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lfunc_lfunctions • Show schema
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{'Lhash': '2833598257126065761726514012561', 'a10': [0.5, -0.8660254037844386], 'a2': [0.7071067811865476, -0.7071067811865476], 'a3': [0.8660254037844386, 0.5], 'a4': [0.0, -1.0], 'a5': [0.9659258262890683, -0.25881904510252074], 'a6': [0.9659258262890683, -0.25881904510252074], 'a7': [-1.224744871391589, -1.224744871391589], 'a8': [-0.7071067811865476, -0.7071067811865476], 'a9': [0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7785414197074838, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]], [3, [[1.0, 0], [-0.8660254037844386, -0.5]]], [5, [[1.0, 0], [-0.9659258262890683, 0.25881904510252074]]], [13, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '1560.467', 'coefficient_field': 'CDF', 'conductor': 1560, 'conductor_radical': 390, 'conjugate': '1780925753003855535411520302756', 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-0.13465094736314315, -0.26621735754187825], 'positive_zeros': ['2.23531488614914960250405145798625', '2.84359757365443044089329818523273', '3.59841505043628997501815685600619', '5.11144187420409908001610359126007', '5.87489516521264916870762739096926', '6.51024226659081480062417178729899', '7.15474048265387852148945429121643', '8.242671449055865882205940035512557', '8.795369196665696930115676170385574', '9.679591992748955645206140062357691'], 'prelabel': '2-1560-1560.467-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8823499417507114, 'root_angle': 0.40712514215854995, 'root_number': '0.28765262894618256226196883904201 + 0.95773480936026848261400471730019*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.20356257107927497', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.23531488614914960250405145799', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.84359757365443044089329818523', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.59841505043628997501815685601', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7785414197074838, 'bad_primes': [2, 3, 5, 13], 'central_character': '1560.467', 'conductor': 1560, 'conductor_radical': 390, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1560/1/cs/f/467/4'], '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': '2-1560-1560.467-c0-0-16', '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': '2-1560-1560.467-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8823499417507114, 'root_angle': 0.20356257107927497, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.23531488614914960250405145799', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2833598257126065761726514012561', 'Lhash_array': ['2833598257126065761726514012561'], 'label': '2-1560-1560.467-c0-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1560/1/cs/f/467/4'}