-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_287.228', 'a10': [0.6691306063588582, -0.7431448254773942], 'a2': [-0.10452846326765347, -0.9945218953682733], 'a3': [0.5, 0.8660254037844386], 'a4': [-0.9781476007338057, 0.20791169081775934], 'a5': [0.6691306063588582, 0.7431448254773942], 'a6': [0.8090169943749475, -0.5877852522924731], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.30901699437494745, 0.9510565162951535], 'a9': [-0.5, 0.8660254037844386], 'algebraic': True, 'analytic_conductor': 1.3328223966973418, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [41, [1]]], 'bad_primes': [7, 41], 'central_character': '287.228', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 287, 'conductor_radical': 287, 'conjugate': 'dirichlet_L_287.107', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^22', 'a^5', 'a^14', 'a^4', 'a^27', 0, 'a^6', 'a^10', 'a^26', 'a^11', 'a^19', 'a^27', 0, 'a^9', 'a^28', 'a^11', 'a^2', 'a^13', 'a^18', 0, 'a^3', 'a^22', 'a^11', 'a^8', 'a^19', 'a^15', 0, 'a^9', 'a^1', 'a^26', 'a^20', 'a^16', 'a^3', 0, 'a^24', 'a^4', 'a^5', 'a^2', 'a^10', 0, 0, 'a^12', 'a^25', 'a^14', 'a^14', 'a^7', 'a^3', 0, 'a^0', 'a^16', 'a^11', 'a^29', 'a^7', 'a^15', 0, 'a^18', 'a^1', 'a^2', 'a^23', 'a^28', 'a^18', 0, 'a^12', 'a^1', 'a^8', 'a^29', 'a^25', 'a^27', 0, 'a^21', 'a^16', 'a^20', 'a^26', 'a^13', 'a^27', 0, 'a^24', 'a^25', 'a^2', 'a^20', 0, 'a^0', 0, 'a^15', 'a^4', 'a^14', 'a^17', 'a^13', 'a^6', 0, 'a^6', 'a^1', 'a^29', 'a^17', 'a^25', 'a^9', 0, 'a^21', 'a^22'], 'euler_factors': [[1, 'a^22'], [1, 'a^5'], [1, 'a^4'], [0], [1, 'a^11'], [1, 'a^27'], [1, 'a^11'], [1, 'a^13'], [1, 'a^22'], [1, 'a^9'], [1, 'a^26'], [1, 'a^4'], [0], [1, 'a^12'], [1, 'a^7'], [1, 'a^29'], [1, 'a^2'], [1, 'a^28'], [1, 'a^29'], [1, 'a^21'], [1, 'a^20'], [1, 'a^25'], [1, 'a^0'], [1, 'a^13'], [1, 'a^9'], [1, 'a^23']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-287-287.228-r0-0-0', 'leading_term': '1.07878972328570107994250272350+0.560395662625883397768712973943*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/287/228', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.2156605470922968, 1.6889745367996978, 2.2604192380645354, 2.4928759062175496, 2.1296206534716653, 1.2458364096330599, 0.21844860467787874, -0.4632076026583623, -0.48239051487405193, 0.08077514016406091, 0.7519060139371002, 0.9430304925816028, 0.37201298719072357, -0.6588651369154096, -1.3698782267978458, -1.0082419180511257, 0.5405283796180538, 2.4772733846626878, 3.438510958142036, 2.3464083207808373, -0.7696734586311936, -4.587935248021048, -7.180960995700463, -7.19797010941496, -4.75245242388233, -1.361996725086477, 1.063457517988912, 1.481155153657418, 0.307860375912458, -1.0768636525041053, -1.4924763898192595, -0.835331151137642, 0.028030334166235047, 0.20822226174225916, -0.29760690986745425, -0.5840000138941894, 0.2514816385354298, 2.1043171179744418, 3.755189386269662, 3.8626300191798544, 2.212358577138107, 0.046710301989805525, -0.9341474254823076, -0.07321578711447688, 1.6211608751133721, 2.389349561870439, 1.4066011338348314, -0.3300235998680778, -0.8413039977280778, 0.9376887738607393, 3.955169348560729, 5.759136429327474, 4.609691616996876, 1.0965269257633004, -2.2715100231967225, -3.2008221432991135, -1.5463727363364164, 0.7199258164262546, 1.4308095102932008, 0.18697207736213128, -1.4751213885864798, -1.761848025265408, -0.40448270721877044, 1.2169647525091256, 1.620034618387581, 0.7414523084979474, -0.15859076115006715, -0.017705442368195833, 0.8252731411164645, 1.1156815407110496, 0.30521776087190494, -0.6082378831002013, -0.16421293938438267, 1.603259063199031, 2.5950912954698264, 0.4581874719452437, -4.808185304874456, -10.183711807727004, -11.914413796951097, -8.781919929802987, -3.209835871812957, 