Formats: - HTML - YAML - JSON - 2026-10-12T02:51:56.681606
  • lfunc_lfunctions • Show schema
    {'Lhash': '2002888339452872674929562141273', 'a10': 0, 'a2': 0, 'a3': 27, 'a4': 0, 'a5': 100, 'a6': 0, 'a7': 343, 'a8': 0, 'a9': 729, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 104.96136856266496, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 7}, 'bad_lfactors': [[2, [1]], [3, [1, -27]], [7, [1, -343]]], 'bad_primes': [2, 3, 7], 'central_character': '336.1', 'coefficient_field': '1.1.1.1', 'conductor': 336, 'conductor_radical': 42, 'degree': 2, 'euler_factors': [[1], [1, -27], [1, -100, 78125], [1, -343], [1, 2774, 19487171], [1, 3294, 62748517], [1, -5900, 410338673], [1, 6644, 893871739], [1, 1982, 3404825447], [1, 208106, 17249876309], [1, -117792, 27512614111], [1, 335686, 94931877133], [1, 265488, 194754273881], [1, -93292, 271818611107], [1, -657516, 506623120463], [1, 608718, 1174711139837], [1, -536120, 2488651484819], [1, 1797090, 3142742836021], [1, 2123176, 6060711605323], [1, -1191214, 9095120158391], [1, -1056430, 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[[[1, 3898004, 27136050989627], 1]], [[[1, 4622352, 44231334895529], 1]], [[[1, -15287710, 80798284478113], 1]], [[[1, -2238688, 107213535210701], 1]], [[[1, 12450224, 122987386542487], 1]], [[[1, -7588602, 160578147647843], 1]], [[[1, -5170966, 182803912081669], 1]], [[[1, 9638678, 235260548044817], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 38, 'label': '2-336-1.1-c7-0-38', 'load_key': 'CMFs-workshop', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [7], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/336/8/a/j', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 24}, 'plot_values': [-2.4016949587995344e-60, 0.3407734513399053, 0.6762762733609317, 1.0013261813130436, 1.3109162443632096, 1.6002992383358439, 1.8650680482065967, 2.1012308685245165, 2.3052800060193634, 2.4742531592237493, 2.6057861352113134, 2.6981560636700994, 2.750314283533792, 2.7619082071610044, 2.733291611248995, 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['1.58000030851740231113528364676427', '2.51537004761033971788287898832552', '3.72792362413569459239708222926188', '4.93400551592568110989801465469177', '5.91144745087680421963489535054388', '7.23692570874761374977242920851625', '7.974848091696007895737898197012162', '8.960628909031010970496542768189115', '9.863031042448714346740560101659739'], 'prelabel': '2-336-1.1-c7-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 10.245065571418515, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c7-0', 'trace_hash': 954064973072121314, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.58000030851740231113528364676', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.51537004761033971788287898833', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.72792362413569459239708222926', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 104.96136856266496, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 336, 'conductor_radical': 42, 'degree': 2, 'dirichlet_coefficients': [1, 0, 27, 0, 100, 0, 343, 0, 729, 0, -2774, 0, -3294, 0, 2700, 0, 5900, 0, -6644, 0, 9261, 0, -1982, 0, -68125, 0, 19683, 0, -208106, 0, 117792, 0, -74898, 0, 34300, 0, -335686, 0, -88938, 0, -265488, 0, 93292, 0, 72900, 0, 657516, 0, 117649, 0, 159300, 0, -608718, 0, -277400, 0, -179388, 0, 536120, 0, -1797090, 0, 250047, 0, -329400, 0, -2123176, 0, -53514, 0, 1191214, 0, 1056430, 0, -1839375, 0, -951482, 0, -998484, 0, 531441, 0, -3898004, 0, 590000, 0, -5618862, 0, -4622352, 0, -1129842, 0, 3180384, 0, -664400, 0, 15287710, 0, -2022246, 0], 'euler11': [1, 2774, 19487171], 'euler13': [1, 3294, 62748517], 'euler17': [1, -5900, 410338673], 'euler19': [1, 6644, 893871739], 'euler2': [1, 0, 0], 'euler23': [1, 1982, 3404825447], 'euler29': [1, 208106, 17249876309], 'euler3': [1, -27, 0], 'euler31': [1, -117792, 27512614111], 'euler37': [1, 335686, 94931877133], 'euler41': [1, 265488, 194754273881], 'euler43': [1, -93292, 271818611107], 'euler47': [1, -657516, 506623120463], 'euler5': [1, -100, 78125], 'euler53': [1, 608718, 1174711139837], 'euler59': [1, -536120, 2488651484819], 'euler61': [1, 1797090, 3142742836021], 'euler67': [1, 2123176, 6060711605323], 'euler7': [1, -343, 0], 'euler71': [1, -1191214, 9095120158391], 'euler73': [1, -1056430, 11047398519097], 'euler79': [1, 998484, 19203908986159], 'euler83': [1, 3898004, 27136050989627], 'euler89': [1, 4622352, 44231334895529], 'euler97': [1, -15287710, 80798284478113], 'euler_factors': [[1, 0, 0], [1, -27, 0], [1, -100, 78125], [1, -343, 0], [1, 2774, 19487171], [1, 3294, 62748517], [1, -5900, 410338673], [1, 6644, 893871739], [1, 1982, 3404825447], [1, 208106, 17249876309], [1, -117792, 27512614111], [1, 335686, 94931877133], [1, 265488, 194754273881], [1, -93292, 271818611107], [1, -657516, 506623120463], [1, 608718, 1174711139837], [1, -536120, 2488651484819], [1, 1797090, 3142742836021], [1, 2123176, 6060711605323], [1, -1191214, 9095120158391], [1, -1056430, 11047398519097], [1, 998484, 19203908986159], [1, 3898004, 27136050989627], [1, 4622352, 44231334895529], [1, -15287710, 80798284478113]], 'index': 38, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/336/8/a/j/1/1', 'ModularForm/GL2/Q/holomorphic/336/8/a/j'], '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': '2-336-1.1-c7-0-38', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [7], 'order_of_vanishing': 1, 'prelabel': '2-336-1.1-c7-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 10.245065571418515, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c7-0', 'trace_hash': 954064973072121314, 'z1': {'__RealLiteral__': 0, 'data': '1.58000030851740231113528364676', 'prec': 100}}
  • lfunc_instances • Show schema
    • id: 20894520
      {'Lhash': '2002888339452872674929562141273', 'Lhash_array': ['2002888339452872674929562141273'], 'factors': ['2-336-1.1-c7-0-38'], 'label': '2-336-1.1-c7-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/336/8/a/j'}
    • id: 24592208
      {'Lhash': '2002888339452872674929562141273', 'Lhash_array': ['2002888339452872674929562141273'], 'factors': ['2-336-1.1-c7-0-38'], 'label': '2-336-1.1-c7-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/336/8/a/j/1/1'}