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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -2, 'A8': 0, 'A9': -3, 'Lhash': '61336035317798443', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.020618556701030927, 0.0], 'a8': [0.0, 0.0], 'a9': [-0.030927835051546393, 0.0], 'algebraic': True, 'analytic_conductor': 2.3504806021792133, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.500000000000000', 'prec': 57}, 'bad_lfactors': [[2, [1]], [3, [1, 0, 3]]], 'bad_primes': [2, 3], 'central_character': '36864.1', 'coefficient_field': '1.1.1.1', 'conductor': 36864, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1, 0, 3], [1, 0, -2, 0, 25], [1, 2, -2, 14, 49], [1, 4, 6, 44, 121], [1, 0, 6, 0, 169], [1, 2, 26, 34, 289], [1, -4, 6, -76, 361], [1, 8, 46, 184, 529], [1, -4, 38, -116, 841], [1, 10, 78, 310, 961], [1, 4, 46, 148, 1369], [1, 2, 26, 82, 1681], [1, -4, 54, -172, 1849], [1, 8, 30, 376, 2209], [1, 4, -26, 212, 2809], [1, 8, 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5.558679057170004, 6.266366039543871, 6.766067517349077, 7.641666036118081, 7.828715101765476, 8.625446620381355, 8.96867725849783, 9.664078295036086, 10.03700208487617, 10.62069897144519, 11.05206816373421, 11.52184648837616, 12.18301383661104, 12.49061904591557, 12.96375493941384, 13.56476381351342, 13.90632883421583, 14.25364298823326, 14.83272008836889, 15.41177428618468, 15.79531073986694, 16.13923336305945, 16.54059422696438, 16.92341924304003, 17.65897349979974, 17.96058719776562, 18.17512494708763, 18.75553585333236, 19.18444234708186, 19.6739216959817], 'prelabel': '4-192e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.2381953475960827, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'USp(4)', 'trace_hash': 61336035317798443, 'z1': {'__RealLiteral__': 0, 'data': '2.03781245881', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.93493481935', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.43795678588', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.3504806021792133, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 36864, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -2, 0, -3, 0, -4, 0, 0, 0, 0, 0, -2, 0, 4, 0, 0, 0, -8, 0, 2, 0, 0, 0, 4, 0, -10, 0, 0, 0, 0, 0, -4, 0, 0, 0, -2, 0, 4, 0, 0, 0, -8, 0, 6, 0, 0, 0, -4, 0, 0, 0, 0, 0, -8, 0, -4, 0, 6, 0, 0, 0, 8, 0, 0, 0, 0, 0, -4, 0, 0, 0, 8, 0, -2, 0, 9, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -16, 0, 12, 0], 'euler11': [1, 4, 6, 44, 121], 'euler13': [1, 0, 6, 0, 169], 'euler17': [1, 2, 26, 34, 289], 'euler19': [1, -4, 6, -76, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 8, 46, 184, 529], 'euler29': [1, -4, 38, -116, 841], 'euler3': [1, 0, 3, 0, 0], 'euler31': [1, 10, 78, 310, 961], 'euler37': [1, 4, 46, 148, 1369], 'euler41': [1, 2, 26, 82, 1681], 'euler43': [1, -4, 54, -172, 1849], 'euler47': [1, 8, 30, 376, 2209], 'euler5': [1, 0, -2, 0, 25], 'euler53': [1, 4, -26, 212, 2809], 'euler59': [1, 8, 54, 472, 3481], 'euler61': [1, 4, 30, 244, 3721], 'euler67': [1, -8, 38, -536, 4489], 'euler7': [1, 2, -2, 14, 49], 'euler71': [1, 0, -18, 0, 5041], 'euler73': [1, 4, 6, 292, 5329], 'euler79': [1, 2, 46, 158, 6241], 'euler83': [1, -4, 54, -332, 6889], 'euler89': [1, -2, -30, -178, 7921], 'euler97': [1, 16, 222, 1552, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 3, 0, 0], [1, 0, -2, 0, 25], [1, 2, -2, 14, 49], [1, 4, 6, 44, 121], [1, 0, 6, 0, 169], [1, 2, 26, 34, 289], [1, -4, 6, -76, 361], [1, 8, 46, 184, 529], [1, -4, 38, -116, 841], [1, 10, 78, 310, 961], [1, 4, 46, 148, 1369], [1, 2, 26, 82, 1681], [1, -4, 54, -172, 1849], [1, 8, 30, 376, 2209], [1, 4, -26, 212, 2809], [1, 8, 54, 472, 3481], [1, 4, 30, 244, 3721], [1, -8, 38, -536, 4489], [1, 0, -18, 0, 5041], [1, 4, 6, 292, 5329], [1, 2, 46, 158, 6241], [1, -4, 54, -332, 6889], [1, -2, -30, -178, 7921], [1, 16, 222, 1552, 9409]], 'index': 12, 'instance_types': ['G2Q'], 'instance_urls': ['Genus2Curve/Q/36864/f'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': True, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-192e2-1.1-c1e2-0-12', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 1, 'prelabel': '4-192e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.2381953475960827, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 61336035317798443, 'z1': {'__RealLiteral__': 0, 'data': '2.03781245881', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': '61336035317798443', 'Lhash_array': ['61336035317798443'], 'label': '4-192e2-1.1-c1e2-0-12', 'type': 'G2Q', 'url': 'Genus2Curve/Q/36864/f'}