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lfunc_lfunctions • Show schema
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{'Lhash': '2190636348638368051003194864619', 'a10': [-8.469141236150206, 4.889660972496282], 'a2': [-2.1380322939989393, -1.2343935204764007], 'a3': [1.4788019246888455, 0.9017454560664921], 'a4': [2.0474547267882444, 3.5462956129942937], 'a5': [1.9805924494034814, -3.4304867514541204], 'a6': [-2.0486175233250243, -3.753384419940903], 'a7': [2.625225967604753, -0.3289203840045287], 'a8': [0.0, -5.17188531095915], 'a9': [1.373710264926868, 2.6670058320210988], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.4788019246888455, -0.9017454560664921]]], [7, [[1.0, 0], [-2.625225967604753, 0.3289203840045287]]], [13, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.131', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': '1824585244749143984240444563269', 'degree': 2, 'euler_factors': [[[1.0, 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'6.63987521587885570357290169849360', '7.35108373603708598776008176873266', '8.087703443102198221989062117892578', '9.047111110793480857006705345534840', '9.987049047314646338440345777339911', '10.63161790708496582618734883804639', '11.66232889372837599532452695836477'], 'prelabel': '2-273-21.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': 0.3416378402222084, 'root_number': '0.47723834481204813 + 0.8787738971095219*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.170818920111', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.72810737299691503285058903488', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.90314700767558762634225365476', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.55676992505910811200273899154', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'bad_primes': [3, 7, 13], 'central_character': '21.5', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/2/bh/a/131/3'], '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': '2-273-21.5-c1-0-13', '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': '2-273-21.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': 0.1708189201111042, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.72810737299691503285058903488', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2190636348638368051003194864619', 'Lhash_array': ['2190636348638368051003194864619'], 'label': '2-273-21.5-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/2/bh/a/131/3'}