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  • lfunc_lfunctions • Show schema
    {'Lhash': '2453457787346880036809728961429', 'a10': [0.6909827500311696, 0.2862144264287686], 'a2': [-0.5288553009739936, -0.5288553009739936], 'a3': [1.1767627582982172, 2.8409566107791284], 'a4': [0.0, -1.4406241412634133], 'a5': [-0.9238795325112867, 0.3826834323650898], 'a6': [0.8801177407328622, -2.1247921861624435], 'a7': [2.9865511514626575, 1.2370699916568164], 'a8': [-1.8195923157662508, 1.8195923157662508], 'a9': [-4.564943531452362, 4.564943531452362], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6787284171808836, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[5, [[1.0, 0], [0.9238795325112867, -0.3826834323650898]]], [17, [[1.0, 0], [3.4715214383556825, 2.224531164770881]]]], 'bad_primes': [5, 17], 'central_character': '85.66', 'coefficient_field': 'CDF', 'conductor': 85, 'conductor_radical': 85, 'conjugate': '3556379770082247222594845734259', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5288553009739936, 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'4.09948290286126213997464928232615', '6.70682957295278224979330017064012', '7.37143188237714541528540026542247', '8.277640514884716915290997025451718', '9.038122943085563692180363056723486', '11.34577158764887912473525712202804', '12.21643197598732643501210002392927', '13.02613305535379477211567049259205', '14.12384495018135912635278722047062'], 'prelabel': '2-85-17.15-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8238497540091176, 'root_angle': -0.08471208355423293, 'root_number': '0.8616614904754062 - 0.507483473456724*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0847120835542', 'prec': 40}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.93543693104800046984715487414', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '4.09948290286126213997464928233', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '6.70682957295278224979330017064', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 0.6787284171808836, 'bad_primes': [5, 17], 'central_character': '17.15', 'conductor': 85, 'conductor_radical': 85, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/85/2/l/a/66/2'], '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': '2-85-17.15-c1-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-85-17.15-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8238497540091176, 'root_angle': -0.08471208355423293, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.93543693104800046984715487414', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '2453457787346880036809728961429', 'Lhash_array': ['2453457787346880036809728961429'], 'factors': ['2-85-17.15-c1-0-0'], 'label': '2-85-17.15-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/85/2/l/a/66/2'}