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lfunc_lfunctions • Show schema
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{'Lhash': '868454611575725519252437068165', 'a10': -1, 'a2': -1, 'a3': 0, 'a4': 1, 'a5': 1, 'a6': 0, 'a7': -1, 'a8': -1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 55.336328600747336, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [5, [1, -1]], [7, [1, 1]], [11, [1, 1]]], 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '6930.1', 'coefficient_field': '1.1.1.1', 'conductor': 6930, 'conductor_radical': 2310, 'degree': 2, 'euler_factors': [[1, 1], [1], [1, -1], [1, 1], [1, 1], [1, -2, 13], [1, 0, 17], [1, 2, 19], [1, -4, 23], [1, -10, 29], [1, 4, 31], [1, 4, 37], [1, 6, 41], [1, -6, 43], [1, 6, 47], [1, -6, 53], [1, -12, 59], [1, 0, 61], [1, -2, 67], [1, 2, 71], [1, 10, 73], [1, 0, 79], [1, -16, 83], [1, 18, 89], [1, 14, 97], [1, 6, 101], [1, 0, 103], [1, -4, 107], [1, 6, 109], [1, -6, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [1], [[[1, -1], 1]], [[[1, 1], 1]], [[[1, 1], 1]], [[[1, -2, 13], 1]], [[[1, 0, 17], 1]], [[[1, 2, 19], 1]], [[[1, -4, 23], 1]], [[[1, -10, 29], 1]], [[[1, 4, 31], 1]], [[[1, 4, 37], 1]], [[[1, 6, 41], 1]], [[[1, -6, 43], 1]], [[[1, 6, 47], 1]], [[[1, -6, 53], 1]], [[[1, -12, 59], 1]], [[[1, 0, 61], 1]], [[[1, -2, 67], 1]], [[[1, 2, 71], 1]], [[[1, 10, 73], 1]], [[[1, 0, 79], 1]], [[[1, -16, 83], 1]], [[[1, 18, 89], 1]], [[[1, 14, 97], 1]], [[[1, 6, 101], 1]], [[[1, 0, 103], 1]], [[[1, -4, 107], 1]], [[[1, 6, 109], 1]], [[[1, -6, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 17, 'label': '2-6930-1.1-c1-0-17', 'leading_term': '1.419032292855017023269283524071500000000000000000000000000000000000000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/6930/2/a/i', 'plot_delta': {'__RealLiteral__': 0, 'data': 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2.161264461365931, 1.7498001993615278, 1.2116426045914028, 0.5793476845453681, -0.10854227251571813, -0.8098601817263364, -1.4814437039023922, -2.0818674182696277, -2.5741024336827545, -2.9279297919595555, -3.1219469982738546, -3.14503079974324, -2.997152562582358, -2.689483253107659, -2.2437705566826964, -1.6910181448208135, -1.069543411080255], 'positive_zeros': ['0.68508989103098903077156499148002', '1.69961732288693581850333296609336', '2.64536652094341162060297480995267', '3.34711559818770167127130244291228', '4.36707879462100514588224343087959', '5.29957965689161254804884714096157', '5.94177224906595788916007559231349', '6.80497317566770523206681840269470', '7.06277172352689287665702293193063', '8.263783043118445658627637948939239'], 'prelabel': '2-6930-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.438839197129303, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 1690293943852683931, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.68508989103098903077156499148', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.69961732288693581850333296609', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.64536652094341162060297480995', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 55.336328600747336, 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '1.1', 'conductor': 6930, 'conductor_radical': 2310, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, 1, 0, -1, -1, 0, -1, -1, 0, 2, 1, 0, 1, 0, 0, -2, 1, 0, 1, 4, 0, 1, -2, 0, -1, 10, 0, -4, -1, 0, 0, -1, 0, -4, 2, 0, -1, -6, 0, 6, -1, 0, -4, -6, 0, 1, -1, 0, 2, 6, 0, -1, 1, 0, -10, 12, 0, 0, 4, 0, 1, 2, 0, 2, 0, 0, 1, -2, 0, -10, 4, 0, -2, 1, 0, 0, 1, 0, 6, 16, 0, 0, -6, 0, 1, -18, 0, -2, 4, 0, 6, -2, 0, -14, -1, 0, 1], 'euler11': [1, 1, 0], 'euler13': [1, -2, 13], 'euler17': [1, 0, 17], 'euler19': [1, 2, 19], 'euler2': [1, 1, 0], 'euler23': [1, -4, 23], 'euler29': [1, -10, 29], 'euler3': [1, 0, 0], 'euler31': [1, 4, 31], 'euler37': [1, 4, 37], 'euler41': [1, 6, 41], 'euler43': [1, -6, 43], 'euler47': [1, 6, 47], 'euler5': [1, -1, 0], 'euler53': [1, -6, 53], 'euler59': [1, -12, 59], 'euler61': [1, 0, 61], 'euler67': [1, -2, 67], 'euler7': [1, 1, 0], 'euler71': [1, 2, 71], 'euler73': [1, 10, 73], 'euler79': [1, 0, 79], 'euler83': [1, -16, 83], 'euler89': [1, 18, 89], 'euler97': [1, 14, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, -1, 0], [1, 1, 0], [1, 1, 0], [1, -2, 13], [1, 0, 17], [1, 2, 19], [1, -4, 23], [1, -10, 29], [1, 4, 31], [1, 4, 37], [1, 6, 41], [1, -6, 43], [1, 6, 47], [1, -6, 53], [1, -12, 59], [1, 0, 61], [1, -2, 67], [1, 2, 71], [1, 10, 73], [1, 0, 79], [1, -16, 83], [1, 18, 89], [1, 14, 97]], 'index': 17, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/6930/i', 'ModularForm/GL2/Q/holomorphic/6930/2/a/i/1/1', 'ModularForm/GL2/Q/holomorphic/6930/2/a/i'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-6930-1.1-c1-0-17', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-6930-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.438839197129303, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1690293943852683931, 'z1': {'__RealLiteral__': 0, 'data': '0.68508989103098903077156499148', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21610301
{'Lhash': '868454611575725519252437068165', 'Lhash_array': ['868454611575725519252437068165'], 'label': '2-6930-1.1-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6930/2/a/i'}
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id: 24577298
{'Lhash': '868454611575725519252437068165', 'Lhash_array': ['868454611575725519252437068165'], 'label': '2-6930-1.1-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6930/2/a/i/1/1'}
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id: 35215
{'Lhash': '1690293943852683931', 'Lhash_array': ['1690293943852683931'], 'label': '2-6930-1.1-c1-0-17', 'type': 'ECQ', 'url': 'EllipticCurve/Q/6930/i'}