Formats: - HTML - YAML - JSON - 2026-08-15T02:14:29.994500
  • lfunc_lfunctions • Show schema
    {'Lhash': '979860785779588699200888892812', 'a10': -10, 'a2': -2, 'a3': 1, 'a4': 4, 'a5': 5, 'a6': -2, 'a7': 0, 'a8': -8, 'a9': -26, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 28.910935902812913, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 7}, 'bad_lfactors': [[2, [1, 2]], [5, [1, -5]], [7, [1]]], 'bad_primes': [2, 5, 7], 'central_character': '490.1', 'coefficient_field': '1.1.1.1', 'conductor': 490, 'conductor_radical': 70, 'degree': 2, 'euler_factors': [[1, 2], [1, -1, 27], [1, -5], [1], [1, 65, 1331], [1, 13, 2197], [1, -73, 4913], [1, -142, 6859], [1, -130, 12167], [1, -111, 24389], [1, 256, 29791], [1, 266, 50653], [1, -424, 68921], [1, -534, 79507], [1, -269, 103823], [1, 132, 148877], [1, -224, 205379], [1, -572, 226981], [1, 108, 300763], [1, -560, 357911], [1, 586, 389017], [1, -57, 493039], [1, 252, 571787], [1, -184, 704969], [1, -605, 912673], [1, -750, 1030301], [1, -337, 1092727], [1, -634, 1225043], [1, 827, 1295029], [1, 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'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/490/4/a/d', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 10}, 'plot_values': [1.3144877474437864, 1.304816538572642, 1.275883679256436, 1.2279325533933088, 1.161372319375897, 1.0767828830026411, 0.9749212621429085, 0.8567287741828751, 0.7233383538097687, 0.576081212037711, 0.4164919810272183, 0.24631145558397988, 0.06748604256769046, -0.1178369358289886, -0.30731887031835803, -0.49844510825936117, -0.6885463645410412, -0.8748266903103319, -1.0543982036292177, -1.2243225773058608, -1.381659052129315, -1.5235185032289649, -1.6471228386289734, -1.7498687583129446, -1.8293946559647483, -1.8836492113328536, -1.9109600067131385, -1.9101003145509143, -1.880352052971952, -1.8215628004140534, -1.7341947073111164, -1.619363149144857, -1.4788630372498293, -1.3151808462746593, -1.1314906331825365, -0.9316326130922424, 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'primitive': True, 'rational': True, 'root_analytic_conductor': 5.3768890543522385, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'trace_hash': 1391774100530356581, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.77297386646065827309668789486', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '2.45786601116675073852589250564', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.19821706227892982147912468797', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 28.910935902812913, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 490, 'conductor_radical': 70, 'degree': 2, 'dirichlet_coefficients': [1, -2, 1, 4, 5, -2, 0, -8, -26, -10, -65, 4, -13, 0, 5, 16, 73, 52, 142, 20, 0, 130, 130, -8, 25, 26, -53, 0, 111, -10, -256, -32, -65, -146, 0, -104, -266, -284, -13, -40, 424, 0, 534, -260, -130, -260, 269, 16, 0, -50, 73, -52, -132, 106, -325, 0, 142, -222, 224, 20, 572, 512, 0, 64, -65, 130, -108, 292, 130, 0, 560, 208, -586, 532, 25, 568, 0, 26, 57, 80, 649, -848, -252, 0, 365, -1068, 111, 520, 184, 260, 0, 520, -256, -538, 710, -32, 605, 0, 1690, 100], 'euler11': [1, 65, 1331], 'euler13': [1, 13, 2197], 'euler17': [1, -73, 4913], 'euler19': [1, -142, 6859], 'euler2': [1, 2, 0], 'euler23': [1, -130, 12167], 'euler29': [1, -111, 24389], 'euler3': [1, -1, 27], 'euler31': [1, 256, 29791], 'euler37': [1, 266, 50653], 'euler41': [1, -424, 68921], 'euler43': [1, -534, 79507], 'euler47': [1, -269, 103823], 'euler5': [1, -5, 0], 'euler53': [1, 132, 148877], 'euler59': [1, -224, 205379], 'euler61': [1, -572, 226981], 'euler67': [1, 108, 300763], 'euler7': [1, 0, 0], 'euler71': [1, -560, 357911], 'euler73': [1, 586, 389017], 'euler79': [1, -57, 493039], 'euler83': [1, 252, 571787], 'euler89': [1, -184, 704969], 'euler97': [1, -605, 912673], 'euler_factors': [[1, 2, 0], [1, -1, 27], [1, -5, 0], [1, 0, 0], [1, 65, 1331], [1, 13, 2197], [1, -73, 4913], [1, -142, 6859], [1, -130, 12167], [1, -111, 24389], [1, 256, 29791], [1, 266, 50653], [1, -424, 68921], [1, -534, 79507], [1, -269, 103823], [1, 132, 148877], [1, -224, 205379], [1, -572, 226981], [1, 108, 300763], [1, -560, 357911], [1, 586, 389017], [1, -57, 493039], [1, 252, 571787], [1, -184, 704969], [1, -605, 912673]], 'index': 5, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/490/4/a/d/1/1', 'ModularForm/GL2/Q/holomorphic/490/4/a/d'], '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': '2-490-1.1-c3-0-5', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-490-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.3768890543522385, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 1391774100530356581, 'z1': {'__RealLiteral__': 0, 'data': '0.77297386646065827309668789486', 'prec': 97}}
  • lfunc_instances • Show schema
    • id: 20615444
      {'Lhash': '979860785779588699200888892812', 'Lhash_array': ['979860785779588699200888892812'], 'factors': ['2-490-1.1-c3-0-5'], 'label': '2-490-1.1-c3-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/490/4/a/d'}
    • id: 24562341
      {'Lhash': '979860785779588699200888892812', 'Lhash_array': ['979860785779588699200888892812'], 'factors': ['2-490-1.1-c3-0-5'], 'label': '2-490-1.1-c3-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/490/4/a/d/1/1'}