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lfunc_lfunctions • Show schema
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{'Lhash': '1503255013133737167517199311577', 'a10': [1.5, -2.598076211353316], 'a2': [-0.5, 0.8660254037844386], 'a3': [-1.5, 2.598076211353316], 'a4': [0.5, 0.8660254037844386], 'a5': [-3.0, 0.0], 'a6': [-1.5, -2.598076211353316], 'a7': [0.0, 0.0], 'a8': [-3.0, 0.0], 'a9': [-3.0, -5.196152422706632], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.086470608755563, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-1.0, -3.4641016151377544]]]], 'bad_primes': [7, 13], 'central_character': '637.295', 'coefficient_field': 'CDF', 'conductor': 637, 'conductor_radical': 91, 'conjugate': '4227031441912545420632597577589', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, -0.8660254037844386], [-1.0, -1.7320508075688772]], [[1.0, 0], [1.5, -2.598076211353316], [-1.5, -2.598076211353316]], [[1.0, 0], [3.0, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.5, 2.598076211353316], [-5.5, 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-4.27437562228978, -2.2542977177634325, 0.7149169113689395, 4.000107287258149], 'positive_zeros': ['1.18585911043870389244667343959628', '2.39667627224644028421078766267526', '3.94114065870228253874817188541515', '5.46005584618270116139243791811441', '6.26385727754423665528886900573563', '7.20892396848169732998825106118259', '7.79567633373124016427401213918920', '8.782157788270012433070236009096126', '10.11119986112905739488476531203130'], 'prelabel': '2-637-13.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.16258476388153328, 'root_number': '0.8723658594356627 + 0.4888535642614029*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0812923819408', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.18585911043870389244667343960', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.39667627224644028421078766268', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.94114065870228253874817188542', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.086470608755563, 'bad_primes': [7, 13], 'central_character': '13.9', 'conductor': 637, 'conductor_radical': 91, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/637/2/f/a/295/1'], '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': '2-637-13.9-c1-0-18', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-637-13.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.08129238194076664, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.18585911043870389244667343960', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1503255013133737167517199311577', 'Lhash_array': ['1503255013133737167517199311577'], 'label': '2-637-13.9-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/f/a/295/1'}