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lfunc_lfunctions • Show schema
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{'Lhash': '3343948027965834484441700388889', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [-0.5, -0.8660254037844386], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.08534011716024341, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 19], 'central_character': '171.46', 'coefficient_field': 'CDF', 'conductor': 171, 'conductor_radical': 57, 'conjugate': '2531645834265837728525070833508', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [-1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [1.5, -0.8660254037844386], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-0.5, 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'7.07924459627109291426730101132114', '8.011942648320657675990551982060416', '8.795959328665294891122447836875384', '10.08883893701692750943633178570216', '11.15249335626099394609718975711307', '12.38075014513968022941096384100929', '12.73573705344168905994537873130738'], 'prelabel': '2-171-19.8-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.29213030852727934, 'root_angle': 0.13550657612455358, 'root_number': '0.91074721581647173872399680010745 + 0.41296429492456735877069994364673*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.06775328806227678', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.63790986835314549134060667019', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.31033340971662668399967222435', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.24356164546940634662966272452', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.08534011716024341, 'bad_primes': [3, 19], 'central_character': '19.8', 'conductor': 171, 'conductor_radical': 57, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/171/1/p/a/46/1'], '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': '2-171-19.8-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-171-19.8-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.29213030852727934, 'root_angle': 0.06775328806227679, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.63790986835314549134060667019', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3343948027965834484441700388889', 'Lhash_array': ['3343948027965834484441700388889'], 'label': '2-171-19.8-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/171/1/p/a/46/1'}