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  • lfunc_lfunctions • Show schema
    {'Lhash': '1270348747154571933201346591258,1600917402173861941314181797019,1958746911496227644022946733292', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 3, 'a6': 0, 'a7': -3, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 380137.2649529088, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1, 3, 3, 1]]], 'bad_primes': [2, 3, 7], 'central_character': '9072.1', 'coefficient_field': '1.1.1.1', 'conductor': 746636341248, 'conductor_radical': 42, 'degree': 6, 'euler_factors': [[1], [1], [1, -3, 9, -21, 45, -75, 125], [1, 3, 3, 1], [1, 6, 36, 123, 396, 726, 1331], [1, 3, 42, 79, 546, 507, 2197], [1, 0, 18, -9, 306, 0, 4913], [1, 3, 21, 65, 399, 1083, 6859], [1, 6, 54, 177, 1242, 3174, 12167], [1, -15, 135, -807, 3915, -12615, 24389], [1, -3, 15, -133, 465, -2883, 29791], [1, 3, 33, 115, 1221, 4107, 50653], [1, -6, 126, -483, 5166, -10086, 68921], [1, 3, 21, -205, 903, 5547, 79507], [1, 15, 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'6.74190547808909234460128251144605', '6.74932178426159151211503723076651', '7.08246219336223730278599909958149', '7.34549541086342559674696814960985', '7.65794578034274710321720655212359'], 'prelabel': '6-9072e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.511185858251809, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c1e3-0', 'trace_hash': 377997448982435089, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.00212846262673386022397324323', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '1.26290115106294334373966191833', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '1.54517886170177523460438817871', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 380137.2649529088, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 746636341248, 'conductor_radical': 42, 'degree': 6, 'dirichlet_coefficients': [1, 0, 0, 0, 3, 0, -3, 0, 0, 0, -6, 0, -3, 0, 0, 0, 0, 0, -3, 0, 0, 0, -6, 0, 0, 0, 0, 0, 15, 0, 3, 0, 0, 0, -9, 0, -3, 0, 0, 0, 6, 0, -3, 0, 0, 0, -15, 0, 6, 0, 0, 0, 18, 0, -18, 0, 0, 0, -3, 0, -6, 0, 0, 0, -9, 0, 6, 0, 0, 0, -15, 0, 9, 0, 0, 0, 18, 0, -3, 0, 0, 0, -18, 0, 0, 0, 0, 0, -6, 0, 9, 0, 0, 0, -9, 0, -15, 0, 0, 0], 'euler11': [1, 6, 36, 123, 396, 726, 1331], 'euler13': [1, 3, 42, 79, 546, 507, 2197], 'euler17': [1, 0, 18, -9, 306, 0, 4913], 'euler19': [1, 3, 21, 65, 399, 1083, 6859], 'euler2': [1, 0, 0, 0, 0, 0, 0], 'euler23': [1, 6, 54, 177, 1242, 3174, 12167], 'euler29': [1, -15, 135, -807, 3915, -12615, 24389], 'euler3': [1, 0, 0, 0, 0, 0, 0], 'euler31': [1, -3, 15, -133, 465, -2883, 29791], 'euler37': [1, 3, 33, 115, 1221, 4107, 50653], 'euler41': [1, -6, 126, -483, 5166, -10086, 68921], 'euler43': [1, 3, 21, -205, 903, 5547, 79507], 'euler47': [1, 15, 177, 1329, 8319, 33135, 103823], 'euler5': [1, -3, 9, -21, 45, -75, 125], 'euler53': [1, -18, 198, -1521, 10494, -50562, 148877], 'euler59': [1, 3, 123, 435, 7257, 10443, 205379], 'euler61': [1, 6, 138, 763, 8418, 22326, 226981], 'euler67': [1, -6, 174, -745, 11658, -26934, 300763], 'euler7': [1, 3, 3, 1, 0, 0, 0], 'euler71': [1, 15, 231, 1833, 16401, 75615, 357911], 'euler73': [1, -9, 207, -1235, 15111, -47961, 389017], 'euler79': [1, 3, 3, -889, 237, 18723, 493039], 'euler83': [1, 18, 324, 3015, 26892, 124002, 571787], 'euler89': [1, 6, 72, -21, 6408, 47526, 704969], 'euler97': [1, 15, 309, 2887, 29973, 141135, 912673], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0], [1, -3, 9, -21, 45, -75, 125], [1, 3, 3, 1, 0, 0, 0], [1, 6, 36, 123, 396, 726, 1331], [1, 3, 42, 79, 546, 507, 2197], [1, 0, 18, -9, 306, 0, 4913], [1, 3, 21, 65, 399, 1083, 6859], [1, 6, 54, 177, 1242, 3174, 12167], [1, -15, 135, -807, 3915, -12615, 24389], [1, -3, 15, -133, 465, -2883, 29791], [1, 3, 33, 115, 1221, 4107, 50653], [1, -6, 126, -483, 5166, -10086, 68921], [1, 3, 21, -205, 903, 5547, 79507], [1, 15, 177, 1329, 8319, 33135, 103823], [1, -18, 198, -1521, 10494, -50562, 148877], [1, 3, 123, 435, 7257, 10443, 205379], [1, 6, 138, 763, 8418, 22326, 226981], [1, -6, 174, -745, 11658, -26934, 300763], [1, 15, 231, 1833, 16401, 75615, 357911], [1, -9, 207, -1235, 15111, -47961, 389017], [1, 3, 3, -889, 237, 18723, 493039], [1, 18, 324, 3015, 26892, 124002, 571787], [1, 6, 72, -21, 6408, 47526, 704969], [1, 15, 309, 2887, 29973, 141135, 912673]], 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9072/2/a/bz'], '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': '6-9072e3-1.1-c1e3-0-9', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 3, 'prelabel': '6-9072e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.511185858251809, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 377997448982435089, 'z1': {'__RealLiteral__': 0, 'data': '1.00212846262673386022397324323', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1270348747154571933201346591258,1600917402173861941314181797019,1958746911496227644022946733292', 'Lhash_array': ['1270348747154571933201346591258', '1600917402173861941314181797019', '1958746911496227644022946733292'], 'factors': ['2-9072-1.1-c1-0-79', '2-9072-1.1-c1-0-108', '2-9072-1.1-c1-0-141'], 'label': '6-9072e3-1.1-c1e3-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9072/2/a/bz'}