-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3157662669977943260482578928183', 'a10': [1.1887912389152873, 0.6863489417980099], 'a2': [0.0, 0.5462082665232075], 'a3': [-0.761913847326238, -1.5554701184055353], 'a4': [1.7016565295817128, 0.0], 'a5': [1.256570037225623, -2.1764431477434942], 'a6': [0.8496106370029358, -0.4161636417880923], 'a7': [-0.6127048635947892, -2.573828422822176], 'a8': [0.0, 2.0218753962871396], 'a9': [-1.83897457850506, 2.370268444630721], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.761913847326238, 1.5554701184055353]]], [7, [[1.0, 0], [0.6127048635947892, 2.573828422822176]]], [13, [[1.0, 0], [-1.897155475711012, -3.066072585732393]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.68', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': '1435246786164929153148912230900', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -0.5462082665232075], [-2.0, 0]], [[1.0, 0], [0.761913847326238, 1.5554701184055353]], [[1.0, 0], [-1.256570037225623, 2.1764431477434942], [-2.5, -4.330127018922194]], [[1.0, 0], [0.6127048635947892, 2.573828422822176]], [[1.0, 0], [5.22008309734271, 3.013816381443029], [5.5, 9.526279441628825]], [[1.0, 0], [-1.897155475711012, -3.066072585732393]], [[1.0, 0], [0.6473027531457587, 0], [17.0, 0]], [[1.0, 0], [-1.9880055799631011, 1.1477755567421746], [9.5, -16.454482671904334]], [[1.0, 0], [0, -1.033311258771008], [-23.0, 0]], [[1.0, 0], [-4.462554575815039, 2.576457085620209], [14.5, -25.11473670974872]], [[1.0, 0], [-9.257454654343174, 5.344793936695786], [15.5, -26.846787517317598]], [[1.0, 0], [3.955324002025386, 0], [37.0, 0]], [[1.0, 0], [-4.486892915613254, -7.77152649796301], [-20.5, 35.50704155516198]], [[1.0, 0], [4.099508919421539, -7.100557734519891], [-21.5, -37.239092362730865]], [[1.0, 0], [-2.0964620689094446, 3.631178819492123], [-23.5, -40.703193977868615]], [[1.0, 0], [-0.040651684252936054, 0.023470260846444303], [26.5, -45.89934640057525]], [[1.0, 0], [1.6622964634235526, 0], [59.0, 0]], [[1.0, 0], [3.111423642484321, -1.7963812775512888], [30.5, -52.827549630850754]], [[1.0, 0], [0.7612537758282957, -1.3185302171882567], [-33.5, -58.023702053557386]], [[1.0, 0], [-11.472911244856327, -6.6238883956064845], [35.5, 61.48780366869514]], [[1.0, 0], [-4.768346887300584, 2.7530063589725065], [36.5, -63.21985447626402]], [[1.0, 0], [2.147961429482197, -3.720378328561439], [-39.5, -68.41600689897065]], [[1.0, 0], [11.881561672820558, 0], [83.0, 0]], [[1.0, 0], [-1.0155371924769347, 0], [89.0, 0]], [[1.0, 0], [8.58147398148515, 4.954516313254222], [48.5, 84.00446416709055]], [[1.0, 0], [-2.6586410688475195, 4.604901410333129], [-50.5, -87.4685657822283]], [[1.0, 0], [-2.4143876378139493, -1.3939473526199884], [51.5, 89.20061658979718]], [[1.0, 0], [0, -19.224057774954186], [-107.0, 0]], [[1.0, 0], [3.025369286042618, 5.240093315084194], [-54.5, 94.39676901250381]], [[1.0, 0], [7.42599080292555, 4.287397789068751], [56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 28, 'label': '2-273-273.68-c1-0-28', '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/273/2/r/b/68/18', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.3282096605064848, 1.4344498414906441, 1.5497713283884802, 1.6738987122559963, 1.8038614663541341, 1.9343116016242536, 2.058016749791707, 2.1664277657940523, 2.250282905625255, 2.3002524826246047, 2.307637565283114, 2.2651234832514753, 2.167566319638083, 2.0127668205380904, 1.8021659932936651, 1.5413827790826646, 1.240508457586985, 0.9140763975422235, 0.580640506240023, 0.26192163727061585, -0.018482372807812848, -0.2367824228136745, -0.3709889339495639, -0.403066614458937, -0.32106727158484644, -0.12102197806434656, 0.19164036447950641, 0.6013713167138389, 1.0826640188694032, 1.6012173956532054, 2.11613215307072, 2.58305625902844, 2.958077258137658, 3.202042353757624, 3.2848899126972064, 3.18951341687749, 2.9146646571427928, 2.4764469484743286, 1.9080551538381525, 1.2575835525325505, 0.5839328913276716, -0.048916036744332723, -0.578760292040856, -0.9524599871202655, -1.1328083270503648, -1.104097063290464, -0.8755511158596605, -0.48198574693289176, 0.018673304797402507, 0.5509972476029876, 1.0303689705226988, 1.3731839995026567, 1.507782593723886, 1.3847453461695862, 0.985137446453623, 0.3254302214732166, -0.5418367379669079, -1.5320909903414153, -2.537290486623008, -3.4382046823066212, -4.119020910878228, -4.482449295808458, -4.463291829764682, -4.038511524207603, -3.232199846547769, -2.1144656586367745, -0.7940838794704954, 0.5943616938341905, 1.9072606975006374, 3.01044114899374, 3.796713781047322, 4.199910715760029, 4.203253679658399, 3.8406688746420508, 3.19070661956026, 2.3638710971544494, 1.4852374318307062, 0.6750481334987509, 0.03038776642782705, -0.389058122193607, -0.568758206806434, -0.5392432502147991, -0.36812403526011067, -0.1455581525701046, 0.03429286164116832, 0.09247512742193051, -0.018448169750105575, -0.30414801646753997, -0.7264849095724527, -1.2103479691838603, -1.6583919479754898, -1.9711196164728997, -2.0685908677291853, -1.9095197710585061, -1.5037855070892656, -0.9154306499843308, -0.25489831862668916, 