-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_49.32', 'a10': [0.07473009358642425, 0.9972037971811801], 'a2': [-0.9888308262251285, 0.14904226617617444], 'a3': [0.8262387743159949, 0.5633200580636221], 'a4': [0.9555728057861407, -0.2947551744109042], 'a5': [0.07473009358642425, -0.9972037971811801], 'a6': [-0.9009688679024191, -0.4338837391175581], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.9009688679024191, 0.4338837391175581], 'a9': [0.36534102436639504, 0.9308737486442042], 'algebraic': True, 'analytic_conductor': 0.22755504333857055, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]]], 'bad_primes': [7], 'central_character': '49.32', 'coeff_info': ['x^21 - 1', '0.955572805786141 + 0.294755174410904*I', '\\\\zeta_{21}'], 'conductor': 49, 'conductor_radical': 7, 'conjugate': 'dirichlet_L_49.23', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^10', 'a^2', 'a^20', 'a^16', 'a^12', 0, 'a^9', 'a^4', 'a^5', 'a^17', 'a^1', 'a^3', 0, 'a^18', 'a^19', 'a^8', 'a^14', 'a^7', 'a^15', 0, 'a^6', 'a^13', 'a^11', 'a^11', 'a^13', 'a^6', 0, 'a^15', 'a^7', 'a^14', 'a^8', 'a^19', 'a^18', 0, 'a^3', 'a^1', 'a^17', 'a^5', 'a^4', 'a^9', 0, 'a^12', 'a^16', 'a^20', 'a^2', 'a^10', 'a^0', 0, 'a^0', 'a^10', 'a^2', 'a^20', 'a^16', 'a^12', 0, 'a^9', 'a^4', 'a^5', 'a^17', 'a^1', 'a^3', 0, 'a^18', 'a^19', 'a^8', 'a^14', 'a^7', 'a^15', 0, 'a^6', 'a^13', 'a^11', 'a^11', 'a^13', 'a^6', 0, 'a^15', 'a^7', 'a^14', 'a^8', 'a^19', 'a^18', 0, 'a^3', 'a^1', 'a^17', 'a^5', 'a^4', 'a^9', 0, 'a^12', 'a^16', 'a^20', 'a^2', 'a^10', 'a^0', 0, 'a^0', 'a^10'], 'euler_factors': [[1, 'a^10'], [1, 'a^2'], [1, 'a^16'], [0], [1, 'a^17'], [1, 'a^3'], [1, 'a^8'], [1, 'a^7'], [1, 'a^13'], [1, 'a^15'], [1, 'a^14'], [1, 'a^1'], [1, 'a^9'], [1, 'a^12'], [1, 'a^10'], [1, 'a^20'], [1, 'a^5'], [1, 'a^1'], [1, 'a^14'], [1, 'a^6'], [1, 'a^11'], [1, 'a^7'], [1, 'a^18'], [1, 'a^4'], [1, 'a^0'], [1, 'a^2']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-7e2-49.32-r0-0-0', 'leading_term': '0.734645782058211998739726436281+0.0788021255558574912164334039938*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/49/32', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.738860068002083, 0.8503437884807383, 1.0463509638220745, 1.1438852353937081, 1.0266648720232452, 0.6406868002609647, -0.0005469110939602674, -0.806728550754747, -1.6149428043619007, -2.216619876517823, -2.4073947913442275, -2.0501441467695427, -1.1330459493754208, 0.19910161975600282, 1.6581041272223014, 2.875865613290908, 3.506396135100847, 3.3374372286274623, 2.373199051617809, 0.8534134075016877, -0.807601520181549, -2.14953391370971, -2.8213480257245447, -2.7058873654129494, -1.9617274782070688, -0.95850905132316, -0.12458291379069948, 0.23421124617128147, 0.06704359657616743, -0.40147186587835426, -0.780905175767645, -0.7133363230287736, -0.0721209200071519, 0.9371896962410847, 1.8353344777848712, 2.077170142860972, 1.3232076743801386, -0.3530348778298685, -2.43321961725415, -4.134934245312054, -4.74049522841495, -3.9289802953999007, -1.9508046838253368, 0.4522733445517856, 2.360441182822743, 3.0836869280794867, 2.4697902675267844, 0.9580728452937578, -0.6533559408907715, -1.6135482699260244, -1.5913374406889331, -0.8203815315661086, 0.06051894262212673, 0.38549733411701625, -0.15012012792377313, -1.3096905740463052, -2.448749859329594, -2.8902852618283537, -2.3273037479209076, -1.0151895787920622, 0.367294911053113, 1.1154229096753905, 0.9215774825514282, 0.06430384482659247, -0.7658117268874962, -0.914394107366528, -0.21919730948550153, 0.8169287427258796, 1.271548369704926, 0.3509470747652662, -2.072947277687827, -5.270136330047311, -7.952691832927323, -8.927076934923068, -7.7375700867759605, -4.9263791086253885, -1.7488448008128301, 0.49956005531939895, 1.1556933764952275, 0.47182536194532954, -0.642141605076511, -1.2377694739829774, -0.9111626721239302, 0.012568831514833312, 0.7893728070595842, 0.8300613261899944, 