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lfunc_lfunctions • Show schema
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{'Lhash': '6562524658038486921940808466044', 'a10': [26.193659437162463, -26.193659437162463], 'a2': [0.0, -5.467672649840779], 'a3': [3.9454584700943536, 3.9454584700943536], 'a4': [-21.89544420581689, 0.0], 'a5': [4.790641487640126, 4.790641487640126], 'a6': [21.572475368017543, -21.572475368017543], 'a7': [3.337609273840324, -3.337609273840324], 'a8': [0.0, 75.97574024153353], 'a9': [0.0, 4.133285078478554], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.003032470097591, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[17, [[1.0, 0], [56.093079320821026, -42.03054189881545]]]], 'bad_primes': [17], 'central_character': '17.13', 'coefficient_field': 'CDF', 'conductor': 17, 'conductor_radical': 17, 'conjugate': '3384980132710508944474735949117', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 5.467672649840779], [-8.0, 0]], [[1.0, 0], [-3.9454584700943536, -3.9454584700943536], [0, 27.0]], [[1.0, 0], [-4.790641487640126, 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'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.253160164858', 'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '5.17691914227545174080496313913', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '6.99890415722263368711418769673', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '8.199066667541582882068144768172', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.003032470097591, 'bad_primes': [17], 'central_character': '17.13', 'conductor': 17, 'conductor_radical': 17, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/17/4/c/a/13/1'], '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': '2-17-17.13-c3-0-3', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-17-17.13-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0015150873040262, 'root_angle': 0.2531601648581443, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '5.17691914227545174080496313913', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '6562524658038486921940808466044', 'Lhash_array': ['6562524658038486921940808466044'], 'label': '2-17-17.13-c3-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/17/4/c/a/13/1'}