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              lfunc_lfunctions •   Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 1, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 0, 'Lhash': '1793612049243716150', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 1391.31340481879, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, -1]], [11, [1]]], 'bad_primes': [2, 3, 5, 11], 'central_character': '174240.1', 'coefficient_field': '1.1.1.1', 'conductor': 174240, 'conductor_radical': 330, 'degree': 2, 'euler_factors': [[1], [1], [1, -1], [1, 0, 7], [1], [1, -2, 13], [1, 2, 17], [1, 0, 19], [1, 0, 23], [1, -6, 29], [1, -4, 31], [1, -6, 37], [1, 2, 41], [1, -8, 43], [1, 0, 47], [1, 10, 53], [1, 12, 59], [1, -2, 61], [1, -4, 67], [1, 8, 71], [1, -6, 73], [1, 8, 79], [1, -4, 83], [1, -6, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 31, 'label': '2-174240-1.1-c1-0-31', 'leading_term': '2.77703753102', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'EllipticCurve/Q/174240/dn', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.777037531020434, 1.944125293397554, -0.02590032833986159, -1.690420674497353, -1.619807004649053, 0.03120877696573657, 1.226607053792321, 0.2095516841219921, -2.066629369162453, -2.790054956862497, -1.07210031542971, 0.4622815055820292, -0.7130221716828811, -2.938536543963275, -2.411110760053114, 0.8983780933306631, 2.680585090356789, 0.7992375209074952, -1.241204411298567, -0.05266364431709325, 1.848776216231464, 0.3552022493788507, -2.851835909836341, -2.960392132487068, -0.3691818612203583, 0.3905408461295751, -0.6813671261501271, 0.7448373749678564, 4.17126546300052, 4.033237373335077, 0.05682081879422548, -1.466964547067504, 1.001720180404147, 1.632822850821653, -1.339038231638119, -2.358424904929733, 0.1345961237199973, 0.660998665132045, -1.873571567691449, -1.941198596142654, 0.8072843696288696, 0.5242289150977479, -2.496862002191532, -2.30063630119959, 0.005448547386903682, -1.32269087332358, -3.739318882841438, -1.286995960888192, 2.246875241077458, 0.590411220968428, -1.997725819569471, 0.1310664222377926, 2.30543274862433, 0.2870100784187466, -0.7386983352116003, 1.520580872215051, 1.385457784044898, -1.082142049366115, 0.2280792756416953, 2.748078996223453, -0.03050037201826912, -3.553257751417163, -1.345691432309505, 1.353116966045692, 0.0670073386268346, 0.8261864659566978, 4.829083823866001, 4.255264992749341, -0.2157651385543916, -0.6890406921129506, 0.835491991502536, -0.9791579110250834, -1.531659292645813, 1.679389534460891, 1.762870316614635, -1.151337647111313, 0.3360307102365668, 2.85031948790306, -0.4663594644182234, -3.460755292096788, -0.9089063273839355, -0.2400315256534314, -3.337264695018499, -2.343398856185155, 1.147463580700887, 0.4887512434075581, 0.07663684045951932, 3.135171488982951, 2.727243740705139, -0.5773475994593783, 0.9177355715043167, 3.210005199320184, 0.5204655052312209, -0.05321807592706613, 3.754687547261453, 3.171241509683022, -0.1290895474384443, 1.768416405408643, 3.391101444035643, -0.3244840277046832, -1.659446532536793, 0.5104739552813915, -0.7296596620051258, -1.635083196808982, 1.834543806289141, 2.086879554627156, -1.108992424342991, 0.3105404911292333, 1.832174140482979, -2.147920104915297, -2.959011979288063, 1.16219609576639, 0.4861476467160201, -2.235016019285647, 0.3529971784336524, 1.901077073345541, -0.2557328840211978, 0.7246381903603117, 1.266135445337095, -3.33099739900494, -4.301454544911816], 'positive_zeros': ['0.4969293557288790', '1.245778168055254', '1.774592228647460', '2.633481962468473', '2.912771309354263', '3.685975583762738', '4.321832818899965', '4.755444291245434', '5.276990003922614', '6.044578670378574', '6.339043697243347', '6.683694284588193', '7.503753551302306', '7.912522061277931', '8.398798113965481', '8.986758145134493', '9.326135321014409', '9.921151317012545', '10.29585207899268', '10.99869012042843', '11.10495492033106', '11.82111111167754', '12.29040151808744', '12.74073540038951', '13.27716508996162', '13.59732912907762', '14.12619210321826', '14.48245180600184', '14.99841667757944', '15.58693516932224', '16.01128232325322', '16.16994271937825', '16.98446048195437', '17.33309943291788', '17.65408323811943', '18.12774714095967', '18.63597577186124', '18.97663828915720', '19.47671261331535'], 'prelabel': '2-174240-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 37.30031373619785, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1793612049243716150, 'z1': {'__RealLiteral__': 0, 'data': '0.4969293557288790', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.245778168055254', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.774592228647460', 'prec': 57}}
           
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              lfunc_search •   Show schema
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{'algebraic': True, 'analytic_conductor': 1391.31340481879, 'bad_primes': [2, 3, 5, 11], 'central_character': '1.1', 'conductor': 174240, 'conductor_radical': 330, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 6, 0, 0, 0, -2, 0, 8, 0, 0, 0, 0, 0, -7, 0, 0, 0, -10, 0, 0, 0, 0, 0, -12, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 0, -8, 0, 6, 0, 0, 0, 0, 0, -8, 0, 0, 0, 4, 0, -2, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0], 'euler11': [1, 0, 0], 'euler13': [1, -2, 13], 'euler17': [1, 2, 17], 'euler19': [1, 0, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, -6, 29], 'euler3': [1, 0, 0], 'euler31': [1, -4, 31], 'euler37': [1, -6, 37], 'euler41': [1, 2, 41], 'euler43': [1, -8, 43], 'euler47': [1, 0, 47], 'euler5': [1, -1, 0], 'euler53': [1, 10, 53], 'euler59': [1, 12, 59], 'euler61': [1, -2, 61], 'euler67': [1, -4, 67], 'euler7': [1, 0, 7], 'euler71': [1, 8, 71], 'euler73': [1, -6, 73], 'euler79': [1, 8, 79], 'euler83': [1, -4, 83], 'euler89': [1, -6, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -1, 0], [1, 0, 7], [1, 0, 0], [1, -2, 13], [1, 2, 17], [1, 0, 19], [1, 0, 23], [1, -6, 29], [1, -4, 31], [1, -6, 37], [1, 2, 41], [1, -8, 43], [1, 0, 47], [1, 10, 53], [1, 12, 59], [1, -2, 61], [1, -4, 67], [1, 8, 71], [1, -6, 73], [1, 8, 79], [1, -4, 83], [1, -6, 89], [1, -2, 97]], 'index': 31, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/174240/dn'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-174240-1.1-c1-0-31', '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': '2-174240-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 37.30031373619785, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1793612049243716150, 'z1': {'__RealLiteral__': 0, 'data': '0.4969293557288790', 'prec': 60}}
           
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              lfunc_instances •   Show schema
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{'Lhash': '1793612049243716150', 'Lhash_array': ['1793612049243716150'], 'factors': ['2-174240-1.1-c1-0-31'], 'label': '2-174240-1.1-c1-0-31', 'type': 'ECQ', 'url': 'EllipticCurve/Q/174240/dn'}