-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2994237056136119354555610954876', 'a10': [0.0, 0.0], 'a2': [0.8420220001241379, -1.1362213478486252], 'a3': [-0.21845504649703962, -1.7182192504625178], 'a4': [-0.5819979026138926, -1.9134467437984863], 'a5': [0.0, 0.0], 'a6': [-2.136221347848625, -1.1985651225510459], 'a7': [3.644264152356288, 0.0], 'a8': [-2.664154076302282, -0.9498858129911903], 'a9': [-2.9045547853199527, 0.7507073325037957], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.791024121276825, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8420220001241379, 1.1362213478486252]]], [3, [[1.0, 0], [0.21845504649703962, 1.7182192504625178]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '600.299', 'coefficient_field': 'CDF', 'conductor': 600, 'conductor_radical': 30, 'conjugate': '1204767370925943111602086429630', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8420220001241379, 1.1362213478486252]], [[1.0, 0], [0.21845504649703962, 1.7182192504625178]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.644264152356288, 0], [7.0, 0]], [[1.0, 0], [0, 5.074027394851169], [-11.0, 0]], [[1.0, 0], [-1.7059393943546175, 0], [13.0, 0]], [[1.0, 0], [4.081174245350367, 0], [17.0, 0]], [[1.0, 0], [-1.2642241792454045, 0], [19.0, 0]], [[1.0, 0], [0, -4.70066268017044], [-23.0, 0]], [[1.0, 0], [1.063767431210166, 0], [29.0, 0]], [[1.0, 0], [0, 4.869502665504143], [-31.0, 0]], [[1.0, 0], [-7.568295209359563, 0], [37.0, 0]], [[1.0, 0], [0, -1.5014146650075915], [-41.0, 0]], [[1.0, 0], [0, -3.4364385009250356], [-43.0, 0]], [[1.0, 0], [0, -10.91755646110937], [-47.0, 0]], [[1.0, 0], [0, 8.872877001850071], [-53.0, 0]], [[1.0, 0], [0, 0.7883284201537756], [-59.0, 0]], [[1.0, 0], [0, 0.627594479019433], [-61.0, 0]], [[1.0, 0], [0, 4.181780640354774], [-67.0, 0]], [[1.0, 0], [-6.21689378093893, 0], [71.0, 0]], [[1.0, 0], [0, 4.21689378093893], [-73.0, 0]], [[1.0, 0], [0, 0.9928531495008017], [-79.0, 0]], [[1.0, 0], [-7.725438397706656, 0], [83.0, 0]], [[1.0, 0], [0, 11.57422727940997], [-89.0, 0]], [[1.0, 0], [0, -7.401325360340881], [-97.0, 0]], [[1.0, 0], [10.153538213999166, 0], [101.0, 0]], [[1.0, 0], [-15.539959314034943, 0], [103.0, 0]], [[1.0, 0], [-14.870663857393811, 0], [107.0, 0]], [[1.0, 0], [0, 10.537583341696484], [-109.0, 0]], [[1.0, 0], [-9.943530060355313, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 64, 'label': '2-600-120.59-c1-0-64', 'load_key': 'CMFs-workshop', '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': 'ModularForm/GL2/Q/holomorphic/600/2/m/c/299/11', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.907862439757241, 2.1901311733713706, 2.4969767871238755, 2.829011673834195, 3.181580848951295, 3.5444571138947394, 3.902153778467421, 4.234699947869495, 4.518785709966895, 4.729246733267004, 4.84087485760716, 4.830513234828238, 4.679339555846727, 4.375177855048184, 3.9146233898035643, 3.304727791847601, 2.5639822051993773, 1.7223610828003433, 0.8202520434160678, -0.09380334246170435, -0.9665030689076368, -1.744109344451636, -2.377351412066699, -2.8264232471590627, -3.065504230028796, -3.0862044925469068, -2.899387637469575, -2.534958312630814, -2.0394155167171606, -1.471246333340259, -0.8945382525278611, -0.37148055359908183, 0.04533963352067556, 0.31980768978218793, 0.43728374801193254, 0.4068636626607476, 0.2603409987090839, 0.04775321476163935, -0.1700920366903336, -0.3312034117645079, -0.3827724206444755, -0.2907285290641876, -0.046864110802940555, 0.3278513384843254, 0.7846522511416885, 1.253237069434262, 1.6522818601371336, 1.9027920613216383, 1.9422472951413534, 1.7371547833157495, 1.2916717410457077, 0.6504220422634233, -0.10551905683372105, -0.8693776361133427, -1.5248587053833118, -1.9653340874684482, -2.112856329333655, -1.9335554460572226, -1.446328939744424, -0.7226983910025537, 0.1228421370801032, 0.950946591076635, 1.6212924744080481, 2.0181879809217325, 2.0732302792023596, 1.780519247878994, 1.2009996659984996, 0.45432920973324914, -0.3010411619510432, -0.8965448303131716, -1.185969005980609, -1.0756406322833976, -0.5462627541299716, 0.33844584365553465, 1.4388749583072766, 2.5620150294652713, 3.4958234738547542, 4.049363145238969, 4.091061823205572, 3.577348246691005, 2.565404927934424, 1.2066420081587954, -0.2787636749024983, -1.6420286864950748, -2.6531506091193187, -3.146193192033599, -3.0531340805967555, -2.418897139470749, -1.393803012941026, -0.20425399393111413, 0.8929124551648494, 1.6633090863674431, 1.9441732891281227, 1.679312915963434, 0.9320356903465252, -0.12720015938729032, -1.2562818716936905, -2.1928530216308575, -2.7107520998202173, -2.6692511348628005, -2.0442209135565124, -0.9341765308008897, 0.4603413155090949, 1.8796314257518323, 3.0604642775762323, 3.792036231875734, 3.959668920879078, 3.5664679791818257, 