-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '50870598945702306441238226273', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.3826834323650898, 0.9238795325112867], 'a8': [0.0, 0.0], 'a9': [-0.3826834323650898, -0.9238795325112867], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.7886490052766808, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0.3826834323650898, -0.9238795325112867]]]], 'bad_primes': [2, 7], 'central_character': '3584.2785', 'coefficient_field': 'CDF', 'conductor': 3584, 'conductor_radical': 14, 'conjugate': '2463276397225590985965498443766', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0.3826834323650898, 0.9238795325112867]], [[1.0, 0], [0, 0], [0.9238795325112867, 0.3826834323650898]], [[1.0, 0], [0.3826834323650898, -0.9238795325112867]], [[1.0, 0], [1.6309863136978342, -1.0897902135516373], [0.3826834323650898, -0.9238795325112867]], [[1.0, 0], [0, 0], [0.9238795325112867, -0.3826834323650898]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0, 0], [-0.9238795325112867, 0.3826834323650898]], [[1.0, 0], [-0.7071067811865476, 0.2928932188134525], [0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [0.32442334882145774, 0.21677275132473922], [0.3826834323650898, 0.9238795325112867]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [1.6309863136978342, 0.32442334882145774], [0.9238795325112867, 0.3826834323650898]], [[1.0, 0], [0, 0], [-0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [0.9238795325112867, 1.3826834323650898], [-0.3826834323650898, 0.9238795325112867]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0.9238795325112867, -0.6173165676349103], [0.3826834323650898, -0.9238795325112867]], [[1.0, 0], [0, 0], [0.9238795325112867, 0.3826834323650898]], [[1.0, 0], [0, 0], [0.3826834323650898, 0.9238795325112867]], [[1.0, 0], [0.6173165676349103, -0.9238795325112867], [-0.3826834323650898, -0.9238795325112867]], [[1.0, 0], [0.541196100146197, -1.3065629648763766], [-0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [0, 0], [0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [1.3065629648763766, 1.3065629648763766], [0, 1.0]], [[1.0, 0], [0, 0], [-0.9238795325112867, 0.3826834323650898]], [[1.0, 0], [0, 0], [-0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-0.9238795325112867, -0.3826834323650898]], [[1.0, 0], [0, 0], [-0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [-0.6173165676349103, -0.9238795325112867], [-0.3826834323650898, 0.9238795325112867]], [[1.0, 0], [-1.9238795325112867, 0.3826834323650898], [0.9238795325112867, -0.3826834323650898]], [[1.0, 0], [-0.541196100146197, -0.541196100146197], [0, 1.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-3584-448.293-c0-0-0', 'leading_term': '0.076223081078838180860265345651112', '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/3584/1/bf/b/2785/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.07622308107883818, -0.020243810743305325, -0.11774778138712863, -0.21841162673594247, -0.32397144186003674, -0.4356568445703877, -0.5541301718533567, -0.6794752851892978, -0.811220581006996, -0.9483815152032677, -1.089512073253605, -1.2327592173365225, -1.3759179125083152, -1.5164865342944651, -1.651723521842979, -1.7787064381629007, -1.8943944523555327, -1.9956948870673363, -2.079534009459371, -2.142931758970015, -2.183079638828196, -2.197420571251969, -2.183729140438398, -2.1401903310133386, -2.065474619408871, -1.958807098041368, -1.820028213181965, -1.6496436824269443, -1.4488612310211817, -1.21961195076678, -0.9645543416674238, -0.6870594432063626, -0.39117589486174587, -0.08157427674844572, 0.23652933938306261, 0.5574700648425459, 0.8752498590615317, 1.1836702601302054, 1.4764795700251305, 1.7475312251849038, 1.9909494766871472, 2.2012979752141537, 2.373746428934708, 2.5042302005852433, 2.589597554173194, 2.6277392691965997, 2.617695524061065, 2.5597353182374447, 2.455404256434882, 2.307537252913747, 2.1202336183578363, 1.898793046721501, 1.649612199464593, 1.38004285731935, 1.0982139370423352, 0.8128210094079846, 0.5328882582206412, 0.26750903936548726, 0.02557228436044408, -0.18451710370433325, -0.3551150375134005, -0.47960298213735725, -0.5526312965694656, -0.5703320486439869, -0.5304927209666997, -0.4326831125683675, -0.27832895486720666, -0.0707272769803044, 0.18499966284366273, 0.4820130657259757, 0.811927935329036, 1.1650418760854535, 1.5306169083174124, 1.8972067032352973, 2.25301964771939, 2.5863064063605643, 2.885759236770809, 3.1409093058909003, 3.342507710656227, 3.4828758720326065, 3.556211475807823, 3.5588371857097543, 3.48938094233136, 3.348878750931534, 3.140793396523682, 2.8709454289462366, 2.54735593804853, 2.180003977802263, 1.7805048736850875, 1.3617189276635855, 0.9373030840994975, 0.5212208049195689, 0.12722759852473386, -0.23164875699149576, -0.5436133517255731, -0.7985745544409413, -0.9885602632201304, -1.108062028584344, -1.1542913300713646, -1.12733526139393, -1.0302024871688515, -0.8687544532229236, -0.6515213128734879, -0.38940670148422885, -0.09529016337090913, 