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lfunc_lfunctions • Show schema
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{'Lhash': '2871838186833021314867067632155', 'a10': [-0.2073748509007054, -2.7672250740447573], 'a2': [-0.6911204271422468, -0.8666376041848839], 'a3': [0.9888308262251285, 0.14904226617617444], 'a4': [0.171628575738595, -0.7519539220000666], 'a5': [2.068434426976082, 1.410234713893171], 'a6': [-0.5542355505109261, -0.9599641328458307], 'a7': [0.1514852756045328, -0.262380193945625], 'a8': [-2.76768346597425, 1.3328461101064493], 'a9': [0.9555728057861407, 0.2947551744109042], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.0300701860745174, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.9888308262251285, -0.14904226617617444]]], [43, [[1.0, 0], [5.249658362458924, -3.9295148654083354]]]], 'bad_primes': [3, 43], 'central_character': '129.52', 'coefficient_field': 'CDF', 'conductor': 129, 'conductor_radical': 129, 'conjugate': '2406410442725621894456991831952', 'degree': 2, 'euler_factors': [[[1.0, 0], 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[14.786088302058664, 2.228644223029223], [79.31254288024968, 24.46467947610505]], [[1.0, 0], [-12.698112451493305, -1.9139325006232961], [85.04597971496652, 26.233210522570474]], [[1.0, 0], [-3.9558225417633883, -17.331590979032633], [-87.39398018653465, 42.086722694403136]], [[1.0, 0], [-5.7773049001845695, -5.360555564897476], [7.54773945222885, 100.7175835152992]], [[1.0, 0], [12.852580497553816, -8.762741010482292], [37.63012550973869, -95.87999611035303]], [[1.0, 0], [1.9328847978417059, -2.4237608737646927], [-23.80973993332564, -104.31728660345513]], [[1.0, 0], [-8.49473596658769, 7.881963120307465], [8.145580200920243, -108.69521389274864]], [[1.0, 0], [18.3546233122973, 8.83912072497535], [70.45434761003689, 88.34695751888736]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-129-43.9-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': 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0.7497236136080468*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.134906783666', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.26548087171336642085263601779', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.23052785837905140386740814051', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.99653628350379422834586336595', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.0300701860745174, 'bad_primes': [3, 43], 'central_character': '43.9', 'conductor': 129, 'conductor_radical': 129, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/129/2/m/a/52/1'], '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': '2-129-43.9-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': '2-129-43.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0149237341172574, 'root_angle': 0.13490678366550238, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.26548087171336642085263601779', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2871838186833021314867067632155', 'Lhash_array': ['2871838186833021314867067632155'], 'label': '2-129-43.9-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/129/2/m/a/52/1'}