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lfunc_lfunctions • Show schema
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{'Lhash': '1184909379147194216970697099619', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-0.706216381252423, 1.5815367282648647], 'a4': [0, 0], 'a5': [-1.2794318284053319, 0.7386803105395935], 'a6': [0, 0], 'a7': [1.340275687959326, -2.281153453905536], 'a8': [0, 0], 'a9': [-2.0025168457014644, -2.233814290106019], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.048920523745066, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.706216381252423, -1.5815367282648647]]], [7, [[1.0, 0], [-1.340275687959326, 2.281153453905536]]]], 'bad_primes': [2, 3, 7], 'central_character': '1008.607', 'coefficient_field': 'CDF', 'conductor': 1008, 'conductor_radical': 42, 'conjugate': '1288896484062503890773512905649', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.706216381252423, -1.5815367282648647]], [[1.0, 0], [1.2794318284053319, -0.7386803105395935], [2.5, -4.330127018922194]], [[1.0, 0], 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'7.58861761765828736597252428643000', '8.087284290928658901131961151449854', '8.749564250017764943505783133790806', '9.842591874586168884547671000557349'], 'prelabel': '2-1008-252.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.837061952750603, 'root_angle': -0.24542504641023727, 'root_number': '0.7171963896582563839861118923682401484840402185148145002 - 0.6968711062034086625362608291538356518509909266428869357*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.12271252320511863', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.934728685438922719344882265731', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.13860675830766737011905513365', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.51305262357101274195270118554', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.048920523745066, 'bad_primes': [2, 3, 7], 'central_character': '252.103', 'conductor': 1008, 'conductor_radical': 42, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1008/2/cz/g/607/6'], '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': '2-1008-252.103-c1-0-19', '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': '2-1008-252.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.837061952750603, 'root_angle': -0.12271252320511863, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.934728685438922719344882265731', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1184909379147194216970697099619', 'Lhash_array': ['1184909379147194216970697099619'], 'label': '2-1008-252.103-c1-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1008/2/cz/g/607/6'}