0.13520245809930065, -0.7120643060566455, -0.9904613648480757, -0.40704548200255297, 0.6277085144072727, 1.2392466441441332, 0.7071893164687938, -0.9562384525609088, -2.8906056769372737, -3.8628997875916466, -3.05722168677908, -0.6613887868200419, 2.163904217800908, 3.9531441308520274, 3.8310800055721836, 2.0533795096668026, -0.1718108824409238, -1.4744129335986624, -1.206003524758768, 0.17078961792966194, 1.4434913357409018, 1.5083786186497734, 0.13450961219131635, -1.8894975403559515, -3.316236460418783, -3.304046655174178, -1.9743663707591401, -0.2784732100079217, 0.7102702646616794, 0.5514250208345457, -0.3108967086062336, -0.9681036384073511, -0.8008795444864688, 0.02347523448051864, 0.7036593776798084, 0.49591203884700513, -0.5997916120319814, -1.727070242172516, -1.7796058320534072, -0.3083458844440806, 1.964975952537507, 3.479165182023278, 2.8521549277781664, -0.1038798113738551, -4.111721815384118, -7.146952959722716, -7.68928703849852, -5.658562056079188, -2.396657639294089, 0.27184220312933965, 1.2212751625944551, 0.6224093865034855, -0.41490635221810107, -0.8123280293705075, -0.3336396169912593, 0.3685895560826419, 0.44732949217810053, -0.31556913327921976, -1.2568879437925262, -1.3706357488769736, -0.19656870321784684, 1.68984723101826, 3.02949636792213, 2.8333346838051616, 1.183892516132287, -0.7840740656723377, -1.7530737354870871, -1.2771914424409525, -0.17081256271004017, 0.1199634656969673, -1.2937607533365334, -3.9290236695294967, -6.171412683193373, -6.439556119564059, -4.401720758715525, -1.2965939204372376, 0.9192205678105213, 0.9694330000956397, -0.8547516224781387, -2.9836146230061567, -3.789163811135765, -2.7800699734988332, -0.8620813566747149, 0.4851143839692299, 0.40737013007783973, -0.7195734297824795, -1.7247242965269447, -1.689158341227191, -0.6925459419116284, 0.36006055745404564, 0.6349067885158837, 0.15958870978705944, -0.2264607274785561, 0.2588078854001805, 1.431801335885346, 2.070695544025506, 0.8630684713299128, -2.35230528343005, -6.120555912739841, -8.193809994590685, -7.109395993301419, -3.3195600293964818, 1.0443499224228443, 3.64076456433484, 3.512420868093257, 1.597795861002474, -0.18385184658762208, -0.4874526679199902, 0.5207544424219308, 1.5398238644584203, 1.4101221930467438, 0.1520442899485247, -1.1086147095572385, -1.2077745307647636, -0.020059419454924923, 1.4207203922013645, 1.8568433112000549, 0.9497355517065651, -0.4049468125417667, -0.8850667065128893, 0.04648711908575259, 1.625230843716374, 2.45382376678812, 1.777183592990479, 0.21010950339261805, -0.7798951721699632, -0.22018525905058828, 1.3890410137122202, 2.399895183935736, 1.4509433028676744, -1.201406140933941, -3.658629507378877, -3.7927027907822697, -0.9828980535093287, 3.2677188055338324, 6.385881057479528, 6.622184591655472, 4.264262882344171, 1.2330104884779927, -0.5204198471286761, -0.4413979500254975, 0.5104502054317466, 0.9952471951999098, 0.5551414804288819, -0.13096036502375322, -0.1303323376653359, 0.6653329026252485, 1.3577159584719163, 0.949949918674792, -0.5485601359055197, -1.9522023182096433, -1.9315804364348002, -0.3393950738330376, 1.4502388851722934, 1.6325715901584883, -0.38698893471921686, -3.276521470906945, -4.726302814045292, -3.3430363164136896, 0.11873448049019746, 3.283921615400132, 4.036615943101886, 2.1692707605507042, -0.5825172950877767, -2.095356703061834, -1.610037001473666, -0.16890033418379036, 0.5539152368255188, -0.11730309842060037, -1.2764448787484541, -1.3881148326608264, 0.16964819249294877, 2.441698946723097, 3.726498555153405, 3.1042602832139132, 1.2245680790944165, -0.3619394634760381, -0.6553754262215838, -0.04137732057270148, 0.2670940385146653, -0.4166760016043643, -1.4926109965846843, -1.717780160313631, -0.6548492189296367, 0.5527209411469703, 0.0015902441774080021, -3.1568024167808373, -7.572373532084403, -10.423040404853607, -9.56382018973271, -5.305708531197404, -0.2585193528152011, 