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lfunc_lfunctions • Show schema
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{'Lhash': '293559023921626043915985066622', 'a10': [0, 0], 'a2': [0, 0], 'a3': [1.8826321864694313, 0], 'a4': [0, 0], 'a5': [0, -2.23606797749979], 'a6': [0, 0], 'a7': [0, 13.390118905981064], 'a8': [0, 0], 'a9': [-5.455696050469328, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 50.136368642294634, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 2.23606797749979]]], [23, [[1.0, 0], [4.243022858049376, -22.605237380440634]]]], 'bad_primes': [2, 5, 23], 'central_character': '1840.321', 'coefficient_field': 'CDF', 'conductor': 1840, 'conductor_radical': 230, 'conjugate': '2265025665243561501944469862529', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.8826321864694313, 0], [9.0, 0]], [[1.0, 0], [0, 2.23606797749979]], [[1.0, 0], [0, -13.390118905981064], [-49.0, 0]], [[1.0, 0], [0, -18.224037700040444], [-121.0, 0]], [[1.0, 0], [-7.918753755129492, 0], [169.0, 0]], 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-2.4465567449697465], 'positive_zeros': ['0.23157723734661057994695710986786', '1.40839096003643390802929349990108', '2.84723243818631961961154419403883', '3.83365512104033944653236853011342', '3.96996123458603743296150427669681', '5.79273297318247443536820661978239', '6.16655043099915785704947909532810', '7.34114694552762711248803565074137', '7.929834730715500333976344136781823', '8.548577789979899733553175082688401'], 'prelabel': '2-1840-23.22-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.080703965164385, 'root_angle': -0.9409401481449376, 'root_number': '-0.98283640784524492008033248596808069213552184347510622195 - 0.18447925469779898726478299479176905225969026950943517453*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4704700740724688', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.23157723734661057994695710987', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.40839096003643390802929349990', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.84723243818631961961154419404', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 50.136368642294634, 'bad_primes': [2, 5, 23], 'central_character': '23.22', 'conductor': 1840, 'conductor_radical': 230, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1840/3/k/e/321/34'], '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': '2-1840-23.22-c2-0-12', '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': '2-1840-23.22-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.080703965164385, 'root_angle': -0.4704700740724688, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.23157723734661057994695710987', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '293559023921626043915985066622', 'Lhash_array': ['293559023921626043915985066622'], 'label': '2-1840-23.22-c2-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1840/3/k/e/321/34'}