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lfunc_lfunctions • Show schema
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{'Lhash': '3609969520388894384884903463980', 'a10': [-3.0, 3.111507638930571e-61], 'a2': [0.5, -0.8660254037844386], 'a3': [1.0, 1.7320508075688772], 'a4': [-0.5, -0.8660254037844386], 'a5': [-1.5, -2.598076211353316], 'a6': [2.0, -3.111507638930571e-61], 'a7': [2.0, 3.4641016151377544], 'a8': [-1.0, 0.0], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5908929749574752, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, 0.8660254037844386]]], [37, [[1.0, 0], [-5.5, -2.598076211353316]]]], 'bad_primes': [2, 37], 'central_character': '74.47', 'coefficient_field': 'CDF', 'conductor': 74, 'conductor_radical': 74, 'conjugate': '3537912555906372436106017927939', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [-1.0, -1.7320508075688772], [-1.5, 2.598076211353316]], [[1.0, 0], [1.5, 2.598076211353316], [-2.5, 4.330127018922194]], [[1.0, 0], [-2.0, 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'data': '4.68609982432455321402057069443', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.89372335788240693191062248397', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5908929749574752, 'bad_primes': [2, 37], 'central_character': '37.10', 'conductor': 74, 'conductor_radical': 74, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/74/2/c/b/47/1'], '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': '2-74-37.10-c1-0-2', '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': '2-74-37.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7686956321961738, 'root_angle': 0.04682406675194775, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.84776382367424505759218468873', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3609969520388894384884903463980', 'Lhash_array': ['3609969520388894384884903463980'], 'label': '2-74-37.10-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/74/2/c/b/47/1'}