-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1614135724880018202441983410595', 'a10': [0.7609815435614865, 1.837171963181753], 'a2': [0.5406408174555976, 0.8412535328311812], 'a3': [0.0, 0.0], 'a4': [-0.41541501300188644, 0.9096319953545183], 'a5': [1.956945088224751, 0.35307174004066205], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-0.9898214418809327, 0.14231483827328514], 'a9': [-0.9369497249997617, -0.3494641795990983], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7046797978377994, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5406408174555976, -0.8412535328311812]]], [353, [[1.0, 0], [0.14231483827328514, -0.9898214418809327]]]], 'bad_primes': [2, 353], 'central_character': '1412.1339', 'coefficient_field': 'CDF', 'conductor': 1412, 'conductor_radical': 706, 'conjugate': '2728068881710002063162991033761', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5406408174555976, -0.8412535328311812]], [[1.0, 0], [0, 0], [0.9369497249997617, 0.3494641795990983]], [[1.0, 0], [-1.956945088224751, -0.35307174004066205], [0.9369497249997617, 0.3494641795990983]], [[1.0, 0], [0, 0], [-0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [0, 0], [0.8412535328311812, -0.5406408174555976]], [[1.0, 0], [0.7353641512939705, -1.4690704286009895], [-0.599277666511347, -0.8005412409243604]], [[1.0, 0], [0.8223733742970273, -0.11823944078331622], [0.9594929736144974, -0.28173255684142967]], [[1.0, 0], [0, 0], [-0.9898214418809327, 0.14231483827328514]], [[1.0, 0], [0, 0], [0.5406408174555976, -0.8412535328311812]], [[1.0, 0], [-1.8146287145670172, 0.8287131663191551], [0.6548607339452851, -0.7557495743542583]], [[1.0, 0], [0, 0], [-0.21256528955297668, 0.9771468659711595]], [[1.0, 0], [-0.47924898672005684, 1.8776789895672557], [-0.8776789895672557, -0.47924898672005684]], [[1.0, 0], [0.2498134869122486, 0.13640848407540132], [0.5406408174555976, 0.8412535328311812]], [[1.0, 0], [0, 0], [-0.5406408174555976, -0.8412535328311812]], [[1.0, 0], [0, 0], [0.7557495743542583, -0.6548607339452851]], [[1.0, 0], [0.8348320276978743, 1.2023867314339094], [-0.3494641795990983, 0.9369497249997617]], [[1.0, 0], [0, 0], [-0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [0.1078291146752006, -0.09343445973781288], [0.14231483827328514, -0.9898214418809327]], [[1.0, 0], [0, 0], [0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [0, 0], [0.07133918319923234, -0.9974521146102535]], [[1.0, 0], [1.28641390459886, 0.5874855454006634], [0.6548607339452851, 0.7557495743542583]], [[1.0, 0], [0, 0], [-0.9369497249997617, 0.3494641795990983]], [[1.0, 0], [0, 0], [-0.9594929736144974, -0.28173255684142967]], [[1.0, 0], [-0.2071493413258132, 0.052871716881170996], [0.8776789895672557, -0.47924898672005684]], [[1.0, 0], [-0.23944572094339864, 1.6653815697087766], [-0.9594929736144974, -0.28173255684142967]], [[1.0, 0], [1.0538188223841578, -0.43650604851556196], [0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [0, 0], [0.9974521146102535, -0.07133918319923234]], [[1.0, 0], [0, 0], [-0.9771468659711595, -0.21256528955297668]], [[1.0, 0], [0.15874646716881882, 0.5406408174555976], [-0.8412535328311812, 0.5406408174555976]], [[1.0, 0], [1.704558895796801, -0.6357675979873152], [0.7557495743542583, -0.6548607339452851]], [[1.0, 0], [0, 0], [-0.28173255684142967, -0.9594929736144974]], [[1.0, 0], [0, 0], [0.9594929736144974, -0.28173255684142967]], [[1.0, 0], [-0.684410391155026, 1.6523128485555385], [-0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [0, 0], [0.599277666511347, -0.8005412409243604]], [[1.0, 0], [-0.8005412409243604, -0.40072233348865305], [0.599277666511347, 0.8005412409243604]], [[1.0, 0], [0, 0], [-0.3494641795990983, -0.9369497249997617]], [[1.0, 0], [1.797993355534614, -0.6706168497105792], [0.7557495743542583, -0.6548607339452851]], [[1.0, 0], [0, 0], [0.599277666511347, -0.8005412409243604]], [[1.0, 0], [0, 0], [0.5406408174555976, 0.8412535328311812]], [[1.0, 0], [1.0308321568137297, -0.7157195577688238], [0.3494641795990983, -0.9369497249997617]], [[1.0, 0], [0, 0], [0.07133918319923234, 0.9974521146102535]], [[1.0, 0], [0.34033456135237183, -0.2547712614092333], [0.28173255684142967, -0.9594929736144974]], [[1.0, 0], [0, 0], [0.9594929736144974, 0.28173255684142967]], [[1.0, 0], [0.8270887575534906, -1.6523128485555385], [-0.599277666511347, -0.8005412409243604]], [[1.0, 0], [-0.9490181727664879, 0.5182031278901967], [0.5406408174555976, -0.8412535328311812]], [[1.0, 0], [0, 0], [-0.599277666511347, 0.8005412409243604]], [[1.0, 0], [0, 