-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '597258145673657524998493275848', 'a10': [0.37496813740426005, 4.736909040896072], 'a2': [-1.1517061642892346, -0.8207148781021206], 'a3': [0.0, 0.0], 'a4': [0.6528541777236424, 1.8904447684682002], 'a5': [-2.159752420670196, -2.5738927064477477], 'a6': [0.0, 0.0], 'a7': [-1.784529114973131, 0.6495154800316293], 'a8': [0.7996199668458722, -2.71304402998208], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.174306050978972, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.1517061642892346, 0.8207148781021206]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '648.397', 'coefficient_field': 'CDF', 'conductor': 648, 'conductor_radical': 6, 'conjugate': '1426386814774173727198981000224', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.1517061642892346, 0.8207148781021206]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.159752420670196, 2.5738927064477477], [-0.8682408883346517, 4.924038765061041]], [[1.0, 0], [1.784529114973131, -0.6495154800316293], [5.362311101832846, -4.499513267805775]], [[1.0, 0], [3.219443369073442, -3.8367832012468814], [-1.9101299543362338, -10.832885283134289]], [[1.0, 0], [-3.6142433706238064, 0.6372886210876814], [12.216004070216808, -4.446261863233693]], [[1.0, 0], [-1.743795303763409, -3.0203420641182284], [-8.5, 14.722431864335457]], [[1.0, 0], [2.73085260311981, 1.5766584855284125], [9.5, 16.454482671904334]], [[1.0, 0], [-2.9342782670101664, -1.0679899482459165], [17.619022191736494, 14.784115022790404]], [[1.0, 0], [-6.616108314728441, -1.1665984031762364], [27.251086002791343, 9.918584156444393]], [[1.0, 0], [-0.8426387906850693, -0.30669543804743415], [23.747377736688318, 19.92641590028272]], [[1.0, 0], [-6.2148498379425625, 3.5881452269092406], [18.5, -32.04293994002423]], [[1.0, 0], [-0.34164934489122545, -1.9375897183659074], [-38.527397452222246, 14.022825876352417]], [[1.0, 0], [5.36405314530849, -6.392629606787664], [-7.466871639678005, -42.34673337952495]], [[1.0, 0], [2.6373272669867074, -0.9599086232017952], [36.00408882659197, -30.211017655267348]], [[1.0, 0], [0, -9.525362682899328], [-53.0, 0]], [[1.0, 0], [-6.136947878735891, -7.313729682046915], [-10.24524248234889, 58.10365742772028]], [[1.0, 0], [-2.9254008900666313, -8.037472888310523], [-46.728711030257664, 39.2100441908789]], [[1.0, 0], [-13.751158826022383, 2.4247003170350867], [62.95940559265586, -22.915349602819806]], [[1.0, 0], [1.5010935668646042, 2.5999703247242842], [-35.5, 61.48780366869514]], [[1.0, 0], [-0.4726626456472183, 0.8186757171009066], [-36.5, -63.21985447626402]], [[1.0, 0], [0.8032093541666215, -4.555226607632043], [-74.23571704208676, -27.01959132272783]], [[1.0, 0], [2.128031175300961, 0.3752293119943046], [77.9944875252304, 28.387671896030504]], [[1.0, 0], [-7.837121201259056, 13.574292105655918], [-44.5, -77.07626093681505]], [[1.0, 0], [-1.6861898249196186, -1.414881260184934], [16.843873233692243, 95.52635204218419]], [[1.0, 0], [6.128302384614808, 16.837372421319103], [-77.37048875501678, 64.92154857834048]], [[1.0, 0], [10.69733098729407, -8.976126486019743], [17.885762299693827, -101.43519856025743]], [[1.0, 0], [0, -12.351783895422084], [-107.0, 0]], [[1.0, 0], [0, -2.184684551951464], [-109.0, 0]], [[1.0, 0], [12.12104467419042, -10.170764115596516], [19.62224407636313, -111.28327609037952]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-648-216.133-c1-0-4', '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/648/2/t/a/397/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.5572120170077243, 0.45524765943231327, 0.3234135219222525, 0.15627356693070996, -0.05198394374303843, -0.30596546111043577, -0.6075576385911428, -0.9546333294502322, -1.34007083826275, -1.7511656741164543, -2.169524344729959, -2.5715351418956724, -2.9294941896857862, -3.2134206425815193, -3.39352481768012, -3.4432040265297066, -3.34234330975775, -3.080605403904905, -2.6603212337168776, -2.0985545783770188, -1.4279261805892045, -0.695853197290459, 0.03800731700625612, 0.7061327189009132, 1.2391177503118735, 1.5728094242791368, 1.6559053214792308, 1.457147772622256, 0.9711562780794324, 0.22196889973291717, -0.736472763576545, -1.8233618638463491, -2.937643387130851, -3.9677847892241496, -4.803786252766761, -5.35009295467649, -5.537787314206889, -5.334357570700711, -4.74950073563602, -3.8358300681206, -2.6839870656997933, -1.412432680947109, -0.15300556221870218, 0.9659400948595023, 1.8364957642035142, 2.3857516491847495, 2.5856356357451613, 2.4563257895335413, 2.062447622402879, 1.502394016932282, 0.8922592864073393, 0.3468602775964174, -0.039061369237121224, -0.20624172603348706, -0.14013161567395935, 0.1278304078098286, 0.5273463239822409, 0.9636982695905909, 1.336992487895735, 1.5626719288769677, 1.5893489019547518, 1.4103379374147218, 1.06632939610108, 0.6382795272625219, 0.2315170258774849, -0.04608826934469207, -0.10766431543458845, 0.09225163002234306, 0.5449061061143776, 1.1852869135589552, 1.9019332906329405, 2.5572436681525472, 3.0146027023892947, 3.1669529535321486, 2.9607794351467516, 2.4100775610092033, 1.5967000742892885, 0.6562185952021472, -0.2484437187728765, -0.9605116854738183, -1.3629855667693551, -1.4049133839252377, -1.113989651823926, -0.5918321972100685, 