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lfunc_lfunctions • Show schema
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{'Lhash': '1309011825124330279554116663511', 'a10': [0.0, 0.0], 'a2': [-0.2859966341581015, 0.4953607011555205], 'a3': [0.0, 0.0], 'a4': [0.8364118505004741, 1.4487078211195252], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.7140033658418985, -1.2366901064133569], 'a8': [-2.100830432684745, 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': '675.451', 'coefficient_field': 'CDF', 'conductor': 675, 'conductor_radical': 15, 'conjugate': '1893425244996074692299621712654', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.2859966341581015, -0.4953607011555205], [-1.0, -1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.7140033658418985, 1.2366901064133569], [-3.5, -6.06217782649107]], [[1.0, 0], [-1.336411850500474, 2.314733224903964], 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-0.39164322689669995, 'root_number': '0.333876272759915 - 0.9426169075971144*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.195821613448', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.03262825331258798862399361285', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.32630054808145339630130504395', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.49258447037491906021984847057', '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': '9.7', 'conductor': 675, 'conductor_radical': 15, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/675/2/e/b/451/2'], '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': '2-675-9.7-c1-0-6', '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': '2-675-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.321616276742655, 'root_angle': -0.19582161344834997, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.03262825331258798862399361285', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1309011825124330279554116663511', 'Lhash_array': ['1309011825124330279554116663511'], 'label': '2-675-9.7-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/675/2/e/b/451/2'}