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lfunc_lfunctions • Show schema
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{'Lhash': '2585046140276147550672546775931', 'a10': [-16.879956929780118, 8.788875041672519], 'a2': [-2.395313682065367, -2.957966054992026], 'a3': [2.9972114160665453, -0.1293202513157715], 'a4': [-2.1803887837245055, 10.257922722279414], 'a5': [0.9964455896025539, -4.899703683587572], 'a6': [-7.5617864265618, -8.555887061014625], 'a7': [-6.100477171923622, -1.6346179316614338], 'a8': [21.99993782343262, -11.209528208333992], 'a9': [8.966552545199251, -0.77520026714445], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.130805948106681, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-2.9972114160665453, 0.1293202513157715]]], [5, [[1.0, 0], [-0.9964455896025539, 4.899703683587572]]]], 'bad_primes': [3, 5], 'central_character': '225.13', 'coefficient_field': 'CDF', 'conductor': 225, 'conductor_radical': 15, 'conjugate': '801380650116694632687581225135', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.395313682065367, 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0.16073537385399678*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.474306715237', 'prec': 50}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.03924183825632442127213051546', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.98686328358453958423982183811', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.08337821244874891473749131316', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.130805948106681, 'bad_primes': [3, 5], 'central_character': '225.13', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'index': 44, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/3/x/a/13/2'], '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': '2-15e2-225.13-c2-0-44', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-15e2-225.13-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4760464349657663, 'root_angle': -0.47430671523749, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.03924183825632442127213051546', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2585046140276147550672546775931', 'Lhash_array': ['2585046140276147550672546775931'], 'label': '2-15e2-225.13-c2-0-44', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/3/x/a/13/2'}