0.9262813051801784, 1.6752985557768256, 0.3191188983181168, -0.4769117380041744, 0.4510046547707515, 1.862743357177092, 1.9128080952073134, 0.4311096159874099, -0.9097683343891249, -0.624824143864194, 0.7912781110722641, 1.4241969524149132, 0.2026639391203786, -1.7910350888146118, -2.5273312031780866, -1.3704257108776903, 0.19561962288947032, 0.34374778790083815, -0.8948985156001421, -1.653051542353231, -0.5241240016370894, 1.5849745786757055, 2.3710657012993632, 0.895301015251089, -1.0815074263051103, -0.9870729497304609, 1.4287781265186645, 3.396157989306654, 1.9791668254431023, -2.496434689871616, -6.331199795560741, -6.026736003063396, -1.8137018011448018, 2.6349385728322257, 3.929570463364654, 2.0769216754888475, -0.18095275654836823, -0.6566010078093546, 0.23369591500288256, 0.688586727074048, 0.05964711798655599, -0.5445559758303351, -0.10201280363440951, 0.7033199449361616, 0.36240178462571476, -1.209514788223738, -2.1675507818758115, -0.9566681810180969, 1.4171300250155965, 2.1662097861237566, -0.0038414453762484063, -3.024578480037414, -3.570200914261144, -0.9669443676362147, 1.7216003524551784, 0.9882780047308445, -3.071835254014565, -6.6696288277341065, -6.387579111602557, -2.7704152351434512, 0.5935448464637121, 1.2145235926858364, 0.12468993166262399, -0.034677666052686254, 1.4422674019945076, 2.624005938394614, 1.7515242048075237, -0.23577140222401705, -0.7700661114710468, 1.0641574063729535, 3.2780701135768595, 3.378162079036078, 1.3619890016487766, -0.4582054765274597, -0.4431527033227821, 0.5107462092101347, 0.546286045477789, -0.46541375437460036, -0.9056967946396272, -0.11159332517905796, 0.10375382754243029, -2.299217939584604, -6.161727491513518, -7.323426019421906, -3.0689311260024574, 4.176527097741351, 8.673856701319371, 7.140974338229839, 2.022698639050957, -1.4340902071033137, -0.7985295954305365, 1.6582730742109688, 2.4624434811944598, 1.0848293814200283, -0.185211057984871, 0.22304118553471985, 1.1818538074442366, 0.8087006222479175, -0.7222495860699599, -1.477992261994959, -0.5997238971384568, 0.4827157385553186, 0.25778185493686606, -0.4091734862496065, 0.6998670774660474, 3.7641153562158967, 5.916992356777797, 4.500826154820288, 0.6140314526085042, -1.878197501911328, -0.9751469772485839, 1.0280458416706724, 0.5649779322883068, -2.513694030479949, -4.675895113291636, -3.279218941469799, -0.042350026427727575, 1.152849729966793, -0.7040773904297244, -2.457912794630609, -0.9366673443387359, 2.8576923732073567, 4.92647010364217, 3.2071280178603265, -0.10687644233827165, -1.5898730352143224, -0.7123431459027375, 0.21060803182924848, -0.3730093826055042, -1.31008601128872, -0.8958878349550936, 0.36134260859082606, 0.4990413269128442, -0.8196945047291361, -1.612134774820131, -0.49253431616429355, 1.072915823558676, 0.8183751113506669, -0.5858589211206289, 0.2504024266702597, 4.745624515836741, 9.297208879689899, 8.675894135521553, 2.350571305320753, -4.193134794492299, -5.24743694350493, -0.9833209871871746, 3.371243646291694, 3.835967239257287, 1.5273520745913665, -0.0510869640874118, 0.19823024300191175, 0.46401345185562953, -0.42565029004428195, -1.108915345419959, -0.10802662960870388, 1.4151175757962888, 1.0166270218631044, -1.3449609557715074, -2.7931805515562096, -1.2858990833860902, 1.5224006792311426, 2.439642953044882, 0.9810116230942398, -0.25905684002182033, 0.44201996687906553, 1.4584313862088383, 0.5084599481548641, -1.4218310757679438, -0.9805654734889835, 2.6051830840908687, 5.569407415433837, 4.041502315529804, -0.6706797827418627, -3.25227671184886, -0.8987607894616699, 3.2490863601912174, 4.247864675223662, 1.548082964754693, -0.817171452250708, 0.12819189082440569, 