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lfunc_lfunctions • Show schema
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{'Lhash': '1482241829730019523341431184317', 'a10': [12.807764064044152, 0.0], 'a2': [0.0, 4.56155281280883], 'a3': [8.68465843842649, 0.0], 'a4': [-12.807764064044152, 0.0], 'a5': [0.0, -2.8077640640441515], 'a6': [0.0, 39.6155281280883], 'a7': [0.0, 9.56155281280883], 'a8': [0.0, -21.93086968966181], 'a9': [48.42329219213246, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.971322790970168, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[13, [[1.0, 0], [0, 0]]]], 'bad_primes': [13], 'central_character': '169.168', 'coefficient_field': 'CDF', 'conductor': 169, 'conductor_radical': 13, 'conjugate': '2847120489997324166217564153593', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -4.56155281280883], [-8.0, 0]], [[1.0, 0], [-8.68465843842649, 0], [27.0, 0]], [[1.0, 0], [0, 2.8077640640441515], [-125.0, 0]], [[1.0, 0], [0, -9.56155281280883], [-343.0, 0]], [[1.0, 0], [0, -39.42329219213246], [-1331.0, 0]], [[1.0, 0], [0, 0]], 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['1.16928263155727204969620560755133', '2.72962649891808148369347214836452', '3.31982572340343047053478756120694', '4.52076312914273031231803941619345', '6.90367541249636820555335747385178', '8.333306117364102748965948730040335', '8.974202582625530949459316984410578', '10.03411706426754121108194766680444', '10.76943041222701393129096120204958', '11.86284048019958281353605904986001'], 'prelabel': '2-13e2-13.12-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.157740139873794, 'root_angle': -0.8128329581890013, 'root_number': '-0.8320502943378437 - 0.5547001962252291*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.406416479095', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.16928263155727204969620560755', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.72962649891808148369347214836', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.31982572340343047053478756121', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.971322790970168, 'bad_primes': [13], 'central_character': '13.12', 'conductor': 169, 'conductor_radical': 13, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/169/4/b/e/168/4'], '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': '2-13e2-13.12-c3-0-16', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-13e2-13.12-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.157740139873794, 'root_angle': -0.4064164790945006, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.16928263155727204969620560755', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1482241829730019523341431184317', 'Lhash_array': ['1482241829730019523341431184317'], 'label': '2-13e2-13.12-c3-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/169/4/b/e/168/4'}