0.008025363083824674, 0.5154451778882473, 0.7849984632981762, 0.7340820791532874, 0.3687113354903719, -0.20996647963367399, -0.821462009536192, -1.242142198701966, -1.255094027553534, -0.7032553881655565, 0.4661183013418998, 2.1764894362484717, 4.223760885031685, 6.306327396857438, 8.078813543177665, 9.219232769858516, 9.495675485795848, 8.817957580413442, 7.262256391080922, 5.062204868307147, 2.567092831033466, 0.17515868687086017, -1.7442465116070092, -2.922987155892113, -3.245193311924303, -2.7657717517996643, -1.6923221527201282, -0.3346812663509858, 0.9662661784366182, 1.9141032509837883, 2.3193897981972786, 2.1350309736951685, 1.4569769810901285, 0.4911575998881937, -0.5042516621658922, -1.2862237805416685, -1.6867996916190204, -1.6506176440377107, -1.2411593548626263, -0.615108853424021, 0.02737412689154071, 0.5023533329241179, 0.6951489825057344, 0.592030949537859, 0.2818643717493353, -0.07261574412022316, -0.28569148530928157, -0.20717359584570735, 0.2283292845925351, 0.9758627521965139, 1.8862542434960723, 2.7429635099787175, 3.319884961499681, 3.4441093059806835, 3.04586406516216, 2.1811199524697518, 1.0198628718848215, -0.1972655122189838, -1.222110735861207, -1.864167597656425, -2.0391217966373447, -1.7866945776467344, -1.2525275931500124, -0.6394289111013711, -0.1425630386937679, 0.111702744168682, 0.10426931572056498, -0.07342569932339182, -0.2532792229276036, -0.2518657129547705, 0.059545744896771065, 0.6988360409499931, 1.5502039992233223, 2.3848103560174683, 2.922011442745329, 2.915303599833822, 2.238127101411259, 0.942708199716945, -0.7288152880140468, -2.3889661341333017, -3.5971238146253994, -3.976537526543919, -3.324402834930064, -1.6830733960242228, 0.6503889736625419, 3.1828758343670236, 5.339691630272, 6.606115604692331, 6.658611380731884, 5.449819554945602, 3.2233053720207705, 0.4530098467672634, -2.276823725440975, -4.418782611473676, -5.596358442591609, -5.688587601675439, -4.843068346171637, -3.4157353326231035, -1.8567304516240395, -0.5768792438913045, 0.1658327344215753, 0.3272287524673274, 0.0692748326557086, -0.31120790484731875, -0.49316121761100074, -0.2453700755705977, 0.49222117789131675, 1.5852802315977308, 2.746565928857833, 3.6281321443268286, 3.934265098972952, 3.51878957086361, 2.435622860476097, 0.9265951442360825, -0.6492941614461796, -1.9223438971537652, -2.620321574309616, -2.644202631962862, -2.0882734350382277, -1.199731328888269, -0.2926038457889741, 0.3546469673381406, 0.5838503382939444, 0.3969698414037744, -0.060341661835256924, -0.5634419488687368, -0.8971951801965098, -0.9360245714476806, -0.6868349852431755, -0.2797847415605909, 0.08908343889558748, 0.24163426909328767, 0.09607540027584256, -0.29041623148962004, -0.7328342917687535, -0.9817405357915155, -0.8177843200951203, -0.14350733747844577, 0.9623169896318098, 2.250853624067774, 3.372246001598386, 3.987227421986723, 3.8843860539187975, 3.061819691864051, 1.7420110662468666, 0.3104487641600583, -0.8052585577453384, -1.2772771130725393, -0.9925319444526495, -0.09966640505306756, 1.0316922769192434, 1.9297192121173024, 2.180218602342144, 1.574616146640489, 0.19486540320630757, -1.5966946392986292, -3.263452566322098, -4.264929285642619, -4.236741871417493, -3.120106966857933, -1.1957470096342564, 0.9923144612938473, 2.8011659226471872, 3.689722048698599, 3.3905693873117917, 1.9961186414683463, -0.07020843514051266, -2.1892605550038233, -3.744050716947326, -4.315444521962029, -3.8114835970269225, -2.4883770886321974, -0.8574759647519903], 'positive_zeros': ['0.47115360144674441090256775919529', '2.74334920218141633996696272597790', '3.65614627756699488639856983432354', '5.26593778036797746194138739939323', '6.48358145811990741147600995358249', '6.82491714778207266784735644429920', '8.096930372933873586135013926401437', '8.335401663262138933135439663187138', '9.713827079298190042205466483196302', '10.49827626562350420903863494368334'], 'prelabel': '2-648-216.133-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2747101026238425, 'root_angle': -0.07699584145622614, 'root_number': '0.8852434649168054 - 0.465127947797258*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0769958414562', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.47115360144674441090256775920', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.74334920218141633996696272598', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.65614627756699488639856983432', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 5.174306050978972, 'bad_primes': [2, 3], 'central_character': '216.133', 'conductor': 648, 'conductor_radical': 6, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/648/2/t/a/397/6'], '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': '2-648-216.133-c1-0-4', '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': '2-648-216.133-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2747101026238425, 'root_angle': -0.07699584145622614, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.47115360144674441090256775920', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '597258145673657524998493275848', 'Lhash_array': ['597258145673657524998493275848'], 'factors': ['2-648-216.133-c1-0-4'], 'label': '2-648-216.133-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/648/2/t/a/397/6'}