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lfunc_lfunctions • Show schema
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{'A10': 4, 'A2': 1, 'A3': 2, 'A4': 1, 'A5': 4, 'A6': 2, 'A7': 1, 'A8': 1, 'A9': 1, 'Lhash': '238933554130836013', 'a10': [1.2649110640673518, 0], 'a2': [0.7071067811865475, 0], 'a3': [1.1547005383792517, 0], 'a4': [0.5, 0], 'a5': [1.7888543819998317, 0], 'a6': [0.8164965809277261, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 928.1970431757679, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [7, [1, -1]], [19, [1]], [23, [1, -1]]], 'bad_primes': [2, 7, 19, 23], 'central_character': '116242.1', 'coefficient_field': '1.1.1.1', 'conductor': 116242, 'conductor_radical': 6118, 'degree': 2, 'euler_factors': [[1, -1], [1, -2, 3], [1, -4, 5], [1, -1], [1, 2, 11], [1, -2, 13], [1, -7, 17], [1], [1, -1], [1, 0, 29], [1, 3, 31], [1, 2, 37], [1, -8, 41], [1, -10, 43], [1, 7, 47], [1, 1, 53], [1, 2, 59], [1, -12, 61], [1, 4, 67], [1, 10, 71], [1, -4, 73], [1, 1, 79], [1, 3, 83], [1, -1, 89], [1, -5, 97]], 'gamma_factors': [[], [0]], 'index': 23, 'label': '2-116242-1.1-c1-0-23', 'leading_term': '13.0107893826', '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/116242/y', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [13.0107893825736, 11.55873757447133, 7.625726052790144, 2.706988264334025, -0.9031731804630064, -1.688340326040822, -0.3706220665812223, 0.7683509410341108, 0.3689868095966651, -0.6276236500471786, -0.6047568445352861, 0.2354036863838396, 0.2163891337003145, -0.9063702088374718, -1.068029003128457, 0.9143836914377379, 2.738508347238131, 1.419162486966361, -1.98187331225018, -3.308903957138428, -1.291049468940365, 0.7161459441383732, 0.3118074721164524, -0.2768786903454955, 1.100686761916907, 1.769534948552198, -1.236516591983941, -4.720239275886683, -3.453764940700153, 0.8559638344799241, 1.800406877528728, -1.016228511890439, -1.532786944742798, 1.70628838831745, 2.95238238042098, 0.01328918514850348, -1.7443797862398, 0.279424124976635, 1.223501358794501, -1.176326747652902, -1.956642426076373, 0.5656387984663517, 0.5796293080375092, -3.189067100359644, -3.214395895124339, 2.43091431237692, 4.29826921568607, -2.167119016311489, -7.779395013869259, -5.185689554560665, -0.1764584404013201, 0.4457446303479417, -0.5932913072436703, 0.3735353920510585, 1.062454836363004, 0.136190937775707, -0.04484589058852544, 0.4347089825095281, 0.02501508939316178, 0.5240814764909739, 1.963321776236534, -0.221739123293103, -4.925314668982048, -4.176061460989296, 1.260510947499189, 1.550485981918307, -2.645134386519031, -0.944384830988462, 5.002280908461171, 4.422224388602848, -0.07567556521285627, 1.568138250503483, 5.110421713174089, 1.725090263219458, -2.270105133728731, 0.8017693573174176, 3.240321559325158, -0.7754527489971643, -2.300833115723268, 2.870426166201588, 5.43235446095258, 1.970448957334752, -0.401431348527175, 0.04955423732465876, -0.1538617837383044, 0.002655484682625608, 0.6209018105660347, -1.361346525323627, -2.544842240242709, 1.379824954522489, 3.915895687229419, 0.5672448565981001, -0.1197105372927829, 4.840107913673239, 5.234386924291282, -0.1628404839667251, -0.973749113562507, 2.429280649988969, 1.784186193092776, -0.6384158468839869, 0.1626473145343917, 0.7771201838581092, -0.0495028949525572, 0.5623739351600942, 0.3381779647568835, -0.5961236008405177, 2.907820918910227, 4.286154403879792, -6.007557631934096, -14.98737917015342, -7.459270457151592, 