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lfunc_lfunctions • Show schema
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{'Lhash': '959257263608965722393367902971', 'a10': [0.4160482318712027, -0.08147526739669496], 'a2': [-0.27178485294650356, -1.387851935081278], 'a3': [-1.0, 0.0], 'a4': [-1.8522659874176948, 0.754394268175171], 'a5': [0.0, 0.29977854362889034], 'a6': [0.27178485294650356, 1.387851935081278], 'a7': [-1.8803473430934248, 0.0], 'a8': [1.550405383909264, 2.3656379996832078], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.419972322510946, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.27178485294650356, 1.387851935081278]]], [3, [[1.0, 0], [1.0, 0]]], [67, [[1.0, 0], [-2.908320683307246, -7.651252891066095]]]], 'bad_primes': [2, 3, 67], 'central_character': '804.535', 'coefficient_field': 'CDF', 'conductor': 804, 'conductor_radical': 402, 'conjugate': '1081244957006884413035060744022', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.27178485294650356, 1.387851935081278]], [[1.0, 0], [1.0, 0]], 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'2.91029007033710530096125756915', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.50915847272661732419653250056', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.419972322510946, 'bad_primes': [2, 3, 67], 'central_character': '268.267', 'conductor': 804, 'conductor_radical': 402, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/804/2/e/a/535/15'], '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': '2-804-268.267-c1-0-15', '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': '2-804-268.267-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.533766430141292, 'root_angle': 0.13063196730563434, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.75672055331039944556574291531', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '959257263608965722393367902971', 'Lhash_array': ['959257263608965722393367902971'], 'label': '2-804-268.267-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/804/2/e/a/535/15'}