Formats: - HTML - YAML - JSON - 2026-09-22T23:37:19.385512
  • lfunc_lfunctions • Show schema
    {'Lhash': '2029897310937659541544057712024', 'a10': 0, 'a2': 22, 'a3': -27, 'a4': 356, 'a5': 0, 'a6': -594, 'a7': 420, 'a8': 5016, 'a9': 729, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.428876911309143, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 7}, 'bad_lfactors': [[3, [1, 27]], [5, [1]]], 'bad_primes': [3, 5], 'central_character': '75.1', 'coefficient_field': '1.1.1.1', 'conductor': 75, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[1, -22, 128], [1, 27], [1], [1, -420, 823543], [1, 2944, 19487171], [1, -11006, 62748517], [1, -16546, 410338673], [1, 25364, 893871739], [1, -5880, 3404825447], [1, -163042, 17249876309], [1, 201600, 27512614111], [1, 120530, 94931877133], [1, 115910, 194754273881], [1, -19148, 271818611107], [1, 841016, 506623120463], [1, 501890, 1174711139837], [1, 1586176, 2488651484819], [1, 372962, 3142742836021], [1, 4561044, 6060711605323], [1, -1512832, 9095120158391], [1, -1522910, 11047398519097], [1, 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-0.044147379867923844, -0.13152234503817084, -0.11720527178581507], 'positive_zeros': ['1.60130663021197977401507554933536', '3.29866953313571255979108238926013', '4.59743156890007725735576346747873', '5.63306850433352736404406217541731', '6.59431903875824013712814002075090', '7.994038182769346481815521741365576', '10.52798791474975947998997701690736', '11.18816141162080707728413033139869', '12.26224215684148444250257101960662', '13.09838024159491212740692389062209'], 'prelabel': '2-75-1.1-c7-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.84033851205772, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c7-0', 'trace_hash': 2012567304129120063, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.60130663021197977401507554934', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '3.29866953313571255979108238926', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '4.59743156890007725735576346748', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 23.428876911309143, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 75, 'conductor_radical': 15, 'degree': 2, 'dirichlet_coefficients': [1, 22, -27, 356, 0, -594, 420, 5016, 729, 0, -2944, -9612, 11006, 9240, 0, 64784, 16546, 16038, -25364, 0, -11340, -64768, 5880, -135432, 0, 242132, -19683, 149520, 163042, 0, -201600, 783200, 79488, 364012, 0, 259524, -120530, -558008, -297162, 0, -115910, -249480, 19148, -1048064, 0, 129360, -841016, -1749168, -647143, 0, -446742, 3918136, -501890, -433026, 0, 2106720, 684828, 3586924, -1586176, 0, -372962, -4435200, 306180, 8938048, 0, 1748736, -4561044, 5890376, -158760, 0, 1512832, 3656664, 1522910, -2651660, 0, -9029584, -1236480, -6537564, 4231920, 0, 531441, -2550020, 1854204, -4037040, 0, 421256, -4402134, -14767104, -6888174, 0, 4622520, 2093280, 5443200, -18502352, 0, -21146400, -3700034, -14237146, -2146176, 0], 'euler11': [1, 2944, 19487171], 'euler13': [1, -11006, 62748517], 'euler17': [1, -16546, 410338673], 'euler19': [1, 25364, 893871739], 'euler2': [1, -22, 128], 'euler23': [1, -5880, 3404825447], 'euler29': [1, -163042, 17249876309], 'euler3': [1, 27, 0], 'euler31': [1, 201600, 27512614111], 'euler37': [1, 120530, 94931877133], 'euler41': [1, 115910, 194754273881], 'euler43': [1, -19148, 271818611107], 'euler47': [1, 841016, 506623120463], 'euler5': [1, 0, 0], 'euler53': [1, 501890, 1174711139837], 'euler59': [1, 1586176, 2488651484819], 'euler61': [1, 372962, 3142742836021], 'euler67': [1, 4561044, 6060711605323], 'euler7': [1, -420, 823543], 'euler71': [1, -1512832, 9095120158391], 'euler73': [1, -1522910, 11047398519097], 'euler79': [1, -4231920, 19203908986159], 'euler83': [1, -1854204, 27136050989627], 'euler89': [1, 6888174, 44231334895529], 'euler97': [1, 3700034, 80798284478113], 'euler_factors': [[1, -22, 128], [1, 27, 0], [1, 0, 0], [1, -420, 823543], [1, 2944, 19487171], [1, -11006, 62748517], [1, -16546, 410338673], [1, 25364, 893871739], [1, -5880, 3404825447], [1, -163042, 17249876309], [1, 201600, 27512614111], [1, 120530, 94931877133], [1, 115910, 194754273881], [1, -19148, 271818611107], [1, 841016, 506623120463], [1, 501890, 1174711139837], [1, 1586176, 2488651484819], [1, 372962, 3142742836021], [1, 4561044, 6060711605323], [1, -1512832, 9095120158391], [1, -1522910, 11047398519097], [1, -4231920, 19203908986159], [1, -1854204, 27136050989627], [1, 6888174, 44231334895529], [1, 3700034, 80798284478113]], 'index': 13, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/75/8/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/75/8/a/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': '2-75-1.1-c7-0-13', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'prelabel': '2-75-1.1-c7-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.84033851205772, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c7-0', 'trace_hash': 2012567304129120063, 'z1': {'__RealLiteral__': 0, 'data': '1.60130663021197977401507554934', 'prec': 100}}
  • lfunc_instances • Show schema
    • id: 20734848
      {'Lhash': '2029897310937659541544057712024', 'Lhash_array': ['2029897310937659541544057712024'], 'factors': ['2-75-1.1-c7-0-13'], 'label': '2-75-1.1-c7-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/75/8/a/c'}
    • id: 24559429
      {'Lhash': '2029897310937659541544057712024', 'Lhash_array': ['2029897310937659541544057712024'], 'factors': ['2-75-1.1-c7-0-13'], 'label': '2-75-1.1-c7-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/75/8/a/c/1/1'}