Formats: - HTML - YAML - JSON - 2026-08-13T22:04:07.319417
  • lfunc_lfunctions • Show schema
    {'Lhash': '1552831204989403414395971655622,3190429918439227447186139083360', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.035965114058884314, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1, 1, 1]], [19, [1, -2, 1]]], 'bad_primes': [2, 5, 19], 'central_character': '380.1', 'coefficient_field': '1.1.1.1', 'conductor': 144400, 'conductor_radical': 190, 'degree': 4, 'euler_factors': [[1], [1, 0, 2, 0, 1], [1, 1, 1], [1, 0, 1, 0, 1], [1, -2, 3, -2, 1], [1, 0, 2, 0, 1], [1, 0, 1, 0, 1], [1, -2, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 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, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, -2, 3, -2, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 1, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 4, 6, 4, 1], [1, 0, 2, 0, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 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'5.99016608629263259011110941331918', '6.77388089486647289399419825957921', '6.94388774149781126870978416757681', '7.79803134088040807684303816901735', '8.101267339385240330948258433041478', '8.559554467746743853534006034563651', '9.043479528725945405742207084891798', '9.564525582866044905900922091310344', '9.680940375097192819510039946258860', '10.63395831016736958726213973442655', '11.21607423167003868914747075070874', '11.39448347991777191910497595919176', '11.73940428663520134005828723224494'], 'prelabel': '4-380e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.4354821521033221, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c0e2-0', 'trace_hash': 436264611465042784, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.22496783002337532100487424725', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.51680543350416782780194495462', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.31492373852692772330478789224', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 0.035965114058884314, 'bad_primes': [2, 5, 19], 'central_character': '1.1', 'conductor': 144400, 'conductor_radical': 190, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, -1, 0, 0, 0, -2, 0, 2, 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, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 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, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -4, 0], 'euler11': [1, -2, 3, -2, 1], 'euler13': [1, 0, 2, 0, 1], 'euler17': [1, 0, 1, 0, 1], 'euler19': [1, -2, 1, 0, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -2, 0, 1], 'euler29': [1, 0, -2, 0, 1], 'euler3': [1, 0, 2, 0, 1], 'euler31': [1, 0, -2, 0, 1], 'euler37': [1, 0, 2, 0, 1], 'euler41': [1, 0, -2, 0, 1], 'euler43': [1, 0, 1, 0, 1], 'euler47': [1, 0, 1, 0, 1], 'euler5': [1, 1, 1, 0, 0], 'euler53': [1, 0, 2, 0, 1], 'euler59': [1, 0, -2, 0, 1], 'euler61': [1, -2, 3, -2, 1], 'euler67': [1, 0, 2, 0, 1], 'euler7': [1, 0, 1, 0, 1], 'euler71': [1, 0, -2, 0, 1], 'euler73': [1, 0, 1, 0, 1], 'euler79': [1, 0, -2, 0, 1], 'euler83': [1, 0, -2, 0, 1], 'euler89': [1, 0, -2, 0, 1], 'euler97': [1, 0, 2, 0, 1], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 2, 0, 1], [1, 1, 1, 0, 0], [1, 0, 1, 0, 1], [1, -2, 3, -2, 1], [1, 0, 2, 0, 1], [1, 0, 1, 0, 1], [1, -2, 1, 0, 0], [1, 0, -2, 0, 1], [1, 0, -2, 0, 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, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, -2, 3, -2, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 1, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/380/1/g/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': '4-380e2-1.1-c0e2-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0], 'nu_real_doubled': [0, 0], 'order_of_vanishing': 0, 'prelabel': '4-380e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.4354821521033221, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e2-0', 'trace_hash': 436264611465042784, 'z1': {'__RealLiteral__': 0, 'data': '1.22496783002337532100487424725', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1552831204989403414395971655622,3190429918439227447186139083360', 'Lhash_array': ['1552831204989403414395971655622', '3190429918439227447186139083360'], 'factors': ['2-380-95.94-c0-0-0', '2-380-95.94-c0-0-1'], 'label': '4-380e2-1.1-c0e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/380/1/g/a'}