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lfunc_lfunctions • Show schema
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{'Lhash': '2322466655119335494693644415327', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.5, -0.8660254037844386], 'a4': [0.0, 0.0], 'a5': [0.0, 1.7320508075688772], 'a6': [0.0, 0.0], 'a7': [-2.366025403784439, -1.3660254037844386], 'a8': [0.0, 0.0], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.9826650861278985, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.5, 0.8660254037844386]]], [13, [[1.0, 0], [2.598076211353316, 2.5]]]], 'bad_primes': [2, 3, 13], 'central_character': '624.49', 'coefficient_field': 'CDF', 'conductor': 624, 'conductor_radical': 78, 'conjugate': '439485337915626435962807053958', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, -1.7320508075688772], [-5.0, 0]], [[1.0, 0], [2.366025403784439, 1.3660254037844386], [3.5, 6.06217782649107]], [[1.0, 0], [-2.366025403784439, 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0.37397952430371667, 'root_number': '-0.7025584230735236 + 0.7116260690618661*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.373979524304', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.83210314790305442979911372314', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.47856226575362933397146902544', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.43993941734565334596465131686', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.9826650861278985, 'bad_primes': [2, 3, 13], 'central_character': '13.10', 'conductor': 624, 'conductor_radical': 78, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/624/2/bv/c/49/1'], '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': '2-624-13.10-c1-0-11', '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': '2-624-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.232188407399317, 'root_angle': 0.37397952430371667, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.83210314790305442979911372314', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2322466655119335494693644415327', 'Lhash_array': ['2322466655119335494693644415327'], 'factors': ['2-624-13.10-c1-0-11'], 'label': '2-624-13.10-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/624/2/bv/c/49/1'}