Formats: - HTML - YAML - JSON - 2026-09-07T11:46:55.330980
  • lfunc_lfunctions • Show schema
    {'Lhash': '937980352166900864953119114611', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.5, -0.8660254037844386], 'a6': [0.0, 0.0], 'a7': [0.0, 1.7320508075688772], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.7068023432048682, 'analytic_normalization': 0, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.5, 0.8660254037844386]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 5, 19], 'central_character': '3420.2089', 'coefficient_field': 'CDF', 'conductor': 3420, 'conductor_radical': 570, 'conjugate': '1892158762530633908633850910193', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, -1.7320508075688772], [-1.0, 0]], [[1.0, 0], [1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, -1.7320508075688772], [-1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], 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'0.50000000000000000000000000000000 - 0.86602540378443864676372317075312*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.16666666666666666', 'prec': 57}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.73993602968990485844533605341', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '2.20634282294789445149447807980', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.13311005417323666772238798720', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 1.7068023432048682, 'bad_primes': [2, 3, 5, 19], 'central_character': '95.94', 'conductor': 3420, 'conductor_radical': 570, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3420/1/h/a/2089/1'], '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': '2-3420-95.94-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3420-95.94-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.306446456309966, 'root_angle': -0.16666666666666666, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.73993602968990485844533605341', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '937980352166900864953119114611', 'Lhash_array': ['937980352166900864953119114611'], 'factors': ['2-3420-95.94-c0-0-1'], 'label': '2-3420-95.94-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3420/1/h/a/2089/1'}