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lfunc_lfunctions • Show schema
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{'Lhash': '922602784632151000951304706488,1233454723887788689125253333927,1314330203820358592048814687207,1480428377501464721002604264744', 'a10': 16, 'a2': 4, 'a3': 0, 'a4': 10, 'a5': 4, 'a6': 0, 'a7': 1, 'a8': 20, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5374990.198265895, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -4, 6, -4, 1]], [3, [1]], [5, [1, -4, 6, -4, 1]], [67, [1, 4, 6, 4, 1]]], 'bad_primes': [2, 3, 5, 67], 'central_character': '6030.1', 'coefficient_field': '1.1.1.1', 'conductor': 1322115048810000, 'conductor_radical': 2010, 'degree': 8, 'euler_factors': [[1, -4, 6, -4, 1], [1], [1, -4, 6, -4, 1], [1, -1, 8, -9, 66, -63, 392, -343, 2401], [1, -3, 24, -67, 398, -737, 2904, -3993, 14641], [1, -2, 32, -50, 486, -650, 5408, -4394, 28561], [1, -2, 36, -22, 678, -374, 10404, -9826, 83521], [1, -2, 44, -34, 982, -646, 15884, -13718, 130321], [1, -12, 100, -624, 3094, -14352, 52900, -146004, 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123869124790948030, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.72780526784434483781654196629', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.973024210035254159172176342806', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.03682371434504502760165639563', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 5374990.198265895, 'bad_primes': [2, 3, 5, 67], 'central_character': '1.1', 'conductor': 1322115048810000, 'conductor_radical': 2010, 'degree': 8, 'dirichlet_coefficients': [1, 4, 0, 10, 4, 0, 1, 20, 0, 16, 3, 0, 2, 4, 0, 35, 2, 0, 2, 40, 0, 12, 12, 0, 10, 8, 0, 10, -2, 0, 10, 56, 0, 8, 4, 0, 3, 8, 0, 80, 0, 0, -6, 30, 0, 48, 14, 0, -7, 40, 0, 20, 10, 0, 12, 20, 0, -8, 0, 0, 9, 40, 0, 84, 8, 0, -4, 20, 0, 16, 9, 0, -14, 12, 0, 20, 3, 0, 12, 140, 0, 0, 25, 0, 8, -24, 0, 60, 9, 0, 2, 120, 0, 56, 8, 0, -3, -28, 0, 100], 'euler11': [1, -3, 24, -67, 398, -737, 2904, -3993, 14641], 'euler13': [1, -2, 32, -50, 486, -650, 5408, -4394, 28561], 'euler17': [1, -2, 36, -22, 678, -374, 10404, -9826, 83521], 'euler19': [1, -2, 44, -34, 982, -646, 15884, -13718, 130321], 'euler2': [1, -4, 6, -4, 1, 0, 0, 0, 0], 'euler23': [1, -12, 100, -624, 3094, -14352, 52900, -146004, 279841], 'euler29': [1, 2, 64, 322, 1918, 9338, 53824, 48778, 707281], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, -10, 140, -878, 6646, -27218, 134540, -297910, 923521], 'euler37': [1, -3, 122, -273, 6346, -10101, 167018, -151959, 1874161], 'euler41': [1, 0, 92, -16, 4358, -656, 154652, 0, 2825761], 'euler43': [1, 6, 92, 518, 6006, 22274, 170108, 477042, 3418801], 'euler47': [1, -14, 116, -762, 4862, -35814, 256244, -1453522, 4879681], 'euler5': [1, -4, 6, -4, 1, 0, 0, 0, 0], 'euler53': [1, -10, 168, -1230, 12542, -65190, 471912, -1488770, 7890481], 'euler59': [1, 0, 164, -16, 12566, -944, 570884, 0, 12117361], 'euler61': [1, -9, 254, -1599, 23518, -97539, 945134, -2042829, 13845841], 'euler67': [1, 4, 6, 4, 1, 0, 0, 0, 0], 'euler7': [1, -1, 8, -9, 66, -63, 392, -343, 2401], 'euler71': [1, -9, 242, -1313, 22814, -93223, 1219922, -3221199, 25411681], 'euler73': [1, 14, 248, 2274, 25134, 166002, 1321592, 5446238, 28398241], 'euler79': [1, -12, 200, -992, 13686, -78368, 1248200, -5916468, 38950081], 'euler83': [1, -25, 324, -3793, 40262, -314819, 2232036, -14294675, 47458321], 'euler89': [1, -9, 122, -783, 10410, -69687, 966362, -6344721, 62742241], 'euler97': [1, 3, 368, 841, 52686, 81577, 3462512, 2738019, 88529281], 'euler_factors': [[1, -4, 6, -4, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, -4, 6, -4, 1, 0, 0, 0, 0], [1, -1, 8, -9, 66, -63, 392, -343, 2401], [1, -3, 24, -67, 398, -737, 2904, -3993, 14641], [1, -2, 32, -50, 486, -650, 5408, -4394, 28561], [1, -2, 36, -22, 678, -374, 10404, -9826, 83521], [1, -2, 44, -34, 982, -646, 15884, -13718, 130321], [1, -12, 100, -624, 3094, -14352, 52900, -146004, 279841], [1, 2, 64, 322, 1918, 9338, 53824, 48778, 707281], [1, -10, 140, -878, 6646, -27218, 134540, -297910, 923521], [1, -3, 122, -273, 6346, -10101, 167018, -151959, 1874161], [1, 0, 92, -16, 4358, -656, 154652, 0, 2825761], [1, 6, 92, 518, 6006, 22274, 170108, 477042, 3418801], [1, -14, 116, -762, 4862, -35814, 256244, -1453522, 4879681], [1, -10, 168, -1230, 12542, -65190, 471912, -1488770, 7890481], [1, 0, 164, -16, 12566, -944, 570884, 0, 12117361], [1, -9, 254, -1599, 23518, -97539, 945134, -2042829, 13845841], [1, 4, 6, 4, 1, 0, 0, 0, 0], [1, -9, 242, -1313, 22814, -93223, 1219922, -3221199, 25411681], [1, 14, 248, 2274, 25134, 166002, 1321592, 5446238, 28398241], [1, -12, 200, -992, 13686, -78368, 1248200, -5916468, 38950081], [1, -25, 324, -3793, 40262, -314819, 2232036, -14294675, 47458321], [1, -9, 122, -783, 10410, -69687, 966362, -6344721, 62742241], [1, 3, 368, 841, 52686, 81577, 3462512, 2738019, 88529281]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6030/2/a/bu'], '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': '8-6030e4-1.1-c1e4-0-0', '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}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '8-6030e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.939005146188616, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 123869124790948030, 'z1': {'__RealLiteral__': 0, 'data': '0.72780526784434483781654196629', 'prec': 103}}
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{'Lhash': '922602784632151000951304706488,1233454723887788689125253333927,1314330203820358592048814687207,1480428377501464721002604264744', 'Lhash_array': ['922602784632151000951304706488', '1233454723887788689125253333927', '1314330203820358592048814687207', '1480428377501464721002604264744'], 'label': '8-6030e4-1.1-c1e4-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6030/2/a/bu'}