-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_1441.299', 'a10': [-0.44319154559924134, 0.8964269372957038], 'a2': [-0.8619696668800493, 0.5069598538135904], 'a3': [-0.9988322268323266, -0.048313379525507065], 'a4': [0.4859834132426061, -0.873968032626518], 'a5': [0.8364701380102267, -0.54801250735467], 'a6': [0.8854560256532099, -0.46472317204376856], 'a7': [0.9895063994510511, -0.14448904956922132], 'a8': [0.024163745236132288, 0.9997080140801929], 'a9': [0.9953316347176486, 0.09651392091451512], 'algebraic': True, 'analytic_conductor': 6.691975866344493, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [131, [1]]], 'bad_primes': [11, 131], 'central_character': '1441.299', 'coeff_info': ['x^130 - 1', '0.998832226832327 + 0.0483133795255071*I', '\\\\zeta_{130}'], 'conductor': 1441, 'conductor_radical': 1441, 'conjugate': 'dirichlet_L_1441.347', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^54', 'a^66', 'a^108', 'a^118', 'a^120', 'a^127', 'a^32', 'a^2', 'a^42', 0, 'a^44', 'a^101', 'a^51', 'a^54', 'a^86', 'a^60', 'a^56', 'a^44', 'a^96', 'a^63', 0, 'a^33', 'a^98', 'a^106', 'a^25', 'a^68', 'a^105', 'a^102', 'a^108', 'a^97', 'a^10', 0, 'a^114', 'a^115', 'a^110', 'a^17', 'a^98', 'a^37', 'a^20', 'a^5', 'a^117', 'a^79', 0, 'a^120', 'a^87', 'a^119', 'a^22', 'a^124', 'a^30', 'a^126', 'a^79', 'a^104', 'a^122', 0, 'a^29', 'a^110', 'a^26', 'a^8', 'a^32', 'a^65', 'a^21', 'a^129', 'a^64', 'a^89', 0, 'a^51', 'a^38', 'a^99', 'a^39', 'a^97', 'a^34', 'a^78', 'a^71', 'a^42', 'a^22', 0, 'a^91', 'a^118', 'a^74', 'a^4', 'a^59', 'a^48', 'a^41', 'a^48', 'a^3', 'a^38', 0, 'a^104', 'a^44', 'a^98', 'a^11', 'a^33', 'a^43', 'a^32', 'a^76', 'a^127', 'a^48', 0, 'a^84'], 'euler_factors': [[1, 'a^54'], [1, 'a^66'], [1, 'a^118'], [1, 'a^127'], [0], [1, 'a^101'], [1, 'a^60'], [1, 'a^44'], [1, 'a^33'], [1, 'a^102'], [1, 'a^97'], [1, 'a^17'], [1, 'a^5'], [1, 'a^79'], [1, 'a^119'], [1, 'a^104'], [1, 'a^8'], [1, 'a^65'], [1, 'a^51'], [1, 'a^97'], [1, 'a^78'], [1, 'a^118'], [1, 'a^48'], [1, 'a^104'], [1, 'a^127'], [1, 'a^17']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-1441-1441.299-r0-0-0', 'leading_term': '0.822560112508240241178535818975-0.376811125245409341306278627034*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/1441/299', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.9047606107685503, 0.5781364210506357, -0.034546625630790785, -0.7060948382495432, -0.7590243178296286, 0.07335320303671543, 0.974051087147202, 0.34248938929284345, -2.8739773015361094, -7.8278576097300245, -11.804550775031258, -12.056217912231919, -8.108542903678781, -2.4132998696280774, 1.5212256473672747, 1.991832241311665, 0.2778503845483465, -1.0035307038296253, -0.6352149155944217, 0.25496441130876524, -0.05181087019826984, -1.5621405457038806, -2.4946210520209022, -1.5336730639197649, 0.3835762332984922, 1.0819309548153178, -0.16031315904427873, -1.612227912019056, -1.1891918933233985, 0.88512354660308, 2.2871147718758893, 1.534369960923306, -0.10937783380206217, -0.3533756690592268, 0.9640642776246418, 1.6002868228833298, 0.13598136612803732, -1.601622383135632, -0.5921753663023308, 3.1159605031609314, 5.698875623248241, 3.9972287505794655, -0.23490110366691438, -2.0049055827477646, 0.9440139825896464, 5.280749704391147, 6.10013884330644, 2.8005197081407642, -0.556280632454482, -0.5617684328261459, 1.624960326148988, 2.5265401427281122, 1.1136330311195797, -0.44472556987737827, -0.3904250803847827, 0.3465123362056871, 0.2483877220260709, -0.15106171295678877, 0.5110815609902722, 1.4384256925058585, 0.26596529467383845, -2.9644407069157785, -4.663373947249886, -2.162882297552617, 2.1018829472488, 3.26334136278821, 0.5540564897221579, -1.50818841152244, 0.5473131353261619, 4.038164640770342, 3.7268507905256674, -0.7375636445072111, -4.113420156939805, -2.6504953001443132, 1.099893436418884, 2.318567263908988, 0.5274843879116431, -0.7040543060006794, 0.3114533074238039, 1.2217240196174157, 0.1251717444653573, -0.95345090838826, 0.6694619091664519, 3.6289726816806143, 4.120463413809749, 