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lfunc_lfunctions • Show schema
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{'Lhash': '2585091633470298771455743736366', 'a10': [4.8483447171925654e-61, 1.4641016151377546], 'a2': [0.36602540378443865, 1.3660254037844386], 'a3': [0.8660254037844386, -1.5], 'a4': [-1.7320508075688772, 1.0], 'a5': [1.0, 0.2679491924311227], 'a6': [2.366025403784439, 0.6339745962155614], 'a7': [2.366025403784439, 1.3660254037844386], 'a8': [-2.0, -2.0], 'a9': [-1.5, -2.598076211353316], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.149845789106438, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.36602540378443865, -1.3660254037844386]]], [3, [[1.0, 0], [-0.8660254037844386, 1.5]]]], 'bad_primes': [2, 3], 'central_character': '144.61', 'coefficient_field': 'CDF', 'conductor': 144, 'conductor_radical': 6, 'conjugate': '2872107867753686271936894120152', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.36602540378443865, -1.3660254037844386]], [[1.0, 0], [-0.8660254037844386, 1.5]], [[1.0, 0], [-1.0, 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'11.02287539217196225562641903973282', '11.57381781142887454534009913712526', '13.23596127546621509435153739730121'], 'prelabel': '2-12e2-144.61-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.072308625865911, 'root_angle': -0.23611111111111113, 'root_number': '0.737277336810124 - 0.6755902076156602*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.118055555556', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.03927772605864394853899138606', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.79695875238478591206756505681', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.65353205644240147684521217007', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.149845789106438, 'bad_primes': [2, 3], 'central_character': '144.61', 'conductor': 144, 'conductor_radical': 6, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/144/2/x/c/61/1'], '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': '2-12e2-144.61-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': '2-12e2-144.61-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.072308625865911, 'root_angle': -0.11805555555555557, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.03927772605864394853899138606', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2585091633470298771455743736366', 'Lhash_array': ['2585091633470298771455743736366'], 'label': '2-12e2-144.61-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/144/2/x/c/61/1'}