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lfunc_lfunctions • Show schema
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{'Lhash': '1711851183513557009853803367262', 'a10': [2.6338064941699897, 1.5206288884024282], 'a2': [0.0, -0.8834133953294439], 'a3': [1.4120209746311554, 1.0030935984252327], 'a4': [1.2195807729525037, 0.0], 'a5': [-1.7213106530214577, 2.981397506642727], 'a6': [0.8861463216180644, -1.2473982434752995], 'a7': [-2.266182618450568, 1.3654363184830438], 'a8': [0.0, -2.8442207821713668], 'a9': [0.9876064655966363, 2.8327784009893398], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.4120209746311554, -1.0030935984252327]]], [7, [[1.0, 0], [2.266182618450568, -1.3654363184830438]]], [13, [[1.0, 0], [-0.14418497819905132, 3.6026671636527485]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.68', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': '3151311183867752899689298007065', 'degree': 2, 'euler_factors': 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'6.20519794071398184326750957470536', '6.94659627377530705252997528037681', '7.896197555999826853038190045633337', '8.782175783659580881947773381152353', '9.413154000188210881996775592154331', '11.12078601239097107040931340406889', '12.09580742939775839416049785839673'], 'prelabel': '2-273-273.68-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': -0.1749640762690833, 'root_number': '0.8526991269254762 - 0.5224023343559354*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0874820381345', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.35041247423016498322690075047', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.30186867773944583011621658561', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.46451383302327247903808552826', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'bad_primes': [3, 7, 13], 'central_character': '273.68', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/2/r/b/68/12'], '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': '2-273-273.68-c1-0-14', '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': '2-273-273.68-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': -0.08748203813454165, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.35041247423016498322690075047', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1711851183513557009853803367262', 'Lhash_array': ['1711851183513557009853803367262'], 'label': '2-273-273.68-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/2/r/b/68/12'}