1.5319459699581264, -0.6871287597306612, -0.22031913436436176, 1.0671647216112583, 0.7411524359042061, -0.21200296525639156, 0.4230495202352027, 1.7779825450328974, 1.24087404145509, -0.5729769951305683, -0.23187876667378463, 2.2344464294777624, 1.579465150160844, -5.213200441954461, -12.670322120167734, -12.398387648452992, -4.024575292377877, 3.9070319191696288, 4.668151810522342, 0.775806628873906, -1.341904691944756, -0.26641626238612315, 0.6259461169259397, -0.06603985194517359, -0.10708118257111196, 1.4413583895316877, 2.2137494801620035, 0.8732729642424263, -0.28795569186339576, 0.6646841421135306, 1.7889245838357613, 0.6856462472462449, -1.009101123712812, -0.2705221747190413, 1.7952526652214658, 1.5494607151085107, -0.48240015170803485, 0.460828153026257, 5.472022576760222, 8.88493282142484, 6.1246812033959825, 0.6849903696155849, -1.0550588740450297, 0.8228315926655559, 0.9936945760859013, -1.8407481905101226, -3.090515567281774, -0.5620524192171282, 1.417410480233409, -0.8240934212956986, -3.8857927853146874, -2.554169122276591, 1.8295890763300837, 3.525133429665668, 1.1961833991638597, -0.9229442509764354, -0.34802143847997524, 0.5933061827657741, 0.02159977510379784, -0.2464947360037735, 1.1156184300015246, 1.9166317623227402, 0.5599239694500271, -0.6009067761548266, 0.48509286083138625, 1.4340692120536631, -0.11768529360560556, -1.0588770345032434, 2.4714515817751286, 6.869995194754434, 4.589414565452884, -3.94653324199664, -9.18519594415887, -5.578763774476677, 0.7176697636997686, 1.4072190857245899, -2.3419509080739824, -3.634555066569103, -1.1026505121726546, 0.5728726155055426, -0.5123295213753476, -1.2478481541120963, -0.09985155433077397, 0.517292830880258, -0.398703184047912, -0.5374428060637813, 0.43239761626988144, -0.7863611347332771, -4.830402347898726, -6.956617538148428, -4.157805074897776, -0.3327013136661534, -0.1132668029558108, -1.7449966187122317, -1.1307903537133055, 0.779027592014597, 0.6340486187767593, -0.2766039774069849, 1.327254753091901, 2.8497721643804943, -1.368293961888389, -9.353500783984124, -11.958174309957977, -6.044763153237361, 0.6234737597664177, 1.1867111859735582, -0.9710608143587318, 0.19917083807801417, 3.0184701775647502, 2.1806694652285388, -1.3582947392695506, -2.260559158447539, -0.012182886465014833, 1.1210161033166468, 0.05961821530553015, -0.11280075787972574, 1.2923019980537156, 1.5718700972013098, 0.3176091307221392, -0.06126456903481965, 0.259678547468234, -1.1288220996666711, -2.786467863253871, -0.6990440830586037, 3.3346223511538797, 2.4345941845172177, -3.7799685468497213, -6.557513547792396, -1.2590367761056354, 4.6567622203107195, 3.0180096218725945, -2.640169702673611, -3.728798575452866, -0.162951511413165, 1.5557922166185771, 0.09416377266910263, -0.18993404715622245, 1.40424588900798, 1.1783240290715313, -0.7746077644596042, -0.21611546089324624, 2.8449276013212144, 3.418618488109609, 0.3628088297474506, -1.6426438347065846, -0.5267153160665476, 0.16363507324710205, -1.3153782571633306, -1.8013830252147776, -0.07295770878949748, 0.3953225058405051, -1.4895674295063814, -1.726100895281208, 1.0464900202390577, 2.3506044119201666, 0.26386375248760563, -0.6182044470501112, 1.6851756757697918, 1.5915075981551314, -3.5323144458674616, -5.983469644949525, 0.6910211085320808, 9.459936920111124, 9.078480043548636, 0.7936716202286924, -4.558821144318591, -2.947465883888494, -0.1496207191088126, -0.048292848204233726, -0.2601688789254718, 0.5408353762030949, 0.1966526975026314, -1.1668275300652342, -0.8118183827033448, 0.6004225644308809, -0.1261305947215021, -1.972639951151042, -1.2174266645986151, 0.8640729082419697, -0.12849299191091948, -2.7337832546249037, -1.4229407755320669, 2.8160798420712236, 3.430396756809574, 0.3431960972556997, 0.49502689796160715, 4.733964149969927, 5.305841807643759, -0.37133857844786267, -4.473157804442777, -1.9337008996347036, 1.6074758559396247, 0.6649500416906874, -1.1163059488472997, 0.5980849300669269, 2.4152323838291117, 