0], [0.8776789895672557, 0.47924898672005684]], [[1.0, 0], [0, 0], [-0.9898214418809327, -0.14231483827328514]], [[1.0, 0], [0, 0], [0.9369497249997617, 0.3494641795990983]], [[1.0, 0], [0.18928020095657233, 0.7415925047846321], [-0.8776789895672557, 0.47924898672005684]], [[1.0, 0], [-0.2547712614092333, 1.1711645873561447], [-0.9096319953545183, -0.41541501300188644]], [[1.0, 0], [0, 0], [-0.599277666511347, 0.8005412409243604]], [[1.0, 0], [-0.43038300863446155, -1.293094002569142], [-0.8005412409243604, 0.599277666511347]], [[1.0, 0], [0, 0], [-0.47924898672005684, 0.8776789895672557]], [[1.0, 0], [-1.3925618789730458, -0.6970667058015417], [0.599277666511347, 0.8005412409243604]], [[1.0, 0], [0, 0], [0.9974521146102535, -0.07133918319923234]], [[1.0, 0], [-0.5182031278901967, -0.8063398063680233], [-0.41541501300188644, 0.9096319953545183]], [[1.0, 0], [0, 0], [0.9898214418809327, -0.14231483827328514]], [[1.0, 0], [0.5595209759897515, -1.500133791070095], [-0.7557495743542583, -0.6548607339452851]], [[1.0, 0], [-0.9365932907867147, -0.2037433992602391], [0.9096319953545183, 0.41541501300188644]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0, 0], [0.5406408174555976, 0.8412535328311812]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-0.4942978463944064, -0.01765389235666213], [0.9974521146102535, 0.07133918319923234]], [[1.0, 0], [-0.7645815764181828, 0.7645815764181828], [0, -1.0]], [[1.0, 0], [0, 0], [0.14231483827328514, 0.9898214418809327]], [[1.0, 0], [-1.2963903918098558, -1.4961142667764662], [-0.14231483827328514, 0.9898214418809327]], [[1.0, 0], [0, 0], [-0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [0.4978978792511027, -1.0902442791202323], [-0.6548607339452851, -0.7557495743542583]], [[1.0, 0], [0.14231483827328514, -0.9898214418809327]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-1412-1412.1339-c0-0-0', 'leading_term': '1.6620485321155816781886406087468', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1412/1/s/a/1339/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.6620485321155816, 1.6127858547052987, 1.5799580125742507, 1.5598829338604367, 1.5483424413509017, 1.5409893485151933, 1.5336730076660667, 1.5226508311617728, 1.5046974403013536, 1.477142660456912, 1.4378697017399096, 1.385296345680425, 1.3183524606878028, 1.2364598901121133, 1.1395161549681687, 1.0278809043908197, 0.9023629019558445, 0.7642049914088077, 0.6150645787096144, 0.4569874890391874, 0.2923734947893557, 0.12393230601538639, -0.045370660366236715, -0.21237887741613307, -0.3738192727792532, -0.5263858247416625, -0.6668307305588775, -0.7920611922324974, -0.8992394103496948, -0.9858829784616081, -1.0499625449527807, -1.0899933727176556, -1.10511729471103, -1.0951715494035619, -1.060741095600888, -1.0031912587800924, -0.9246779546218193, -0.8281332684030852, -0.7172248345321341, -0.5962882461037075, -0.47023261133437466, -0.34442033767387104, -0.22452323539925426, -0.1163580559113805, -0.02570557723882268, 0.0418817207708906, 0.08127752882678466, 0.0879785968033241, 0.05829363009122792, -0.010483064874919193, -0.11992043779488018, -0.27032902095770917, -0.4606751151849413, -0.6885363565085396, -0.9501030336307745, -1.2402281157303607, -1.55252731610499, -1.8795287075271874, -2.2128694794910757, -2.543535455046095, -2.8621370426792447, -3.159213468815256, -3.425555502993006, -3.6525355331429283, -3.8324328498637628, -3.958741424326733, -4.026447369751722, -4.032263700332593, -3.974810963719933, -3.8547338216046003, -3.674745662064964, -3.43959579747611, -3.1559566594287833, -2.8322315513596563, -2.4782868447008206, -2.105115873399885, -1.7244450512785516, -1.3482957576864878, -0.9885181605538153, -0.6563152308103772, -0.36177662103600017, -0.11344272804581515, 0.08208094470523829, 0.22044010903206382, 0.29976168661191016, 0.32078334056250996, 0.28687208154363986, 0.2039258407148135, 0.0801567836779183, -0.07423964050343364, -0.2475205796067064, -0.4269220253588503, -0.5992559984000431, -0.7515549809215538, -0.871736482715858, -0.9492582468357709, -0.9757334374875373, -0.9454753302192977, -0.8559426126711884, -0.7080594108071242, -0.5063885220140307, -0.25914193648221406, 0.02198063008346317, 0.3221270385580257, 0.6237957938400519, 0.9074927526083811, 1.1525195217074167, 1.3378643843875753, 1.443160362550385, 1.4496701238116916, 1.3412541732822814, 1.1052773699386287, 0.7334094374917474, 