2.67784610426144, 2.481492699418263, 0.5300435836256611, -0.8528020406546751, -0.43587655228516775, 1.0947912634634358, 2.1058550133689686, 1.6989038807260206, 0.4682048351034852, -0.28988908321375995, 0.0038838090436168066, 0.6491743807708144, 0.5139843601999453, -0.6232380633017203, -1.6810895313502328, -1.320211718032436, 0.5809823561549846, 2.551613307790367, 2.765162912976707, 0.7903971111092243, -1.8464685824811513, -2.9350572370930057, -1.5794308579189127, 0.9512517111441268, 2.3733233380787215, 1.5112475549314104, -0.5929213525288985, -1.65206889749901, -0.30259285691449517, 2.5616268928826305, 4.5531279173943044, 3.9494021158462456, 1.2388064859632477, -1.3615735413865653, -1.9195138373482052, -0.43123289988424923, 1.385326470125408, 1.8294492429620202, 0.7527534712723328, -0.5381823170898075, -0.7716297676871922, -0.005003220030346231, 0.5725273915069596, 0.03829161758430896, -1.1979820600803028, -1.8208067587061205, -1.088283907344303, 0.24160398168224487, 0.6312738771595525, -0.498294577369918, -1.8193066205038302, -1.1042555419732452, 2.574750410306755, 7.542044826029931, 10.527090678955837, 9.27416621731639, 4.467427437771301, -0.7809893647362345, -3.4402506803610686, -2.8337960724827527, -0.735407454214468, 0.5837979184478252, 0.3864726810677394, -0.2776813339067736, -0.08764965909773931, 0.990132951346913, 1.7189614617477105, 1.069307336383772, -0.4983351263688253, -1.3691591170411173, -0.42113965877046355, 1.7381232446176829, 3.279646205676503, 2.9375913181405537, 1.2488370374391449, -0.047859192468606315, 0.14845770309272371, 1.1402757641834567, 1.2067353577816227, -0.4385827400589031, -2.5605141905849353, -2.9373425726765574, -0.6079988975080021, 2.916658539038838, 4.818692779174029, 3.5268226719876954, 0.22936533336034529, -2.157444858876787, -1.6344546994249367, 1.1143071751385532, 3.4716906550233055, 3.364363879246656, 1.0687632903766229, -1.2934979445959374, -1.9046016357527908, -0.8493600853907586, 0.31172738107548154, 0.3406107582272332, -0.4810373118506587, -0.9310804798492601, -0.4010758980389819, 0.396185968817391, 0.377866559145801, -0.4032396137427646, -0.512585576557152, 1.368713010830722, 4.707439726549535, 7.122150277977552, 6.426541152596526, 2.8330742210333466, -0.9410547460777139, -1.9726536537316592, 0.25450186740248615, 3.4213064516492455, 4.5593141849304235, 2.7528101914766725, -0.21067089396746294, -1.7556448140300167, -1.008013522270234, 0.5896268589598296, 0.99485989989418, -0.2816468368038805, -1.8073210322253996, -1.904576414432929, -0.49510027779036636, 0.8602887976200637, 0.7106066895415895, -0.6801462780039874, -1.6157113193945238, -0.821430125567822, 1.1495331587073225, 2.486997697595324, 2.0513450794336237, 0.5557759961505623, -0.29199295944705084, 0.26008139437930017, 1.1573028013595132, 0.8157848631626211, -0.8138713177047672, -1.7497732346033006, 0.14706985216110358, 4.694892770596566, 8.94078112600046, 9.483290393211405, 5.508843437715688, -0.36506835986371633, -4.2970233804913605, -4.406481761676554, -1.9872111064595623, 0.1809334122161354, 0.5331214818988942, -0.23401694218501395, -0.5167248900121134, 0.1909191241829021, 0.8570817494497953, 0.34169009368085534, -1.1001612596164119, -2.0304867859391478, -1.5150382373597173, -0.3049741502751528, -0.06302479615460241, -1.4148174810167142, -3.039681403555009, -2.9761043611044835, -0.8568701265652, 1.391289860302365, 1.3430601417775596, -1.3610736535381576, -4.386867782665178, -4.830713069626963, -2.049675485576851, 1.6688029642019981, 3.3082025494658645, 1.9775435284621332, -0.4468254810976955, -1.4467509508456162, -0.4640773277327678, 0.7185495957713022, 0.1029744858058935, -2.24643106257998, -4.206727736994069, -3.821671840540077, -1.3313930959707658, 1.1250810069315162, 1.7231872573374458, 0.6648220970672194, -0.36031126874111186, -0.19180700150677993, 0.6346408618018309, 0.807191580999251, 0.03407964575759552, -0.49752606994719406, 