-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2957870866523065804060725416848', 'a10': [9.558105474872457, 4.602941000583856], 'a2': [0.7770616906500636, 0.9744045399923053], 'a3': [-0.18954752500442185, 0.09128127709991496], 'a4': [1.4345281351688344, -6.285078419007553], 'a5': [7.669122491018297, -3.6932547402003806], 'a6': [-0.23623501106092404, -0.1137647854006568], 'a7': [18.37682134461005, 2.300529779916895], 'a8': [16.2220192192105, -7.812112721779701], 'a9': [-16.806628657499495, 21.074845746329743], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.8910935902812915, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [-18.37682134461005, -2.300529779916895]]]], 'bad_primes': [7], 'central_character': '49.8', 'coefficient_field': 'CDF', 'conductor': 49, 'conductor_radical': 7, 'conjugate': '2343809852967613824493295718539', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.7770616906500636, -0.9744045399923053], [-1.7801674716505151, 7.799423297454589]], [[1.0, 0], [0.18954752500442185, -0.09128127709991496], [16.834224650185806, -21.109450026636804]], [[1.0, 0], [-7.669122491018297, 3.6932547402003806], [77.9362252323417, -97.72893530850372]], [[1.0, 0], [-18.37682134461005, -2.300529779916895]], [[1.0, 0], [-2.584426478271103, -3.240768299357265], [-296.1753630958545, 1297.6290511140073]], [[1.0, 0], [11.776966351233375, 14.767848702434902], [-488.87849190202274, 2141.9166230634664]], [[1.0, 0], [4.871086645238224, 21.3416250267545], [-4426.460048004586, 2131.6708102845632]], [[1.0, 0], [46.47722386624813, 0], [6859.0, 0]], [[1.0, 0], [18.353493281648294, -80.4119080761783], [-10962.088215768734, -5279.06345384333]], [[1.0, 0], [-44.663481859487916, -195.68349973126507], [-21973.7297192721, 10581.990513338125]], [[1.0, 0], [276.70312673888935, 0], [29791.0, 0]], [[1.0, 0], [-48.37839210696103, -211.95958498364342], [-45636.77606586124, 21977.513037521672]], [[1.0, 0], [-386.6626049407642, 186.20689658147458], [42971.54063390577, -53884.60760317908]], [[1.0, 0], [-188.2629461850588, -90.66265654465197], [49571.803676382326, 62161.07567658565]], [[1.0, 0], [258.85454474518974, 324.59333233420364], [-23102.79092614643, 101219.94062645348]], [[1.0, 0], [-39.28022153840813, 172.09789521195313], [-134133.54214670844, -64595.3094286047]], [[1.0, 0], [-149.79188945681028, -72.13597206562288], [128051.71201594484, 160571.7680378015]], [[1.0, 0], [72.43628326599145, 317.3640931445508], [-204502.814605359, 98483.36498864245]], [[1.0, 0], [809.2913106406614, 0], [300763.0, 0]], [[1.0, 0], [-44.78339902384801, 196.2088911567177], [-322466.66847982275, -155291.76295130435]], [[1.0, 0], [391.20972113802856, -490.56147401517444], [-86564.42616488357, -379263.53161323647]], [[1.0, 0], [-69.4560469416215, 0], [493039.0, 0]], [[1.0, 0], [-441.2868308148954, 553.3561833747507], [-127234.57726407914, -557451.1061227084]], [[1.0, 0], [-537.9473797746007, 674.564677986925], [-156870.36029024902, -687293.955322908]], [[1.0, 0], [-1059.435752963191, 0], [912673.0, 0]], [[1.0, 0], [-889.7826558085118, 428.4967432925345], [642382.166344855, -805521.7582182935]], [[1.0, 0], [766.9897372417389, -369.36279034147697], [681304.1407156884, -854328.3703428428]], [[1.0, 0], [-1011.6301259408657, 1268.5440543145714], [-272597.7124966453, -1194328.6143229578]], [[1.0, 0], [-743.1162367830273, -931.8382871990826], [-288171.0625805119, 1262559.9191849148]], [[1.0, 