2.728264189859397, 1.6434104473348194, 0.5449183859406791, -0.35344465076904846, -0.904146154493899, -1.0548499144411514, -0.8528155409773931, -0.42441798563218247, 0.06423817138172487, 0.4548693807423888, 0.6399967828794246, 0.5899671667952933, 0.35697553579866653, 0.05532802204134881, -0.17627410899572513, -0.2196024239354508, -0.015954521043229537, 0.4121438161654124, 0.9634150082899394, 1.4845311852421197, 1.8140616117148793, 1.8313872009605925, 1.4963041685579337, 0.8670604299789578, 0.09023235350289913, -0.6362718083148362, -1.117834741592858, -1.2203656377144223, -0.9133491208880943, -0.28486592451440595, 0.4780921925978519, 1.1410861022644263, 1.4930711648049164, 1.4175787867333662, 0.9434774823873511, 0.25858204642764104, -0.3215677294784207, -0.4255418068802168, 0.277371128899169, 1.9797309093685014, 4.66377511781597, 8.075794017223597, 11.75748837260851, 15.130457600108583, 17.615911937793406, 18.76168029624838, 18.345466527102246, 16.428206716857833, 13.343279160472095, 9.623260834698769, 5.881762599483371, 2.679376843792213, 0.4067822801978479, -0.7866025054194075, -1.0021645053828647, -0.5399644663044189, 0.19878708017112362, 0.8268373387469272, 1.0720380080720524, 0.8380102378232075, 0.21008631049046358, -0.5917417254344361, -1.2960832558668582, -1.6730284774727069, -1.608267815334161, -1.1367166974351353, -0.42689505944991774, 0.27733624195204704, 0.7380278776521443, 0.8009378262557094, 0.44493810855123017, -0.21259074691057667, -0.9558171166986258, -1.5427992566465536, -1.7865181168438682, -1.6180996941464638, -1.1113132318795291, -0.4598199844065065, 0.08605305339171793, 0.3029078976258575, 0.07109914641555874, -0.5806992396066333, -1.4786902494225815, -2.35517145980378, -2.93234431693298, -3.0122428562416714, -2.543615704528644, -1.643335368263227, -0.5641293250773136, 0.3823119095512503, 0.9230433649983792, 0.9112232072472122, 0.37457901354278345, -0.4915401924979085, -1.3853335698476732, -1.9949978660865655, -2.099564408261397, -1.6411660292599441, -0.7445344750867569, 0.323503015800538, 1.241990724742697, 1.7426664313929083, 1.7001156155677117, 1.1745493349740994, 0.3917694769263394, -0.334199747393909, -0.710645838940136, -0.5709265963704683, 0.06208398076700045, 0.9775114350295709, 1.8451300676227542, 2.330200536419176, 2.216576197953886, 1.4953547031759349, 0.38589308951629037, -0.7226753136091121, -1.3948273182894093, -1.2994081054351403, -0.3386674366702074, 1.2893123671998765, 3.120372740816598, 4.54308745141757, 4.974423212216938, 4.040122320668315, 1.703723022077442, -1.6980093275292085, -5.527716913356646, -9.009528520883261, -11.43400094424836, -12.345551289896724, -11.65698891600213, -9.658091990291833, -6.91782398014118, -4.112328788898142, -1.8328731166345922, -0.4324480628436541, 0.04443882469912174, -0.1677437472650715, -0.6688539885104005, -1.0480995993213653, -1.027298515927302, -0.5456283803387812, 0.23879724969035865, 1.025666543729223, 1.4959904579955745, 1.4361326433850397, 0.818003102760508, -0.19149658918735865, -1.2923399769683628], 'positive_zeros': ['2.36203655454983665483009812217664', '3.98421460625580394937876385019241', '4.65142582409321561082516692382721', '5.26804044053297538820062939500924', '6.48304971966589660918948127964656', '7.48218079169907086853778604587053', '8.448544629183750854656932267921975', '9.081825078249147466951913158599384', '10.22639247822971483265082463290640', '11.14669970474609071683079889919269'], 'prelabel': '2-600-120.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.188840816797061, 'root_angle': 0.921180886673705, 'root_number': '-0.9694990995507714 + 0.24509487136666777*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.460590443337', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.36203655454983665483009812218', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.98421460625580394937876385019', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.65142582409321561082516692383', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.791024121276825, 'bad_primes': [2, 3, 5], 'central_character': '120.59', 'conductor': 600, 'conductor_radical': 30, 'degree': 2, 'index': 64, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/600/2/m/c/299/11'], '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': '2-600-120.59-c1-0-64', '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': '2-600-120.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.188840816797061, 'root_angle': 0.4605904433368525, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.36203655454983665483009812218', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2994237056136119354555610954876', 'Lhash_array': ['2994237056136119354555610954876'], 'label': '2-600-120.59-c1-0-64', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/600/2/m/c/299/11'}