0.21645948730016712, 0.5305425030492257, 0.831337360473882, 1.1035371043704738, 1.332787383943556, 1.506299836958725, 1.6134147141540396, 1.6460879894848197, 1.5992806552300056, 1.4712313892218847, 1.2635981910166645, 0.9814597561621802, 0.6331730943598997, 0.2300899670220563, -0.21385913250640393, -0.6826987752247756, -1.1590399910243174, -1.6247843055823863, -2.061871642534483, -2.4530406517525214, -2.7825686789921154, -3.0369586666489345, -3.205541812519115, -3.280967790717479, -3.259558667007342, -3.1415081653614703, -2.9309144488091654, -2.6356417980357008, -2.267014196114497, -1.839351518251009, -1.369366428170519, -0.8754468461543995, -0.37685464443711025, 0.10712425478187382, 0.5580402033967479, 0.959111102175002, 1.2959856726298933, 1.5574021309050246, 1.7357098082170574, 1.8272270364442345, 1.8324157964346424, 1.755861906556055, 1.6060585436522934, 1.39500022507626, 1.1376035980001553, 0.8509800325176425, 0.5535926641977416, 0.2643367818092244, 0.0015869657498306835, -0.21774311348665545, -0.3790820045625883, -0.47097859045776114, -0.48573685474775957, -0.41987336028804023, -0.27437153239792583, -0.05471633246774132, 0.2292965696305009, 0.5639719626273519, 0.9323303925217067, 1.3149008980479089, 1.6906550996392988, 2.038038766457912, 2.336051220966506, 2.5653195418013284, 2.709113721492206, 2.75425082796206, 2.6918407749855415, 2.5178333572369986, 2.2333354485507333, 1.8446782758008387, 1.3632269420486567, 0.804937280723915, 0.1896780288638482, -0.4596514526099885, -1.1181667558780461, -1.760157122484203, -2.3603004720490275, -2.8948741752180265, -3.3429002449753535, -3.6871660481253614, -3.9150671693153964, -4.019227466176546, -3.9978622518123026, -3.8548634053873245, -3.599599402454099, -3.2464380488193516, -2.8140143222552716, -2.3242793946852762, -1.801378877270474, -1.2704179309039352, -0.7561775569530701, -0.2818497156344132, 0.1321413281469065, 0.4691679108350563, 0.7172219738493493, 0.8694865270525629, 0.924623085430134, 0.8867577080032721, 0.7651645570031617, 0.5736624860998581, 0.3297561532371429, 0.05356764565587806, -0.23338322406672848, -0.5094826558619997, -0.7543377976800727, -0.9500284681031007, -1.0822238061430534, -1.1410985952465456, -1.1219943750778765, -1.0257840678105485, -0.8589150002550759, -0.6331230373728878, -0.36482908332113656, -0.07424742100788577, 0.21574778369992342, 0.48093696865588664, 0.6971784908787448, 0.8418611906198575, 0.8953035964770732, 0.8420187777231324, 0.6717700959045344, 0.3803537123081159, -0.02994185660768283, -0.5502313340715074, -1.1652959896950972, -1.8542065425016725, -2.5912769939038554, -3.347301480145802, -4.0910094231338565, -4.790660888109564, -5.415694952066081, -5.9383396417334104, -6.335092936722922, -6.5879904792691, -6.685586711902136, -6.623591611430168, -6.405124170791823, -6.040565248367712, -5.547015143329925, -4.947383957507219, -4.269164142166161, -3.542953334278816, -2.800810528556969, -2.0745388805611524, -1.3939933274126666, -0.7855103880783849, -0.2705509406337189, 0.13536521399669518, 0.42337095912600703, 0.591568204019309, 0.6449307875646324, 0.5948003326229079], 'positive_zeros': ['0.04012982673344177023518815895654', '1.68889835546375257805968472714258', '2.95107037858127961539664201829828', '3.41732769081169518564636350730557', '4.68923058375528641411177510176890', '5.29696469899440133083283734571212', '6.01897764665087254095402628712102', '6.99633614331423540647865670870999', '7.76986214010241196719825771541986', '8.135665737138150986015284509213308'], 'prelabel': '2-3584-448.293-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3374038302908664, 'root_angle': 0.9687500000000001, 'root_number': '-0.99518472667219688624483695310913 + 0.098017140329560601994195563888964*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.484375', 'prec': 27}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.04012982673344177023518815896', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.68889835546375257805968472714', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.95107037858127961539664201830', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.7886490052766808, 'bad_primes': [2, 7], 'central_character': '448.293', 'conductor': 3584, 'conductor_radical': 14, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3584/1/bf/b/2785/1'], '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': '2-3584-448.293-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': '2-3584-448.293-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3374038302908664, 'root_angle': 0.48437500000000006, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.04012982673344177023518815896', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '50870598945702306441238226273', 'Lhash_array': ['50870598945702306441238226273'], 'label': '2-3584-448.293-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3584/1/bf/b/2785/1'}