0.22227787154214582, -0.42606354741189856, -1.2038806694723034, -2.097740877673212, -3.0887426625288694, -4.152993690975279, -5.262326812800659, -6.385232074661179, -7.487971990825685, -8.535837594833051, -9.494494681981456, -10.331363607350552, -11.016972404304008, -11.526222105970682, -11.83950513592863, -11.943622497158886, -11.832453100723603, -11.507338665919738, -10.977159785968231, -10.25809246256104, -9.373049046533055, -8.350822389027396, -7.224966379771392, -6.0324591980460776, -4.812206836347408, -3.603453159674803, -2.4441684270095796, -1.369490457499461, -0.4102912674225053, 0.40806298951554304, 1.0666994138024528, 1.5539253130656274, 1.865581145504003, 2.005042016847254, 1.9828675706995469, 1.8161176595487118, 1.5273680926147921, 1.143476128967907, 0.6941583817369302, 0.21045369059044267, -0.27685027628015374, -0.7387458081738091, -1.1494105877735572, -1.4874174033582441, -1.736686071097916, -1.8871292513527655, -1.9349603355002258, -1.882649948154794, -1.7385368651623838, -1.5161182327468528, -1.2330618189712497, -0.9099986159922765, -0.5691665298836547, -0.23298439689885161, 0.07736038616580314, 0.34322802557872734, 0.5496691594567858, 0.6863272006224198, 0.7480470146902868, 0.73515395873855, 0.6533867762634645, 0.5134884641546179, 0.3304797928750924, 0.12265944941742682, -0.08960838420419205, -0.2852448488920413, -0.4438624394221629, -0.5471389953270739, -0.5800735923375749, -0.532044736350034, -0.39760267454941867, -0.17694337805026833, 0.12396908335280236, 0.493643588423173, 0.9156557730062477, 1.3695618303211141, 1.8320791685526838, 2.2784634648277065, 2.6839984955568568, 3.0255070202884253, 3.2827885377584787, 3.439893162648711, 3.486150066684962, 3.4168833982211826, 3.2337675068286234, 2.9447955222359274, 2.563859506804911, 2.1099650044172518, 1.6061262771989124, 1.0780093298541134, 0.5524065876939613, 0.055638672590362086, -0.3880157199961511, -0.7577617552474464, -1.0375095482051389, -1.2167953152255342, -1.2913423974502243, -1.2632250483783145, -1.1406236828224219, -0.9371871478162814, -0.6710437304565131, -0.36352630922508683, -0.037696660195915485, 0.28323193466165497, 0.5774670058858642, 0.8260968837198113, 1.0143379031268303, 1.1324821420831923, 1.1764789209112922, 1.148108099236146, 1.054731301823298, 0.9086367140182194, 0.7260220015649335, 0.5256862129332117, 0.3275233324918156, 0.1509258529986928, 0.013215092605389198, -0.07178475980172887, -0.09491993783164801, -0.052534794976155236, 0.053116006301154726, 0.21391212037452859, 0.4163779446198779, 0.6426339751299768, 0.8717311788870254, 1.0812806003981519, 1.2492659310834773, 1.355909553145748, 1.3854540671206936, 1.3277223975521601, 1.1793304728182987, 0.9444467408974412, 0.6350212906767634, 0.2704423638868186, -0.1233826786505218, -0.5154839449855327, -0.8717453983211505, -1.157167505978311, -1.3383334541691727, -1.38591594607175, -1.2770519024096767, -0.9974143032812449, -0.5428242041147454, 0.07972893100627501], 'positive_zeros': ['1.27332856907842522633015826080806', '2.59794112185846907187991205469914', '2.86399092100264983833415320337124', '4.77802765285175138182878131196220', '5.18784105677734693899982683054649', '5.97216101274212258942116381190625', '6.64259662654711432861741365546182', '8.289742592933928355013488507900458', '8.931397687633661899996678756351160', '9.769872815061661981085290376689333'], 'prelabel': '2-1412-1412.1339-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8394520819187951, 'root_angle': -0.5645981903639451, 'root_number': '-0.20155103942500923955109671254171 - 0.97947801328396257737461102607842*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.28229909518197255', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.27332856907842522633015826081', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.59794112185846907187991205470', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.86399092100264983833415320337', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.7046797978377994, 'bad_primes': [2, 353], 'central_character': '1412.1339', 'conductor': 1412, 'conductor_radical': 706, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1412/1/s/a/1339/1'], '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': '2-1412-1412.1339-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1412-1412.1339-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8394520819187951, 'root_angle': -0.28229909518197255, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.27332856907842522633015826081', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1614135724880018202441983410595', 'Lhash_array': ['1614135724880018202441983410595'], 'label': '2-1412-1412.1339-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1412/1/s/a/1339/1'}