2.637998028230736, -0.2202326322706867, -3.609103757066246, 2.333072401517312, 5.038324649976233, 0.1404922885913166, -1.317956711087103, 0.6198705986630397, -0.7471172686167004, -1.324261638726397], 'positive_zeros': ['0.9184463945435938', '1.559154379893065', '2.085186481357756', '2.675803731114739', '3.058903996997183', '3.656718024489166', '4.356022049849561', '5.128629513744128', '5.571353119169153', '5.833834569471103', '6.424225937841360', '7.195073991547879', '7.665672600954054', '8.131639804438444', '8.750964156397550', '9.222915999660962', '9.645091382056464', '10.19613498047891', '10.54703863399058', '11.15113214819657', '11.68346188028553', '12.51479800044168', '12.83106917709787', '13.18611529441972', '13.79106363818340', '14.02020239487885', '14.51613184105471', '14.61889659739659', '15.23766663725551', '15.93616964868883', '16.34004964791201', '16.78927601453082', '17.49218598239604', '17.64510368334619', '18.32510747158406', '18.70881219055852', '19.21086144840783', '19.62993679342246'], 'prelabel': '2-116242-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 30.46632638136354, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 238933554130836013, 'z1': {'__RealLiteral__': 0, 'data': '0.9184463945435938', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.559154379893065', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.085186481357756', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 928.1970431757679, 'bad_primes': [2, 7, 19, 23], 'central_character': '1.1', 'conductor': 116242, 'conductor_radical': 6118, 'degree': 2, 'dirichlet_coefficients': [1, 1, 2, 1, 4, 2, 1, 1, 1, 4, -2, 2, 2, 1, 8, 1, 7, 1, 0, 4, 2, -2, 1, 2, 11, 2, -4, 1, 0, 8, -3, 1, -4, 7, 4, 1, -2, 0, 4, 4, 8, 2, 10, -2, 4, 1, -7, 2, 1, 11, 14, 2, -1, -4, -8, 1, 0, 0, -2, 8, 12, -3, 1, 1, 8, -4, -4, 7, 2, 4, -10, 1, 4, -2, 22, 0, -2, 4, -1, 4, -11, 8, -3, 2, 28, 10, 0, -2, 1, 4, 2, 1, -6, -7, 0, 2, 5, 1, -2, 11], 'euler11': [1, 2, 11], 'euler13': [1, -2, 13], 'euler17': [1, -7, 17], 'euler19': [1, 0, 0], 'euler2': [1, -1, 0], 'euler23': [1, -1, 0], 'euler29': [1, 0, 29], 'euler3': [1, -2, 3], 'euler31': [1, 3, 31], 'euler37': [1, 2, 37], 'euler41': [1, -8, 41], 'euler43': [1, -10, 43], 'euler47': [1, 7, 47], 'euler5': [1, -4, 5], 'euler53': [1, 1, 53], 'euler59': [1, 2, 59], 'euler61': [1, -12, 61], 'euler67': [1, 4, 67], 'euler7': [1, -1, 0], 'euler71': [1, 10, 71], 'euler73': [1, -4, 73], 'euler79': [1, 1, 79], 'euler83': [1, 3, 83], 'euler89': [1, -1, 89], 'euler97': [1, -5, 97], 'euler_factors': [[1, -1, 0], [1, -2, 3], [1, -4, 5], [1, -1, 0], [1, 2, 11], [1, -2, 13], [1, -7, 17], [1, 0, 0], [1, -1, 0], [1, 0, 29], [1, 3, 31], [1, 2, 37], [1, -8, 41], [1, -10, 43], [1, 7, 47], [1, 1, 53], [1, 2, 59], [1, -12, 61], [1, 4, 67], [1, 10, 71], [1, -4, 73], [1, 1, 79], [1, 3, 83], [1, -1, 89], [1, -5, 97]], 'index': 23, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/116242/y'], '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': '2-116242-1.1-c1-0-23', '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': '2-116242-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 30.46632638136354, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 238933554130836013, 'z1': {'__RealLiteral__': 0, 'data': '0.9184463945435938', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '238933554130836013', 'Lhash_array': ['238933554130836013'], 'label': '2-116242-1.1-c1-0-23', 'type': 'ECQ', 'url': 'EllipticCurve/Q/116242/y'}