2.6292975750363334, 3.0808816107000236, 0.9648932071332319, -0.9354736082795864, -0.7156773313126121, 0.3581158606823948, 0.3284410043462302, -0.46298127888918783, -0.4073018193242223, 0.3384161968826516, -0.028101009075813796, -1.6640528735188294, -2.052195317556045, 0.36735487036448156, 2.96360299548248, 1.5812084184598947, -3.6356084195703677, -7.353812434466996, -5.189471037629435, 0.7661211263415871, 4.426104759961398, 3.0959496849190593, 0.15544980455129903, -0.10117479868050909, 1.9047052383555698, 2.3968452817393917, 0.027232842670201478, -2.3210364882422008, -1.8920212287244973, 0.09809907836214846, 0.6012749470862346, -0.6579306363946751, -1.0326526385889936, 0.7357330750853979, 2.413465708484732, 1.5773080420077665, -0.6977694015192204, -1.3645230205955547, 0.14224534477258483, 1.225327082157918, 0.18756200644750065, -1.2024705907352975, -0.5781093921950937, 1.1884334410748965, 1.2760718231979862, -0.4919717235458768, -1.0741356397469506, 0.8139436285270225, 1.541738795023438, -3.115513553693198, -11.345205342497806, -15.90137069161408, -12.226108025928989, -3.8846814987464766, 1.732533757112598, 1.7455419464612216, -0.3686928648268546, -0.63830185835871, 0.5858090847691317, 0.7413220088123533, -0.3898938927069176, -0.7297464640439506, 0.32630372011828734, 0.913745977896454, 0.0012793002590751215, -0.6339773101765056, 0.7406036351813261, 2.605061920993512, 2.0851219228780202, -0.5619089802261927, -1.940588197565466, -0.5290056584949412, 0.7825808020529866, -1.0395412912959694, -4.08888147319865, -3.537618146484748, 1.4826035464034417, 5.972199988879387, 5.3323234503679675, 1.2990565888415073, -0.6960929787310557, 1.125837116549121, 3.1584809554845727, 2.204796047987254, -0.049606946575068776, -0.2000255399922958, 1.3470725371397494, 0.9928513695162893, -2.3517227721439182, -5.23716184345919, -4.418755694241787, -1.3034268170152308, 0.31101893209719067, -0.493198075923297, -1.2501190192411356, -0.4442586495034172, 0.4257928382373371, -0.08796784075154336, -0.7492622753102611, -0.0043581078144005626, 0.7397864062450553, -0.9716087671699855, -3.943130716955414, -3.7995446198404337, 0.6899125393097899, 4.521561802121468, 2.298520916106722, -4.242271425389035, -7.746840826203411, -4.396491506882442, 1.5229433718884438, 3.599757089514762, 1.2847100637282827, -0.7386545294904097, 0.25047737151819555, 1.9352847453943258, 1.461953587555173, -0.22972621641449018, -0.5454723474824246, 0.4335017495948462, 0.5448739016006072, -0.4066934593857646, -0.25148789164172475, 1.510944788915637, 2.17256288245793, -0.06988871268429228, -2.6568200353547304, -1.858498431619642, 1.6957078692404135, 3.646930381193286, 2.076168845024278, -0.03204461391106096, 0.258586203291377, 1.2528992961517191, -0.2918117729013545, -3.2140111726780205, -2.8641201466473163, 1.8034868098098618, 5.705631119745759, 4.1934470941963085, -0.4444244748770924, -2.0863231586241238, 0.8527261000580779, 3.703813037613319, 2.487646142829992, -0.8638502849614096, -2.0570568244477965, -0.6061601392115177, 0.5054592210670255, 0.07348287996127295, 0.1280879961434165, 1.8534956697315945, 3.2272772393268827, 2.2942184174677203, 0.41302287918906366, -0.0438815878048283, 0.40729561930221414, -0.3568367634983278, -1.6703858612398501, -0.5159290578011462, 2.9152025725716766, 3.6575787131552806, -1.4523724263765434, -7.976094318691709, -8.34852046098542, -1.6164325962671595, 5.006666433707395, 5.213787326597267, 0.8906355912887981, -1.80803230643465, -0.9355255765784654, 0.23750462377804205, -0.5063975534093381, -1.31107426704459, -0.4142209612672942, 0.33441900298445665, -1.3500062721872137, -3.8141527394455217, -3.518598133621981, -0.5281754785345436, 1.401099010805971, 0.4330204096946842, -0.8757504053986325, 