0.37959062217239986, 2.114563443397107, 2.700323156069762, 0.8939362795412331, -1.9784078540721153, -2.849823682230226, 0.12953809521093906, 5.443165002272603, 9.23134682380835, 8.697428357383886, 4.618263457646417, 0.5044597158122229, -0.7054265819189086, 0.8720373348854427, 2.708178311263117, 2.6779413490345756, 1.0187901178194942, -0.4114421729355126, -0.4241654901696818, 0.32842726227884633, 0.4655312355881864, -0.2405977125241568, -0.5341182154883216, 0.6962915241795614, 2.796573786754562, 3.768730441355276, 2.419654981848989, -0.16318887767675272, -1.588212326260409, -0.6467196400741745, 1.4061496634616513, 2.250548382445653, 1.0883702792932448, -0.466751147861001, -0.2617387302799228, 1.7891601722183061, 3.322464972440465, 1.9669757296459665, -1.9324062127451533, -5.306542833370808, -5.24733216034885, -1.8615823396728304, 1.8568091543685161, 2.9788567430372495, 1.3444402172573433, -0.6794819202194948, -0.9018954643941057, 0.522947009060426, 1.6507873587656063, 1.1362612632720837, -0.3319591734950509, -1.0441696298985794, -0.35852552033192525, 0.6417479640203613, 0.616357863598807, -0.30801920748255346, -0.7103309127783431, 0.23198339717250757, 1.4859677118888326, 1.2757595768654815, -0.5283795667845376, -1.5989653281646263, 0.7450886230089728, 6.4764269377926365, 12.177534428873216, 13.805326191779196, 10.33169224040488, 4.624465169829925, 0.691971765877635, 0.11132198961674564, 1.1689985363659252, 1.2685628900505033, -0.22470932384088754, -1.711310337309462, -1.6206937019003087, -0.39618695641446855, 0.07974511843639238, -1.1763517962174317, -2.9743197209135293, -3.26364421112833, -1.5050344435815441, 0.6692651721043934, 1.2797193219155227, 0.18889019517323533, -0.8795071940404392, -0.4790122013942463, 0.8156227560837186, 1.1534573038691531, -0.22127182075206348, -1.8361774755461722, -1.592673976642579, 0.6431554123006612, 2.5497736855097095, 1.7903236504566673, -1.196416867584972, -3.278316825427984, -1.7761249115179862, 2.577401952299048, 6.0984874087804, 5.684510010584617, 1.7880937762692881, -2.1939583504778186, -3.3351141819064547, -1.7657541225013116, 0.06934836575399414, 0.29301674309667797, -0.6792620623697957, -1.2121030569054043, -0.6682263691362429, -0.019087529522224946, -0.29146489323077446, -1.0061663157600553, -0.7140479630107062, 0.9694611814032525, 2.4503865349594167, 1.7673562301859231, -0.9706331776200886, -3.277202957394697, -2.792805901326913, 0.0404202542215705, 2.2342726032901448, 1.3945199213204393, -1.6055328515891458, -3.4241854069132205, -1.7707513669135877, 2.1361979099565698, 4.833510098623209, 4.19962482113394, 1.4705358320961688, -0.37873656202963324, 0.08384276400184816, 1.4762221376953686, 1.5702482615403226, 0.03081315144910795, -1.267544789046828, -0.5888677622864353, 1.5170168537466133, 2.8059802491287114, 1.9274126663914117, -0.06037730075746779, -0.9865278731049175, -0.07278555266576862, 1.3243648206590952, 1.5140696337623756, 0.5156999748426864, -0.18989944993732766, 0.15498488347664172, 0.3250780812223133, -1.3873814110453446, -4.53452203155948, -6.090727208025455, -3.2989523019703095, 3.0445161701031247, 8.62475573698141, 9.352273883714604, 5.138182472897373, -0.17484663339314946, -2.595174742045673, -1.5073216498814925, 0.5288166251297406, 1.021424170309181, 0.04376618625350069, -0.540615124665396, 0.2604078368441703, 1.367729914368321, 1.1710285652907924, -0.32065760627742995, -1.4712875600135562, -1.1236763673699501, -0.10558959317214217, -0.15920724568680245], 