-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1355878984213763109617748470659', 'a10': [-2.1213203435596424, -1.224744871391589], 'a2': [-0.8660254037844386, 0.5], 'a3': [0.0, 0.0], 'a4': [0.5, -0.8660254037844386], 'a5': [1.224744871391589, 2.1213203435596424], 'a6': [0.0, 0.0], 'a7': [-1.0, -2.449489742783178], 'a8': [0.0, 1.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.0183451964044, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.8660254037844386, -0.5]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.0, 2.449489742783178]]]], 'bad_primes': [2, 3, 7], 'central_character': '378.269', 'coefficient_field': 'CDF', 'conductor': 378, 'conductor_radical': 42, 'conjugate': '1985071011582033146955489390167', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.8660254037844386, -0.5]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.224744871391589, -2.1213203435596424], [-2.5, 4.330127018922194]], [[1.0, 0], [1.0, 2.449489742783178]], [[1.0, 0], [-3.6742346141747673, -2.1213203435596424], [5.5, 9.526279441628825]], [[1.0, 0], [0, -4.1815405503520555], [-13.0, 0]], [[1.0, 0], [-1.224744871391589, 2.1213203435596424], [-8.5, -14.722431864335457]], [[1.0, 0], [-4.242640687119285, 2.449489742783178], [9.5, -16.454482671904334]], [[1.0, 0], [5.196152422706632, -3.0], [11.5, -19.91858428704209]], [[1.0, 0], [0, -10.242640687119286], [-29.0, 0]], [[1.0, 0], [-4.863961030678928, -2.8082092103903284], [15.5, 26.846787517317598]], [[1.0, 0], [-1.6213203435596426, -2.8082092103903284], [-18.5, 32.04293994002423]], [[1.0, 0], [-2.449489742783178, 0], [41.0, 0]], [[1.0, 0], [-7.0, 0], [43.0, 0]], [[1.0, 0], [3.9714075513150426, 6.878679656440357], [-23.5, 40.703193977868615]], [[1.0, 0], [2.1523168056429025, 1.2426406871192852], [26.5, 45.89934640057525]], [[1.0, 0], [1.224744871391589, -2.1213203435596424], [-29.5, -51.09549882328188]], [[1.0, 0], [0.6213203435596426, -0.3587194676071504], [30.5, -52.827549630850754]], [[1.0, 0], [-1.7426406871192852, 3.018342209427341], [-33.5, -58.023702053557386]], [[1.0, 0], [0, 12.727922061357855], [-71.0, 0]], [[1.0, 0], [13.242640687119286, 7.64564216548981], [36.5, 63.21985447626402]], [[1.0, 0], [4.621320343559643, 8.004361633096961], [-39.5, 68.41600689897065]], [[1.0, 0], [-5.493325359846907, 0], [83.0, 0]], [[1.0, 0], [8.870387036881398, 15.363961030678928], [-44.5, 77.07626093681505]], [[1.0, 0], [0, 6.631030293135233], [-97.0, 0]], [[1.0, 0], [-3.6742346141747673, 6.363961030678928], [-50.5, -87.4685657822283]], [[1.0, 0], [-5.378679656440357, 3.1053821475306043], [51.5, -89.20061658979718]], [[1.0, 0], [12.544621651056167, -7.242640687119285], [53.5, -92.66471820493493]], [[1.0, 0], [3.8639610306789276, -6.692576823602108], [-54.5, -94.39676901250381]], [[1.0, 0], [0, 1.7573593128807148], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-378-21.17-c1-0-1', '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/378/2/k/d/269/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.120539301128421, 1.0527405921914184, 0.977926526118066, 0.891564759737718, 0.7882377024762987, 0.6627584711819334, 0.5111934076978567, 0.33171289735982307, 0.12525249877523198, -0.10402095970390832, -0.348458946342865, -0.5969364025266921, -0.8351616721701584, -1.046334383359701, -1.2121733621609871, -1.3143025580453982, -1.3359393015710654, -1.2637805007470417, -1.0899342085911017, -0.8137028860006957, -0.4429976468802558, 0.0048434374539232826, 0.5030397158112504, 1.0163118512102811, 1.5028623209015766, 1.9173638989561106, 2.21480404123057, 2.3549042847594377, 2.30671534171839, 2.052898059920809, 1.5931550941662251, 0.9462924292793842, 0.15047281144192295, -0.7386241421798749, -1.6518061929694094, -2.5123508618284878, -3.2435070607888545, -3.77680365418056, -4.060256068588222, -4.065458110566999, -3.792562945663436, -3.2723098965127995, -2.5645401182646856, -1.75304230929813, -0.9370378933557777, -0.22009586855268778, 0.3023067054380348, 0.5550601160913756, 0.4938943421880092, 0.1125095962391489, -0.5548427405977014, -1.4359990310394966, -2.428726883255193, -3.413012890084249, -4.266337038352361, -4.879938476229245, -5.173797175093391, -5.1081005760939755, -4.689355203701297, -3.970008091519153, -3.0413749815533095, -2.020699453079191, -1.0341294872686173, -0.19813225739851245, 0.39776470644846196, 0.704105578480578, 0.7182713967480436, 0.483608072763647, 0.08088709683315717, -0.38661875529533873, -0.8120035182058987, -1.1043090341617505, -1.205332605190745, -1.100534277689838, -0.8218639338140057, -0.4417263279433006, -0.058919874737198875, 0.22106649212280877, 0.3078310975261132, 0.1457750344184248, -0.2721899892897813, -0.899922946632882, -1.6437070474937363, -2.3776974937219797, -2.966623365086717, -3.2916281722117486, -3.2742824163109288, -2.8938908159937036, -2.1942890739697316, -1.278227026503062, -0.2898347176591278, 0.6118909394151101, 1.283654789530071, 1.626467926691794, 1.6063467336239317, 1.2624748339095138, 0.700543404026802, 