0.4870204145756904, -1.7366122911674768, -0.41994370131991626, 1.1134314866021329, -0.9391795812208241, -3.2223470007187895, -1.5294236823846898, 1.320405012587798, 0.9564267983587278, -0.8597534986348702, -0.6369630622588006, 0.3246706721407088, -0.10343693505523936, -0.2502759080485758, 0.45971846801610766, -1.2743542786213993, -5.022311899971001, -4.34207958090204, 1.442573872448851, 2.348318352417307, -7.048735461781307, -16.541308150254256, -14.489262637113159, -4.994741209500367, 0.1738539765668242, -0.37139460466867885, 0.25147033662726587, 2.7931367887738707, 2.2649207636769835, -0.83892108386454, -1.3877494331353393, 0.6029514757608351, 0.9953580875748866, -0.06745204456522894, 0.39558630563399566, 1.3432596345022167, 0.46303609284173325, 0.04799168385566679, 2.264990225426821, 3.1692256902703746, -0.5292737847170059, -4.023823359699424, -2.1110874864708427, 1.4673016142112698, 1.1011225037643009, -0.6313851101888557, 0.6942799608472963, 1.7189417957517228, -1.807836244385395, -5.224182685041087, -2.858418939057924, 0.8261994924174405, -0.7354971794617782, -3.5659350344685516, -0.5441511316898793, 4.656897436049933, 3.715891153057217, -1.3922705831114814, -2.30307424027083, 1.096845757487991, 2.1717143372973164, 0.1465392962633641, -0.26971560855825444, 1.1701636445965966, 1.0093704997105835, -0.23769673024086427, -0.10821059953114992, -0.14842444675749314, -2.0130154213761604, -2.502321359044571, 0.3272366244511254, 2.231262741203385, 0.6395491734278221, -0.2414036845244849, 1.2542331790800514, -0.4825533665862158, -6.223541473117714, -6.274652343195409, 3.5945478153558827, 11.89570239706755, 8.04561341048378, -1.284756157194894, -3.9677126210595657, -0.6814397481366711, 0.5509027315854433, -0.8457145553898758, -0.606091139463302, 0.43869637665359457, -0.30176128979993583, -0.6205074087159624, 0.9762276896816204, 0.4304092334705234, -3.8165259107743386, -6.011590461370116, -2.9020937679852956, 0.35465692745950034, -0.12970306791298009, -0.7772547103956826, 0.8693137722882087, 1.3375246687037272, -0.5241512114201188, -0.7971422893202954, 0.5768545912617931, -0.9519307072907399, -4.143362262075951, -2.905392694220298, 1.0429006399186047, -0.03571821528282824, -4.498797675726166, -2.7427572259598687, 4.684276683397148, 6.420975928832005, -0.12314304628997838, -4.657405672966712, -2.228326301168111, 0.1832324603109356, -1.5968289142064473, -2.5221862286062517, 0.012708469642368304, 1.5112553239158681, 0.15154520104369223, -0.44601074462428986, 0.48195449565980314, 0.13904589164172435, -0.8054940222616467, 0.09417182288539311, 0.9638782784531571, -0.130051861181681, 0.11855077555532086, 2.782378157831481, 1.5302611755038504, -5.816253735188851, -9.96721244014364, -4.623334480231246, 2.166243905866924, 1.8520067528371582, -0.7358375751041571, 1.3416731269898634, 3.881102407581439, 1.4979852399668145, -0.792778000478618, 2.1911414266947267, 5.074320242246964, 2.355448309691941, -1.2890055171338175, -0.768248865846803, 0.30147154010669364, -1.4489405121568608, -2.191204436072695, 0.09483987981402635, 0.833735012255036, -1.4518840768501453, -1.8863726510255479, 0.5438852213534157, 0.928472923400004, -1.2734213770931975, -1.3535705545602061, 0.7382254788346331, 0.8823937784173297, -0.2706594149836597, 0.19933681931639485, -0.011960246921666145, -2.4294403446115633, -1.1091533303765435, 6.069516142223859, 8.59847366794947, -0.5207751829602736, -10.129422861986885, -7.399754660664986, 1.5658440035910697, 3.2761857282159736, -1.3795870031661006, -2.7556167495212707, -0.32719471334560674, 0.13428351812389042, -0.991451287240266, -0.37405175058522416, 0.27853578648949284, -0.8596526252634958, -0.9584482874720563, 0.6726884118395575, 0.29370857019739066, -1.745324257863982, -0.7902093631404429, 2.0105509931596965, 1.1381260078219506, -1.938175775451087, -1.4486682685591288, 0.7826876914660141, -0.5810232547456824, -2.592802534111459, -0.285229961153767, 1.3162928523400943, -3.8330090974702937, -9.21371939528291, -6.2351802394179865, 0.03204780530693548, 0.42628385527606893, -2.3546758944250845, -1.5619817280289214, 