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lfunc_lfunctions • Show schema
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{'Lhash': '734669718157312713129536687065', 'a10': [-460.42688164676963, 0.0], 'a2': [0.9308595942384071, 0.0], 'a3': [23.44780464133324, 0.0], 'a4': [-127.13350041581431, 0.0], 'a5': [-494.62548863072396, 0.0], 'a6': [21.8266139142129, 0.0], 'a7': [343.0, 0.0], 'a8': [-237.4934666736894, 0.0], 'a9': [-1637.2004575018714, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 28.427037319055092, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [-343.0, 0]]], [13, [[1.0, 0], [-2197.0, 0]]]], 'bad_primes': [7, 13], 'central_character': '91.1', 'coefficient_field': 'CDF', 'conductor': 91, 'conductor_radical': 91, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.9308595942384071, 0], [128.0, 0]], [[1.0, 0], [-23.44780464133324, 0], [2187.0, 0]], [[1.0, 0], [494.62548863072396, 0], [78125.0, 0]], [[1.0, 0], [-343.0, 0]], [[1.0, 0], [2423.999740189521, 0], [19487171.0, 0]], [[1.0, 0], [-2197.0, 0]], [[1.0, 0], 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'z3': {'__RealLiteral__': 0, 'data': '4.10714538922132723131700884267', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 28.427037319055092, 'bad_primes': [7, 13], 'central_character': '1.1', 'conductor': 91, 'conductor_radical': 91, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/91/8/a/e/1/6'], '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': '2-91-1.1-c7-0-5', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'prelabel': '2-91-1.1-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.331701165580746, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '0.57955221890404332003864515888', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '734669718157312713129536687065', 'Lhash_array': ['734669718157312713129536687065'], 'label': '2-91-1.1-c7-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/91/8/a/e/1/6'}