0.07194590208709052, -0.4575033945914337, -0.7432578758701457, -0.6948011381999859, -0.29836032287068204, 0.3758230658264283, 1.184081983611156, 1.9365245272048095, 2.435985383252625, 2.521080885421373, 2.1044074599348064, 1.1974509598573349, -0.08386471297132443, -1.5352718492001407, -2.8996978127173416, -3.9158083524449294, -4.370040169710155, -4.141423600291854, -3.229551868166275, -1.7592243603482873, 0.04001663332967619, 1.8759801331602137, 3.449380224515679, 4.511591619716969, 4.912608044682919, 4.629050973422724, 3.7661842485258976, 2.533414585675089, 1.1985060832324863, 0.030426725309510152, -0.7567042991118167, -1.0463116442628957, -0.8394261698537908, -0.24795902741236292, 0.536854939674842, 1.2931833666593109, 1.8228766610633111, 1.9984380028035305, 1.7916088672516721, 1.2769393718109205, 0.6097769901345337, -0.015654075476689643, -0.417515871090037, -0.47406485483023747, -0.15575604530371254, 0.4664415847901888, 1.2387397327331922, 1.9638582948068954, 2.4520326463939672, 2.570630347093432, 2.2794931474324716, 1.6426296369181275, 0.8128827559904972, -0.006813339763837989, -0.6157856196283852, -0.8680328773178623, -0.710874665972115, -0.1993883158869356, 0.5176016166226222, 1.2367284930984914, 1.7544240684781158, 1.9220472266319837, 1.6869069224819122, 1.1077391991370187, 0.3398462912720475, -0.4067475495678978, -0.9252845660697541, -1.0708047517883226, -0.8029729863604707, -0.20075393565771063, 0.5561449199390647, 1.2350893444536903, 1.6153081360029924, 1.552119537121851, 1.0224438277876426, 0.1378461438560725, -0.8802368596524742, -1.7581496674629284, -2.246207956631761, -2.193189152975492, -1.5982848604129543, -0.6247747725008864, 0.43066094588674014, 1.2072981110856293, 1.3719316119144196, 0.7093976649908933, -0.8119854997596755, -3.018451921712635, -5.5598951635747325, -7.984445168645232, -9.840793407203334, -10.782813949453967, -10.64988815829522, -9.502258067456834, -7.602259372651483, -5.346404400525329, -3.1662112790024217, -1.4238783348841701, -0.3300946695918713, 0.09492696160042355, 0.00805227667056652, -0.31727078292735456, -0.5804589631002236, -0.5462917129514907, -0.11412298910951496, 0.6555234279679711, 1.5638386759352534, 2.338588011055672, 2.7212920369750546, 2.5506620146326, 1.8174079675276549, 0.6739993929897616, -0.6037590696026887, -1.692251974286905, -2.310612698829452, -2.2997711448405957, -1.6668093707438518, -0.5816915226534525, 0.6724668127988869, 1.7806732275824262, 2.4846795495754512, 2.652745504504416, 2.310232742304794, 1.6227365941576695, 0.8379606335046305, 0.20508011128157538, -0.10294250951818068, -0.03983352713234054, 0.3061902443473473, 0.7490940825095314, 1.0736999590818368, 1.1135266415597425, 0.811850158908631, 0.24528674345925436, -0.3987375348978899, -0.8841411777131238, -1.0081096615778633, -0.6757007600745479, 0.05851794745787352, 0.997542913798236, 1.8580116592229843, 2.3593930477875604, 2.318707321051961, 1.7199494592435174, 0.7339885564194776, -0.3205602773414415, -1.0665355949559088, -1.1821047256235608, -0.5048284831171809, 0.9071183522092756, 2.7776548698882864, 4.681447719917893, 6.160104585479828, 6.8521111346940495, 6.597371818928325, 5.483919704483792, 3.821372677089154, 2.0479871857812944, 0.5988467757098506, -0.2247135768518745], 'positive_zeros': ['1.06959992285701514232957566219287', '2.62373335655672969775321743652408', '4.02184673082405158798424180172436', '5.67115433977394478877763176126961', '6.15002507497308426124982565082722', '7.910786034727351312592677985364135', '8.522053799215442722204693595578612', '9.521733626978708691569834001245889', '9.927480983839679859080684248166487', '11.28791587350375458888908271821581'], 'prelabel': '2-378-21.17-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.737338538225754, 'root_angle': -0.3303884299889839, 'root_number': '0.507990683148011 - 0.8613625635206218*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.165194214994', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.06959992285701514232957566219', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.62373335655672969775321743652', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.02184673082405158798424180172', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.0183451964044, 'bad_primes': [2, 3, 7], 'central_character': '21.17', 'conductor': 378, 'conductor_radical': 42, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/378/2/k/d/269/2'], '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': '2-378-21.17-c1-0-1', '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': '2-378-21.17-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.737338538225754, 'root_angle': -0.16519421499449194, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.06959992285701514232957566219', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1355878984213763109617748470659', 'Lhash_array': ['1355878984213763109617748470659'], 'label': '2-378-21.17-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/378/2/k/d/269/2'}