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  • lfunc_lfunctions • Show schema
    {'Lhash': '1107816199549095365576044933353,1584916436723391048149249668465,2009892517076271205909665499125', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, '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, 0, 0, -2, 0, 0, 125], [1, 3, 3, 1], [1, 3, 15, 30, 165, 363, 1331], [1, 6, 36, 132, 468, 1014, 2197], [1, -6, 42, -154, 714, -1734, 4913], [1, 0, 33, -8, 627, 0, 6859], [1, 6, 33, 68, 759, 3174, 12167], [1, -6, 42, -86, 1218, -5046, 24389], [1, 0, 69, -8, 2139, 0, 29791], [1, 15, 162, 1107, 5994, 20535, 50653], [1, 6, 135, 500, 5535, 10086, 68921], [1, 3, 9, -142, 387, 5547, 79507], [1, -6, -15, 572, -705, 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'6.22187572460583309282778633961132', '6.51897492476161439373747194842448', '6.61386861219166735562167230588846', '7.21186820361115461805083030298014', '7.30963077239234002357814343960955', '7.31694947569133429037066443329322', '7.35364312944121214261949264328939'], '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': 937369775901235181, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.873912889994800420346329979746', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '1.25027861497327474001887598039', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '1.58552563041772523140189025820', '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, 0, 0, -3, 0, 0, 0, -3, 0, -6, 0, 0, 0, 6, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, -15, 0, 0, 0, -6, 0, -3, 0, 0, 0, 6, 0, 6, 0, 0, 0, 9, 0, 0, 0, 0, 0, -24, 0, -6, 0, 0, 0, 0, 0, 9, 0, 0, 0, -21, 0, -12, 0, 0, 0, 9, 0, -15, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 30, 0, 0, 0], 'euler11': [1, 3, 15, 30, 165, 363, 1331], 'euler13': [1, 6, 36, 132, 468, 1014, 2197], 'euler17': [1, -6, 42, -154, 714, -1734, 4913], 'euler19': [1, 0, 33, -8, 627, 0, 6859], 'euler2': [1, 0, 0, 0, 0, 0, 0], 'euler23': [1, 6, 33, 68, 759, 3174, 12167], 'euler29': [1, -6, 42, -86, 1218, -5046, 24389], 'euler3': [1, 0, 0, 0, 0, 0, 0], 'euler31': [1, 0, 69, -8, 2139, 0, 29791], 'euler37': [1, 15, 162, 1107, 5994, 20535, 50653], 'euler41': [1, 6, 135, 500, 5535, 10086, 68921], 'euler43': [1, 3, 9, -142, 387, 5547, 79507], 'euler47': [1, -6, -15, 572, -705, -13254, 103823], 'euler5': [1, 0, 0, -2, 0, 0, 125], 'euler53': [1, -9, 39, -110, 2067, -25281, 148877], 'euler59': [1, 24, 345, 3144, 20355, 83544, 205379], 'euler61': [1, 6, 120, 344, 7320, 22326, 226981], 'euler67': [1, -9, 171, -1218, 11457, -40401, 300763], 'euler7': [1, 3, 3, 1, 0, 0, 0], 'euler71': [1, 21, 345, 3222, 24495, 105861, 357911], 'euler73': [1, 12, 246, 1748, 17958, 63948, 389017], 'euler79': [1, 15, 291, 2374, 22989, 93615, 493039], 'euler83': [1, -12, 273, -1968, 22659, -82668, 571787], 'euler89': [1, 0, 162, -388, 14418, 0, 704969], 'euler97': [1, -30, 399, -3940, 38703, -282270, 912673], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0], [1, 0, 0, -2, 0, 0, 125], [1, 3, 3, 1, 0, 0, 0], [1, 3, 15, 30, 165, 363, 1331], [1, 6, 36, 132, 468, 1014, 2197], [1, -6, 42, -154, 714, -1734, 4913], [1, 0, 33, -8, 627, 0, 6859], [1, 6, 33, 68, 759, 3174, 12167], [1, -6, 42, -86, 1218, -5046, 24389], [1, 0, 69, -8, 2139, 0, 29791], [1, 15, 162, 1107, 5994, 20535, 50653], [1, 6, 135, 500, 5535, 10086, 68921], [1, 3, 9, -142, 387, 5547, 79507], [1, -6, -15, 572, -705, -13254, 103823], [1, -9, 39, -110, 2067, -25281, 148877], [1, 24, 345, 3144, 20355, 83544, 205379], [1, 6, 120, 344, 7320, 22326, 226981], [1, -9, 171, -1218, 11457, -40401, 300763], [1, 21, 345, 3222, 24495, 105861, 357911], [1, 12, 246, 1748, 17958, 63948, 389017], [1, 15, 291, 2374, 22989, 93615, 493039], [1, -12, 273, -1968, 22659, -82668, 571787], [1, 0, 162, -388, 14418, 0, 704969], [1, -30, 399, -3940, 38703, -282270, 912673]], 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9072/2/a/bw'], '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-c1e3-0-7', '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': 937369775901235181, 'z1': {'__RealLiteral__': 0, 'data': '0.873912889994800420346329979746', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1107816199549095365576044933353,1584916436723391048149249668465,2009892517076271205909665499125', 'Lhash_array': ['1107816199549095365576044933353', '1584916436723391048149249668465', '2009892517076271205909665499125'], 'factors': ['2-9072-1.1-c1-0-53', '2-9072-1.1-c1-0-106', '2-9072-1.1-c1-0-142'], 'label': '6-9072e3-1.1-c1e3-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9072/2/a/bw'}