-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2172145596302983318704222184411', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -5.196152422706632], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [10.0, 15.588457268119896], 'a8': [0, 0], 'a9': [-27.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.824641761928856, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 5.196152422706632]]], [7, [[1.0, 0], [-10.0, -15.588457268119896]]]], 'bad_primes': [2, 3, 7], 'central_character': '336.209', 'coefficient_field': 'CDF', 'conductor': 336, 'conductor_radical': 42, 'conjugate': '528881798392908371550255524712', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 5.196152422706632]], [[1.0, 0], [0, 0], [125.0, 0]], [[1.0, 0], [-10.0, -15.588457268119896]], [[1.0, 0], [0, 0], [-1331.0, 0]], [[1.0, 0], [0, 62.353829072479584], [-2197.0, 0]], [[1.0, 0], [0, 0], [4913.0, 0]], [[1.0, 0], [0, 155.88457268119896], [-6859.0, 0]], [[1.0, 0], [0, 0], [-12167.0, 0]], [[1.0, 0], [0, 0], [-24389.0, 0]], [[1.0, 0], [0, 155.88457268119896], [-29791.0, 0]], [[1.0, 0], [110.0, 0], [50653.0, 0]], [[1.0, 0], [0, 0], [68921.0, 0]], [[1.0, 0], [520.0, 0], [79507.0, 0]], [[1.0, 0], [0, 0], [103823.0, 0]], [[1.0, 0], [0, 0], [-148877.0, 0]], [[1.0, 0], [0, 0], [205379.0, 0]], [[1.0, 0], [0, 935.3074360871938], [-226981.0, 0]], [[1.0, 0], [-880.0, 0], [300763.0, 0]], [[1.0, 0], [0, 0], [-357911.0, 0]], [[1.0, 0], [0, -374.1229744348775], [-389017.0, 0]], [[1.0, 0], [884.0, 0], [493039.0, 0]], [[1.0, 0], [0, 0], [571787.0, 0]], [[1.0, 0], [0, 0], [704969.0, 0]], [[1.0, 0], [0, 1371.7842395945509], [-912673.0, 0]], [[1.0, 0], [0, 0], [1030301.0, 0]], [[1.0, 0], [0, 1028.8381796959131], [-1092727.0, 0]], [[1.0, 0], [0, 0], [-1225043.0, 0]], [[1.0, 0], [-646.0, 0], [1295029.0, 0]], [[1.0, 0], [0, 0], [-1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 39, 'label': '2-336-21.20-c3-0-39', 'leading_term': '1.207626642379131904189637397053523091267321190317026893', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/336/4/k/a/209/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 30}, 'plot_values': [1.207626642379132, 1.3976859591239825, 1.5785868715200086, 1.7483702769921667, 1.9050834084247428, 2.0467809686874876, 2.1715313815066057, 2.277428875101918, 2.3626118460267684, 2.4252876602790616, 2.463763747315092, 2.476484539763864, 2.4620735161463765, 2.419379323496399, 2.3475246983333653, 2.245956674204269, 2.114496367887888, 1.9533864801225762, 1.7633345361824744, 1.5455498326254655, 1.30177205481841, 1.0342895908173217, 0.7459456955498716, 0.4401308585969815, 0.12076000119353644, -0.20776652668971393, -0.540618762690301, -0.8726098946762111, -1.1982855652799937, -1.5120287319019095, -1.8081784837557418, -2.0811605936918705, -2.325626967674321, -2.5366005720511655, -2.7096218929328035, -2.8408925387164468, -2.9274112615981296, -2.967097471154519, -2.958897264792917, -2.9028671245823197, -2.800230741512967, -2.6534049345775976, -2.465991334372063, -2.2427313926415713, -1.9894233455313934, -1.7128009758160516, -1.4203753560791823, -1.1202421705186898, -0.820858660202663, -0.5307956614833855, -0.258471551632071, -0.011876118788121686, 0.20170662598302183, 0.375966936984022, 0.505818939679412, 0.5876211057595035, 0.6193576785646119, 0.6007718754196603, 0.5334428609131101, 0.42080006321640656, 0.26807036423999764, 0.08215598487948325, -0.12855655862622437, -0.3544533168821355, -0.5850096637558907, -0.8091582410661763, -1.0156967563828578, -1.1937219456548527, -1.3330740571751725, -1.4247747705215843, -1.461440634724036, -1.4376539761426461, -1.3502738461494388, -1.198670980372236, -0.9848729208417057, -0.7136083704132268, -0.39224342946085833, -0.030606496413026745, 0.3592968488768336, 0.7636728910528573, 1.16742186406676, 1.5546975619739523, 1.9095247410583114, 2.216450975379182, 2.4612068473387834, 2.6313465770907247, 2.7168405648237783, 2.710591939234373, 2.608851122670763, 2.4115056289896564, 2.12222673264956, 1.7484601527333912, 1.3012542886866436, 0.7949265757569283, 0.24657590116565742, -0.3245435941916484, -0.8977649610662883, -1.4518384215539752, -1.965814866111186, -2.4199448994273607, -2.7965531317335754, -3.0808468919122216, -3.2616199523644793, -3.331815231949638, -3.2889157143750816, -3.135139817838087, -2.877425913638892, -2.527200264557024, -2.0999329103885955, -1.6144964832811137, -1.0923530693374337, -0.5566035155702956, -0.030941500457564868, 0.4614392244689989, 0.8989321489993578, 1.2625462554551505, 1.536822937944506, 1.7105934101856626, 1.7775351494395621, 1.7364950418893397, 1.591558016853536, 1.3518525714717533, 1.0310980782104493, 