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lfunc_lfunctions • Show schema
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{'Lhash': '1392134903405633181529779128539', 'a10': [0.0, 0.0], 'a2': [-1.618033988749895, 0.0], 'a3': [0.0, 0.0], 'a4': [0.6180339887498949, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.0, 0.0], 'a8': [2.23606797749979, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 44.91585113697024, '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': '5625.1', 'coefficient_field': 'CDF', 'conductor': 5625, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.618033988749895, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.0, 0], [7.0, 0]], [[1.0, 0], [-3.0, 0], [11.0, 0]], [[1.0, 0], [1.0, 0], [13.0, 0]], [[1.0, 0], [-4.23606797749979, 0], [17.0, 0]], [[1.0, 0], [6.708203932499369, 0], [19.0, 0]], [[1.0, 0], [5.381966011250105, 0], [23.0, 0]], [[1.0, 0], [-3.618033988749895, 0], [29.0, 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'label': '2-75e2-1.1-c1-0-108', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/5625/2/a/b/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.0, 0.10318281554994871, 0.2051609074373832, 0.30470016013227635, 0.40051105223748534, 0.491229116016831, 0.5754044415270071, 0.6515020992108196, 0.7179145683145045, 0.772986462496388, 0.815051101557229, 0.8424778293461895, 0.8537284399593424, 0.8474206472955612, 0.8223962065771777, 0.777791056888927, 0.7131046890957975, 0.6282658460876703, 0.5236916298634547, 0.40033712487201234, 0.25973275486695563, 0.10400677838614043, -0.06410939733461482, -0.24129503759847754, -0.4236745296425142, -0.6068734004921876, -0.7860962051035166, -0.9562258735777335, -1.1119433347126115, -1.2478654239496332, -1.3586982619510914, 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'2-75e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.701928911661943, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.09820080009033362205797219087', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.08136400647833211258189485686', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.14195708488296106043979789671', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 44.91585113697024, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 5625, 'conductor_radical': 15, 'degree': 2, 'index': 108, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5625/2/a/b/1/1'], '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': '2-75e2-1.1-c1-0-108', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-75e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.701928911661943, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.09820080009033362205797219087', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1392134903405633181529779128539', 'Lhash_array': ['1392134903405633181529779128539'], 'label': '2-75e2-1.1-c1-0-108', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5625/2/a/b/1/1'}