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lfunc_lfunctions • Show schema
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{'Lhash': '2745852817351437961415246307697', 'a10': [3.49465993840233, 3.6156348522088635], 'a2': [-0.3892106989554361, 1.3596010561258847], 'a3': [1.7260754412201715, -0.14374829117798302], 'a4': [-1.6970300636372417, -1.0583425547106093], 'a5': [1.7778309631957978, -3.0792935555242367], 'a6': [-0.4763667004252388, 2.40272236571893], 'a7': [-0.7934555116166296, 2.523970750837892], 'a8': [2.09942591234415, -1.8953656213453731], 'a9': [2.9586728575668197, -0.49624079023936546], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.341486753957511, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.3892106989554361, -1.3596010561258847]]], [3, [[1.0, 0], [-1.7260754412201715, 0.14374829117798302]]], [7, [[1.0, 0], [0.7934555116166296, -2.523970750837892]]]], 'bad_primes': [2, 3, 7], 'central_character': '168.107', 'coefficient_field': 'CDF', 'conductor': 168, 'conductor_radical': 42, 'conjugate': 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'3.18733309352038886421432989423562', '4.43289653265045351907557347859608', '6.72295003717251523640886803235351', '7.52454480173692302594736229977083', '9.096868576061271843069791207926832', '9.695172078425514049974316975851570', '10.68432455633231926383174035485421', '11.27596167371403372940779689150526', '13.20552204411596049068405390036552'], 'prelabel': '2-168-168.107-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': -0.18342260174947378, 'root_number': '0.8385177936725963 - 0.5448742145618943*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0917113008747', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.16609593909952094185110894725', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.18733309352038886421432989424', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.43289653265045351907557347860', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.341486753957511, 'bad_primes': [2, 3, 7], 'central_character': '168.107', 'conductor': 168, 'conductor_radical': 42, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/168/2/v/a/107/12'], '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': '2-168-168.107-c1-0-16', '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': '2-168-168.107-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': -0.09171130087473689, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.16609593909952094185110894725', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2745852817351437961415246307697', 'Lhash_array': ['2745852817351437961415246307697'], 'label': '2-168-168.107-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/168/2/v/a/107/12'}