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lfunc_lfunctions • Show schema
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{'Lhash': '920003763292894393799417370538', 'a10': [-0.5972386467970178, 1.1157648647542595], 'a2': [1.0082978982608104, 0.9916326680595151], 'a3': [-1.6951643908056313, -0.3555526517192255], 'a4': [0.033329303274335045, 1.9997222701023378], 'a5': [0.25211720871888355, 0.8586323604382792], 'a6': [-1.3566530677959139, -2.0394833791036238], 'a7': [-1.9222044365849869, 1.6655996256570502], 'a8': [-1.9493840636376025, 2.0493661879800174], 'a9': [2.7471646237108542, 1.2054403885018954], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.2038710957873398, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0082978982608104, -0.9916326680595151]]], [3, [[1.0, 0], [1.6951643908056313, 0.3555526517192255]]], [23, [[1.0, 0], [0.5787613258752766, -4.7607809577495885]]]], 'bad_primes': [2, 3, 23], 'central_character': '276.35', 'coefficient_field': 'CDF', 'conductor': 276, 'conductor_radical': 138, 'conjugate': 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1.484544070005111, 'root_angle': -0.7971916427583299, 'root_number': '-0.8037997133420542 - 0.594900009103405*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.398595821379', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.72575500151797014427298193856', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.86946900961548281944125931553', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.45410394646086071355085737516', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.2038710957873398, 'bad_primes': [2, 3, 23], 'central_character': '276.35', 'conductor': 276, 'conductor_radical': 138, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/276/2/o/a/35/34'], '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': '2-276-276.35-c1-0-4', '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': '2-276-276.35-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.484544070005111, 'root_angle': -0.39859582137916494, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.72575500151797014427298193856', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '920003763292894393799417370538', 'Lhash_array': ['920003763292894393799417370538'], 'label': '2-276-276.35-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/276/2/o/a/35/34'}