-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2870024087696926270136051351291', 'a10': [6.972863555349226, -4.025784650703407], 'a2': [1.3660254037844386, 0.36602540378443865], 'a3': [0.8660254037844386, 1.5], 'a4': [1.7320508075688772, 1.0], 'a5': [4.025784650703407, -4.025784650703407], 'a6': [0.6339745962155614, 2.366025403784439], 'a7': [-4.999324103026317, 1.3395648561073485], 'a8': [2.0, 2.0], 'a9': [-1.5, 2.598076211353316], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.125346062010316, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.3660254037844386, -0.36602540378443865]]], [3, [[1.0, 0], [-0.8660254037844386, -1.5]]], [13, [[1.0, 0], [-3.8131043084302583, 12.428203230275509]]]], 'bad_primes': [2, 3, 13], 'central_character': '78.67', 'coefficient_field': 'CDF', 'conductor': 78, 'conductor_radical': 78, 'conjugate': '3304301477365964943182280691140', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.3660254037844386, -0.36602540378443865]], [[1.0, 0], [-0.8660254037844386, -1.5]], [[1.0, 0], [-4.025784650703407, 4.025784650703407], [0, -25.0]], [[1.0, 0], [4.999324103026317, -1.3395648561073485], [42.4352447854375, -24.5]], [[1.0, 0], [3.4111805197835743, -12.73069901362151], [-104.78907385791707, -60.5]], [[1.0, 0], [-3.8131043084302583, 12.428203230275509]], [[1.0, 0], [16.328956331023093, 9.427527333301827], [144.5, 250.28134169370276]], [[1.0, 0], [7.8559116696256, 29.318661490815987], [-312.63517076618234, 180.5]], [[1.0, 0], [10.483966871358902, -6.05292109535418], [264.5, -458.12743860196804]], [[1.0, 0], [-18.472187658375542, -31.994767551253208], [-420.5, 728.3273645827129]], [[1.0, 0], [6.482482498582647, -6.482482498582647], [0, -961.0]], [[1.0, 0], [-13.609367012416847, 50.79084914919153], [-1185.5887777808964, -684.5]], [[1.0, 0], [6.380525632429906, 1.7096566904956718], [1455.7887037616413, 840.5]], [[1.0, 0], [-11.782581999905478, -6.802676889394267], [924.5, 1601.280971597427]], [[1.0, 0], [-61.60598114854284, -61.60598114854284], [0, 2209.0]], [[1.0, 0], [-4.644094709379991, 0], [2809.0, 0]], [[1.0, 0], [-24.10178680886626, 6.458054311582801], [3014.634430573631, -1740.5]], [[1.0, 0], [19.271286529085753, -33.37884739559421], [-1860.5, -3222.4805274818964]], [[1.0, 0], [-91.8346460922377, -24.607019257613054], [3887.5880375883453, 2244.5]], [[1.0, 0], [-10.51061319484045, -39.226142461848404], [-4365.634060477355, 2520.5]], [[1.0, 0], [-60.44857432618386, -60.44857432618386], [0, 5329.0]], [[1.0, 0], [94.28537601841532, 0], [6241.0, 0]], [[1.0, 0], [63.48903393257541, -63.48903393257541], [0, -6889.0]], [[1.0, 0], [-40.36553061285902, 150.64621112166674], [-6859.787223376538, -3960.5]], [[1.0, 0], [39.27355490203623, 146.57090228824495], [-8148.433024207783, 4704.5]], [[1.0, 0], [-39.81379763317132, 22.986506780972746], [5100.5, -8834.325144005059]], [[1.0, 0], [0, 92.80992973638308], [-10609.0, 0]], [[1.0, 0], [37.620161313305566, 65.16003078358234], [-5724.5, 9915.124847928038]], [[1.0, 0], [46.05514265033468, -46.05514265033468], [0, -11881.0]], [[1.0, 0], [78.24669466380502, -135.52725068203884], [-6384.5, -11058.278380923497]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-78-13.2-c2-0-2', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/78/3/l/c/67/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.9826598595172569, 1.9547784415874305, 1.929412048578895, 1.90494596311869, 1.8791080127491917, 1.8491185886795967, 1.81186244551603, 1.764072359871555, 1.7025185535884415, 1.6242011707586468, 1.526544776233713, 1.4075935429528263, 1.2662039290273222, 1.1022288939206937, 0.9166847279127648, 0.7118888990080319, 0.49155534894799185, 0.26083268682598104, 0.02627095792830618, -0.20429572640798996, -0.4219603202350983, -0.6170527578828019, -0.7795476447589662, -0.8995614612847453, -0.9679228811909015, -0.9767912793850113, -0.9202902165464572, -0.7951153779602872, -0.6010709237711296, -0.3414852994233369, -0.023458019510578614, 0.3421066087704959, 0.740714032340966, 1.1547642182463476, 1.5643112126374261, 1.9480813326724284, 2.2847109440974886, 2.554141362198167, 2.739086442109605, 2.8264700887502587, 2.8087184604223623, 2.6847871496525575, 2.4608087976367594, 2.150262508414233, 1.773593310916717, 1.3572470004607111, 0.9321311046608781, 0.531563492493726, 0.18882232767315493, -0.06554003716202277, -0.2064161052646968, -0.21666496601451718, -0.08919714475364161, 0.17160518495387866, 0.5493257951544541, 1.0159459986024517, 1.533329789720782, 2.055730815831009, 2.533190821474098, 2.915602111382408, 3.1571209330867243, 3.2205544552869236, 3.081310179049981, 2.730500035756252, 2.176835861978274, 1.4470382549681653, 0.5846024891786641, -0.3530857054164709, -1.2991280033069887, -2.1826660467826278, -2.935146000857136, -3.4967244369648314, -3.822187734389202, -3.885761689799996, -3.684259211397611, -3.2381498779367397, -2.5903262979877013, -1.80257198336478, -0.9499812918161747, -0.1138174744147611, 0.626507550485611, 1.201513854531965, 1.558926062542678, 1.6693141075923768, 1.5294203287328727, 1.1627200350064675, 