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  • lfunc_lfunctions • Show schema
    {'Lhash': '1380109709160289363340734891099', 'a10': [0.0, 0.0], 'a2': [2.0, 0.0], 'a3': [-9.712116046324176, 0.0], 'a4': [4.0, 0.0], 'a5': [0.0, 0.0], 'a6': [-19.424232092648353, 0.0], 'a7': [-33.128757515974605, 0.0], 'a8': [8.0, 0.0], 'a9': [67.32519809726755, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 67.85219650660174, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 7}, 'bad_lfactors': [[2, [[1.0, 0], [-2.0, 0]]], [5, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [23.0, 0]]]], 'bad_primes': [2, 5, 23], 'central_character': '1150.1', 'coefficient_field': 'CDF', 'conductor': 1150, 'conductor_radical': 230, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.0, 0]], [[1.0, 0], [9.712116046324176, 0], [27.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [33.128757515974605, 0], [343.0, 0]], [[1.0, 0], [-1.5970472146313588, 0], [1331.0, 0]], [[1.0, 0], [-15.123841161082519, 0], [2197.0, 0]], [[1.0, 0], [-63.966074131956816, 0], [4913.0, 0]], [[1.0, 0], 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'6.34771995493651488144917614593335', '6.68508563298757123131148901683711', '7.87490516899741304820167837858421', '9.393373521622475278510054931253465'], 'prelabel': '2-1150-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.237244472917006, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.08871459447249319571461712656', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.82911248129271160349714659363', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.98825732862814895833999621705', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 67.85219650660174, 'bad_primes': [2, 5, 23], 'central_character': '1.1', 'conductor': 1150, 'conductor_radical': 230, 'degree': 2, 'index': 48, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1150/4/a/x/1/1'], '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': '2-1150-1.1-c3-0-48', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-1150-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.237244472917006, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.08871459447249319571461712656', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1380109709160289363340734891099', 'Lhash_array': ['1380109709160289363340734891099'], 'factors': ['2-1150-1.1-c3-0-48'], 'label': '2-1150-1.1-c3-0-48', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1150/4/a/x/1/1'}