0.6469124440278221, 0.21991182119703173, -0.22735407735278845, -0.6715776248730261, -1.0899191631032192, -1.4612181839062435, -1.7671240943478612, -1.993083667293446, -2.129128667808342, -2.170416873896961, -2.117492349378481, -1.9762457648472984, -1.7575720315683434, -1.4767396261716605, -1.1525027822383591, -0.8060032298502281, -0.4595214342386775, -0.13514747177814027, 0.14655191472402165, 0.36779142435077034, 0.5146742579833138, 0.5780789350886802, 0.5542680031169275, 0.4451758925864193, 0.2583513024370905, 0.0065496629114715, -0.29300772535737335, -0.619670576388691, -0.9506361423165385, -1.262392732160163, -1.5322452406567146, -1.7398301627757533, -1.8685254596460372, -1.9066642766673274, -1.848470867806654, -1.6946517704291435, -1.4525945768693538, -1.1361495238832227, -0.7649942706180958, -0.3636081724760224, 0.040092507773782475, 0.4163842755717144, 0.7355379579041753, 0.9696855044880176, 1.0946380250875045, 1.0915405773849238, 0.948255908324574, 0.6603830113792758, 0.23183635170394387, -0.3250631352377906, -0.9900050856907809, -1.7356034270212097, -2.5287640572983774, -3.3324342309946244, -4.1076356174975315, -4.815662736675601, -5.4203151875318865, -5.890026822537961, -6.199758343050124, -6.332531719979153, -6.28050483777778, -6.045511735183745, -5.639026200977228, -5.081542305650108, -4.401402457580479, -3.6331393723985665, -2.815430559438262, -1.9887903569084138, -1.1931433124967779, -0.4654323961856432, 0.1625846940223214, 0.6662082119480475, 1.0292150808295013, 1.2447291687904787, 1.3154838621039648, 1.2534574060046386, 1.0789031216550944, 0.8188373646295237, 0.505085171043953, 0.1720143384727869, -0.1458890182822542, -0.41643830015445016, -0.6119916266586676, -0.7113689795352048, -0.7013073822765974, -0.5773513535489185, -0.34411461437279395, -0.0148927714356118, 0.3893475643367093, 0.841533244248615, 1.3104925394923361, 1.7632637295826195, 2.1675385171928214, 2.4940631631456203, 2.71882159253126, 2.824838860980925, 2.803469485357196, 2.65507154296871, 2.3890116487880015, 2.022994828169723, 1.5817633993858453, 1.0952565898201159, 0.5963641608205461, 0.11843960951911275, -0.307241030391277, -0.6538819102426406, -0.9012462540690703, -1.0372476823897365, -1.0589246345201528, -0.9727133843183385, -0.7939872528899189, -0.5458852220768733, -0.25750810949074526, 0.03838940269002888, 0.3080412009907732, 0.5194476421310016, 0.6450752050663352, 0.6642654911708631, 0.5651587904807971, 0.3459703861553763, 0.015503892305977198, -0.4071580113804999, -0.8937831328132001, -1.4088740667312492, -1.912182014841797, -2.3616734214917408, -2.7167335837496593, -2.9413678941661505, -3.0071556747967976, -2.89572450877789, -2.600544000748532, -2.127885023132509, -1.4968504681019599, -0.7384519966645041], 'positive_zeros': ['1.71352074137140589484897419981840', '3.58956220414985624183442629107835', '4.31729940070952066850243266248229', '5.41973963683204377947770294298618', '6.63992962171986762516218060969058', '7.87925110755520057981937380345334', '8.753491919803755979967730197629659', '9.875874426186003541709374045324744', '10.40789804648586078280810315332173', '11.45382503926397097422445012845422'], 'prelabel': '2-336-21.20-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.452487143376032, 'root_angle': 0.4092217112572425, 'root_number': '-0.8416975766245420420263760151745321714461246773655458597 + 0.5399492471560388960207379089059715154510733026698877919*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.4092217112572425', 'prec': 60}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.71352074137140589484897419982', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.58956220414985624183442629108', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.31729940070952066850243266248', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 19.824641761928856, 'bad_primes': [2, 3, 7], 'central_character': '21.20', 'conductor': 336, 'conductor_radical': 42, 'degree': 2, 'index': 39, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/336/4/k/a/209/1'], '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': '2-336-21.20-c3-0-39', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-336-21.20-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.452487143376032, 'root_angle': 0.4092217112572425, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.71352074137140589484897419982', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2172145596302983318704222184411', 'Lhash_array': ['2172145596302983318704222184411'], 'factors': ['2-336-21.20-c3-0-39'], 'label': '2-336-21.20-c3-0-39', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/336/4/k/a/209/1'}