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lfunc_lfunctions • Show schema
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{'Lhash': '1359128459177009151016197553449', 'a10': [-0.6054704603365525, 0.0], 'a2': [-2.2478815676447628, 0.0], 'a3': [0.0, 0.0], 'a4': [3.0529715421570756, 0.0], 'a5': [0.2693515837540051, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.5238002077581788, 0.0], 'a8': [-2.36695532086937, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 47.934196333374636, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [-1.0, 0]]], [29, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 23, 29], 'central_character': '6003.1', 'coefficient_field': 'CDF', 'conductor': 6003, 'conductor_radical': 2001, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.2478815676447628, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.2693515837540051, 0], [5.0, 0]], [[1.0, 0], [0.5238002077581788, 0], [7.0, 0]], [[1.0, 0], [5.548702783006189, 0], [11.0, 0]], [[1.0, 0], [-3.853352027981315, 0], [13.0, 0]], [[1.0, 0], 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'5.01945626272103483529460124975636', '5.79275194065132095464563475543728', '6.47881934445695036301267776533619', '7.47561507606019012463421016211515', '7.74884349520729546397084711633670'], 'prelabel': '2-6003-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.923452630976444, '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': '1.07216330661801442861309088917', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.09625837622109623231047969072', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.87044207821374903326988219958', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 47.934196333374636, 'bad_primes': [3, 23, 29], 'central_character': '1.1', 'conductor': 6003, 'conductor_radical': 2001, 'degree': 2, 'index': 137, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6003/2/a/o/1/3'], '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': '2-6003-1.1-c1-0-137', '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': '2-6003-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.923452630976444, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.07216330661801442861309088917', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1359128459177009151016197553449', 'Lhash_array': ['1359128459177009151016197553449'], 'label': '2-6003-1.1-c1-0-137', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6003/2/a/o/1/3'}