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lfunc_lfunctions • Show schema
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{'Lhash': '1103942370718606657703422079482', 'a10': [-626.0923798911144, 2.335489322942027e-59], 'a2': [-4.898979485566356, -2.8284271247461903], 'a3': [0.0, 0.0], 'a4': [16.0, 27.712812921102035], 'a5': [95.85042891112461, -55.339270933778884], 'a6': [0.0, 0.0], 'a7': [-163.1690163552285, 282.61702654829287], 'a8': [0.0, -181.01933598375618], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.422920515471954, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [4.898979485566356, 2.8284271247461903]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '54.35', 'coefficient_field': 'CDF', 'conductor': 54, 'conductor_radical': 6, 'conjugate': '1706275383352939569830350194460', 'degree': 2, 'euler_factors': [[[1.0, 0], [4.898979485566356, 2.8284271247461903]], [[1.0, 0], [0, 0]], [[1.0, 0], [-95.85042891112461, 55.339270933778884], [7812.5, -13531.646934131853]], [[1.0, 0], 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'7.79602024714311554289579078650767', '9.543658502860764388203867186787306', '10.18920761557483737743406435213871', '11.43776675662403056035341702429095', '13.27310846399026669710177564834658', '13.94589460920070672807799394265125'], 'prelabel': '2-54-9.2-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.5246163642972483, 'root_angle': -0.10452105493956779, 'root_number': '0.9465716701233047 - 0.32249352446208557*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0522605274698', 'prec': 54}, 'spectral_label': 'c6-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.870856977876909844757969776172', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.98588262674021069536167170950', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.33593178995569891443533345066', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.422920515471954, 'bad_primes': [2, 3], 'central_character': '9.2', 'conductor': 54, 'conductor_radical': 6, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/54/7/d/a/35/3'], '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': '2-54-9.2-c6-0-3', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'prelabel': '2-54-9.2-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.5246163642972483, 'root_angle': -0.05226052746978389, 'self_dual': False, 'spectral_label': 'c6-0', 'z1': {'__RealLiteral__': 0, 'data': '0.870856977876909844757969776172', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1103942370718606657703422079482', 'Lhash_array': ['1103942370718606657703422079482'], 'label': '2-54-9.2-c6-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/54/7/d/a/35/3'}