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lfunc_lfunctions • Show schema
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{'Lhash': '3508164884928531370905535484153', 'a10': [0.6893486551595477, -0.5784322022969305], 'a2': [0.9730448705798238, 0.23061587074244017], 'a3': [1.7074701861612043, 0.29076719789313005], 'a4': [0.8936326403234123, 0.44879918020046217], 'a5': [0.5373715269459237, -0.7218152277779684], 'a6': [1.594389575786673, 0.6766992541911013], 'a7': [-3.9567856771973053, -2.602418879390761], 'a8': [0.766044443118978, 0.6427876096865394], 'a9': [2.8309088732587546, 0.992952643032309], '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], [-1.7074701861612043, -0.29076719789313005]]]], 'bad_primes': [2, 3], 'central_character': '162.97', 'coefficient_field': 'CDF', 'conductor': 162, 'conductor_radical': 6, 'conjugate': '3224296629442151437014520729458', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'0.9840970460786885 - 0.17763165230104547*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0284217792693', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.76745412678928797247351510067', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.10460446898260012657750010895', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.20912162212214439184039484586', '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': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/162/2/g/b/97/5'], '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-c1-0-8', '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': -0.028421779269324363, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.76745412678928797247351510067', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3508164884928531370905535484153', 'Lhash_array': ['3508164884928531370905535484153'], 'label': '2-162-81.16-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/2/g/b/97/5'}