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lfunc_lfunctions • Show schema
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{'Lhash': '1484259662520614394468115893696', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [3.0, -4.0], 'a6': [0, 0], 'a7': [7.0, 7.0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.61857903394138, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-3.0, 4.0]]]], 'bad_primes': [2, 3, 5], 'central_character': '720.577', 'coefficient_field': 'CDF', 'conductor': 720, 'conductor_radical': 30, 'conjugate': '1523125329042159451651795633234', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.0, 4.0]], [[1.0, 0], [-7.0, -7.0], [0, 49.0]], [[1.0, 0], [-10.0, 0], [121.0, 0]], [[1.0, 0], [-9.0, 9.0], [0, -169.0]], [[1.0, 0], [1.0, 1.0], [0, 289.0]], [[1.0, 0], [0, -8.0], [-361.0, 0]], [[1.0, 0], [23.0, -23.0], [0, -529.0]], [[1.0, 0], [0, -8.0], [-841.0, 0]], [[1.0, 0], [-14.0, 0], [961.0, 0]], 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'root_analytic_conductor': 4.4292865152235725, 'root_angle': 0.02862457352435009, 'root_number': '0.995959313953112109360633848559134822163619882357858574387 + 0.08980559531591707448838903035950535751584249646421670388*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.014312286762175046', 'prec': 67}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.17087442095904536008962883593', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.32025632687975471213759164623', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.84683340037927167750113122166', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.61857903394138, 'bad_primes': [2, 3, 5], 'central_character': '5.2', 'conductor': 720, 'conductor_radical': 30, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/720/3/bh/e/577/1'], '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': '2-720-5.2-c2-0-18', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-720-5.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.4292865152235725, 'root_angle': 0.014312286762175046, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.17087442095904536008962883593', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1484259662520614394468115893696', 'Lhash_array': ['1484259662520614394468115893696'], 'label': '2-720-5.2-c2-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/720/3/bh/e/577/1'}