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lfunc_lfunctions • Show schema
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{'Lhash': '2856740267848795463285298499511', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.5, 0.8660254037844386], 'a4': [0.0, 0.0], 'a5': [-0.5, -2.179449471770337], 'a6': [0.0, 0.0], 'a7': [2.6374586088176875, 0.2093133697914896], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.1179056282979258, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0.5, 2.179449471770337]]], [7, [[1.0, 0], [-2.6374586088176875, -0.2093133697914896]]]], 'bad_primes': [2, 5, 7], 'central_character': '140.109', 'coefficient_field': 'CDF', 'conductor': 140, 'conductor_radical': 70, 'conjugate': '2726200305235111316122256085012', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.5, -0.8660254037844386], [1.5, 2.598076211353316]], [[1.0, 0], [0.5, 2.179449471770337]], [[1.0, 0], [-2.6374586088176875, -0.2093133697914896]], [[1.0, 0], [1.1374586088176875, 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'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/140/2/q/b/109/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.3842152577422098, 1.3895505131148185, 1.4080646987887169, 1.4370224174308783, 1.4722659880518687, 1.5086387657943012, 1.540388382874623, 1.561508624294882, 1.5660309089128563, 1.548298195289601, 1.5032511136778546, 1.4267418434802375, 1.3158752498222814, 1.1693630743003005, 0.9878664288142357, 0.7742943450302711, 0.5340215584817529, 0.27498718637815, 0.007637819760753315, -0.2553158380414228, -0.49935004847412306, -0.7087945101816242, -0.8677047420991933, -0.9609109843594594, -0.9751928833598501, -0.9005082099655629, -0.731185280472425, -0.4669749333896223, -0.11385118976298061, 0.31554783066314196, 0.8019340027572504, 1.3199089483997686, 1.839064354365316, 2.3256324578187315, 2.744624317008747, 3.06233895156423, 3.2490745161824894, 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'root_analytic_conductor': 1.0573105637881075, 'root_angle': -0.02640139469829123, 'root_number': '0.9965622483466144 - 0.08284736067214639*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0132006973491', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.25357071367651651651678217180', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.53518049086950142524561968582', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.42045278587186085757282105169', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.1179056282979258, 'bad_primes': [2, 5, 7], 'central_character': '35.4', 'conductor': 140, 'conductor_radical': 70, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/140/2/q/b/109/1'], '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': '2-140-35.4-c1-0-2', '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': '2-140-35.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0573105637881075, 'root_angle': -0.013200697349145614, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.25357071367651651651678217180', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2856740267848795463285298499511', 'Lhash_array': ['2856740267848795463285298499511'], 'label': '2-140-35.4-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/140/2/q/b/109/1'}