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lfunc_lfunctions • Show schema
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{'Lhash': '1510183851562052003589841602076', 'a10': [0.31748328070619397, 0.1832990575789266], 'a2': [0.8660254037844386, 0.5], 'a3': [0, 0], 'a4': [0.5, 0.8660254037844386], 'a5': [0.3665981151578532, 0], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 1.0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21.1284163748308, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, -0.5]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '2646.2285', 'coefficient_field': 'CDF', 'conductor': 2646, 'conductor_radical': 42, 'conjugate': '1104347322698236372892404265637', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.3665981151578532, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0.6694533992560775], [-11.0, 0]], [[1.0, 0], [-0.8673804534429738, -0.5007823382851205], [6.5, 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'9.015322298095191857450343714948285'], 'prelabel': '2-2646-63.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.596565715273828, 'root_angle': -0.01758774680898439, 'root_number': '0.998473911686080277928946011413243784495834404370064255070 - 0.05522542604903616134645931812350246197499575101413327774*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.008793873404492196', 'prec': 70}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.19132500019339446674631270835', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.10184343161515355806777110848', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.40837113647807716816057132764', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.1284163748308, 'bad_primes': [2, 3, 7], 'central_character': '63.59', 'conductor': 2646, 'conductor_radical': 42, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2646/2/t/a/2285/7'], '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': '2-2646-63.59-c1-0-27', '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': '2-2646-63.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.596565715273828, 'root_angle': -0.008793873404492196, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.19132500019339446674631270835', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1510183851562052003589841602076', 'Lhash_array': ['1510183851562052003589841602076'], 'label': '2-2646-63.59-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2646/2/t/a/2285/7'}