0.2320233763068634, -0.9558806366768358, -0.38228803928063737, 5.130494731042237, 8.30717605784812, 3.9527883115390505, -1.327988662168238, -1.1519480633987054, 0.8511981747336059, 0.43673592497185854, -0.1131528817188634, 0.6249764852127142, 0.22386706825529942, -0.7126349870639306, 0.5074939366301957, 1.7013294987158298, 0.21479989110023895, -0.21602157060533314, 2.512416984903548, 2.065926234916091, -4.1254585253860165, -7.054690542943373, -2.2424423748687454, 0.04628085044227147, -6.712319448792243, -11.896564999787296, -6.203695337331008, 2.0967997201181423, 2.6054503485652436, -0.7632394883691431, -0.8403195741293563, 0.015159064587816212, -1.4718800344289398, -1.8381604800868074, 0.42617246688087457, 1.1849137781928254, -0.14387599705159956, 0.15339145987024722, 1.1057014200114614, -0.5300556098758823, -1.5949424787381434, 1.6451953186037305, 4.452528924596391, 2.0546610679060864, -0.7374057026884293, 0.8609364386459736, 2.4333007852295845, 0.35471575105905173, -0.9535569175193328, 0.44669504603817634, -0.16962139772582516, -2.425370753868774, -0.5169232864132938, 2.3114423978516916, -3.0790505456862425, -12.646640790381534, -12.905254738876724, -4.162006702538694, 0.2046804176986643, -3.007084061963814, -4.405432596684032, -1.1635542545135191, 0.49545021279796436, -0.4939100331209359, -0.09610896253483159, 0.4698834289113651, -1.7549071580830962, -3.5060463993624076, -1.6731280696055173, 0.2663971379909618, -0.13390279277770825, -0.034756801110637885, 0.9261045023642671, 0.034934827918478406, -0.44511264711412296, 2.561370882985698, 3.671933519983913, -1.6236688499715142, -4.914144990682843, 1.5867664544778999, 8.661933051929951, 4.885180657723128, -3.1309399178217863, -3.281362434128777, 1.2871414269831618, 1.3872106512770692, -0.9248010619063265, -0.09403789393081168, 0.7580511126799386, -1.5508864239898998, -2.5443339709810173, -0.3697882884025444, -0.12142029610853869, -2.3200774522761716, -1.5623579311097646, 1.185796810901536, -0.09973921845700347, -3.7073476263336, -3.2868416673473937, -0.2131106921938009, 0.4263349065370531, -0.09396784670155298, 0.5980224177767313, -0.32330030505113255, -3.0471710480410485, -2.579811192191384, 0.18966572593156195, -0.9668912433885115, -3.6491226914454535, -0.3333519631202189, 4.858686545893673, 2.3020148319491778, -3.4140296555931875, -1.0459408199807896, 5.213114984030465, 3.1939945876307667, -4.240201144692525, -5.256479693585479, -0.6628727504011912, 0.398557152267251, -1.9010167852681448, -1.7436519062628442, -0.04449838196090546, -0.05687512362217396, -0.21013354245484406, 0.29447850036942635, -0.7042007897323579, -1.5426425606808278, 0.6010258910007841, 1.6498076344100876, -2.2545172311052473, -5.231294182782569, -2.0456364446743933, 1.3749907412200184, 0.015415981136914463, -0.5000126485631068, 2.6990851487542953, 2.544349043990753, -2.252504099789018, -2.5417087450112525, 2.778113052749341, 3.473293123510228, -1.9076388665184443, -3.4118877952321083, 0.5701903576970806, 1.7241541916640064, -0.616626787063078, -0.2249843606179248, 1.2635609758829531, -1.3593257860002408, -4.256775404964792, -2.1580049659697575, 0.5061789135434734, -0.9191403928005499, -2.155481685635038, -0.11626122042854385, 0.8738885464603318, -0.7158222770514602, -0.8647495209980303, 0.28479899251361257], 'positive_zeros': ['0.61036151471226207844068146692', '1.54152167160921266523946520848', '2.23841371954664510883927957226', '4.22261355725140502534758143314', '5.0470816723844250898304361912', '5.82452292622603856085422028579', '6.23489245064462004451945763693', '7.43210669660127173812661096723', '8.09651882499780916108968650865', '8.93921954251755259270531579268', '9.973651600237798642604208982917', '10.41784213316048362230522817572', '11.269668665904312987691427292496', '11.935800002977155998031134254612', '13.10612055330174145273587895971', '13.68207751219938599833928063343', '14.92567617306427386902279673066', '15.4028059140788368151887523793', '16.443092071885643470601875774430', '17.02448459554490019