0.009531292201952228, 1.6001525752839714, 1.1963429450707248, -0.3812112423619659, -0.16651630477597584, 1.722803195383786, 2.0014161462531264, -0.07141289889752392, -0.6518702599461585, 2.819515137931695, 6.69031789468343, 5.63389994629787, 0.6565354178246567, -1.7036820488099609, 1.4508194229275009, 5.139579273360091, 3.5642223992362307, -1.8053339758315787, -4.658283589378161, -2.6392925466494175, 0.3517846147307982, 0.5975670279966893, -0.7161764351517961, -0.764257621954457, 0.22067398917087547, 0.2874413259365483, -0.2712142133071952, 0.35938591392705743, 1.7051842070741718, 1.4317128788509264, -0.2134670782695344, 0.057642137227792024, 3.167754746935553, 5.04975661287591, 2.1500713445677215, -2.770877279538243, -4.0481604709304095, -1.30427282328659, 0.05065243929928167, -2.8667186047325486, -5.88067967944163, -4.055075374413676, 0.7590768199746649, 2.6204136197714645, 0.15163049440178605, -2.0102123884742147, -0.6106751400503914, 1.764729433016234, 1.533823143353523, -0.19111582021705903, -0.06331928923299243, 1.5776697544014002, 1.3214707696713106, -1.3652739946035792, -2.9013844904616044, -1.1901683109597114, 1.1082210252806048, 0.8588898600713155, -0.8583491754339723, -1.1125720091593903, -0.09903248463946378, -0.26701007931278575, -1.520465757418264, -1.2735939376627383, 0.5137386536081624, 0.6135857342679513, -1.3857656122224964, -0.28704576308342145, 7.661467434759311, 17.340616508142954, 19.26156029470039, 11.317682098689465, 1.544392158520942, -2.0604263779676013, -0.35901837217429083, 0.7792263683710657, -0.4843636538483398, -1.1168782475565535, 0.29951785807225756, 1.2739524711006167, 0.19547155477163966, -0.8399941201759309, 0.0877636803486679, 1.2991553362466366, 0.6300017473620989, -0.5191328007217391, 0.43489198748656, 2.4137611741345553, 2.0816633237265894, -0.37498063110025986, -1.041346608334506, 1.3071331415713887, 2.7030046436875192, 0.23117991198721594, -2.741403605103842, -1.3295740167633112, 3.1062183213015104, 4.621904768405965, 1.5393183653721512, -1.32383410355231, -0.4393444691421078, 1.15021410082222, -0.6255024144750186, -3.7097949619314665, -2.8964702324019447, 1.7737952766430733, 4.6734190760503695, 2.8644500089087144, 0.011101761858036562, 0.2878499569089226, 2.364137979985371, 2.4507683557255366, 0.4598409902813272, -0.6714858005405819, -0.20983955032337687, -0.08514374794059786, -0.5543798672367307, 0.43539391394325133, 2.8435068797907563, 3.499359609269419, 1.2747495587575275, -0.3713500541030604, 1.0612497585756144, 2.1788465397389025, -1.3663474796443782, -6.847872780841751, -6.818073652144555, 0.15054073727952214, 6.386393442088343, 5.142001001332058, -0.6328165229095686, -3.275557117350485, -1.0296139714330987, 1.2198661754615114, 0.4063174702077217, -0.9987651613856756, -0.4307869381239612, 0.5658185474438718, -0.050509365168113586, -0.8523409911436475, 0.08772877767309858, 1.0027184389383192, -0.835070120224751, -3.777494000421112, -3.5377417243938476, 0.08247865120705, 2.5373318571883385, 1.3505748199461485, -0.6098853999207118, -0.4600825481664485, 0.11387284156452085, -1.2837025349786377, -2.6757513641192916, -1.003029700128279, 1.4850496368516528, -0.4075596407809668, -6.123378754341453, -8.607670209273968, -4.222295816264599, 1.4768580986585658, 1.4483896848671929, -3.0375224634713502, -5.086145431127831, -2.509659864302942, 0.10310099539388572, -0.5372521458796469, -1.8514956470656077, -0.7134190631681161, 1.306539925311765, 1.214602556007277, -0.1851667301020835, -0.1441540119443568, 1.069536944870114, 1.0822192866800835, 0.06836886063378214, 0.27801265985267803, 1.339453136060891, 0.6059092028042236, -1.1716095399886943, 0.5658971887608215, 6.622008781888915, 10.581705389111795, 