0], [918.6307213125996, -1151.9264894844805], [-321074.7880427642, -1406720.5597034167]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-7e2-49.8-c3-0-6', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/49/4/e/a/8/9', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.7790067408682229, 1.796826784196136, 1.8075266095935472, 1.8107224246864262, 1.8056282626771527, 1.791102791578841, 1.7657154148252707, 1.7278296195068867, 1.6757014108058788, 1.6075906478740398, 1.5218830067717795, 1.4172200097092595, 1.2926340096514908, 1.147684209201249, 0.9825887866429925, 0.7983471063620388, 0.5968449362575218, 0.38093472254868643, 0.15448242436307416, -0.07762767879624807, -0.3095383043606373, -0.534521541588567, -0.7451433112102941, -0.9334922671838208, -1.0914720922349748, -1.2111520860270202, -1.2851664003363554, -1.30714746432751, -1.2721743566300145, -1.1772124695135218, -1.0215171672746663, -0.8069716801821238, -0.5383286033560291, -0.2233254510956803, 0.12735196426712986, 0.5002788386236501, 0.879685743692049, 1.2480400642903888, 1.5868042969277327, 1.877347537393286, 2.1019725812363266, 2.245007701571575, 2.293900464069021, 2.240242055596742, 2.0806456743075477, 1.8174025540650787, 1.4588449316262313, 1.0193571196278761, 0.5189937900713852, -0.01731194055428248, -0.5609400896596441, -1.0811337393460325, -1.5468345034050857, -1.9287009518440372, -2.201182070843382, -2.344499586012923, -2.3463842530324657, -2.2034139602182305, -1.9218168896070444, -1.5176312906115328, -1.0161537689752964, -0.45065833942100225, 0.13957436134344803, 0.7118185542731716, 1.222898937087748, 1.6324141510898345, 1.9059449796383978, 2.017984914239807, 1.9543326138317438, 1.7137107956239923, 1.3084242627297022, 0.7639389390986534, 0.11734956214643501, -0.5852003561905855, -1.291984626136457, -1.9497937935468892, -2.508340378173467, -2.924592636222283, -3.1666416665841854, -3.21672519102225, -3.0730874641024184, -2.750446040288419, -2.2789562723120382, -1.7017036457426469, -1.0708997484387, -0.4430954448941604, 0.12616010890165785, 0.5877072482048507, 0.9036715391034374, 1.05135115469293, 1.0256575744995529, 0.8398003810492772, 0.5240767689102169, 0.12282136935934011, -0.3102274645896599, -0.7177043796649821, -1.0449495202670807, -1.24621946822267, -1.2900796585501089, -1.163339002036433, -0.8730209397024283, -0.44606404460607396, 0.07330917755531016, 0.6283499943327966, 1.1562044358423007, 1.5953160096353278, 1.8929781569461113, 2.012144096333254, 1.9366442275085407, 1.674107973707171, 1.2561265462114197, 0.7355022525840681, 0.1807751997471781, -0.3314405231477338, -0.7254840696821953, -0.9360017371668172, -0.9164976583305608, -0.6459931456854581, -0.13288581555675655, 0.5845981982560744, 1.4415716280938733, 2.353044609884757, 3.223211089057699, 3.9564270458227893, 4.468584872755652, 4.697481152142729, 4.610842347612161, 4.210914847308186, 3.5349198120209047, 2.6511755807012882, 1.6512404781859706, 0.6389566915274228, -0.28228936325703735, -1.0224951085229474, -1.5164830757627348, -1.732319245927032, -1.6755217437414827, -1.3883949694560445, -0.9444551474720956, -0.438572035642286, 0.025950682258784934, 0.35168151951409465, 0.46084040195082976, 0.30665402460599683, -0.11933046078819577, -0.7850784129899415, -1.6214689697615676, -2.530922364465202, -3.400171676669497, -4.115488415587138, -4.5782840528291695, -4.71890699605232, -4.5066607047946645, -3.9545638968703036, -3.1180953488721763, -2.088015448817981, -0.9782138015108027, 0.08972917156529424, 1.0030713191781127, 1.6731391926014139, 2.0470276462967067, 2.1140309040207996, 1.9058336911151754, 1.4904201114112778, 0.9606122448457802, 