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lfunc_lfunctions • Show schema
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{'Lhash': '550406033640688074679757721538', 'a10': [10.0, 0], 'a2': [-1.0, 1.7320508075688772], 'a3': [0, 0], 'a4': [-2.0, -3.4641016151377544], 'a5': [-2.5, -4.330127018922194], 'a6': [0, 0], 'a7': [-7.0, 12.12435565298214], 'a8': [8.0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 47.79154710464992, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, -1.7320508075688772]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [2.5, 4.330127018922194]]]], 'bad_primes': [2, 3, 5], 'central_character': '810.541', 'coefficient_field': 'CDF', 'conductor': 810, 'conductor_radical': 30, 'conjugate': '989988457604225829432687902865', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, -1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.5, 4.330127018922194]], [[1.0, 0], [7.0, -12.12435565298214], [-171.5, -297.04671349806245]], [[1.0, 0], [-3.0, 5.196152422706632], [-665.5, -1152.6798124370878]], [[1.0, 0], 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0.9848077530122080593667430245895230136706432517198424188*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2222222222222222', 'prec': 64}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.43419380193689987061901834077', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.93059209658484318798592657299', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.99504874152822162071524140063', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 47.79154710464992, 'bad_primes': [2, 3, 5], 'central_character': '9.7', 'conductor': 810, 'conductor_radical': 30, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/810/4/e/a/541/1'], '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': '2-810-9.7-c3-0-12', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-810-9.7-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.913143069881451, 'root_angle': -0.2222222222222222, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.43419380193689987061901834077', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '550406033640688074679757721538', 'Lhash_array': ['550406033640688074679757721538'], 'label': '2-810-9.7-c3-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/810/4/e/a/541/1'}