Table lfunc_lfunctions
L-functions
{'Lhash': '1840964134276421482485035280869', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0.5, -0.8660254037844386], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0.5, -2.598076211353316], 'a8': [0, 0], 'a9': [1.0, 1.7320508075688772], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.837569529021748, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-0.5, 2.598076211353316]]], [11, [[1.0, 0], [0.5, -0.8660254037844386]]]], 'bad_primes': [2, 7, 11], 'central_character': '1232.529', 'coefficient_field': 'CDF', 'conductor': 1232, 'conductor_radical': 154, 'conjugate': '1050393638628897139123082934624', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.5, 0.8660254037844386], [-1.5, -2.598076211353316]], [[1.0, 0], [0, 0], [-2.5, 4.330127018922194]], [[1.0, 0], [-0.5, 2.598076211353316]], [[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [1.0, 0], [13.0, 0]], [[1.0, 0], [-3.0, 5.196152422706632], [-8.5, -14.722431864335457]], [[1.0, 0], [-1.0, -1.7320508075688772], [-9.5, 16.454482671904334]], [[1.0, 0], [3.0, 5.196152422706632], [-11.5, 19.91858428704209]], [[1.0, 0], [-9.0, 0], [29.0, 0]], [[1.0, 0], [2.0, -3.4641016151377544], [-15.5, -26.846787517317598]], [[1.0, 0], [1.0, 1.7320508075688772], [-18.5, 32.04293994002423]], [[1.0, 0], [6.0, 0], [41.0, 0]], [[1.0, 0], [-4.0, 0], [43.0, 0]], [[1.0, 0], [3.0, 5.196152422706632], [-23.5, 40.703193977868615]], [[1.0, 0], [0, 0], [-26.5, -45.89934640057525]], [[1.0, 0], [1.5, -2.598076211353316], [-29.5, -51.09549882328188]], [[1.0, 0], [5.5, 9.526279441628825], [-30.5, 52.827549630850754]], [[1.0, 0], [-5.5, 9.526279441628825], [-33.5, -58.023702053557386]], [[1.0, 0], [0, 0], [71.0, 0]], [[1.0, 0], [1.0, -1.7320508075688772], [-36.5, -63.21985447626402]], [[1.0, 0], [-2.5, -4.330127018922194], [-39.5, 68.41600689897065]], [[1.0, 0], [-6.0, 0], [83.0, 0]], [[1.0, 0], [-9.0, -15.588457268119896], [-44.5, 77.07626093681505]], [[1.0, 0], [13.0, 0], [97.0, 0]], [[1.0, 0], [-7.5, 12.99038105676658], [-50.5, -87.4685657822283]], [[1.0, 0], [8.0, 13.856406460551018], [-51.5, 89.20061658979718]], [[1.0, 0], [-6.0, -10.392304845413264], [-53.5, 92.66471820493493]], [[1.0, 0], [1.0, -1.7320508075688772], [-54.5, -94.39676901250381]], [[1.0, 0], [-9.0, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 23504287, 'index': 30, 'label': '2-1232-7.4-c1-0-30', 'leading_term': '1.8427619525584800401471940085296358724625150669443315044', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1232/2/q/d/529/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 24}, 'plot_values': [1.84276195255848, 1.9232095748581903, 1.998211864473965, 2.0674459150690008, 2.1303190430926278, 2.1859699840594566, 2.233285975713809, 2.2709340780012623, 2.2974044596962493, 2.3110631157382024, 2.310211500091384, 2.2931507606674133, 2.2582485383373547, 2.2040065572525784, 2.1291274377997293, 2.032579287527378, 1.9136566742653276, 1.7720365789234727, 1.6078278890126994, 1.4216129543238674, 1.2144797072215525, 0.9880428710723058, 0.7444528559873217, 0.48639108111371077, 0.21705067253366503, -0.05989823324382802, -0.3403590005791832, -0.6198748286674749, -0.8937104497629951, -1.1569482252494019, -1.4045971382551474, -1.6317126370103967, -1.8335247483203112, -2.0055713762213805, -2.1438332488500325, -2.244866598765068, -2.3059293798350255, -2.3250966573036203, -2.3013607744213602, -2.234712013473615, -2.126195741408842, -1.9779424658929312, -1.7931678261514354, -1.5761402978676045, -1.3321152895664932, -1.067235329513025, -0.7883971607797663, -0.5030877452113189, -0.21919238645284972, 0.05522062455211811, 0.3121333069559361, 0.5438226739277479, 0.743109381976925, 0.9036022622733683, 1.0199302323041273, 1.0879529475334073, 1.104941721233431, 1.0697227341300164, 0.9827753803974707, 0.8462797466722672, 0.6641086765304846, 0.44176160092190786, 0.18623926846183206, -0.09413937139223293, -0.38997466535564274, -0.6910724381611081, -0.9867710078004617, -1.2662991895322604, -1.519153704278604, -1.7354830076126977, -1.906463575650096, -2.024654191421531, -2.0843138220137045, -2.0816692965073034, -2.0151201995937433, -1.8853701741788946, -1.6954761419187878, -1.450809742063876, -1.1589284706148026, -0.8293574658278173, -0.4732865057087101, -0.10319041660335053, 0.26761541205153794, 0.6254695084080609, 0.9568911374219428, 1.24911963059094, 1.4906449402963804, 1.6717074906315665, 1.784745643237826, 