-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2912139989444511419787031169511', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.2928932188134525, -0.7071067811865476], 'a4': [0.0, 0.0], 'a5': [1.7071067811865475, -0.7071067811865476], 'a6': [0.0, 0.0], 'a7': [-0.2928932188134525, -0.12132034355964258], 'a8': [0.0, 0.0], 'a9': [1.7071067811865475, -1.7071067811865475], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.0859654674894137, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [-1.0, -4.0]]]], 'bad_primes': [2, 17], 'central_character': '136.49', 'coefficient_field': 'CDF', 'conductor': 136, 'conductor_radical': 34, 'conjugate': '2093639215759173537455156013152', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.2928932188134525, 0.7071067811865476], [-2.1213203435596424, 2.1213203435596424]], [[1.0, 0], [-1.7071067811865475, 0.7071067811865476], [3.5355339059327378, -3.5355339059327378]], [[1.0, 0], [0.2928932188134525, 0.12132034355964258], [4.949747468305833, 4.949747468305833]], [[1.0, 0], [-0.2928932188134525, 0.7071067811865476], [-7.7781745930520225, -7.7781745930520225]], [[1.0, 0], [0, 0], [-13.0, 0]], [[1.0, 0], [-1.0, -4.0]], [[1.0, 0], [1.5857864376269049, 1.5857864376269049], [0, 19.0]], [[1.0, 0], [2.5355339059327378, -6.121320343559643], [-16.263455967290593, -16.263455967290593]], [[1.0, 0], [5.121320343559643, -2.1213203435596424], [20.506096654409877, -20.506096654409877]], [[1.0, 0], [-0.8786796564403574, -2.1213203435596424], [-21.920310216782973, 21.920310216782973]], [[1.0, 0], [-0.2928932188134525, -0.7071067811865476], [-26.16295090390226, 26.16295090390226]], [[1.0, 0], [2.2928932188134525, 0.9497474683058327], [28.991378028648448, 28.991378028648448]], [[1.0, 0], [-7.242640687119285, 7.242640687119285], [0, -43.0]], [[1.0, 0], [0, -12.82842712474619], [-47.0, 0]], [[1.0, 0], [-2.1715728752538097, -2.1715728752538097], [0, 53.0]], [[1.0, 0], [-5.585786437626905, 5.585786437626905], [0, -59.0]], [[1.0, 0], [9.121320343559642, 3.778174593052023], [43.1335136523794, 43.1335136523794]], [[1.0, 0], [-9.65685424949238, 0], [67.0, 0]], [[1.0, 0], [-3.7071067811865475, -8.949747468305832], [-50.204581464244875, 50.204581464244875]], [[1.0, 0], [-7.363961030678928, 3.0502525316941673], [51.61879502661797, -51.61879502661797]], [[1.0, 0], [-5.464466094067262, 13.192388155425117], [-55.86143571373726, -55.86143571373726]], [[1.0, 0], [7.242640687119285, 7.242640687119285], [0, 83.0]], [[1.0, 0], [0, -1.6568542494923801], [-89.0, 0]], [[1.0, 0], [14.778174593052023, -6.121320343559643], [68.58935777509511, -68.58935777509511]], [[1.0, 0], [-10.0, 0], [101.0, 0]], [[1.0, 0], [2.34314575050762, 0], [103.0, 0]], [[1.0, 0], [13.363961030678928, -5.535533905932738], [75.66042558696059, -75.66042558696059]], [[1.0, 0], [10.778174593052023, 4.464466094067262], [77.07463914933368, 77.07463914933368]], [[1.0, 0], [-3.1213203435596424, 7.535533905932738], [-79.90306627407988, -79.90306627407988]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-136-17.15-c1-0-3', '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/136/2/n/a/49/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.1555280943457316, 1.1945383092832218, 1.244711534206609, 1.3049076847724745, 1.3723866519933474, 1.4430871200579287, 1.5119253797428807, 1.5730655498049448, 1.6201604092349169, 1.6465879952505347, 1.6457128516288249, 1.6111921032045262, 1.5373337491601908, 1.4195018900648777, 1.2545523902568883, 1.0412729747565594, 0.7807940658950188, 0.47693106806872343, 0.13641581316241164, -0.2310248966033984, -0.6127816676227815, -0.9936955284320697, -1.3566285636545428, -1.683272241606294, -1.9551731178876757, -2.154932947466141, -2.2675170489920196, -2.281583185964369, -2.1907256999421914, -1.9945186817266956, -1.6992399622822876, -1.3181665527348487, -0.8713530068793771, -0.3848371226691597, 0.1107387181979812, 0.5820499915204906, 0.9954588953283019, 1.3196761024749453, 1.5285122144174947, 1.6034788571299818, 1.5359811898333093, 1.3288489926454823, 0.9969855235439794, 0.5669725911570729, 0.07555443740109748, -0.432973435865333, -0.9103299578949058, -1.3085139341907859, -1.5844130856301903, -1.7043249610304918, -1.6479201479518197, -1.411187199882842, -1.0079594548674204, -0.46973592756260524, 0.15633493335439883, 0.8112514362183175, 1.4294756758239862, 1.9453189988767907, 2.299782665793402, 2.447134807116485, 2.3604729016977797, 2.035574565264636, 1.49248076009751, 0.7744762114323532, -0.055587489984042324, -0.9213689341266376, -1.740950289441555, -2.4357608001061632, -2.9395032320583865, -3.2060072518650835, -3.2149956544296434, -2.974945375911725, -2.5225411056512597, -1.9186234395299944, -1.2409794996506807, -0.5747555227491709, -0.0016288116807904878, 0.4108936728684352, 0.6186222036217353, 0.6069786491488364, 0.39345686150221554, 0.02574047969035411, -0.4244564547491495, -0.8711594788267457, -1.226303049390831, -1.412682001087328, -1.3758687329437598, -1.0933305670872608, -0.5792920532768072, 0.11557140098219273, 0.9098140662503896, 1.7016998227614761, 2.3831663239351517, 