6.956208683887338, -0.38311878030633884, -3.001449709405569, 0.5029709824913735, 3.382737255548128, 1.2764579581201183, -2.088001560648248, -1.8845238143584664, 0.3998565663520381, 0.6078000554416809, -0.7764412165194754, -0.15499770958568154, 2.2188761311822223, 2.3279570973661246], 'positive_zeros': ['1.952389315794181945107230962289', '2.776993209610220686489571378623', '3.868409230954415517418754907587', '4.90941846428608741513284421058', '6.18465921666965894525417973637', '7.96011937991650972794509881058', '8.81238340633699081421966519212', '9.98615213205249005576995889287', '10.46777579895086994372656400518', '11.192388312651867257255098683866', '12.82062060665897106846300170929', '13.45195928213285318008988117497', '14.62162376416582997635181966877', '15.19208458374014598727690947248', '16.651245489298459756016562232623', '17.70093362750455561184107393445', '18.469550646028029186064719466587', '19.44488455477279490780167099018', '20.542948208724376020206886421061', '20.94561673578605437740696302623', '21.95924373744535499552155254776', '22.53683129334024068080520097665', '23.47184968457397661441277089393', '25.2172743515638651489358130250', '26.010239149000869854175781590956', '26.461286169675808944020710273362', '27.57847667613985907893741468428', '28.27039954150002653642388088470', '29.09438288229634837446164935137', '30.26081279035463133296897487381', '30.7328940084292139407909601122', '31.64108016530980048231714824811', '32.62531049418476004140685707047', '33.2747436554310218368646330061', '34.21481198041533025928180965914', '35.42577005372727441561527733396', '36.52798785526309897281586693659', '37.11418262116502815933226032701', '37.83381806230255775386840362981', '38.47283853404039427253372333790', '39.148343442920608092600592557850', '40.1249632557104539133812570445', '40.93712218079605491873544805239', '41.966269057036613747424134054759', '42.59317047534726069988954836938', '43.987762073144077232231987352802', '44.73007407936081497844414375876', '45.01273971451398895794583130286', '46.20806122603111041204208533121', '46.73131056926057311247623607737', '48.01645622633771940224902391478', '48.57974814939789222984671736146', '49.24282938427558191880146503374', '50.03803205281591658194593147519', '50.342504110069230962837275665184', '51.69694993224753464886016495535', '52.95306644664564055143958442299', '53.53979632519785019144739222277', '54.606376627407652985805332833835', '54.92710455662936688437359129169', '55.7962266459746379072115210619', '56.70589049682076596189958359316', '57.28141799999895706953096122100', '57.69814127101141741090848640087', '59.11447385040953836418269441576', '59.823066881587531676102584452314', '60.38396647081579855657758489835', '61.56730721957201831456652340140', '62.09872401419340686920108995148', '62.895777200301824018789321585067', '64.0508149555957202458322065411', '64.87673776617826822634934529207', '65.194768871019533684825019431012', '66.15203917122713637567384192227', '66.70293495477604930584289568385', '67.58416231815732751432200361128', '68.29487253025296742369642195828', '68.7204306288235089371590196652', '70.097295527064295755475783710517', '70.9958656684818089484904552146', '72.16139100044580353767552814576', '72.39755798012362860404012190704', '73.00776785209229197899435083252', '73.76980707622684937608932875403', '74.52352015134341173374216785741', '75.45037944723405433316408102009', '76.44561175740743733455593167080', '76.76055512014129824012290994215', '77.57724113831443821700121429629', '78.23130101800081580143112682979', '79.3304570456664302250889117497', '80.06489386633261321074686461669', '81.09868166392969262090944451022', '81.545152603038742982947207391016', '82.62563929096556587369770423563', '83.3168