Formats: - HTML - YAML - JSON - 2026-08-15T02:12:28.923746
  • lfunc_lfunctions • Show schema
    {'Lhash': '610471442439210446829856920787', 'a10': [66.04807179985042, 0.0], 'a2': [-2.641922871994017, 0.0], 'a3': [6.665343643170264, 0.0], 'a4': [-25.020243538434887, 0.0], 'a5': [-25.0, 0.0], 'a6': [-17.60932382059145, 0.0], 'a7': [12.880167212877463, 0.0], 'a8': [150.64308557086017, 0.0], 'a9': [-198.57319411844975, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 97.0322109868533, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 7}, 'bad_lfactors': [[5, [[1.0, 0], [25.0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 11], 'central_character': '605.1', 'coefficient_field': 'CDF', 'conductor': 605, 'conductor_radical': 55, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.641922871994017, 0], [32.0, 0]], [[1.0, 0], [-6.665343643170264, 0], [243.0, 0]], [[1.0, 0], [25.0, 0]], [[1.0, 0], [-12.880167212877463, 0], [16807.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-485.166703868196, 0], [371293.0, 0]], [[1.0, 0], [266.66109434987504, 0], 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2.5091997455000197], 'positive_zeros': ['0.48157705469417235621744734632288', '1.83845906849806565650435669895141', '3.30816119961775258030121866390628', '4.11749504103314156394810269504939', '5.23411303961112226660731322437767', '6.27889669609778865954084275779292', '7.63872478912060923491486570895008', '8.264812775868235978315032746429688', '8.864191099771209038191500749952706', '9.687938288064523197167890096645906'], 'prelabel': '2-605-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.850492931161025, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.48157705469417235621744734632', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '1.83845906849806565650435669895', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.30816119961775258030121866391', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 97.0322109868533, 'bad_primes': [5, 11], 'central_character': '1.1', 'conductor': 605, 'conductor_radical': 55, 'degree': 2, 'index': 31, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/605/6/a/c/1/2'], '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': '2-605-1.1-c5-0-31', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-605-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.850492931161025, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.48157705469417235621744734632', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '610471442439210446829856920787', 'Lhash_array': ['610471442439210446829856920787'], 'factors': ['2-605-1.1-c5-0-31'], 'label': '2-605-1.1-c5-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/605/6/a/c/1/2'}