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lfunc_lfunctions • Show schema
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{'Lhash': '3008852505878776384304592373516', 'a10': [0.5135920265255528, -0.88956748430452], 'a2': [0.16853197674585607, 0.29190594642383927], 'a3': [0.9269577977849812, -1.6055380022357448], 'a4': [0.9431939456282684, -1.6336598352195182], 'a5': [-1.5237227867446266, -2.639165283292131], 'a6': [0.6248881200827536, 0], 'a7': [0.6756652317723233, -2.5580219886807174], 'a8': [1.3099612674292467, 0], 'a9': [-0.21850151774876433, -0.37845573027177265], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.99302524233017, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [-0.6756652317723233, 2.5580219886807174]]], [11, [[1.0, 0], [0.5, -0.8660254037844386]]], [13, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [7, 11, 13], 'central_character': '1001.144', 'coefficient_field': 'CDF', 'conductor': 1001, 'conductor_radical': 1001, 'conjugate': '1192777861597740202998199753831', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'3.73576950816557190521687602163101', '4.76863724205845306117605347632492', '6.10888274185183536323413306575844', '7.08672306693009842248661124820327', '7.85971658495593198680210047641116', '8.605490639310296090211016796311941', '9.462329600243253377483136716849081', '10.42861022295631839098027992604742'], 'prelabel': '2-1001-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.827193881277011, 'root_angle': 0.7690393540182197, 'root_number': '-0.74811184495775546384538227124666587770216830168965157012 + 0.66357265422401430568568422250562988182455943820409950336*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.38451967700910983', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.37356611146404128335702054071', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.12245607949133339895279179344', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.73576950816557190521687602163', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.99302524233017, 'bad_primes': [7, 11, 13], 'central_character': '7.4', 'conductor': 1001, 'conductor_radical': 1001, 'degree': 2, 'index': 72, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1001/2/i/d/144/16'], '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': '2-1001-7.4-c1-0-72', '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': '2-1001-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.827193881277011, 'root_angle': 0.38451967700910983, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.37356611146404128335702054071', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3008852505878776384304592373516', 'Lhash_array': ['3008852505878776384304592373516'], 'label': '2-1001-7.4-c1-0-72', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1001/2/i/d/144/16'}