Formats: - HTML - YAML - JSON - 2026-08-15T00:53:15.338528
  • lfunc_lfunctions • Show schema
    {'Lhash': '2809057133559912079607513603978', 'a10': 0, 'a2': 0, 'a3': 6561, 'a4': 0, 'a5': 130950, 'a6': 0, 'a7': -14846776, 'a8': 0, 'a9': 43046721, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21.986650481347176, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '8.5', 'prec': 7}, 'bad_lfactors': [[2, [1]], [3, [1, -6561]]], 'bad_primes': [2, 3], 'central_character': '12.1', 'coefficient_field': '1.1.1.1', 'conductor': 12, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[1], [1, -6561], [1, -130950, 762939453125], [1, 14846776, 232630513987207], [1, 845469684, 505447028499293771], [1, -1751414990, 8650415919381337933], [1, 47147886, 827240261886336764177], [1, 56973573100, 5480386857784802185939], [1, 371395374696, 141050039560662968926103], [1, 3681168479586, 7257147736730073114838109], [1, 5479889229856, 22550116774162743178682911], [1, 5446958938138, 456487940826035155404146917], [1, -29773337634090, 2614120267500775228203738281], [1, 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'euler_factors_factorization': [[1], [[[1, -6561], 1]], [[[1, -130950, 762939453125], 1]], [[[1, 14846776, 232630513987207], 1]], [[[1, 845469684, 505447028499293771], 1]], [[[1, -1751414990, 8650415919381337933], 1]], [[[1, 47147886, 827240261886336764177], 1]], [[[1, 56973573100, 5480386857784802185939], 1]], [[[1, 371395374696, 141050039560662968926103], 1]], [[[1, 3681168479586, 7257147736730073114838109], 1]], [[[1, 5479889229856, 22550116774162743178682911], 1]], [[[1, 5446958938138, 456487940826035155404146917], 1]], [[[1, -29773337634090, 2614120267500775228203738281], 1]], [[[1, -98485895466284, 5874403106360420018879553643], 1]], [[[1, -107861800207536, 26647936506962193439322192687], 1]], [[[1, -626472886328118, 205442259656281392806087233013], 1]], [[[1, 1260971066668356, 1271991467017507741703714391419], 1]], [[[1, 956343149707138, 2241853325254885342546716970621], 1]], [[[1, 5519389511567164, 11047694236668359048016134593027], 1]], [[[1, -9303053873586120, 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'trace_hash': 1687075235199758505, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.21595535319761290343238653419', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '3.75104139256951575123332277807', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '5.90251445011244815841131151825', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 21.986650481347176, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 12, 'conductor_radical': 6, 'degree': 2, 'dirichlet_coefficients': [1, 0, 6561, 0, 130950, 0, -14846776, 0, 43046721, 0, -845469684, 0, 1751414990, 0, 859162950, 0, -47147886, 0, -56973573100, 0, -97409697336, 0, -371395374696, 0, -745791550625, 0, 282429536481, 0, -3681168479586, 0, -5479889229856, 0, -5547126596724, 0, -1944185317200, 0, -5446958938138, 0, 11491033749390, 0, 29773337634090, 0, 98485895466284, 0, 5636968114950, 0, 107861800207536, 0, -12203756393031, 0, -309337280046, 0, 626472886328118, 0, -110714255119800, 0, -373803613109100, 0, -1260971066668356, 0, -956343149707138, 0, -639105024221496, 0, 229347792940500, 0, -5519389511567164, 0, -2436725053380456, 0, 9303053873586120, 0, 3692590926453962, 0, -4893138363650625, 0, 12552499013138784, 0, -2597720120860912, 0, 1853020188851841, 0, 26266742515599444, 0, -6174015671700, 0, -24152146394563746, 0, 63717157489864410, 0, -26002866039572240, 0, -35953553237085216, 0, -7460689397445000, 0, -78558896505972382, 0, -36394697601106164, 0], 'euler11': [1, 845469684, 505447028499293771], 'euler13': [1, -1751414990, 