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lfunc_lfunctions • Show schema
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{'Lhash': '2698485340918784286985539746116', 'a10': [0.8349769505457066, -0.7006288512444324], 'a2': [0.6862416378687336, -0.7273736415730487], 'a3': [0.9162965771642203, 1.4698301203462711], 'a4': [-0.05814482891047583, -0.9983081582712682], 'a5': [1.082614909045931, 0.12653953473192142], 'a6': [1.6979165510167087, 0.34216865108236405], 'a7': [-0.38748509975006545, 0.19460233127203916], 'a8': [-0.766044443118978, -0.6427876096865394], 'a9': [-1.3208011653542684, 2.6936006165723243], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.293576512744743, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.6862416378687336, 0.7273736415730487]]], [3, [[1.0, 0], [-0.9162965771642203, -1.4698301203462711]]]], 'bad_primes': [2, 3], 'central_character': '162.151', 'coefficient_field': 'CDF', 'conductor': 162, 'conductor_radical': 6, 'conjugate': '3045969713287096917052335112583', 'degree': 2, 'euler_factors': [[[1.0, 0], 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[-4.593441483927591, -78.86634450343018]], [[1.0, 0], [-6.2229482919900585, 6.595939842011477], [-4.826020799569494, -82.85957713651526]], [[1.0, 0], [8.272011400222766, 6.9410417150211785], [15.4546878123568, 87.64789001808651]], [[1.0, 0], [-14.229701459039314, 1.6632135646347221], [94.38535244624292, -22.369739462016696]], [[1.0, 0], [0.8466711444506229, -14.536782147546115], [-100.31707413193624, -11.725384326648253]], [[1.0, 0], [-4.421955532301586, -10.251245182936827], [-70.68288870047957, 74.91948508202401]], [[1.0, 0], [8.829953438940287, -15.293927984712107], [-53.5, -92.66471820493493]], [[1.0, 0], [4.579873371385688, 7.932573371471777], [-54.5, 94.39676901250381]], [[1.0, 0], [-1.7301104152147186, 2.3239415950017714], [-32.408765296353195, -108.25281489165025]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-162-81.70-c1-0-4', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': 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1.1373550513119213, 'root_angle': 0.01862752331753452, 'root_number': '0.9982881881156476 + 0.058486694801275114*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.00931376165877', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.12872958876282282120473697756', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.77529388168501467580365562052', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.44845059753908093286296374127', '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': '81.70', 'conductor': 162, 'conductor_radical': 6, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/162/2/g/a/151/3'], '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': '2-162-81.70-c1-0-4', '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': '2-162-81.70-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1373550513119213, 'root_angle': 0.00931376165876726, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.12872958876282282120473697756', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2698485340918784286985539746116', 'Lhash_array': ['2698485340918784286985539746116'], 'label': '2-162-81.70-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/2/g/a/151/3'}