Formats: - HTML - YAML - JSON - 2026-09-09T18:34:12.037503
  • lfunc_lfunctions • Show schema
    {'Lhash': '2028730794253092076782429994752,2745958581162122501843733047976', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 1, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.04843858273743684, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]]], 'bad_primes': [3, 7], 'central_character': '441.1', 'coefficient_field': '1.1.1.1', 'conductor': 194481, 'conductor_radical': 21, 'degree': 4, 'euler_factors': [[1, 0, -1, 0, 1], [1], [1, 0, 1, 0, 1], [1], [1, 0, -1, 0, 1], [1, 0, -2, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, -1, 0, 1], [1, 0, 2, 0, 1], [1, 0, 1, 0, 1], [1, -2, 3, -2, 1], [1, 0, -2, 0, 1], [1, 4, 6, 4, 1], [1, 0, 1, 0, 1], [1, 0, -1, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 2, 3, 2, 1], [1, 0, 2, 0, 1], [1, 0, 1, 0, 1], [1, 2, 3, 2, 1], [1, 0, -2, 0, 1], [1, 0, 1, 0, 1], [1, 0, -2, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, -1, 0, 1], [1, -2, 3, -2, 1], [1, 0, 2, 0, 1]], 'euler_factors_factorization': 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'6.52676742060248642637602831358551', '6.87834066262158608905266997487743', '7.45134713216296716150282292033619', '7.78623839517945642711281070580184', '8.549787287379746596472714024378443', '8.591224729354076119968779401601982', '9.609722008000977215470084698991377', '9.698700915356889802984301980440014', '10.26463573503206159132979439772461', '10.67421072164152299370820510375181', '11.33626292852082760209850477604900', '11.49438970359066473817352013659400'], 'prelabel': '4-21e4-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.4691350238163359, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c0e2-0', 'trace_hash': 719039733210388411, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.60038641080423647027116313974', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.16617937203495717213378069952', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.05249497320041956745119721480', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 0.04843858273743684, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 194481, 'conductor_radical': 21, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1], 'euler11': [1, 0, -1, 0, 1], 'euler13': [1, 0, -2, 0, 1], 'euler17': [1, 0, 1, 0, 1], 'euler19': [1, 0, 1, 0, 1], 'euler2': [1, 0, -1, 0, 1], 'euler23': [1, 0, -1, 0, 1], 'euler29': [1, 0, 2, 0, 1], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, 1, 0, 1], 'euler37': [1, -2, 3, -2, 1], 'euler41': [1, 0, -2, 0, 1], 'euler43': [1, 4, 6, 4, 1], 'euler47': [1, 0, 1, 0, 1], 'euler5': [1, 0, 1, 0, 1], 'euler53': [1, 0, -1, 0, 1], 'euler59': [1, 0, 1, 0, 1], 'euler61': [1, 0, 1, 0, 1], 'euler67': [1, 2, 3, 2, 1], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 0, 2, 0, 1], 'euler73': [1, 0, 1, 0, 1], 'euler79': [1, 2, 3, 2, 1], 'euler83': [1, 0, -2, 0, 1], 'euler89': [1, 0, 1, 0, 1], 'euler97': [1, 0, -2, 0, 1], 'euler_factors': [[1, 0, -1, 0, 1], [1, 0, 0, 0, 0], [1, 0, 1, 0, 1], [1, 0, 0, 0, 0], [1, 0, -1, 0, 1], [1, 0, -2, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, -1, 0, 1], [1, 0, 2, 0, 1], [1, 0, 1, 0, 1], [1, -2, 3, -2, 1], [1, 0, -2, 0, 1], [1, 4, 6, 4, 1], [1, 0, 1, 0, 1], [1, 0, -1, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 2, 3, 2, 1], [1, 0, 2, 0, 1], [1, 0, 1, 0, 1], [1, 2, 3, 2, 1], [1, 0, -2, 0, 1], [1, 0, 1, 0, 1], [1, 0, -2, 0, 1]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/441/1/m/a'], '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': '4-21e4-1.1-c0e2-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0], 'nu_real_doubled': [0, 0], 'order_of_vanishing': 0, 'prelabel': '4-21e4-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.4691350238163359, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e2-0', 'trace_hash': 719039733210388411, 'z1': {'__RealLiteral__': 0, 'data': '1.60038641080423647027116313974', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '2028730794253092076782429994752,2745958581162122501843733047976', 'Lhash_array': ['2028730794253092076782429994752', '2745958581162122501843733047976'], 'factors': ['2-21e2-7.5-c0-0-0', '2-21e2-7.3-c0-0-0'], 'label': '4-21e4-1.1-c0e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/1/m/a'}