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lfunc_lfunctions • Show schema
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{'Lhash': '1970936678734852215230164964261', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.5, -0.8660254037844386], 'a4': [2.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [2.0, 1.7320508075688772], 'a8': [0.0, 0.0], 'a9': [1.5, 2.598076211353316], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.5, 0.8660254037844386]]], [7, [[1.0, 0], [-2.0, -1.7320508075688772]]], [13, [[1.0, 0], [1.0, 3.4641016151377544]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.68', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': '1900247327140228155737495307718', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-2.0, 0]], [[1.0, 0], [1.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-2.5, -4.330127018922194]], [[1.0, 0], [-2.0, -1.7320508075688772]], [[1.0, 0], [0, 0], [5.5, 9.526279441628825]], [[1.0, 0], [1.0, 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['1.55479489252007004726710845250121', '3.56940680954281740674240294168280', '4.83483730757439600057775632918303', '5.91618307430411832413316018983218', '6.99803199730055645006653172378622', '7.75752812144092765319546872156704', '9.358892255116999374650434056433943', '10.34030112497915912392582765463805', '11.04352919388191984109753968111537', '11.80201489812834484710536665063784'], 'prelabel': '2-273-273.68-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': 0.09270095969946383, 'root_number': '0.9578918159858807 + 0.28712935911757903*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0463504798497', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.55479489252007004726710845250', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.56940680954281740674240294168', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.83483730757439600057775632918', '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': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/2/r/a/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-c1-0-15', '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': 0.04635047984973192, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.55479489252007004726710845250', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1970936678734852215230164964261', 'Lhash_array': ['1970936678734852215230164964261'], 'label': '2-273-273.68-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/2/r/a/68/1'}