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lfunc_lfunctions • Show schema
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{'Lhash': '392987758474974609014437903641', 'a10': [-0.5734977821889429, -0.3311090989264395], 'a2': [0.0, -2.7314560208895378], 'a3': [-1.5276133800611242, 0.8163316489382406], 'a4': [-5.460851994053708, 0.0], 'a5': [0.12122073223738344, -0.20996046716585065], 'a6': [2.229773997535042, 4.172608764559376], 'a7': [-2.1333454943831924, 1.5648760339384498], 'a8': [0.0, 9.453165016565562], 'a9': [1.6672052778835462, -2.494078298970834], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.5276133800611242, -0.8163316489382406]]], [7, [[1.0, 0], [2.1333454943831924, -1.5648760339384498]]], [13, [[1.0, 0], [3.558841414884746, -0.5784874965815087]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.68', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': '2251342663758268705675521093790', 'degree': 2, 'euler_factors': 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9.470076697512038], [-54.5, 94.39676901250381]], [[1.0, 0], [8.185238618701602, 4.72574971988869], [56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-273-273.68-c1-0-3', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/273/2/r/b/68/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.3551424948584542, 0.2301243685682066, 0.08185475848709052, -0.09801769971463678, -0.31874056730681116, -0.5896213720250114, -0.9192202909870419, -1.3145845533739748, -1.7805061047489565, -2.3187910488571446, -2.927555617885086, -3.6005917354246004, -4.32686690032563, -5.090235259759577, -5.869438783869251, -6.638469329118776, -7.367344121884275, -8.023319194593833, -8.572528667311285, -8.981994599491848, -9.221905693223752, -9.268017753730085, 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'6.60905355167509036448717830370732', '7.51513059110997239330712876665417', '8.702676607286509037780077303247776', '9.642951479791944986377159545291334', '10.72913169709064446204572200951522', '12.22343031232795093512208677221250'], 'prelabel': '2-273-273.68-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': -0.12065716547706819, 'root_number': '0.9290144947526824 - 0.37004333332654193*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0603285827385', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.31001267889134482392441311437', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.00044528362193315523797726954', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.05246036845848969229383665960', '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': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/2/r/b/68/1'], '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-c1-0-3', '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': -0.060328582738534094, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.31001267889134482392441311437', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '392987758474974609014437903641', 'Lhash_array': ['392987758474974609014437903641'], 'label': '2-273-273.68-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/2/r/b/68/1'}