0.6170575171059413, -0.04047060892950617, -0.7308853187986523, -1.3721636786453353, -1.8885557172041165, -2.2192938486478964, -2.325641750297179, -2.19539407616949, -1.8442214203227107, -1.3136272086659235, -0.6657018879050789, 0.024726731022970287, 0.6795940569328006, 1.2275524402091509, 1.6130828420908372, 1.8035401403148625, 1.7931462037303187, 1.6033272493422779, 1.2792734685985931, 0.883118203117364, 0.4846208211615078, 0.1506219629245658, -0.06523771659790757, -0.13102406054126242, -0.04192596582191676, 0.1783374670654074, 0.4804894247951946, 0.7967864765421352, 1.0513416435928054, 1.1722651678915563, 1.1038625132235522, 0.8170261879754052, 0.3161277439299667, -0.3588505993999229, -1.1355581882113432, -1.9177289835961266, -2.59788559845697, -3.072636391504682, -3.2584195243392933, -3.105355800177427, -2.6070223678048903, -1.8044488261423817, -0.7834107164264501, 0.3349490615995352, 1.4091384437872376, 2.2960437822738675, 2.870785898668705, 3.044832633698271, 2.77962740864501, 2.093548004169924, 1.060922463566275, -0.1970246104560765, -1.5282091300245082, -2.770527726546206, -3.7745213708072125, -4.424514869923391, -4.6550233930756155, -4.459859995138828, -3.89244214663442, -3.0571267843293173, -2.0927994712526083, -1.1511826792594615, -0.37320676004378944, 0.13284818898694842, 0.30795519431482654, 0.15099655223187214, -0.2819700991178152, -0.8877688665150539, -1.5338894336959488, -2.0811063392400118, -2.407204455523573, -2.4278524076252994, -2.111098868208879, -1.483004109398788, -0.6233978189885883, 0.3475695768955592, 1.2898255330412838, 2.067242300172447, 2.5708509092430067, 2.7373515448275554, 2.559653138346137, 2.087548185153531, 1.418360171229872, 0.679189001590487, 0.0039047508294271166, -0.49097876824212927, -0.7271712427640494, -0.67838100907133, -0.37442346612529326, 0.10515743421025368, 0.6468370801389997, 1.125344385448244, 1.4282390086928567, 1.4781816258601472, 1.2486077091813663, 0.7696964679724487, 0.12332563828700589, -0.5722065403903375, -1.1849201002204355, -1.5950744036099314, -1.7192743350817126, -1.5279949139901823, -1.0529205463099272, -0.38239288463177473, 0.3544529963754011, 1.0120446327181505, 1.4566468488284543, 1.5930729465157412, 1.3844938174821142, 0.8612092154903551, 0.11630637996793025, -0.711327397629053, -1.4636362376190921, -1.9946428042688726, -2.2001864128279336, -2.0401131383254425, -1.54817335889284, -0.8271724597591443, -0.02978745767713422, 0.6716438964189178, 1.1207106050819053, 1.2109350513579584, 0.91127243666321, 0.277589573575328, -0.552825761071599, -1.3834254169624478, -1.9936213283057946, -2.1807384867136363, -1.8008088436227223, -0.8002518039787433, 0.7680140524869603, 2.7476720145879137, 4.901359788170548, 6.948604776146243, 8.612594160505951, 9.66720464851507, 9.975529490000838, 9.512661234803021, 8.368444623144082, 6.729738418951958, 4.845666752399853, 2.982613243278754, 1.3776531802186611, 0.19933113450316556, -0.4768768683163375, -0.6741121943749342, -0.5002718115012839, -0.11824684783782684, 0.293058539173924, 0.5785010358743882, 0.6388754667835935, 0.448915346222316, 0.057727256415014645, -0.4278453927175943, -0.8726944483703906, -1.1487395294911584, -1.1678122546621577, -0.9045269943006505, -0.40386030980756676, 0.22831896344515146, 0.8495965682355222, 1.3146054330607808, 1.510033465911174, 1.38279091240949, 0.9545526550264029, 0.3189515229558972, -0.37832456415859766, -0.9722818100296737, -1.3168683413155795, -1.3199076581004576, -0.9664487810597572], 'positive_zeros': ['2.26404979982670582837484680997507', '3.75848604698402290349650874034357', '6.08742647797107526928395949236599', '6.55011400135775077158026706075502', '8.328557056663830287523161360046769', '9.892924643009544628558941781214921', '10.86763285361494331761247741347204', '12.12049479701729260829120512036783', '13.45267820216474587961072514926996', '13.77970767469074200095028040316189'], 'prelabel': '2-78-13.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4578566671694155, 'root_angle': -0.14703205393166413, 'root_number': '0.8952007744159022 - 0.44566307170907593*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0735160269658', 'prec': 54}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.26404979982670582837484680998', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.75848604698402290349650874034', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.08742647797107526928395949237', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2.125346062010316, 'bad_primes': [2, 3, 13], 'central_character': '13.2', 'conductor': 78, 'conductor_radical': 78, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/78/3/l/c/67/2'], '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': '2-78-13.2-c2-0-2', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-78-13.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4578566671694155, 'root_angle': -0.07351602696583207, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.26404979982670582837484680998', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2870024087696926270136051351291', 'Lhash_array': ['2870024087696926270136051351291'], 'label': '2-78-13.2-c2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/78/3/l/c/67/2'}