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lfunc_lfunctions • Show schema
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{'Lhash': '2950905031602645894718229521985', 'a10': [0.0, 0.0], 'a2': [-0.5, -0.8660254037844386], 'a3': [0.0, 0.0], 'a4': [0.5, -0.8660254037844386], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.5, -2.598076211353316], 'a8': [-3.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.389902136436429, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '675.226', 'coefficient_field': 'CDF', 'conductor': 675, 'conductor_radical': 15, 'conjugate': '431838965819249028835407495392', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, 0.8660254037844386], [-1.0, 1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.5, 2.598076211353316], [-3.5, 6.06217782649107]], [[1.0, 0], [1.0, 1.7320508075688772], [-5.5, 9.526279441628825]], [[1.0, 0], [1.0, -1.7320508075688772], [-6.5, -11.258330249197702]], [[1.0, 0], 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-1.4076115073567113], 'positive_zeros': ['2.32785361445130168953501196762583', '3.22906221062972436043939803167017', '4.68635528239629710217673204112015', '5.99612353950498737137371204888492', '6.44108223885072474479195228378993', '7.66024324288023754575593224678705', '8.226927594636734235714688426152532', '9.133939079565944715854203308097645', '9.895183945586868705403190120067826', '10.91405946265766374870851749679171'], 'prelabel': '2-675-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.321616276742655, 'root_angle': -0.8888888888888888, 'root_number': '-0.9396926207859083 - 0.3420201433256689*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.444444444444', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.32785361445130168953501196763', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.22906221062972436043939803167', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.68635528239629710217673204112', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.389902136436429, 'bad_primes': [3, 5], 'central_character': '9.4', 'conductor': 675, 'conductor_radical': 15, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/675/2/e/a/226/1'], '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': '2-675-9.4-c1-0-15', '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': '2-675-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.321616276742655, 'root_angle': -0.4444444444444444, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.32785361445130168953501196763', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2950905031602645894718229521985', 'Lhash_array': ['2950905031602645894718229521985'], 'label': '2-675-9.4-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/675/2/e/a/226/1'}