Formats: - HTML - YAML - JSON - 2026-08-15T00:43:35.015655
  • lfunc_lfunctions • Show schema
    {'Lhash': '3595033003765547351658645003783', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, -2.288245611270737], 'a4': [0.0, 0.0], 'a5': [-2.23606797749979, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, -2.8284271247461903], 'a8': [0.0, 0.0], 'a9': [-2.23606797749979, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.034315276808656, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [2.23606797749979, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 5, 19], 'central_character': '380.229', 'coefficient_field': 'CDF', 'conductor': 380, 'conductor_radical': 190, 'conjugate': '530861864179002480172972330999', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 2.288245611270737], [-3.0, 0]], [[1.0, 0], [2.23606797749979, 0]], [[1.0, 0], [0, 2.8284271247461903], [-7.0, 0]], [[1.0, 0], [5.23606797749979, 0], [11.0, 0]], [[1.0, 0], [0, -4.036309709066021], [-13.0, 0]], [[1.0, 0], 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'10.06705981094389970561365768546078', '10.82859514215923855997715543252836', '11.60450118938691524018470651589309'], 'prelabel': '2-380-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7419286084132886, 'root_angle': 0.5, 'root_number': '-1.0 + 1.2246467991473532e-16*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.83598098964990282632676514655', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '3.71737393637441797905767167907', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '5.16370653955465194142215282014', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 3.034315276808656, 'bad_primes': [2, 5, 19], 'central_character': '5.4', 'conductor': 380, 'conductor_radical': 190, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/380/2/c/a/229/1'], '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': '2-380-5.4-c1-0-9', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-380-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7419286084132886, 'root_angle': 0.5, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.83598098964990282632676514655', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '3595033003765547351658645003783', 'Lhash_array': ['3595033003765547351658645003783'], 'factors': ['2-380-5.4-c1-0-9'], 'label': '2-380-5.4-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/380/2/c/a/229/1'}