0.3387155525895, 0.7226168564752661, 0.7781079077561169, 0.4360139174614043, -0.3053486450579315, -1.3736369993865192, -2.629399416432158, -3.8859973321190444, -4.9395590679380295, -5.6038993382168005, -5.744114600865645, -5.302498176639361, -4.311586983569689, -2.891388084870181, -1.2307496258853448, 0.44410859272452813, 1.908306082414917, 2.977076621096289, 3.537216487195179, 3.565067883813219, 3.1274231471781406, 2.365065524060213, 1.4621474079223138, 0.6075349357079256, -0.044007449654201954, -0.4027620257297427, -0.4606199294915348, -0.28967685522939113, -0.023044212015778272, 0.1781163124138065, 0.16425962683267883, -0.16487032030525375, -0.8330319161582432, -1.7771229789661278, -2.8564899669538724, -3.880443108080587, -4.648403706902739, -4.994104513050053, -4.824068847248058, -4.141541164413891, -3.049996659327034, -1.7347305337608634, -0.42588708265110137, 0.6494420677819611, 1.3157265681832875, 1.487332675170978, 1.1878674778242635, 0.5457305222766888, -0.2337045931283858, -0.9135763697015076, -1.2788557197634607, -1.1856637989970495, -0.5953966729358272, 0.4143142428089319, 1.6646579333339304, 2.913684654236942, 3.9089996083727168, 4.443303919598222, 4.400182015606986, 3.7796573497639576, 2.697635625252396, 1.3593849321362876, 0.013259342284720288, -1.104486092958887, -1.8208471602564738, -2.0612397103431968, -1.8606148174565424, -1.3483026643083333, -0.7107869002949558, -0.14201730353546638, 0.20609396334723465, 0.2604683892735247, 0.04171694602677403, -0.3465041342708709, -0.7505556082569973, -1.0132941115849017, -1.0213164173001348, -0.7399379674186206, -0.2259443970833376, 0.3860397203985799, 0.9206309530381415, 1.212744193352629, 1.1589244267361283, 0.7545382689708185, 0.10554648273640627, -0.5901097691874744, -1.088527682111512, -1.162734845913197, -0.6667869640023654, 0.415850399700346, 1.9534207855907832, 3.683375845697498, 5.264097208778221, 6.349780364446991, 6.67097077147763, 6.101021374979497, 4.6914864953865365, 2.666651961139873, 0.37732371520094216, -1.7758138120702376, -3.4311205760018444, -4.345653460919868, -4.44601588054443, -3.8379106602054063, -2.772238916423224, -1.576598436491247, -0.5698659432524538, 0.01813682076613152, 0.1012791001123784, -0.24777004515645212, -0.825345019168621, -1.3595182850320158, -1.5905184896696465, -1.3469103764182508, -0.5968206173767755, 0.539708353379384, 1.8205717582265464, 2.945486771332419, 3.636427905117064, 3.7125994409073217, 3.139437249884707, 2.0382934256048593, 0.654315829578044, -0.7084115491531092, -1.7663739844562925, -2.3287216128582697, -2.3421366550758784, -1.8964801358773946, -1.1904405484282778, -0.46782316089243314, 0.05653661402238569, 0.25940083873485736, 0.14196473107365662, -0.17654991239974913, -0.5022832318521114, -0.6337236624105788, -0.4316655209201125, 0.12964413999605645, 0.9465722294918683, 1.811349126308942, 2.4719952751434735, 2.709592643792624, 2.4096801647700183, 1.6055036477972149, 0.4785550112686154, -0.6858115138552342, -1.5764497209136035, -1.9463814714690704, -1.6884212790468711, -0.8734600508097787, 0.26144192556505924, 1.3737051809675696, 2.1088417154025394, 2.201103269463638, 1.5524072232751924, 0.2662761097079253, -1.3740513195634227, -2.978319431766865, -4.153031976643339, -4.6073426747882085], 'positive_zeros': ['2.49095663222139737807598242096424', '3.17862935720565567065456974106426', '5.11473035873486468141401519990546', '5.99559221975512183480252527856511', '6.92490329518123810391948277662452', '8.321410699480761795509515624810135', '9.757142587515229333789836830530450', '10.47026433678583017906240785368801', '10.73802193476037886903900774687827', '12.05024717876947192707935955791167'], 'prelabel': '2-273-273.68-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': 0.39255745650177737, 'root_number': '0.3311675744743136 + 0.9435719567774362*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.196278728251', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.49095663222139737807598242096', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.17862935720565567065456974106', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.11473035873486468141401519991', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'bad_primes': [3, 7, 13], 'central_character': '273.68', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 28, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/2/r/b/68/18'], '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': '2-273-273.68-c1-0-28', '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': '2-273-273.68-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': 0.19627872825088868, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.49095663222139737807598242096', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3157662669977943260482578928183', 'Lhash_array': ['3157662669977943260482578928183'], 'label': '2-273-273.68-c1-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/2/r/b/68/18'}