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  • lfunc_lfunctions • Show schema
    {'Lhash': '1248509044314449329905796627963,1431771855502665466194321321112,2465767661223638235807706248205', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -2, 'a5': 0, 'a6': 0, 'a7': -4, 'a8': 2, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 172768.2590114603, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[3, [1]], [5, [1]], [31, [1, 3, 3, 1]]], 'bad_primes': [3, 5, 31], 'central_character': '6975.1', 'coefficient_field': '1.1.1.1', 'conductor': 339338109375, 'conductor_radical': 465, 'degree': 6, 'euler_factors': [[1, 0, 2, -2, 4, 0, 8], [1], [1], [1, 4, 21, 52, 147, 196, 343], [1, -7, 36, -117, 396, -847, 1331], [1, 0, 5, -62, 65, 0, 2197], [1, 7, 44, 179, 748, 2023, 4913], [1, 11, 84, 419, 1596, 3971, 6859], [1, 5, 12, -9, 276, 2645, 12167], [1, -5, 92, -289, 2668, -4205, 24389], [1, 3, 3, 1], [1, 26, 333, 2546, 12321, 35594, 50653], [1, -8, 107, -526, 4387, -13448, 68921], [1, 8, 57, 320, 2451, 14792, 79507], [1, -10, 121, 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'6.43094850572234982010121189738920', '6.62231512788487208306731639059732', '6.74330396197272121037271470402105', '7.10730485608184475359562226659587', '7.17078238487953464802892689032860', '7.66375059652808199255190352443509', '7.74829403040151654082862336656957'], 'prelabel': '6-6975e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.4629521913143115, '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': 2027668123683192120, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.984899974874516840922938564223', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '1.12946884200180039229664387211', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '1.92589493521627963105639112957', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 172768.2590114603, 'bad_primes': [3, 5, 31], 'central_character': '1.1', 'conductor': 339338109375, 'conductor_radical': 465, 'degree': 6, 'dirichlet_coefficients': [1, 0, 0, -2, 0, 0, -4, 2, 0, 0, 7, 0, 0, 0, 0, 0, -7, 0, -11, 0, 0, 0, -5, 0, 0, 0, 0, 8, 5, 0, -3, -8, 0, 0, 0, 0, -26, 0, 0, 0, 8, 0, -8, -14, 0, 0, 10, 0, -5, 0, 0, 0, -11, 0, 0, -8, 0, 0, 14, 0, 12, 0, 0, 4, 0, 0, -3, 14, 0, 0, 26, 0, -12, 0, 0, 22, -28, 0, 10, 0, 0, 0, -5, 0, 0, 0, 0, 14, 9, 0, 0, 10, 0, 0, 0, 0, 5, 0, 0, 0], 'euler11': [1, -7, 36, -117, 396, -847, 1331], 'euler13': [1, 0, 5, -62, 65, 0, 2197], 'euler17': [1, 7, 44, 179, 748, 2023, 4913], 'euler19': [1, 11, 84, 419, 1596, 3971, 6859], 'euler2': [1, 0, 2, -2, 4, 0, 8], 'euler23': [1, 5, 12, -9, 276, 2645, 12167], 'euler29': [1, -5, 92, -289, 2668, -4205, 24389], 'euler3': [1, 0, 0, 0, 0, 0, 0], 'euler31': [1, 3, 3, 1, 0, 0, 0], 'euler37': [1, 26, 333, 2546, 12321, 35594, 50653], 'euler41': [1, -8, 107, -526, 4387, -13448, 68921], 'euler43': [1, 8, 57, 320, 2451, 14792, 79507], 'euler47': [1, -10, 121, -948, 5687, -22090, 103823], 'euler5': [1, 0, 0, 0, 0, 0, 0], 'euler53': [1, 11, 120, 1191, 6360, 30899, 148877], 'euler59': [1, -14, 181, -1350, 10679, -48734, 205379], 'euler61': [1, -12, 167, -1400, 10187, -44652, 226981], 'euler67': [1, 3, 44, 671, 2948, 13467, 300763], 'euler7': [1, 4, 21, 52, 147, 196, 343], 'euler71': [1, -26, 401, -3940, 28471, -131066, 357911], 'euler73': [1, 12, 251, 1768, 18323, 63948, 389017], 'euler79': [1, -10, 255, -1546, 20145, -62410, 493039], 'euler83': [1, 5, 208, 651, 17264, 34445, 571787], 'euler89': [1, -9, 102, -79, 9078, -71289, 704969], 'euler97': [1, -5, 114, -1529, 11058, -47045, 912673], 'euler_factors': [[1, 0, 2, -2, 4, 0, 8], [1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0], [1, 4, 21, 52, 147, 196, 343], [1, -7, 36, -117, 396, -847, 1331], [1, 0, 5, -62, 65, 0, 2197], [1, 7, 44, 179, 748, 2023, 4913], [1, 11, 84, 419, 1596, 3971, 6859], [1, 5, 12, -9, 276, 2645, 12167], [1, -5, 92, -289, 2668, -4205, 24389], [1, 3, 3, 1, 0, 0, 0], [1, 26, 333, 2546, 12321, 35594, 50653], [1, -8, 107, -526, 4387, -13448, 68921], [1, 8, 57, 320, 2451, 14792, 79507], [1, -10, 121, -948, 5687, -22090, 103823], [1, 11, 120, 1191, 6360, 30899, 148877], [1, -14, 181, -1350, 10679, -48734, 205379], [1, -12, 167, -1400, 10187, -44652, 226981], [1, 3, 44, 671, 2948, 13467, 300763], [1, -26, 401, -3940, 28471, -131066, 357911], [1, 12, 251, 1768, 18323, 63948, 389017], [1, -10, 255, -1546, 20145, -62410, 493039], [1, 5, 208, 651, 17264, 34445, 571787], [1, -9, 102, -79, 9078, -71289, 704969], [1, -5, 114, -1529, 11058, -47045, 912673]], 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6975/2/a/bc'], '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': '6-6975e3-1.1-c1e3-0-6', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 3, 'prelabel': '6-6975e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.4629521913143115, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 2027668123683192120, 'z1': {'__RealLiteral__': 0, 'data': '0.984899974874516840922938564223', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1248509044314449329905796627963,1431771855502665466194321321112,2465767661223638235807706248205', 'Lhash_array': ['1248509044314449329905796627963', '1431771855502665466194321321112', '2465767661223638235807706248205'], 'factors': ['2-6975-1.1-c1-0-121', '2-6975-1.1-c1-0-148', '2-6975-1.1-c1-0-235'], 'label': '6-6975e3-1.1-c1e3-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6975/2/a/bc'}