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lfunc_lfunctions • Show schema
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{'Lhash': '933319366547052112775099854322', 'a10': [3.363075807949438, 1.9416727230247262], 'a2': [-0.9659258262890683, -0.25881904510252074], 'a3': [1.694381220768221, 0.35926630611287985], 'a4': [0.8660254037844386, 0.5], 'a5': [-3.751023658741208, -1.0050837601497418], 'a6': [-1.5436616184335785, -0.7855627331887791], 'a7': [1.1820443194513333, 2.36701736936019], 'a8': [-0.7071067811865476, -0.7071067811865476], 'a9': [2.741855442584013, 1.2174681646648613], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.359831950361911, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.9659258262890683, 0.25881904510252074]]], [3, [[1.0, 0], [-1.694381220768221, -0.35926630611287985]]], [7, [[1.0, 0], [-1.1820443194513333, -2.36701736936019]]], [13, [[1.0, 0], [2.0200475419067163, -2.9865377828577078]]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '546.515', 'coefficient_field': 'CDF', 'conductor': 546, 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-3.5172783244835233], 'positive_zeros': ['0.73625916035460885299222218115837', '2.66126581751852586716844505627663', '3.77324280887123247480866423056589', '4.64459136975930880925297144600414', '6.75376056877397386601000665709527', '7.25686559411191018305033799133959', '8.042730152962628152850555017600621', '8.486180839083100499711049981369612', '9.720794442811671686414686459336785', '10.59507873584841343861174994595694'], 'prelabel': '2-546-273.242-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': -0.36119648998262566, 'root_number': '0.4223751515588246 - 0.9064211114849764*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.180598244991', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.73625916035460885299222218116', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.66126581751852586716844505628', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.77324280887123247480866423057', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.359831950361911, 'bad_primes': [2, 3, 7, 13], 'central_character': '273.242', 'conductor': 546, 'conductor_radical': 546, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/546/2/bv/a/515/17'], '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': '2-546-273.242-c1-0-7', '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': '2-546-273.242-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': -0.18059824499131283, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.73625916035460885299222218116', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '933319366547052112775099854322', 'Lhash_array': ['933319366547052112775099854322'], 'label': '2-546-273.242-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/546/2/bv/a/515/17'}