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lfunc_lfunctions • Show schema
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{'Lhash': '1809570105870169007572158295790', 'a10': [-1.3929346738479709, 0.0], 'a2': [4.138061726564863, 0.0], 'a3': [-5.8363695588845665, 0.0], 'a4': [9.123554852860973, 0.0], 'a5': [-0.3366152478842529, 0.0], 'a6': [-24.151257493708478, 0.0], 'a7': [10.521602899277948, 0.0], 'a8': [4.64933933432021, 0.0], 'a9': [7.063209627874435, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 92.81000443903002, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-13.0, 0]]]], 'bad_primes': [11, 13], 'central_character': '1573.1', 'coefficient_field': 'CDF', 'conductor': 1573, 'conductor_radical': 143, 'degree': 2, 'euler_factors': [[[1.0, 0], [-4.138061726564863, 0], [8.0, 0]], [[1.0, 0], [5.8363695588845665, 0], [27.0, 0]], [[1.0, 0], [0.3366152478842529, 0], [125.0, 0]], [[1.0, 0], [-10.521602899277948, 0], [343.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-13.0, 0]], [[1.0, 0], [-28.096882576468158, 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'3.77717951411812477023084061686708', '4.69419479032542366675010859742380', '5.34495476167974335172722460819292', '5.85204808798781205825728787630545', '6.69140269526900818730681212656559', '7.49679280087194992500830181895985', '8.638606534474573033292772179579498'], 'prelabel': '2-1573-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.633794913689519, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.42749911177762369193378349751', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.79315791869474533196932794216', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.77717951411812477023084061687', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 92.81000443903002, 'bad_primes': [11, 13], 'central_character': '1.1', 'conductor': 1573, 'conductor_radical': 143, 'degree': 2, 'index': 253, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1573/4/a/o/1/30'], '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': '2-1573-1.1-c3-0-253', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-1573-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.633794913689519, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.42749911177762369193378349751', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1809570105870169007572158295790', 'Lhash_array': ['1809570105870169007572158295790'], 'label': '2-1573-1.1-c3-0-253', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1573/4/a/o/1/30'}