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  • lfunc_lfunctions • Show schema
    {'Lhash': '1793193767556770318581044975246', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.766044443118978, 0.6427876096865394], 'a4': [0.0, 0.0], 'a5': [2.2057370639048863, -0.8028226358791068], 'a6': [0.0, 0.0], 'a7': [1.786988976119769, 3.0951556992049274], 'a8': [0.0, 0.0], 'a9': [0.17364817766693036, 0.984807753012208], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.282356664340774, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-0.766044443118978, -0.6427876096865394]]], [19, [[1.0, 0], [1.0111443532371651, 4.239998478409703]]]], 'bad_primes': [2, 3, 19], 'central_character': '912.625', 'coefficient_field': 'CDF', 'conductor': 912, 'conductor_radical': 114, 'conjugate': '1922281593403367402154825934670', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.766044443118978, -0.6427876096865394]], [[1.0, 0], [-2.2057370639048863, 0.8028226358791068], 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-0.8080105178109808, 0.9204192399911713], 'positive_zeros': ['1.41458045871151046441376280028847', '2.18871816553686500591652462504098', '3.80250240178029009434576367534794', '4.47446856265032892073162926553727', '6.01409736151798036393196112228379', '6.54964547510504129503269014009013', '7.58846219502611489626254530472573', '8.171258247459167109130063505330490', '9.503515880773729719836220200401317', '9.790699208524700471456781143896841'], 'prelabel': '2-912-19.17-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.698584196266771, 'root_angle': -0.06252119136367988, 'root_number': '0.9238285703041198 - 0.3828064428531029*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0625211913637', 'prec': 40}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.41458045871151046441376280029', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.18871816553686500591652462504', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.80250240178029009434576367535', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 7.282356664340774, 'bad_primes': [2, 3, 19], 'central_character': '19.17', 'conductor': 912, 'conductor_radical': 114, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/912/2/bo/d/625/1'], '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': '2-912-19.17-c1-0-12', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-912-19.17-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.698584196266771, 'root_angle': -0.06252119136367988, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.41458045871151046441376280029', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1793193767556770318581044975246', 'Lhash_array': ['1793193767556770318581044975246'], 'factors': ['2-912-19.17-c1-0-12'], 'label': '2-912-19.17-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/912/2/bo/d/625/1'}