1.8247702707417282, 1.7896480320800399, 1.680277932672685, 1.5006495458996645, 1.2577757481440435, 0.9614978180143762, 0.624166079253052, 0.26020470885599667, -0.11442534732413, -0.48284645138158444, -0.8279440857282881, -1.1330796121643087, -1.3828066792980727, -1.5635606545184269, -1.6642904309363402, -1.6770032954695828, -1.5971962438677165, -1.4241511314566178, -1.1610762308942943, -0.8150829456564905, -0.3969933604924553, 0.07901828876159475, 0.5959395957020233, 1.1345714328457985, 1.6742920845916938, 2.1939033609300904, 2.672523271877374, 3.090486594900472, 3.430213100634748, 3.67700345562736, 3.8197249526503505, 3.851353199072076, 3.769341600827964, 3.575797703767806, 3.2774539031613448, 2.8854293418629875, 2.4147895673487594, 1.883920248687214, 1.3137404908217232, 0.7267895560000335, 0.14622767169906456, -0.40520331447075586, -0.9062106896817134, -1.3379236289766832, -1.6847602875567906, -1.9351457351746153, -2.0820436718431408, -2.123273319329818, -2.0615929894844083, -1.9045431233128254, -1.6640535319064171, -1.3558315583819163, -0.9985593030022399, -0.6129383048684554, -0.22062858764620338, 0.1568647388430465, 0.499300465699892, 0.7887482273847473, 1.0105179946331497, 1.1539219120096642, 1.2128262485802914, 1.1859616297154503, 1.0769720515633021, 0.894196836657432, 0.6501939685828279, 0.36102738965120884, 0.04535408654260364, -0.27664162055034386, -0.5844099069207431, -0.8582303467053898, -1.0803738056176004, -1.2361657767555163, -1.3148897964057369, -1.3104772683138213, -1.221940888827162, -1.0535223783255738, -0.814540699186099, -0.5189435594857393, -0.1845818586682982, 0.16775711938078688, 0.5155074521771351, 0.8356109494070577, 1.1058610913101081, 1.3062285756858638, 1.4200918360681727, 1.4352995885541633, 1.345000436168468, 1.148186461339336, 0.8499129861288406, 0.4611744831620025, -0.0015639858670671684, -0.5171605257641073, -1.0608768130659851, -1.60568911357217, -2.123759220601318, -2.5879837357101043, -2.97353372769007, -3.2592954092023594, -3.4291262715464272, -3.472850023858367, -3.386927296318521, -3.1747567011431044, -2.846581556880007, -2.4190002196543534, -1.914101233463132, -1.3582670429986077, -0.7807104480630815, -0.2118250502586941, 0.31855644848214665, 0.7828949483264586, 1.1575661012151892, 1.4242720479883904, 1.57115653391528, 1.5935522937377904, 1.4943102969883606, 1.2836845939855963, 0.9787727158958873, 0.6025383135374114, 0.18246835643167608, -0.25105982720566733, -0.6666075627932092, -1.0335923293513567, -1.3241790254301153, -1.5150299889311714, -1.5888054896395218, -1.5353198896946432, -1.3522781900629317, -1.04554216150087, -0.6289032769525348, -0.12336954968915484, 0.443996681976691, 1.0416248564276884, 1.635276477487141, 2.190070544959199, 2.672572220748755, 3.0528173628269863, 3.3061479625346206, 3.4147437655402664, 3.3687529229975297, 3.1669484128060676, 2.816865776963674, 2.3344096873738, 1.7429499944455973, 1.0719601364736768, 0.3552800227831237, -0.37089016261708946, -1.0701409856764568, -1.7080153214734812, -2.254044623033888, -2.6835312640698454, -2.9789638738229227, -3.1309755940389383, -3.138784249305898, -3.010086705852307, -2.760415068589487, -2.4119975301508045, -1.9921993171367929, -1.5316470894326546, -1.0621614314810324, -0.6146352364360971, -0.2169998523716471, 0.10758454395567534, 0.34219250362275583, 0.4771519166305289, 0.5105486589713285, 0.4481830646758858, 0.3029814651351922, 0.09390361774252762], 'positive_zeros': ['1.45226463344471417784925838315074', '2.85905336288879770823024735656303', '3.67218872598461066213710518050484', '4.76231918368796292041647115323632', '5.66571763480823976660190355906153', '6.43598085356043037046923057859364', '7.57374038880333160460192713465765', '8.412662959080484984361178184545909', '9.090267695284946990880242048173773', '9.815991239653955782599352048980222'], 'prelabel': '2-1232-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.13649000142225, 'root_angle': 0.20701257277455892, 'root_number': '0.2668258571384815647106987959345095138142320105440431027 + 0.9637447597586793761438043440821124880542606995232854472*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.20701257277455892', 'prec': 57}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.45226463344471417784925838315', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.85905336288879770823024735656', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.67218872598461066213710518050', 'prec': 100}}