466565353534', '17.64307788291407640777275261315', '17.95626899018727819038911607754', '18.78090117295460537241197767286', '19.83844956779473319737717088414', '20.678542196961247561901034160768', '21.20172777984762813041528769088', '22.14161337545576464984816346351', '23.02615805513937170741972407300', '23.83230598144017924549787706246', '24.31074017045542524909159271849', '25.02322251532374325511030709127', '25.54644754802892841512531764162', '26.73746147710948951454712471260', '27.23382138317657258514561877194', '28.02207123540409788215438277067', '28.33097289882814981124599815747', '29.2636197432668094499705304433', '29.72192382984093930914080082533', '30.41173784760381210098066130647', '31.69633811497305817052431253898', '32.56808231071695458279438980366', '33.17914958644948241576684076667', '33.72572592269092390572846750166', '34.09468665995043016063679436223', '35.17440309721926970807803627232', '35.47968226774272541284186445226', '36.354280095663114085327983342427', '36.915144150115414699673138183430', '37.724952694488315435462367305109', '38.0785307174371979702366232149', '39.42972127578658935501742439670', '39.87938171340973188288002996707', '40.44067103674120207184881340747', '41.30505703931887340042495964823', '41.80231928325180715236384861045', '42.68160894526223774098696435663', '43.5705572631822333699444460713', '44.14369085576310442804903941963', '44.695103686447450355932197765083', '45.084446556028276733644039339188', '46.03675381554973442943951935593', '46.47020842831165095989555325261', '47.1706176666188077930049076009', '47.642371545414906927667296846584', '48.61444733322826664969670606890', '49.640263097099042039854609235260', '50.1286674698895251925106666958', '51.07423583201698443225236213991', '51.45969668447540478155284333322', '52.21055872731806867777415799638', '52.69627802036985783713030250636', '53.28601188206774851108775439985', '53.65168478351853606494489719887', '55.05288174324482151269002485089', '55.287644775817141473325772368068', '56.1058260530613734063530354198', '56.720190303047344404259688599197', '56.99249025278269054403737627769', '57.75014539190859829501506636344', '59.01854882416693551492951489176', '59.52634771951380763564654375099', '59.97849207068080827774087362745', '60.81403356898548440649189109866', '61.5641041471488705540573931778', '62.20426000942925555068663484436', '62.53398643252336834054882350247', '63.545147442970649261214451534500', '63.7940197663756950170003476192', '64.17731635341344272990388758064', '65.05121862455654468022193732190', '65.75987762741632940108715953813', '66.61476053462079114930651859676', '67.34766282980358254486842056621', '68.13932736436653593046050229847', '68.76932231227718650834525872760', '69.10819322178232173935584628958', '69.86634906886689812488547847026', '70.33871928230868667931392096596', '71.28406670372341051304428929941', '71.99086271103091175704704858917', '72.24593437484508442132863037596', '73.13809698709368134955686457191', '73.52256741073795752288117164615', '74.269901071312896982103278025098', '75.035071148132491977637660166003', '75.42151803629603495989406295535', '76.056571109440376733939763251821', '76.85299999282854911203831345443', '77.84221963716424355580971192833', '78.78807904403163497782582406021', '79.0389861395953696088043210331', '79.48849125351407783784180330180', '80.0452042717935513448668493207', '80.783304273912799558954966063595', '81.2292153591589311270655580036', '82.03443766423184505065688785859', '82.48496369089254062116530964336', '83.230250545740697836313694394952', '84.11045710400336707026312500140', '84.31427275216562334524746400274', '85.29489117967969474254974946246', '86.074128246657595177861586912', '86.64418522121334910830349030822', '87.11935271583846694072643793848', '87.861472477432777026385850167817', '88.491559956700922738361689491152', '88.96630940172119757105662302587', '89.83139576646077488924321216622', '90.458648478718704342221538274', '91.1045316612877424146130073659', '91.5200539483523358717081988064', '91.973315089487141