0.4189840377851514, -0.03852304998685821, -0.3377250091911279, -0.4376673380073034, -0.33659508824637224, -0.07142107387794823, 0.28927966241750636, 0.6576733032844386, 0.9424926226688984, 1.0657049482615875, 0.9772436069032663, 0.6652725102833875, 0.1601246977201834, -0.4689467182170883, -1.1238953795664568, -1.6934180813551434, -2.071478613582234, -2.1758122874496855, -1.9632990032275808, -1.4395012934504527, -0.6605370320143129, 0.2733339703301649, 1.2316737362884735, 2.0733619292170453, 2.6686136185410745, 2.9199843015022857, 2.778874474064192, 2.254676955948711, 1.414839472865921, 0.3755700254050095, -0.7155405265197213, -1.7023231364348395, -2.444630245200602, -2.840703953678048, -2.8435594758902134, -2.46854555208515, -1.7906636303750187, -0.9319256942592372, -0.04072440541014823, 0.7334115721892988, 1.2654480884304922, 1.4764820607242162, 1.3476036441473938, 0.923469220158889, 0.3047999839302234, -0.36907447682862465, -0.9447561328921288, -1.2822407625129264, -1.28055078923072, -0.8970159044597208, -0.15670560438347242, 0.8498202929587447, 1.9802597780484616, 3.0636089324620595, 3.9286177841129537, 4.4327721959461215, 4.486749685462411, 4.070029759582245, 3.2348519739517902, 2.0977490478567447, 0.8200800076378917, -0.41904508053898254, -1.4526815661911612, -2.1535143227188267, -2.454006248718478, -2.355687826567479, -1.9260216113720752, -1.2835520138161565, -0.5742070838880988, 0.05674838132297877, 0.49181178741217746, 0.662294174094185, 0.5593892317072489, 0.23324626132869059, -0.21964762074527966, -0.6781951392424622, -1.023153390740957, -1.1630080746192295, -1.0540122121604198, -0.710262454213372, -0.2016384182684546, 0.3601531044301574, 0.8447758575005972, 1.1311226400142966, 1.134202986718499, 0.8254845455069627, 0.2422909563518609, -0.5160480014287737, -1.304985454807173, -1.9615535291345592, -2.336124755095516, -2.3229380366681696], 'positive_zeros': ['2.33334868929224427395091330294575', '4.20577787623093149001537846003574', '6.12102826221404966808036347563592', '7.72044003466933334126838454833574', '9.021338551592049019626468491322579', '10.72053389437073119308054892570020', '11.66066911363262985136183694527397', '12.73317948396254368454333845232608', '14.04201395914871787303614372155645', '14.77575474599426987437728614581852'], 'prelabel': '2-7e2-49.8-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.700321613778197, 'root_angle': 0.0384674164449779, 'root_number': '0.9927066480707847 + 0.12055501182475678*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0192337082225', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.33334868929224427395091330295', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.20577787623093149001537846004', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.12102826221404966808036347564', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2.8910935902812915, 'bad_primes': [7], 'central_character': '49.8', 'conductor': 49, 'conductor_radical': 7, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/49/4/e/a/8/9'], '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': '2-7e2-49.8-c3-0-6', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-7e2-49.8-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.700321613778197, 'root_angle': 0.01923370822248895, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.33334868929224427395091330295', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2957870866523065804060725416848', 'Lhash_array': ['2957870866523065804060725416848'], 'label': '2-7e2-49.8-c3-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/49/4/e/a/8/9'}