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lfunc_lfunctions • Show schema
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{'Lhash': '964861198859121645001029481877', 'a10': [0.0, 0.0], 'a2': [-0.7366272604026631, -1.2758758412576825], 'a3': [0.0, 0.0], 'a4': [-0.08523944153666584, 0.14763904355030216], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [1.932914569747178, 3.3479062414922485], 'a8': [-2.6953502564210243, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.389902136436429, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '675.226', 'coefficient_field': 'CDF', 'conductor': 675, 'conductor_radical': 15, 'conjugate': '1911530990620460503873580531876', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7366272604026631, 1.2758758412576825], [-1.0, 1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.932914569747178, -3.3479062414922485], [-3.5, 6.06217782649107]], [[1.0, 0], [-0.13013893201518326, 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'root_analytic_conductor': 2.321616276742655, 'root_angle': 0.009241449243042573, 'root_number': '0.9995785758603937 + 0.029028790551918742*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.00462072462152', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.76114127874463738391218017558', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.78990631505765155350396978147', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.06406061164483134410964251451', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.389902136436429, 'bad_primes': [3, 5], 'central_character': '9.4', 'conductor': 675, 'conductor_radical': 15, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/675/2/e/c/226/2'], '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': '2-675-9.4-c1-0-2', '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': '2-675-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.321616276742655, 'root_angle': 0.004620724621521286, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.76114127874463738391218017558', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '964861198859121645001029481877', 'Lhash_array': ['964861198859121645001029481877'], 'label': '2-675-9.4-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/675/2/e/c/226/2'}