Formats: - HTML - YAML - JSON - 2026-07-18T15:19:25.294163
  • lfunc_lfunctions • Show schema
    {'Lhash': '2745958581162122501843733047976', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.5, -0.8660254037844386], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.22008767057115408, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '441.325', 'coefficient_field': 'CDF', 'conductor': 441, 'conductor_radical': 21, 'conjugate': '2028730794253092076782429994752', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-0.5, 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-21e2-7.3-c0-0-0', 'leading_term': '0.92939903991260832771569426888125', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/441/1/m/a/325/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 30}, 'plot_values': [0.9293990399126083, 0.9529495032174592, 0.9932586854967691, 1.0493407945570434, 1.119286244967962, 1.2006362186907913, 1.2906907926635285, 1.3866974510488177, 1.4859352768630134, 1.5857344249089476, 1.6834665670467257, 1.776529674721062, 1.8623396584337517, 1.9383343289838777, 2.0019912006499676, 2.0508586404858375, 2.082598883948962, 2.095040948621143, 2.0862412027670576, 2.0545491510742036, 1.9986758330577237, 1.9177620775143034, 1.811443725665611, 1.6799108414593562, 1.5239578881789553, 1.3450218844050645, 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'7.78623839517945642711281070580184', '8.549787287379746596472714024378443', '9.609722008000977215470084698991377', '10.67421072164152299370820510375181', '11.49438970359066473817352013659400'], 'prelabel': '2-21e2-7.3-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.4691350238163359, 'root_angle': 0.0934198098603064, 'root_number': '0.83262043355876010118361245995543 + 0.55384403365967783611687467980447*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.09341980986030639', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.16617937203495717213378069952', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.39923831260526179066932882330', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.48029662965645927091740316497', 'prec': 103}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 0.22008767057115408, 'bad_primes': [3, 7], 'central_character': '7.3', 'conductor': 441, 'conductor_radical': 21, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/441/1/m/a/325/1'], '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': '2-21e2-7.3-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-21e2-7.3-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.4691350238163359, 'root_angle': 0.0934198098603064, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.16617937203495717213378069952', 'prec': 103}}
  • lfunc_instances • Show schema
    {'Lhash': '2745958581162122501843733047976', 'Lhash_array': ['2745958581162122501843733047976'], 'factors': ['2-21e2-7.3-c0-0-0'], 'label': '2-21e2-7.3-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/1/m/a/325/1'}