Formats: - HTML - YAML - JSON - 2026-10-17T02:16:45.319470
  • lfunc_lfunctions • Show schema
    {'Lhash': '118962512104987230885431352979', 'a10': [0, 0], 'a2': [0, 0], 'a3': [99.20433458271872, 99.20433458271872], 'a4': [0, -512.0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [-1256.5882380477703, 1256.5882380477703], 'a8': [0, 0], 'a9': [0, 19683.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 38.627687712290495, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.5', 'prec': 7}, 'bad_lfactors': [[3, [[1.0, 0], [-99.20433458271872, -99.20433458271872]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '75.68', 'coefficient_field': 'CDF', 'conductor': 75, 'conductor_radical': 15, 'conjugate': '2275521978345984867424935617089', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [0, 512.0]], [[1.0, 0], [-99.20433458271872, -99.20433458271872]], [[1.0, 0], [0, 0]], [[1.0, 0], [1256.5882380477703, -1256.5882380477703], [0, -40353607.0]], [[1.0, 0], [0, 0], [-2357947691.0, 0]], [[1.0, 0], [119177.47394537275, 119177.47394537275], [0, 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'positive_zeros': ['0.093844874986505801546363170257752', '2.05002086155482247184820147514370', '3.14578044074516842061387578902572', '4.53191575359585932695404139154824', '6.78567365751891155390584756703619', '7.37245134327516390497639798200470', '8.675046737623734136584123105403676', '9.508818482861755860764298602181498', '11.40829267787463308060616683721176', '12.31634297752545486394480761815697'], 'prelabel': '2-75-15.8-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.2151176748546355, 'root_angle': -0.4631040955873917, 'root_number': '-0.9732489894677301 - 0.22975292054736132*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4631040955873917', 'prec': 54}, 'spectral_label': 'c9-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.093844874986505801546363170257752', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.05002086155482247184820147514370', 'prec': 110}, 'z3': {'__RealLiteral__': 0, 'data': '3.14578044074516842061387578902572', 'prec': 110}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 38.627687712290495, 'bad_primes': [3, 5], 'central_character': '15.8', 'conductor': 75, 'conductor_radical': 15, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/75/10/e/b/68/2'], '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': '2-75-15.8-c9-0-3', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [9], 'order_of_vanishing': 0, 'prelabel': '2-75-15.8-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.2151176748546355, 'root_angle': -0.4631040955873917, 'self_dual': False, 'spectral_label': 'c9-0', 'z1': {'__RealLiteral__': 0, 'data': '0.093844874986505801546363170257752', 'prec': 107}}
  • lfunc_instances • Show schema
    {'Lhash': '118962512104987230885431352979', 'Lhash_array': ['118962512104987230885431352979'], 'factors': ['2-75-15.8-c9-0-3'], 'label': '2-75-15.8-c9-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/75/10/e/b/68/2'}