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lfunc_lfunctions • Show schema
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{'Lhash': '1071517570472915277821684087179', 'a10': [0.16602093066783216, -2.2298961972657354], 'a2': [0.5, 0.8660254037844386], 'a3': [0.6868327580795662, 2.5632947494556046], 'a4': [-0.5, 0.8660254037844386], 'a5': [-1.8481362893005266, -1.2587264421511453], 'a6': [-1.8764619913760383, 1.8764619913760383], 'a7': [0.5242098762756722, 1.9563778920902035], 'a8': [-1.0, 0.0], 'a9': [-3.500664523662171, 2.0211096050789275], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.9544648747873756, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, -0.8660254037844386]]], [5, [[1.0, 0], [1.8481362893005266, 1.2587264421511453]]], [37, [[1.0, 0], [-4.850454174971004, -3.6705713855619746]]]], 'bad_primes': [2, 5, 37], 'central_character': '370.103', 'coefficient_field': 'CDF', 'conductor': 370, 'conductor_radical': 370, 'conjugate': '3672044302371143834454700481663', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, 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'7.42551939539688601407153577217877', '7.74359479983343381422076537334740', '9.011098295134260608430394058677241', '10.46820620425621469306572283936301', '11.01491110815263696803527392617629'], 'prelabel': '2-370-185.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7188556875978203, 'root_angle': -0.9374919121454697, 'root_number': '-0.9807803230865091 - 0.19511524247562748*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.468745956073', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.845278320603483256831348238766', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.46190135682844976209466728264', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.46357518513701517600991697144', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.9544648747873756, 'bad_primes': [2, 5, 37], 'central_character': '185.103', 'conductor': 370, 'conductor_radical': 370, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/370/2/q/f/103/8'], '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': '2-370-185.103-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': '2-370-185.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7188556875978203, 'root_angle': -0.46874595607273484, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.845278320603483256831348238766', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1071517570472915277821684087179', 'Lhash_array': ['1071517570472915277821684087179'], 'label': '2-370-185.103-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/370/2/q/f/103/8'}