Formats: - HTML - YAML - JSON - 2026-08-15T00:56:08.281938
  • lfunc_lfunctions • Show schema
    {'Lhash': '114444222084109448642617691699,2401874983918228218396222226677', 'a10': -1, 'a2': 1, 'a3': -1, 'a4': 0, 'a5': -1, 'a6': -1, 'a7': 0, 'a8': -1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8616683420922173, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1, -1, 1]], [3, [1, 1, 1]], [5, [1, 1, 1]], [31, [1, -2, 1]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '1860.1', 'coefficient_field': '1.1.1.1', 'conductor': 3459600, 'conductor_radical': 930, 'degree': 4, 'euler_factors': [[1, -1, 1], [1, 1, 1], [1, 1, 1], [1, 0, -1, 0, 1], [1, 0, 1, 0, 1], [1, 0, -1, 0, 1], [1, 3, 4, 3, 1], [1, 3, 4, 3, 1], [1, 4, 6, 4, 1], [1, 0, 2, 0, 1], [1, -2, 1], [1, 0, -1, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, -1, 0, 1], [1, 0, 1, 0, 1], [1, 0, -1, 0, 1], [1, 0, -1, 0, 1], [1, 0, -1, 0, 1], [1, 1, 0, 1, 1], [1, 1, 0, 1, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -1, 0, 1], [1, 0, 1, 0, 1], [1, 4, 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'10.10823562432668908806115536355493'], 'prelabel': '4-1860e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.9634629850167492, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c0e2-0', 'trace_hash': 531989325604792893, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.090280572630585089917016260268', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '1.89474527404143668492961564638', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.44701808039901576161071865951', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 0.8616683420922173, 'bad_primes': [2, 3, 5, 31], 'central_character': '1.1', 'conductor': 3459600, 'conductor_radical': 930, 'degree': 4, 'dirichlet_coefficients': [1, 1, -1, 0, -1, -1, 0, -1, 0, -1, 0, 0, 0, 0, 1, -1, -3, 0, -3, 0, 0, 0, -4, 1, 0, 0, 1, 0, 0, 1, 2, 0, 0, -3, 0, 0, 0, -3, 0, 1, 0, 0, 0, 0, 0, -4, 0, 1, 1, 0, 3, 0, 0, 1, 0, 0, 3, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1, 0, -1, 0, 3, 0, 0, 0, 0, 0, 0, 0, -2, 0, 3, 0, 0, 1, 0, 0], 'euler11': [1, 0, 1, 0, 1], 'euler13': [1, 0, -1, 0, 1], 'euler17': [1, 3, 4, 3, 1], 'euler19': [1, 3, 4, 3, 1], 'euler2': [1, -1, 1, 0, 0], 'euler23': [1, 4, 6, 4, 1], 'euler29': [1, 0, 2, 0, 1], 'euler3': [1, 1, 1, 0, 0], 'euler31': [1, -2, 1, 0, 0], 'euler37': [1, 0, -1, 0, 1], 'euler41': [1, 0, 1, 0, 1], 'euler43': [1, 0, 1, 0, 1], 'euler47': [1, 0, 1, 0, 1], 'euler5': [1, 1, 1, 0, 0], 'euler53': [1, 0, 1, 0, 1], 'euler59': [1, 0, -1, 0, 1], 'euler61': [1, 0, 1, 0, 1], 'euler67': [1, 0, -1, 0, 1], 'euler7': [1, 0, -1, 0, 1], 'euler71': [1, 0, -1, 0, 1], 'euler73': [1, 0, -1, 0, 1], 'euler79': [1, 1, 0, 1, 1], 'euler83': [1, 1, 0, 1, 1], 'euler89': [1, 0, 2, 0, 1], 'euler97': [1, 0, -2, 0, 1], 'euler_factors': [[1, -1, 1, 0, 0], [1, 1, 1, 0, 0], [1, 1, 1, 0, 0], [1, 0, -1, 0, 1], [1, 0, 1, 0, 1], [1, 0, -1, 0, 1], [1, 3, 4, 3, 1], [1, 3, 4, 3, 1], [1, 4, 6, 4, 1], [1, 0, 2, 0, 1], [1, -2, 1, 0, 0], [1, 0, -1, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, -1, 0, 1], [1, 0, 1, 0, 1], [1, 0, -1, 0, 1], [1, 0, -1, 0, 1], [1, 0, -1, 0, 1], [1, 1, 0, 1, 1], [1, 1, 0, 1, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1860/1/be/c'], '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': '4-1860e2-1.1-c0e2-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0], 'nu_real_doubled': [0, 0], 'order_of_vanishing': 0, 'prelabel': '4-1860e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.9634629850167492, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e2-0', 'trace_hash': 531989325604792893, 'z1': {'__RealLiteral__': 0, 'data': '0.090280572630585089917016260268', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '114444222084109448642617691699,2401874983918228218396222226677', 'Lhash_array': ['114444222084109448642617691699', '2401874983918228218396222226677'], 'factors': ['2-1860-1860.719-c0-0-0', '2-1860-1860.119-c0-0-2'], 'label': '4-1860e2-1.1-c0e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1860/1/be/c'}