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lfunc_lfunctions • Show schema
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{'Lhash': '1116497956008742185265986970833', 'a10': [0.0, 0.0], 'a2': [0.766044443118978, 0.6427876096865394], 'a3': [0.0, 0.0], 'a4': [0.17364817766693036, 0.984807753012208], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-0.5, 0.8660254037844386], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9701823845585568, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.766044443118978, -0.6427876096865394]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1944.379', 'coefficient_field': 'CDF', 'conductor': 1944, 'conductor_radical': 6, 'conjugate': '2514130713121029193142355735951', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.766044443118978, -0.6427876096865394]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-0.766044443118978, -0.6427876096865394]], [[1.0, 0], [0, 0], [0.9396926207859084, 0.3420201433256687]], [[1.0, 0], [1.4396926207859084, -0.5240052604587699], 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'9.432871347566459421053345805051091'], 'prelabel': '2-1944-216.43-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9849783675586773, 'root_angle': -0.6481481481481481, 'root_number': '-0.44879918020046217278504033473295 - 0.89363264032341224819257418686639*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.32407407407407407', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.880761588254465777176600955243', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.59575344926785343145080441703', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.93715750199233864845552312308', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9701823845585568, 'bad_primes': [2, 3], 'central_character': '216.43', 'conductor': 1944, 'conductor_radical': 6, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1944/1/r/a/379/1'], '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': '2-1944-216.43-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1944-216.43-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9849783675586773, 'root_angle': -0.32407407407407407, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.880761588254465777176600955243', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1116497956008742185265986970833', 'Lhash_array': ['1116497956008742185265986970833'], 'label': '2-1944-216.43-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1944/1/r/a/379/1'}