837810550016906319905333', '83.87684164621014589601958456632', '84.53589864981002976510702346561', '84.99289196264021401067758961271', '85.90206492628590774608313384534', '86.67120219218725304948270611587', '87.7721006740919071746808936654', '88.77580523577354258461218663379', '89.083750043014932000177162600475', '90.00280867624604695851244695543', '90.91935899078568935807349051838', '91.417912379329550496703636024938', '92.08443645371114307557725853974', '93.02355234923030909959242089180', '93.72578025654711701574015025911', '94.40861507679047651233063516745', '95.09967237496305026225166312208', '95.85549583173570243213715701465', '96.45145331326194566656178395133', '97.028516840765990883563063770687', '98.61506290675661080196652573950', '99.30973954387623391838391873336', '99.85320727154118402106334153543', '100.52307683737006091497460181893', '101.16815717501458111676884946756', '101.87532702657126895563940551069', '102.38095324259194833926297171445', '103.37328711720876244516221991382', '104.144275132139242021760711661333', '104.57229744208163203399714568489', '105.54570293898676245656628606541', '106.68891081180195047648927880781', '107.04877799287913758939148733917', '108.115383605729540976410247025905', '108.4844420132491183210762076872', '109.17738784715079278130991477049', '110.49804077747403128657829966081', '110.81063702499330835078994614287', '111.67967154308137968973363319598', '112.15885705745150023189202970396', '112.813604678177977086523722437039', '113.3194698415423975155026076382', '114.334787230157419115759558153197', '115.117006469293171233624873169991', '116.16038116215602949668079485105', '117.02280438361948959822125972615', '117.45949000075136750431603011781', '118.38733766461453042658928561904', '118.92977516443955835014790364068', '119.555415847709382350582519406676', '120.05729741993765853828122128082', '120.93056230893086113771415442460', '121.73324583315572462355960782782', '122.80334919354985278419053786325', '123.05478334392280903344136426188', '123.71758174164506369005754081166', '124.58336501511555909624269896318', '125.591907576253267788341626472669', '126.181269833492763040398353378489', '127.10083649552302514164261283387', '127.929097177763846046783977731926', '128.4769074407519052682281946915', '128.7016290119927585204483175312', '130.12786190743573980312347550510', '130.34511151097441851283071688431', '130.85498901108379879719686511239', '131.61541910495423724025365688177', '132.43426505326141183490185196369', '133.499808663873953838747223258437', '134.44225415523138128666605237004', '135.19551541566659351853500673715', '135.48951313436054712550141640819', '136.350311832294040037301966916765', '136.67956349655318551702184959417', '137.867570532369566958949975380106', '138.51356251675416127424571254998', '139.06083044477350639101488912790', '139.9104056891925161748615137299', '140.34545401359625464364736285632', '141.239678892264148191679966057333', '141.65521130882942396501997675583', '142.85765021492631876369520998210', '143.33550463361330070222599025709', '144.27169825266902791231435737309', '145.260456541209940883174720337206', '145.76461732643537049530763016746', '146.484202840066388652161936591695', '147.012384481717693070000416200588', '147.40426154449579763986066931025', '148.38988645659981053721404259336', '148.74081181955852376209787624943', '149.81700520877932033924837082759', '150.8064291595355695716758252890', '150.952544064226633691247556475798', '152.134325496049669168039967656162', '152.82704731135391566376858575547', '153.506874282007059989221167919135', '154.3303874691102652289901060177', '154.70151837646777310173304210683', '155.48022384263845285638337825236', '156.387319962289606499484813564395', '157.026593411346369431222021724535', '157.86188527302895566476821942004', '158.02144004661987472873550014003', '158.969448653207872465346125010853', '159.48045136840623886607505499293', '160.01878170532626907173722901952', '161.63667079828874347235155298667', '162.23891187349557349847124840659', '162.71835510622899540950023073340', '163.38470261931917101704390803481', '164.10119630835712453088127174747', '164.670083278965556123614627738249', '165.44774007401554211942300830589', '165.86351911242990144100611795488', '166.82559825856038754477831102488', '167.35290856752939027721920226233', '168.14430054941773904178616701989', '168.84784951855679472281692565476', '169.81594363425468083268244246421', '170.37492065053523505920245868710', '170.87492125765656395811896946054', '171.76469626174029941046103305533', '172.81470248533979098483449966798', '173.07040728520091136568567775880', '174.14029545463383481019269333340', '174.861691891566421084120737580873', '174.89670716423288338556860159821', '175.55094243965733644673234801162', '176.73809807571223722049161711548', '177.023173757376802247442165598841', '177.73161017253219995236702133484', '178.74431155045456144444906490592', '179.65130577261666314713821468898', '180.4175676657359163114249184579', '181.00748678161991807031217736407', '181.66518782372678851998541392787', '182.17418293435100563802193392175', '182.794384970494398556837901018508', '183.34530369664521485012692061066', '184.36838689528324940849970147844', '185.18646753292056955908500309441', '185.783614796564994027910602292087', '186.000090917268558054272787278006', '186.97753649358820644332296216311', '187.47131479644157382765283327025', '188.6470588161096079073783270493', '189.17504956047908390267574664581', '190.28513737303401779741476317143', '190.51321752491105807925493988419', '191.34753975330541344385220438889', '192.13628502681050945567119468667', '192.54121602633319535085493820732', '193.47302730396203975675968153402', '193.64159610554561592850947320556', '194.46859556759939997913393551708', '194.9568154488885564665284630430', '196.23091873407327152268927847017', '196.840491239669054877464584193', '197.601880394871979709010211196776', '198.37319718759702415459590321912', '198.8814014719411820913380085018', '199.39784464845107191688956203341'], 'prelabel': '1-287-287.228-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3328223966973418, 'root_angle': 0.1525021546225351, 'root_number': '0.574994175967536636080509324975+0.818157501709428509456279287981*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.152502154623', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(30)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.08635407407094658017467279462+0.122388091122083301790968062465*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.95238931579', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.77699320961', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.86840923095', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.3328223966973418, 'bad_primes': [7, 41], 'central_character': '287.228', 'conductor': 287, 'conductor_radical': 287, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/287/228'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-287-287.228-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-287-287.228-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3328223966973418, 'root_angle': 0.1525021546225351, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.95238931579', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_287.228', 'Lhash_array': ['dirichlet_L_287.228'], 'factors': ['1-287-287.228-r0-0-0'], 'label': '1-287-287.228-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/287/228'}