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lfunc_lfunctions • Show schema
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{'Lhash': '1213263318277600112514718690178', 'a10': [2.465180611124594, -2.068532141580029], 'a2': [-0.9730448705798238, -0.23061587074244017], 'a3': [-1.1393059754301007, -1.304600281446109], 'a4': [0.8936326403234123, 0.44879918020046217], 'a5': [-1.921695007718419, 2.5812843631658238], 'a6': [0.8077343055366752, 1.5321766515840087], 'a7': [2.724212075523414, 1.7917424685554688], 'a8': [-0.766044443118978, -0.6427876096865394], 'a9': [-0.403963788698534, 2.9726777923986862], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.293576512744743, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.9730448705798238, 0.23061587074244017]]], [3, [[1.0, 0], [1.1393059754301007, 1.304600281446109]]]], 'bad_primes': [2, 3], 'central_character': '162.97', 'coefficient_field': 'CDF', 'conductor': 162, 'conductor_radical': 6, 'conjugate': '2234250144934435563286356577509', 'degree': 2, 'euler_factors': [[[1.0, 0], 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[[1.0, 0], [-14.558503953770602, -3.4504288214431718], [74.17150914684322, 37.25033195663836]], [[1.0, 0], [0.5929539644711767, 0.4975474528928704], [15.4546878123568, 87.64789001808651]], [[1.0, 0], [10.550619999008399, 14.171942121803937], [-27.819913572975754, 92.92498269460242]], [[1.0, 0], [-1.812280575459217, 0.9101615136449818], [60.3130177619814, -81.01444246825942]], [[1.0, 0], [-1.3583032917555142, -0.15876288523963786], [100.22362166972185, 23.753434686471337]], [[1.0, 0], [-1.201539856187669, 2.0811280782360444], [-53.5, -92.66471820493493]], [[1.0, 0], [2.4298388002633806, 4.208604256258381], [-54.5, 94.39676901250381]], [[1.0, 0], [-4.763976617974244, -11.044139182289133], [-77.5453050791669, 82.19322149775451]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-162-81.16-c1-0-1', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 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-0.1856199677899678, 'root_number': '0.8347364525388834 - 0.5506496661242976*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.092809983895', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.957095999527916182398819869034', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '4.21690935587045545352773285085', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.75237399343772646762894790183', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.293576512744743, 'bad_primes': [2, 3], 'central_character': '81.16', 'conductor': 162, 'conductor_radical': 6, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/162/2/g/a/97/1'], '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': '2-162-81.16-c1-0-1', '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': '2-162-81.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1373550513119213, 'root_angle': -0.0928099838949839, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.957095999527916182398819869034', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1213263318277600112514718690178', 'Lhash_array': ['1213263318277600112514718690178'], 'label': '2-162-81.16-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/2/g/a/97/1'}