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lfunc_lfunctions • Show schema
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{'Lhash': '746827956319262293358590719999,1250896218404519208172678322630,1284023146992454857806267576732', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 3, 'a6': 0, 'a7': 2, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 36127.03704423913, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, -3, 3, -1]], [23, [1, 3, 3, 1]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '4140.1', 'coefficient_field': '1.1.1.1', 'conductor': 70957944000, 'conductor_radical': 690, 'degree': 6, 'euler_factors': [[1], [1], [1, -3, 3, -1], [1, -2, 6, -4, 42, -98, 343], [1, 4, 19, 40, 209, 484, 1331], [1, -2, 21, -64, 273, -338, 2197], [1, 0, 30, -18, 510, 0, 4913], [1, -10, 71, -328, 1349, -3610, 6859], [1, 3, 3, 1], [1, 0, 66, 18, 1914, 0, 24389], [1, -10, 110, -616, 3410, -9610, 29791], [1, -2, 48, -256, 1776, -2738, 50653], [1, 8, 22, 74, 902, 13448, 68921], [1, -16, 149, -1072, 6407, -29584, 79507], [1, 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'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.986783123188129510261269133541', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.01291566206120024120795033286', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 36127.03704423913, 'bad_primes': [2, 3, 5, 23], 'central_character': '1.1', 'conductor': 70957944000, 'conductor_radical': 690, 'degree': 6, 'dirichlet_coefficients': [1, 0, 0, 0, 3, 0, 2, 0, 0, 0, -4, 0, 2, 0, 0, 0, 0, 0, 10, 0, 0, 0, -3, 0, 6, 0, 0, 0, 0, 0, 10, 0, 0, 0, 6, 0, 2, 0, 0, 0, -8, 0, 16, 0, 0, 0, 4, 0, -2, 0, 0, 0, -8, 0, -12, 0, 0, 0, 0, 0, 10, 0, 0, 0, 6, 0, 10, 0, 0, 0, 8, 0, 18, 0, 0, 0, -8, 0, 14, 0, 0, 0, -10, 0, 0, 0, 0, 0, -2, 0, 4, 0, 0, 0, 30, 0, -20, 0, 0, 0], 'euler11': [1, 4, 19, 40, 209, 484, 1331], 'euler13': [1, -2, 21, -64, 273, -338, 2197], 'euler17': [1, 0, 30, -18, 510, 0, 4913], 'euler19': [1, -10, 71, -328, 1349, -3610, 6859], 'euler2': [1, 0, 0, 0, 0, 0, 0], 'euler23': [1, 3, 3, 1, 0, 0, 0], 'euler29': [1, 0, 66, 18, 1914, 0, 24389], 'euler3': [1, 0, 0, 0, 0, 0, 0], 'euler31': [1, -10, 110, -616, 3410, -9610, 29791], 'euler37': [1, -2, 48, -256, 1776, -2738, 50653], 'euler41': [1, 8, 22, 74, 902, 13448, 68921], 'euler43': [1, -16, 149, -1072, 6407, -29584, 79507], 'euler47': [1, -4, 91, -160, 4277, -8836, 103823], 'euler5': [1, -3, 3, -1, 0, 0, 0], 'euler53': [1, 8, 58, 266, 3074, 22472, 148877], 'euler59': [1, 0, 156, -18, 9204, 0, 205379], 'euler61': [1, -10, 161, -928, 9821, -37210, 226981], 'euler67': [1, -10, 218, -1336, 14606, -44890, 300763], 'euler7': [1, -2, 6, -4, 42, -98, 343], 'euler71': [1, -8, 112, -554, 7952, -40328, 357911], 'euler73': [1, -18, 153, -1136, 11169, -95922, 389017], 'euler79': [1, -14, 237, -2116, 18723, -87374, 493039], 'euler83': [1, 10, 232, 1432, 19256, 68890, 571787], 'euler89': [1, 2, 67, -556, 5963, 15842, 704969], 'euler97': [1, 20, 203, 1544, 19691, 188180, 912673], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0], [1, -3, 3, -1, 0, 0, 0], [1, -2, 6, -4, 42, -98, 343], [1, 4, 19, 40, 209, 484, 1331], [1, -2, 21, -64, 273, -338, 2197], [1, 0, 30, -18, 510, 0, 4913], [1, -10, 71, -328, 1349, -3610, 6859], [1, 3, 3, 1, 0, 0, 0], [1, 0, 66, 18, 1914, 0, 24389], [1, -10, 110, -616, 3410, -9610, 29791], [1, -2, 48, -256, 1776, -2738, 50653], [1, 8, 22, 74, 902, 13448, 68921], [1, -16, 149, -1072, 6407, -29584, 79507], [1, -4, 91, -160, 4277, -8836, 103823], [1, 8, 58, 266, 3074, 22472, 148877], [1, 0, 156, -18, 9204, 0, 205379], [1, -10, 161, -928, 9821, -37210, 226981], [1, -10, 218, -1336, 14606, -44890, 300763], [1, -8, 112, -554, 7952, -40328, 357911], [1, -18, 153, -1136, 11169, -95922, 389017], [1, -14, 237, -2116, 18723, -87374, 493039], [1, 10, 232, 1432, 19256, 68890, 571787], [1, 2, 67, -556, 5963, 15842, 704969], [1, 20, 203, 1544, 19691, 188180, 912673]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4140/2/a/s'], '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': '6-4140e3-1.1-c1e3-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '6-4140e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.749614459840772, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 976184641886723066, 'z1': {'__RealLiteral__': 0, 'data': '0.58914337766637151662930508360', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '746827956319262293358590719999,1250896218404519208172678322630,1284023146992454857806267576732', 'Lhash_array': ['746827956319262293358590719999', '1250896218404519208172678322630', '1284023146992454857806267576732'], 'label': '6-4140e3-1.1-c1e3-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4140/2/a/s'}