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lfunc_lfunctions • Show schema
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{'Lhash': '1236157624913316279980206887048', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.2212317420824743, -0.2212317420824743], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [1.260073510670101, 1.260073510670101], 'a8': [0.0, 0.0], 'a9': [0.0, 0.9021130325903072], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.9962600505320096, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '4000.1057', 'coefficient_field': 'CDF', 'conductor': 4000, 'conductor_radical': 10, 'conjugate': '1915707004570660853807365179564', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.2212317420824743, 0.2212317420824743], [0, -1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.260073510670101, -1.260073510670101], [0, 1.0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0, 0], [-1.0, 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'group': 'GL2', 'index': 2, 'label': '2-4000-5.2-c0-0-2', 'leading_term': '1.6244626211555110843985538873073', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/4000/1/p/b/1057/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.624462621155511, 1.5872087270533344, 1.5577505031704728, 1.5338375775472315, 1.5126635613101123, 1.4911260050708919, 1.4660719707352938, 1.4344996988500534, 1.3937069711478955, 1.3413911383090138, 1.2757121970161245, 1.1953307449882207, 1.099430110867477, 0.987728683007527, 0.8604855945693599, 0.7185008323202863, 0.5631095012429944, 0.39616923858339, 0.22003946057392232, 0.03755110728423794, -0.1480342704780958, -0.3330769283896562, -0.513623297977758, -0.685482299558535, -0.8443130973941377, -0.985723285224613, -1.105375979039775, 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'7.11362745063964175260237132486709', '7.75614858012828256769888070842006', '8.633808838135999941808845730093247'], 'prelabel': '2-4000-5.2-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4128906718256757, 'root_angle': -0.25, 'root_number': '0.70710678118654752440084436210459 - 0.70710678118654752440084436210459*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.125', 'prec': 20}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.975156422984974655631985791947', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.90343164351988354093423999321', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.39727445270167248855976893761', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.9962600505320096, 'bad_primes': [2, 5], 'central_character': '5.2', 'conductor': 4000, 'conductor_radical': 10, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4000/1/p/b/1057/2'], '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': '2-4000-5.2-c0-0-2', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-4000-5.2-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4128906718256757, 'root_angle': -0.125, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.975156422984974655631985791947', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1236157624913316279980206887048', 'Lhash_array': ['1236157624913316279980206887048'], 'label': '2-4000-5.2-c0-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4000/1/p/b/1057/2'}