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lfunc_lfunctions • Show schema
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{'Lhash': '2158083562489253864725416731916', 'a10': [-2.1213203435596424, 3.6742346141747673], 'a2': [-0.5, -0.8660254037844386], 'a3': [-0.7071067811865476, 1.224744871391589], 'a4': [-0.5, 0.8660254037844386], 'a5': [-2.1213203435596424, -3.6742346141747673], 'a6': [1.4142135623730951, 0], 'a7': [0, 0], 'a8': [1.0, 0], 'a9': [0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.607873337894029, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, 0.8660254037844386]]], [7, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-0.5, 0.8660254037844386]]]], 'bad_primes': [2, 7, 11], 'central_character': '1078.67', 'coefficient_field': 'CDF', 'conductor': 1078, 'conductor_radical': 154, 'conjugate': '163241068663650674479364480411', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0.7071067811865476, -1.224744871391589], [-1.5, -2.598076211353316]], [[1.0, 0], 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2.9339177455910432, 'root_angle': -0.856451189731629, 'root_number': '-0.9000239394702092709052918408255008826836703319730454082 - 0.4358404620735953176193279339569067765431043146877962002*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4282255948658145', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.70242775264785880087716475833', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.30474698474347804759164360260', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.08065735938503601543205085087', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.607873337894029, 'bad_primes': [2, 7, 11], 'central_character': '7.4', 'conductor': 1078, 'conductor_radical': 154, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1078/2/e/p/67/1'], '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': '2-1078-7.4-c1-0-27', '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': '2-1078-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9339177455910432, 'root_angle': -0.4282255948658145, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.70242775264785880087716475833', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2158083562489253864725416731916', 'Lhash_array': ['2158083562489253864725416731916'], 'label': '2-1078-7.4-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1078/2/e/p/67/1'}