556416208717525', '92.35533061563267104250880503138', '93.3605474357718946507690499180', '93.85950543424223260504382378727', '95.28058903994835075072851917391', '95.52376331838820844374659678673', '95.90092054717661424139316160608', '96.78424625101668567626589482151', '97.40495508457700507307608652636', '98.09419097370285529352840364859', '98.321424330219177452527982143027', '99.19068391454614864431193465651', '99.35929744906498934733119851278', '100.27878766651981153639785116171', '101.09757844585007909839088711333', '101.719010129633522710557007140476', '102.089470272270055435376415606116', '102.690952640994031468107056608817', '103.64474193045273582800976641284', '103.996461593196550481842206601592', '104.716728959062546336822828900813', '105.532664528669104495805655659641', '106.15320547373963218601368135913', '106.90053716633861343939938445897', '107.25358460529860016600640327807', '108.04517703647563231195706696147', '108.49673523107544719027244096512', '108.69785080740546179221442394379', '109.65723879810258608908579528728', '110.41839175819274939992980125555', '110.69159325346954707966025471890', '111.21584061109387728999412979121', '112.09215196185036568727036805464', '113.07403046878763413655205567647', '113.82457800342545691848744807411', '114.19454795499167706816461336605', '114.82847069705862160578330732941', '115.233945934881168841551180382975', '115.762552344965584755562047043550', '116.29243225599530263801964874004', '117.437723779883296019526868171785', '117.78495059453805748082748752253', '118.29791099113002176803980481646', '118.97805144359337664287088939942', '119.535648476173952221620884216039', '119.89647654068787448541433165567', '120.83661703570838115529227404028', '121.247357521909995635736638693616', '121.994919096912763482506158923412', '122.80737849425756358983945588132', '123.67055783555104652372963318258', '123.83732996258580843745065694949', '124.68614128896068467471245987492', '125.34288228232334558015070273733', '125.778710433619396407564918673555', '126.285811645340470768224499315823', '126.85570422714404573355695249929', '127.46805631675603350396046241654', '127.79318581443699802318430589949', '128.518114597748092415284129107855', '129.55877459410739900940301770140', '130.1788973809620553204014569720', '130.50160814283680524678828810914', '131.38364305611215797281779303669', '131.70308447798176079465853822259', '132.668041151681304292650287896154', '133.26210266706204510617203314622', '133.53214681189898110064757493028', '134.362954901580833876070937420482', '134.821119141737931205814962476905', '135.55546927983996211960823373571', '136.0763709934334749675996738220', '136.75920170318456133465246099900', '137.39697128729912198792003983869', '137.74457872007061023570955384433', '138.12284437071918707447307621178', '138.81039841097663457351090477345', '139.674322300193900621833673432843', '140.56079725847328531897365335108', '141.159128988109669451196169503214', '141.92997292078399852500235215075', '142.22439336709025327121206993078', '142.90924091944382617981898724161', '143.23591298169040287337020835515', '143.93094894094304214063754617676', '144.41947853654156732806235808928', '145.08093803684554261262085873910', '145.731497972070814811875639487587', '146.420857826278038943651362867837', '146.80911323433587938536721545642', '147.52535077453709670636231895269', '147.9373171000463073643311118739', '149.06005966113047900760759056702', '149.42144759547500484896615383434', '150.223302670388589456963720699308', '150.44313273293850858209204705860', '150.96910741858203974064888160460', '152.07940880285345400538336992570', '152.650521392164633608770821329299', '153.26208679865076199645324595627', '153.505368673598666042056836394182', '154.11749590577166005543209042355', '154.60476589390786914089713291309', '155.34885959762041278873933323480', '155.66161853140054985163099253777', '156.37247978198273297230414292360', '157.34085615025229890566492123623', '157.505178143541092463973693840372', '158.648623492615734874611411573103', '159