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lfunc_lfunctions • Show schema
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{'Lhash': '2111805537847278414482079720442', 'a10': [0, 0], 'a2': [-0.5, 0.8660254037844386], 'a3': [0.8240300095857624, -1.5234744970960585], 'a4': [-0.5, -0.8660254037844386], 'a5': [0, 0], 'a6': [0.9073526117100275, 1.475368170330034], 'a7': [1.3534224760459843, -2.2733780154944663], 'a8': [1.0, 0], 'a9': [-1.6419490866041766, -2.5107774088914594], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.384292212234444, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, -0.8660254037844386]]], [3, [[1.0, 0], [-0.8240300095857624, 1.5234744970960585]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-1.3534224760459843, 2.2733780154944663]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1050.299', 'coefficient_field': 'CDF', 'conductor': 1050, 'conductor_radical': 210, 'conjugate': '1068957425844587818044662619652', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], 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'6.67346179326006318264323977262791', '8.152881985555839084701510803306805', '8.684017098436732651956213788495328', '9.052758100760194149537575031097052', '10.18372070221383346044359559940307'], 'prelabel': '2-1050-105.89-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8955642303762565, 'root_angle': 0.38818055535454765, 'root_number': '0.3441103884611717443229007456487570426545146762134950200 + 0.9389291989032514266449924250628068852188002672191405736*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.19409027767727383', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.66592082823694975643341199553', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.67748691565613724513273182306', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.90560025463735582900352291086', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.384292212234444, 'bad_primes': [2, 3, 5, 7], 'central_character': '105.89', 'conductor': 1050, 'conductor_radical': 210, 'degree': 2, 'index': 38, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1050/2/u/e/299/4'], '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': '2-1050-105.89-c1-0-38', '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': '2-1050-105.89-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8955642303762565, 'root_angle': 0.19409027767727383, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.66592082823694975643341199553', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2111805537847278414482079720442', 'Lhash_array': ['2111805537847278414482079720442'], 'label': '2-1050-105.89-c1-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1050/2/u/e/299/4'}