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lfunc_lfunctions • Show schema
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{'Lhash': '628966252726794952510277379554', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -2.0], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, -49.0], 'a8': [0, 0], 'a9': [239.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 112.26867386908647, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 49.0]]]], 'bad_primes': [2, 5, 7], 'central_character': '700.449', 'coefficient_field': 'CDF', 'conductor': 700, 'conductor_radical': 70, 'conjugate': '961766370609314640812314454828', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 2.0], [-243.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 49.0]], [[1.0, 0], [720.0, 0], [161051.0, 0]], [[1.0, 0], [0, -572.0], [-371293.0, 0]], [[1.0, 0], [0, 1254.0], [-1419857.0, 0]], [[1.0, 0], [-94.0, 0], [2476099.0, 0]], [[1.0, 0], [0, -96.0], [-6436343.0, 0]], [[1.0, 0], [-4374.0, 0], [20511149.0, 0]], [[1.0, 0], 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'7.88655519999573719184279539079590', '8.649360719332333577174406183918236', '9.832570293895776412158818852838624'], 'prelabel': '2-700-5.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.59569128792862, 'root_angle': -0.07379180882521663, 'root_number': '0.8944271909999158785636694674925104941762473438446102897 - 0.4472135954999579392818347337462552470881236719223051449*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.07379180882521663', 'prec': 67}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.49616688747952715104488793260', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.92846793092497751727320626817', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.95206904774621332742341164589', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 112.26867386908647, 'bad_primes': [2, 5, 7], 'central_character': '5.4', 'conductor': 700, 'conductor_radical': 70, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/700/6/e/d/449/1'], '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': '2-700-5.4-c5-0-15', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-700-5.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.59569128792862, 'root_angle': -0.07379180882521663, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.49616688747952715104488793260', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '628966252726794952510277379554', 'Lhash_array': ['628966252726794952510277379554'], 'factors': ['2-700-5.4-c5-0-15'], 'label': '2-700-5.4-c5-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/700/6/e/d/449/1'}