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  • lfunc_lfunctions • Show schema
    {'Lhash': '619583089684647495983259219726,940427728496828658853805122166,1082870214926141898244593986911', 'a10': 0, 'a2': 0, 'a3': 3, 'a4': 0, 'a5': -3, 'a6': 0, 'a7': -4, 'a8': 0, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 209676.67819583448, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [1]], [3, [1, -3, 3, -1]], [5, [1, 3, 3, 1]], [31, [1, -3, 3, -1]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '7440.1', 'coefficient_field': '1.1.1.1', 'conductor': 411830784000, 'conductor_radical': 930, 'degree': 6, 'euler_factors': [[1], [1, -3, 3, -1], [1, 3, 3, 1], [1, 4, 15, 38, 105, 196, 343], [1, -2, 13, -20, 143, -242, 1331], [1, -4, 33, -86, 429, -676, 2197], [1, 2, 43, 56, 731, 578, 4913], [1, 4, 25, 56, 475, 1444, 6859], [1, -2, 61, -80, 1403, -1058, 12167], [1, 0, 39, 34, 1131, 0, 24389], [1, -3, 3, -1], [1, -6, -3, 278, -111, -8214, 50653], [1, 8, 123, 608, 5043, 13448, 68921], [1, 18, 165, 1124, 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'6.69333408640981534234942318573413', '6.71999209539449819791135887968915', '7.03828718849902434381234136434518', '7.05892858886548697412600362069655', '7.45497876752233407989397025782621', '7.80558038775716669567579980588716', '8.026578060983832656364775960726307', '8.076865273444481139271379341106547'], 'prelabel': '6-7440e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.707703880133994, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e3-0', 'trace_hash': 1565121461223885634, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.48876487698826236554111861339', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '0.74186666919694817558768396944', 'prec': 97}, 'z3': {'__RealLiteral__': 0, 'data': '0.854233977983507907235061486468', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 209676.67819583448, 'bad_primes': [2, 3, 5, 31], 'central_character': '1.1', 'conductor': 411830784000, 'conductor_radical': 930, 'degree': 6, 'dirichlet_coefficients': [1, 0, 3, 0, -3, 0, -4, 0, 6, 0, 2, 0, 4, 0, -9, 0, -2, 0, -4, 0, -12, 0, 2, 0, 6, 0, 10, 0, 0, 0, 3, 0, 6, 0, 12, 0, 6, 0, 12, 0, -8, 0, -18, 0, -18, 0, 4, 0, 1, 0, -6, 0, 26, 0, -6, 0, -12, 0, 6, 0, 18, 0, -24, 0, -12, 0, -10, 0, 6, 0, 0, 0, 22, 0, 18, 0, -8, 0, 0, 0, 15, 0, -6, 0, 6, 0, 0, 0, 10, 0, -16, 0, 9, 0, 12, 0, 4, 0, 12, 0], 'euler11': [1, -2, 13, -20, 143, -242, 1331], 'euler13': [1, -4, 33, -86, 429, -676, 2197], 'euler17': [1, 2, 43, 56, 731, 578, 4913], 'euler19': [1, 4, 25, 56, 475, 1444, 6859], 'euler2': [1, 0, 0, 0, 0, 0, 0], 'euler23': [1, -2, 61, -80, 1403, -1058, 12167], 'euler29': [1, 0, 39, 34, 1131, 0, 24389], 'euler3': [1, -3, 3, -1, 0, 0, 0], 'euler31': [1, -3, 3, -1, 0, 0, 0], 'euler37': [1, -6, -3, 278, -111, -8214, 50653], 'euler41': [1, 8, 123, 608, 5043, 13448, 68921], 'euler43': [1, 18, 165, 1124, 7095, 33282, 79507], 'euler47': [1, -4, 21, 116, 987, -8836, 103823], 'euler5': [1, 3, 3, 1, 0, 0, 0], 'euler53': [1, -26, 347, -3000, 18391, -73034, 148877], 'euler59': [1, -6, 141, -586, 8319, -20886, 205379], 'euler61': [1, -18, 291, -2412, 17751, -66978, 226981], 'euler67': [1, 10, 155, 1378, 10385, 44890, 300763], 'euler7': [1, 4, 15, 38, 105, 196, 343], 'euler71': [1, 0, 9, 954, 639, 0, 357911], 'euler73': [1, -22, 369, -3518, 26937, -117238, 389017], 'euler79': [1, 0, 153, 164, 12087, 0, 493039], 'euler83': [1, 6, 153, 1032, 12699, 41334, 571787], 'euler89': [1, -10, 195, -1882, 17355, -79210, 704969], 'euler97': [1, -4, 35, 200, 3395, -37636, 912673], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0], [1, -3, 3, -1, 0, 0, 0], [1, 3, 3, 1, 0, 0, 0], [1, 4, 15, 38, 105, 196, 343], [1, -2, 13, -20, 143, -242, 1331], [1, -4, 33, -86, 429, -676, 2197], [1, 2, 43, 56, 731, 578, 4913], [1, 4, 25, 56, 475, 1444, 6859], [1, -2, 61, -80, 1403, -1058, 12167], [1, 0, 39, 34, 1131, 0, 24389], [1, -3, 3, -1, 0, 0, 0], [1, -6, -3, 278, -111, -8214, 50653], [1, 8, 123, 608, 5043, 13448, 68921], [1, 18, 165, 1124, 7095, 33282, 79507], [1, -4, 21, 116, 987, -8836, 103823], [1, -26, 347, -3000, 18391, -73034, 148877], [1, -6, 141, -586, 8319, -20886, 205379], [1, -18, 291, -2412, 17751, -66978, 226981], [1, 10, 155, 1378, 10385, 44890, 300763], [1, 0, 9, 954, 639, 0, 357911], [1, -22, 369, -3518, 26937, -117238, 389017], [1, 0, 153, 164, 12087, 0, 493039], [1, 6, 153, 1032, 12699, 41334, 571787], [1, -10, 195, -1882, 17355, -79210, 704969], [1, -4, 35, 200, 3395, -37636, 912673]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7440/2/a/bt'], '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': '6-7440e3-1.1-c1e3-0-2', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '6-7440e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.707703880133994, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 1565121461223885634, 'z1': {'__RealLiteral__': 0, 'data': '0.48876487698826236554111861339', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '619583089684647495983259219726,940427728496828658853805122166,1082870214926141898244593986911', 'Lhash_array': ['619583089684647495983259219726', '940427728496828658853805122166', '1082870214926141898244593986911'], 'factors': ['2-7440-1.1-c1-0-8', '2-7440-1.1-c1-0-30', '2-7440-1.1-c1-0-41'], 'label': '6-7440e3-1.1-c1e3-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7440/2/a/bt'}