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lfunc_lfunctions • Show schema
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{'Lhash': '2537389743776168817936831316392', 'a10': [1.1627731461080586, -2.0139821667358673], 'a2': [2.325546292216117, 0.0], 'a3': [-1.6692522576572906, 0.4621654468975781], 'a4': [3.4081655572401304, 0.0], 'a5': [0.5, -0.8660254037844386], 'a6': [-3.8819233985682953, 1.0747871414230676], 'a7': [2.0266983955918287, -1.7007332575408487], 'a8': [3.2747541904662283, 0.0], 'a9': [2.572806199387924, -1.5429414312899459], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.515287663670333, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.6692522576572906, -0.4621654468975781]]], [5, [[1.0, 0], [-0.5, 0.8660254037844386]]], [7, [[1.0, 0], [-2.0266983955918287, 1.7007332575408487]]]], 'bad_primes': [3, 5, 7], 'central_character': '315.151', 'coefficient_field': 'CDF', 'conductor': 315, 'conductor_radical': 105, 'conjugate': '2316306561633371448928444641945', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.325546292216117, 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'6.28656160986397473918479875959872', '7.32238665337980444549845330392977', '8.717318132912460806546945128015454', '10.35487787187361387623262204373074', '11.33610134157708554429568130860280', '11.63312513707605515283809128221846'], 'prelabel': '2-315-63.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5859658456821613, 'root_angle': 0.014874177137629993, 'root_number': '0.9989084173581679 + 0.046711601674533657*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.00743708856881', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.00164757017377973945560341029', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.54226760939269210545549995296', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.82741410929448607275564418514', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.515287663670333, 'bad_primes': [3, 5, 7], 'central_character': '63.25', 'conductor': 315, 'conductor_radical': 105, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/315/2/l/b/151/11'], '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': '2-315-63.25-c1-0-21', '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': '2-315-63.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5859658456821613, 'root_angle': 0.0074370885688149965, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.00164757017377973945560341029', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2537389743776168817936831316392', 'Lhash_array': ['2537389743776168817936831316392'], 'label': '2-315-63.25-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/315/2/l/b/151/11'}