Formats: - HTML - YAML - JSON - 2026-07-26T20:20:12.195433
  • lfunc_lfunctions • Show schema
    {'Lhash': '1439825468640309112456718954869', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-537.0977745780135, 0.0], 'a6': [0.0, 0.0], 'a7': [-343.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 78.72102642199872, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [343.0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '252.1', 'coefficient_field': 'CDF', 'conductor': 252, 'conductor_radical': 42, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [537.0977745780135, 0], [78125.0, 0]], [[1.0, 0], [343.0, 0]], [[1.0, 0], [-2419.019002741134, 0], [19487171.0, 0]], [[1.0, 0], [-5190.961291644865, 0], [62748517.0, 0]], [[1.0, 0], [-25751.586939783618, 0], [410338673.0, 0]], [[1.0, 0], [34136.3419579627, 0], [893871739.0, 0]], [[1.0, 0], [-93525.69935933684, 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['1.13582202255186179223433697523151', '3.19372785401240981995850190577496', '3.82574341543921192698948856484299', '4.97208592264084290486570141197567', '6.53580384491488422215690756299549', '7.38897798401130006308341552390075', '8.344970414571502587369838789718617', '9.104695967605969306161676816502519', '10.64691483109122279997255709782919'], 'prelabel': '2-252-1.1-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.87248704828577, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c7-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.13582202255186179223433697523', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.19372785401240981995850190577', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.82574341543921192698948856484', 'prec': 103}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 78.72102642199872, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 252, 'conductor_radical': 42, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/252/8/a/g/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': '2-252-1.1-c7-0-9', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 1, 'prelabel': '2-252-1.1-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.87248704828577, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '1.13582202255186179223433697523', 'prec': 103}}
  • lfunc_instances • Show schema
    {'Lhash': '1439825468640309112456718954869', 'Lhash_array': ['1439825468640309112456718954869'], 'factors': ['2-252-1.1-c7-0-9'], 'label': '2-252-1.1-c7-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/252/8/a/g/1/1'}