8650415919381337933], 'euler17': [1, 47147886, 827240261886336764177], 'euler19': [1, 56973573100, 5480386857784802185939], 'euler2': [1, 0, 0], 'euler23': [1, 371395374696, 141050039560662968926103], 'euler29': [1, 3681168479586, 7257147736730073114838109], 'euler3': [1, -6561, 0], 'euler31': [1, 5479889229856, 22550116774162743178682911], 'euler37': [1, 5446958938138, 456487940826035155404146917], 'euler41': [1, -29773337634090, 2614120267500775228203738281], 'euler43': [1, -98485895466284, 5874403106360420018879553643], 'euler47': [1, -107861800207536, 26647936506962193439322192687], 'euler5': [1, -130950, 762939453125], 'euler53': [1, -626472886328118, 205442259656281392806087233013], 'euler59': [1, 1260971066668356, 1271991467017507741703714391419], 'euler61': [1, 956343149707138, 2241853325254885342546716970621], 'euler67': [1, 5519389511567164, 11047694236668359048016134593027], 'euler7': [1, 14846776, 232630513987207], 'euler71': [1, -9303053873586120, 29606831241262271996845213307591], 'euler73': [1, -3692590926453962, 47477585226700098686074966922953], 'euler79': [1, 2597720120860912, 181827912146592045345270516890959], 'euler83': [1, -26266742515599444, 421044084813170691455703581173523], 'euler89': [1, -63717157489864410, 1379209096840925342723840168019929], 'euler97': [1, 78558896505972382, 5958260438588051333281183456765537], 'euler_factors': [[1, 0, 0], [1, -6561, 0], [1, -130950, 762939453125], [1, 14846776, 232630513987207], [1, 845469684, 505447028499293771], [1, -1751414990, 8650415919381337933], [1, 47147886, 827240261886336764177], [1, 56973573100, 5480386857784802185939], [1, 371395374696, 141050039560662968926103], [1, 3681168479586, 7257147736730073114838109], [1, 5479889229856, 22550116774162743178682911], [1, 5446958938138, 456487940826035155404146917], [1, -29773337634090, 2614120267500775228203738281], [1, -98485895466284, 5874403106360420018879553643], [1, -107861800207536, 26647936506962193439322192687], [1, -626472886328118, 205442259656281392806087233013], [1, 1260971066668356, 1271991467017507741703714391419], [1, 956343149707138, 2241853325254885342546716970621], [1, 5519389511567164, 11047694236668359048016134593027], [1, -9303053873586120, 29606831241262271996845213307591], [1, -3692590926453962, 47477585226700098686074966922953], [1, 2597720120860912, 181827912146592045345270516890959], [1, -26266742515599444, 421044084813170691455703581173523], [1, -63717157489864410, 1379209096840925342723840168019929], [1, 78558896505972382, 5958260438588051333281183456765537]], 'index': 1, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/12/18/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/12/18/a/b'], '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': '2-12-1.1-c17-0-1', 'motivic_weight': 17, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [17], 'order_of_vanishing': 1, 'prelabel': '2-12-1.1-c17-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.688992480410603, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c17-0', 'trace_hash': 1687075235199758505, 'z1': {'__RealLiteral__': 0, 'data': '2.21595535319761290343238653419', 'prec': 100}}
  • lfunc_instances • Show schema
    • id: 18978266
      {'Lhash': '2809057133559912079607513603978', 'Lhash_array': ['2809057133559912079607513603978'], 'factors': ['2-12-1.1-c17-0-1'], 'label': '2-12-1.1-c17-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/12/18/a/b'}
    • id: 24558636
      {'Lhash': '2809057133559912079607513603978', 'Lhash_array': ['2809057133559912079607513603978'], 'factors': ['2-12-1.1-c17-0-1'], 'label': '2-12-1.1-c17-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/12/18/a/b/1/1'}