfunctions • Show schema
    {'Lhash': '4869420999683932500799286456578', 'a10': [1.7320508075688772, -4.701954038432138e-61], 'a2': [-0.8660254037844386, -0.5], 'a3': [-1.3660254037844386, -2.366025403784439], 'a4': [0.5, 0.8660254037844386], 'a5': [-1.5, 0.8660254037844386], 'a6': [7.813461677362708e-61, 2.732050807568877], 'a7': [-2.0, -3.4641016151377544], 'a8': [0.0, -1.0], 'a9': [-2.232050807568877, 3.866025403784439], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5908929749574752, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0.8660254037844386, 0.5]]], [37, [[1.0, 0], [0.5, -6.06217782649107]]]], 'bad_primes': [2, 37], 'central_character': '74.27', 'coefficient_field': 'CDF', 'conductor': 74, 'conductor_radical': 74, 'conjugate': '1088680085243616484844461720627', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.8660254037844386, 0.5]], [[1.0, 0], [1.3660254037844386, 2.366025403784439], [-1.5, 2.598076211353316]], [[1.0, 0], 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'root_angle': 0.39325463329069277, 'root_number': '-0.7833862120526781 + 0.6215352305105128*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.393254633291', 'prec': 40}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.84129585771287123298936841095', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '5.41074817060273860177902105043', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '6.47761877574681070624724372865', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 0.5908929749574752, 'bad_primes': [2, 37], 'central_character': '37.27', 'conductor': 74, 'conductor_radical': 74, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/74/2/e/a/27/1'], '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': '2-74-37.27-c1-0-3', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-74-37.27-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7686956321961738, 'root_angle': 0.39325463329069277, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.84129585771287123298936841095', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '4869420999683932500799286456578', 'Lhash_array': ['4869420999683932500799286456578'], 'factors': ['2-74-37.27-c1-0-3'], 'label': '2-74-37.27-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/74/2/e/a/27/1'}