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lfunc_lfunctions • Show schema
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{'Lhash': '1375506496688248746771978417346,1509515813621914353491420327743,1711038717525872287937817937634', 'a10': 0, 'a2': -3, 'a3': 0, 'a4': 6, 'a5': 0, 'a6': 0, 'a7': -3, 'a8': -10, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 139691.64836573237, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 3, 3, 1]], [3, [1]], [19, [1]]], 'bad_primes': [2, 3, 19], 'central_character': '6498.1', 'coefficient_field': '1.1.1.1', 'conductor': 274371577992, 'conductor_radical': 114, 'degree': 6, 'euler_factors': [[1, 3, 3, 1], [1], [1, 0, 6, -9, 30, 0, 125], [1, 3, 21, 41, 147, 147, 343], [1, 0, 30, 1, 330, 0, 1331], [1, -6, 48, -159, 624, -1014, 2197], [1, 6, 42, 187, 714, 1734, 4913], [1], [1, 6, 24, 7, 552, 3174, 12167], [1, 6, 42, 135, 1218, 5046, 24389], [1, -9, 93, -531, 2883, -8649, 29791], [1, -9, 54, -305, 1998, -12321, 50653], [1, 9, 111, 629, 4551, 15129, 68921], [1, -15, 183, -1347, 7869, -27735, 79507], [1, 3, 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'1.19079801117921549999386540851', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.34977155157565873006680932687', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 139691.64836573237, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 274371577992, 'conductor_radical': 114, 'degree': 6, 'dirichlet_coefficients': [1, -3, 0, 6, 0, 0, -3, -10, 0, 0, 0, 0, 6, 9, 0, 15, -6, 0, 0, 0, 0, 0, -6, 0, -6, -18, 0, -18, -6, 0, 9, -21, 0, 18, 0, 0, 9, 0, 0, 0, -9, 0, 15, 0, 0, 18, -3, 0, -12, 18, 0, 36, 3, 0, 0, 30, 0, 18, 12, 0, -33, -27, 0, 28, 0, 0, 12, -36, 0, 0, -15, 0, 3, -27, 0, 0, 0, 0, 15, 0, 0, 27, -27, 0, 0, -45, 0, 0, 15, 0, -18, -36, 0, 9, 0, 0, -12, 36, 0, -36], 'euler11': [1, 0, 30, 1, 330, 0, 1331], 'euler13': [1, -6, 48, -159, 624, -1014, 2197], 'euler17': [1, 6, 42, 187, 714, 1734, 4913], 'euler19': [1, 0, 0, 0, 0, 0, 0], 'euler2': [1, 3, 3, 1, 0, 0, 0], 'euler23': [1, 6, 24, 7, 552, 3174, 12167], 'euler29': [1, 6, 42, 135, 1218, 5046, 24389], 'euler3': [1, 0, 0, 0, 0, 0, 0], 'euler31': [1, -9, 93, -531, 2883, -8649, 29791], 'euler37': [1, -9, 54, -305, 1998, -12321, 50653], 'euler41': [1, 9, 111, 629, 4551, 15129, 68921], 'euler43': [1, -15, 183, -1347, 7869, -27735, 79507], 'euler47': [1, 3, 117, 229, 5499, 6627, 103823], 'euler5': [1, 0, 6, -9, 30, 0, 125], 'euler53': [1, -3, 6, -11, 318, -8427, 148877], 'euler59': [1, -12, 144, -1399, 8496, -41772, 205379], 'euler61': [1, 33, 543, 5323, 33123, 122793, 226981], 'euler67': [1, -12, 210, -1605, 14070, -53868, 300763], 'euler7': [1, 3, 21, 41, 147, 147, 343], 'euler71': [1, 15, 159, 1681, 11289, 75615, 357911], 'euler73': [1, -3, 105, -475, 7665, -15987, 389017], 'euler79': [1, -15, 87, -245, 6873, -93615, 493039], 'euler83': [1, 27, 471, 4985, 39093, 186003, 571787], 'euler89': [1, -15, 231, -2563, 20559, -118815, 704969], 'euler97': [1, 12, 336, 2381, 32592, 112908, 912673], 'euler_factors': [[1, 3, 3, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0], [1, 0, 6, -9, 30, 0, 125], [1, 3, 21, 41, 147, 147, 343], [1, 0, 30, 1, 330, 0, 1331], [1, -6, 48, -159, 624, -1014, 2197], [1, 6, 42, 187, 714, 1734, 4913], [1, 0, 0, 0, 0, 0, 0], [1, 6, 24, 7, 552, 3174, 12167], [1, 6, 42, 135, 1218, 5046, 24389], [1, -9, 93, -531, 2883, -8649, 29791], [1, -9, 54, -305, 1998, -12321, 50653], [1, 9, 111, 629, 4551, 15129, 68921], [1, -15, 183, -1347, 7869, -27735, 79507], [1, 3, 117, 229, 5499, 6627, 103823], [1, -3, 6, -11, 318, -8427, 148877], [1, -12, 144, -1399, 8496, -41772, 205379], [1, 33, 543, 5323, 33123, 122793, 226981], [1, -12, 210, -1605, 14070, -53868, 300763], [1, 15, 159, 1681, 11289, 75615, 357911], [1, -3, 105, -475, 7665, -15987, 389017], [1, -15, 87, -245, 6873, -93615, 493039], [1, 27, 471, 4985, 39093, 186003, 571787], [1, -15, 231, -2563, 20559, -118815, 704969], [1, 12, 336, 2381, 32592, 112908, 912673]], 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6498/2/a/bn'], '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': '6-6498e3-1.1-c1e3-0-7', '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': 3, 'prelabel': '6-6498e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.2032486583088335, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 992848607579697473, 'z1': {'__RealLiteral__': 0, 'data': '1.08508330011487458343229041718', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1375506496688248746771978417346,1509515813621914353491420327743,1711038717525872287937817937634', 'Lhash_array': ['1375506496688248746771978417346', '1509515813621914353491420327743', '1711038717525872287937817937634'], 'label': '6-6498e3-1.1-c1e3-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6498/2/a/bn'}