.28804464691727069853307734482', '159.90938886797437662497852047779', '160.01025370489639566933215430117', '160.88159459858968697646961759694', '161.52194572297430661719164337060', '161.83748549654449122814126798544', '162.43066671918200056866611289509', '163.003219995091496526847768521007', '163.928740110738379596403379471029', '164.27462750181280152663547548460', '165.04236127919287216806560937620', '165.53118598112034578318026508692', '165.914281911732114442820031527108', '166.60187266054366722405040492093', '167.07327218285397194001009841123', '168.35512223972704508505579259949', '168.49070184544432591161852765022', '169.50333743988088470588528858882', '169.85660241331447685132517126755', '170.3366666406995347979830114568', '170.73049482109533042575669719814', '171.79203013485134673184249215314', '172.13308259539327844115868093288', '172.51070567391290898009455236610', '173.13196751528647537560598332519', '173.51103145037217331408841603750', '174.29817102277266800008260061094', '174.94692677060875747658868382871', '175.797142174864430403284275924056', '176.46136896234195876210173160141', '177.035686744372118883527840184154', '177.51534208223044642284410526431', '177.9481966304188293030147921281', '178.81374294308166543866330324920', '179.03890679452309124399491044848', '179.84465148162329361654210830791', '180.30375246022691999597929082420', '181.28125424135083387311160945384', '181.74102393270618299827678313636', '181.949207395052921270075901324052', '182.455836002291931410720717375759', '183.40382542723429693476263797020', '183.641770137014407950622124937419', '184.39174749569921344974217874314', '185.10740885888478513951739626591', '185.67254111941879498722520543714', '186.37990885927630448540978770699', '187.24774846657039071554679066757', '187.56210483594598517090078153314', '188.4524916228771692993969560914', '188.71928754751783855819845845225', '189.17083964460732954714689956649', '189.53687891394591875056225281320', '190.24618225807789784576208421274', '190.79252099107002267482936519908', '191.70218871095922281681329809805', '192.18958645930983000576480377155', '192.56451436230832175589607891138', '193.29443824072766977904753570569', '193.90632815720771928003210433852', '194.58182893833874534799995148639', '195.26855957577140159503037189691', '195.847464251329730234803268091348', '196.28280061842312826223314208600', '196.76488364500796502365798028383', '197.704763244427657356421441766690', '198.002239129163884305307736605138', '198.765196169651051433532079857667', '199.24764411452019314240399225362', '199.88989366318412609519891872290'], 'prelabel': '1-1441-1441.299-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.691975866344493, 'root_angle': -0.27347005355625237, 'root_number': '0.653095399779388466397057776931-0.757275642541737080739159355728*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.136735026778', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(130)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.701344108747235545680304358262-0.0412187878444229763759845795561*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.610361514712', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.54152167161', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.23841371955', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 6.691975866344493, 'bad_primes': [11, 131], 'central_character': '1441.299', 'conductor': 1441, 'conductor_radical': 1441, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1441/299'], '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': '1-1441-1441.299-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': '1-1441-1441.299-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.691975866344493, 'root_angle': -0.13673502677812618, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.610361514712', 'prec': 47}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_1441.299', 'Lhash_array': ['dirichlet_L_1441.299'], 'label': '1-1441-1441.299-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1441/299'}