'positive_zeros': ['1.87477066186703555028755686561', '4.01937694936721663672995033725', '6.09580393980426574834670957512', '8.19289207499894776053676421584', '8.80243212592907273664511344483', '10.024974875402790407666301132341', '11.50602299006584212380386479379', '13.37728242222239024348209326304', '14.86513028836035638632047805480', '16.22368625890618663543349913677', '16.82115678715897378821291277663', '18.65824174946895463215534535692', '19.70818323076858278999327857732', '20.6912915274959466278915371478', '21.6211366176202009578040723279', '23.97202117047838411379662537577', '24.81738552530008975728125598051', '25.933500915403930600734360998571', '26.92148015160090313985594185967', '27.938403196128757102061269010780', '28.90257479253227193779614496080', '30.38381212526101821765200913863', '31.848126367508526217620097975761', '32.77813261768192280132165653089', '33.771893969647963234841978405620', '35.37435906185371655445440286912', '36.14584560048106496036278137681', '37.17944367567385956851030784847', '37.9746510796401008890453828081', '39.10737805972744052175214190034', '40.3039115271947242845413133661', '42.14534069793885339143508825570', '42.99141267995062176457009795847', '43.88586698636421976399548050086', '44.58558889894293130064955062737', '45.66009315833820708165340740975', '47.05423277698385348946663282792', '48.18893792262854102957113270854', '48.49273402456660224633566913395', '50.46416533185867795709538660818', '51.127519480171582365328668670775', '52.66471728041538554844880967330', '53.25675079811903574627356948694', '54.56272411432541845000459903792', '55.39909101108557358021690806707', '55.83983674693431094155779463063', '56.97637019209341371752109956501', '58.66881669949842403996607207717', '59.95463377265202306173681678446', '60.491429790780249937365524344963', '61.59433869670303015640619269143', '62.504044270029068752721322761410', '63.64799160195698381825898383172', '64.365076534181333284843613826803', '65.6693431300225295817787010849', '66.29967334467352995131265514909', '67.37143449488941298917120915459', '68.51260158384941714115874116004', '70.17820118642502001745732410436', '70.77573815381340156242461594973', '71.79942010595777602905786942048', '72.25827750832187124190829763815', '73.33633229755726107020914913147', '74.4274422357479609361353683603', '75.26836723425228217214636280905', '76.55264309008347556904729448671', '77.741305221369004103335698172211', '78.791732065656318110851462271397', '79.342848540923166757093239251486', '80.287876841975889333853111535894', '81.781054785394817352955247948365', '82.51981078156783133296433663851', '82.986227356887606563583641045901', '84.20635819646528790103590553201', '84.68776332906344806031324081995', '86.581275918697968045847866406183', '87.587183324236675679671566649611', '88.22333067812774166383817468157', '89.517060474500688171457501874666', '89.99818444738347413409931516611', '90.78838433426588733974704072052', '91.79379881905001351106077257053', '92.9021133737291118637374716291', '93.94389001146256874945883187583', '94.911222297180930746096412321590', '95.66230081377361799329328542199', '97.00519603602887831680455550330', '97.87908210685912000320453328964', '98.9139648931982349711383574045', '99.689235119880527511067579584214', '100.32353879327656126101556815629', '101.49898505765611327321735372766', '102.08375137162548590905630348610', '102.93330325077713725559221980209', '104.63375191086648594313197501690', '105.75527863557254532698912046735', '106.4119566923927482832813959550', '106.90840701267636430350160590178', '108.02737212731258454269428637476', '108.817945103866070643314703838344', '110.28961586278423550345379228120', '110.56361235046317915994219362729', '111.499272468123698485077826964245', '112.55480609402519950663639694718', '113.77167456546955983165223499421', '114.573207234166203824881578090507', '115.74978793643795839943633342899', '116.76617757107884479767847437956', '117.3308470489166928245371929154', '118.26564566539060608610708245308', '118.91155436675984681736114730519', '119.504034324601341569840959554250', '121.15695059717276245802155471028', '121.85012320198741227855322667820', '123.100314838407259720439209917095', '123.938378258017097680407465102394', '124.635875649373249483874571506157', '125.71782182737848185291979988184', '126.423038804444134671852783713690', '127.32522679566416746153445