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lfunc_lfunctions • Show schema
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{'Lhash': '2657401346351968714982082046462', 'a10': [-0.370807718392465, -0.23830365064366088], 'a2': [-0.22040278299663021, -1.5329350270656], 'a3': [0.9096319953545183, 0.41541501300188644], 'a4': [-0.38232646322295727, 0.11226117855368638], 'a5': [0.18638198147119842, -0.21509627293660646], 'a6': [0.43631880092058967, -1.4859653723827113], 'a7': [0.025075316147287495, -2.6456324817555656], 'a8': [-1.0303503433024406, -2.2561525447039052], 'a9': [0.6548607339452851, 0.7557495743542583], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.9096319953545183, -0.41541501300188644]]], [7, [[1.0, 0], [-0.025075316147287495, 2.6456324817555656]]], [23, [[1.0, 0], [0.5981811518053892, 4.758379903877451]]]], 'bad_primes': [3, 7, 23], 'central_character': '483.181', 'coefficient_field': 'CDF', 'conductor': 483, 'conductor_radical': 483, 'conjugate': 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[-32.817786027149026, -71.86092763300695]], [[1.0, 0], [-10.158675598653456, -11.723736607983588], [-11.812131576682667, 82.15517967611741]], [[1.0, 0], [5.286008205632699, -11.574743427792763], [-58.28260532113037, -67.26171211752899]], [[1.0, 0], [-6.115811581425123, 7.058022812952867], [-13.804539312508659, -96.01267986245047]], [[1.0, 0], [-11.844781748650885, 10.263561810102036], [14.373798665601798, -99.9719656299742]], [[1.0, 0], [2.3312050281837675, -16.21388711334459], [-98.82777628229323, -29.01845335466726]], [[1.0, 0], [-1.863288610266262, 0.8509353960865832], [70.07009853214551, -80.86520445590564]], [[1.0, 0], [-3.2708972931484803, 11.13965317099317], [-91.69663507859875, -58.929849102660135]], [[1.0, 0], [-5.470927747467959, 0.7866006581007053], [108.4227060184382, -31.835778923081556]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 27, 'label': '2-483-161.20-c1-0-27', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': 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'root_analytic_conductor': 1.9638672097745928, 'root_angle': 0.6861206765475473, 'root_number': '-0.5519620439195484 + 0.8338692355952189*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.343060338274', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.09632003161874955829325911667', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.23599387201745155484934912893', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.99613725236886579330043921150', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'bad_primes': [3, 7, 23], 'central_character': '161.20', 'conductor': 483, 'conductor_radical': 483, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/483/2/r/a/181/10'], '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': '2-483-161.20-c1-0-27', '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': '2-483-161.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9638672097745928, 'root_angle': 0.34306033827377364, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.09632003161874955829325911667', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2657401346351968714982082046462', 'Lhash_array': ['2657401346351968714982082046462'], 'label': '2-483-161.20-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/483/2/r/a/181/10'}