2.8553715657221432, 3.0435864916359763, 2.909181399762494, 2.4567787866913666, 1.7352817060497838, 0.8323552318389384, -0.13708172974185137, -1.0468523841436717, -1.7777440806520768, -2.235249810508117, -2.3640802029359778, -2.1570859994790825, -1.6570122714755977, -0.9505746190136835, -0.1555468286823526, 0.5973086910091632, 1.1847407360191686, 1.5107216886232, 1.5221692191802534, 1.218015423145288, 0.6499644684166357, -0.08540183017491391, -0.862084364886498, -1.5453076520789524, -2.0140102034069884, -2.18143756695908, -2.0102996103409656, -1.5197765567156618, -0.7829790837705428, 0.08492272104023112, 0.9460581753318085, 1.663496929305662, 2.125121618545708, 2.2635251924273443, 2.068312404479648, 1.588438764990116, 0.923941662154716, 0.20831415489189128, -0.4154955992779165, -0.8212296798753848, -0.9228672402660215, -0.691171468651664, -0.16000209512776217, 0.5790347231716407, 1.3928937986168892, 2.131576583438037, 2.6563941527665835, 2.8667592254133405, 2.720375832267502, 2.2427904041312154, 1.5241695386270109, 0.7035442370681656, -0.056829643283661434, -0.6023616683452732, -0.816476247479911, -0.6445499463130813, -0.1066191134754539, 0.703937036833252, 1.6359009223789045, 2.507323734809384, 3.139320373103551, 3.3901969469630875, 3.1833175963430835, 2.5231673219568376, 1.496238086499698, 0.25626011365389695, -1.0036355767569431, -2.0866107487773866, -2.828806397874693, -3.1298427017316697, -2.9710706522422123, -2.4178753799653547, -1.6054882866637854, -0.7110923046366523, 0.08217636080824893, 0.6220084806920042, 0.8169264138808006, 0.6532847352410408, 0.19569161146725692, -0.42927366643153037, -1.0626322458163642, -1.5495711200102031, -1.7751140016945381, -1.691075346962983, -1.3282278417147593, -0.7907188345438741, -0.23359374987933487, 0.1719845089258162, 0.2784049972515462, -0.0025283821249151963, -0.6756463870738384, -1.6560974222394786, -2.782674764754137, -3.8485377305067345, -4.643184420861071, -4.996877560763602, -4.817925922894589, -4.11451212515049, -2.995908883244691, -1.6522965970209562, -0.31705259896856786, 0.7806969573890289, 1.4631762258296068, 1.640504192600957, 1.3286154948522046, 0.6444576783937213, -0.22067806035721507, -1.0439795175772075, -1.6207136837640017, -1.8096086358186503, -1.5638504071249522, -0.9406660622815894, -0.08724143245545411, 0.7939203355468056, 1.4923700075132635, 1.8389902707369612, 1.745813402040213, 1.2270854172164767, 0.3965405115402315, -0.5586622216248919, -1.4214272294300991, -1.9955688770370452, -2.1520980513760533, -1.859961506461428, -1.1937875367308624, -0.31655214648240937, 0.5589796702831574, 1.2210662253094462, 1.5100274143021517, 1.3572556290632831, 0.8026585988910756, -0.013951506570060094, -0.8857841012212124, -1.5886601325157341, -1.9354517099865394, -1.8221888036316003, -1.2544657646335229, -0.34740183280173925, 0.7012336070004457, 1.6585476622654647, 2.313336937202663, 2.5283313090105515, 2.2748844793232896, 1.641217717871021, 0.8116925411127703, 0.021712041201882675, -0.5010165915185355, -0.5945243092648512, -0.20547048571106405, 0.5941141703262356, 1.620965457400789, 2.622772546529722, 3.338568769988432, 3.5627766601954924, 3.1971792866751714, 2.277799032657523, 0.9696568897254897, -0.4697786804802875, -1.7498927066888859, -2.6146887772842007, -2.902499575471955, -2.582993056440794, -1.7623780030136498, -0.6555946228354348], 'positive_zeros': ['2.29727338820350504257485595163052', '4.22183942878266038100927665633866', '5.51855675954712629303288004227293', '6.71979159039829428066635544095532', '7.991922040003695595499183319479316', '9.500405471843425007995337275832540', '10.13257147492482251612701421889631', '11.10579186374486947590134654985062', '12.35723454683904325862665090905377', '13.39958871091039145432193388427642'], 'prelabel': '2-136-17.15-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0420966689752988, 'root_angle': 0.19619938372174234, 'root_number': '0.8159773091968405 + 0.5780839306501121*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0980996918609', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.29727338820350504257485595163', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.22183942878266038100927665634', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.51855675954712629303288004227', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.0859654674894137, 'bad_primes': [2, 17], 'central_character': '17.15', 'conductor': 136, 'conductor_radical': 34, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/136/2/n/a/49/1'], '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': '2-136-17.15-c1-0-3', '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': '2-136-17.15-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0420966689752988, 'root_angle': 0.09809969186087117, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.29727338820350504257485595163', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2912139989444511419787031169511', 'Lhash_array': ['2912139989444511419787031169511'], 'label': '2-136-17.15-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/136/2/n/a/49/1'}