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lfunc_lfunctions • Show schema
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{'Lhash': '1056162706095043430920440210071', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.027835131044698192, 0.0], 'a4': [0.0, 0.0], 'a5': [-0.12240765218287943, 0.0], 'a6': [0.0, 0.0], 'a7': [0.8775923478171206, 0.0], 'a8': [0.0, 0.0], 'a9': [-2.9992252054797244, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26.701974435916174, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-1.0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 11, 19], 'central_character': '3344.1', 'coefficient_field': 'CDF', 'conductor': 3344, 'conductor_radical': 418, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.027835131044698192, 0], [3.0, 0]], [[1.0, 0], [0.12240765218287943, 0], [5.0, 0]], [[1.0, 0], [-0.8775923478171206, 0], [7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.6843601187592494, 0], [13.0, 0]], [[1.0, 0], [-6.3403974007113515, 0], [17.0, 0]], [[1.0, 0], [1.0, 0]], 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'3.19353872488499630600546846898617', '3.72734332934737422427595096203715', '5.01588857882208054029501169664568', '5.48402374491544367836492081648598', '6.36333455574032149992190114945106', '7.13839353313720723913643066359174', '8.048810452510903664341350242738535', '8.534894117364714417986308700456657'], 'prelabel': '2-3344-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.167395324137313, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.833165468390809403412805853022', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.01236809741968421995085304345', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.19353872488499630600546846899', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 26.701974435916174, 'bad_primes': [2, 11, 19], 'central_character': '1.1', 'conductor': 3344, 'conductor_radical': 418, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3344/2/a/z/1/3'], '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': '2-3344-1.1-c1-0-27', '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': '2-3344-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.167395324137313, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.833165468390809403412805853022', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1056162706095043430920440210071', 'Lhash_array': ['1056162706095043430920440210071'], 'label': '2-3344-1.1-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3344/2/a/z/1/3'}