243596', '128.58047095316559628147250806824', '128.97592131275191237536641380139', '129.85698072962968713437757893976', '130.611708733980410122745571354541', '132.16690122363658744336585767313', '133.3984594680244704807448549971', '133.97304282753749916889343087383', '134.623071342238841310535692871209', '135.39553146095909730105633790803', '136.698277385561662696272225800', '136.83623074635204138572973908560', '138.22732099565036629217028465312', '138.930761326741843574734658705775', '140.16418415296525013545034165864', '141.18602615368445806753583798549', '141.97265018666223982848307218757', '142.51818878656730760211359312271', '143.89994443369825204667671953167', '144.85545123966203685992635299779', '145.38853604210981000349290510879', '146.261628910939866546796673438599', '146.79136326409552704738507317434', '147.90791848842767590572920321260', '148.74129612458076213131336832206', '150.37277048466065634795662804841', '150.80506986054582444466692256242', '152.06656033654889000797532986627', '152.67512139395609436228939959387', '153.34444325617714666916366899227', '153.9338064085675755028192848446', '155.291494019512833464802712083809', '156.03692079495074800864911334460', '157.07095119823193669983543307817', '157.55340182497966828923802496239', '158.60776846054315454413407112074', '159.8290774582111288018029400956', '160.812025285205937586396621118', '161.46361002620467961720195778023', '162.42756801231699219339384227498', '163.22312850195742710684241544398', '163.96482274220595722673144922273', '164.634454918821424451728847802345', '165.543185605067245542406621224595', '166.191938175334280664643908712264', '168.30532572050709985101177170837', '168.36714598358848242607213806559', '169.33692827249815555602110040189', '170.44484087107678680770112888708', '170.67040063767804698216438628012', '172.07700501877167803945486228325', '172.854038198161237514991898074', '173.55555316579148218459978973600', '174.33785173895794309874871415068', '175.2346389897206164014077223929', '176.13445985996867894353445543997', '177.014637649556794002226804161213', '178.24930910576951015999842215117', '179.35714082485099572487726213358', '179.799220012721614073235622741224', '180.96605574668325866384814322272', '181.05427089624831945378552546391', '182.02866806635818516342708794851', '183.02569117294860156622346134609', '184.058417028109519140281628921091', '184.841544200522478726748959480147', '185.77320362724240405380539885081', '187.081421033241645966881773671629', '187.479842275460055763060553489196', '188.44279470792978475148593418878', '189.15886937345803144193394442022', '190.30198826206263226617722305954', '190.952574733531720870180423649078', '192.04646751769683623933934339115', '192.417305506532367956585912314359', '192.91786455390914722435999280168', '194.2354536173457807229768800578', '195.61253155764645207367981727596', '196.467863511187562796221551471615', '197.19998593968054492867802331184', '197.7452631757331223524423144253', '198.68971427248819787011556037094', '199.74169724815414814814116589478', '199.92957276073545105237383589776'], 'prelabel': '1-7e2-49.32-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.22755504333857055, 'root_angle': 0.06802721088435375, 'root_number': '0.977249996460544025203400005578+0.212090651415536677850867082620*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0340136054422', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(21)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.853764662218301879329680622298+0.0783125287921836762520054407495*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.87477066187', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.01937694937', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '6.0958039398', 'prec': 40}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.22755504333857055, 'bad_primes': [7], 'central_character': '49.32', 'conductor': 49, 'conductor_radical': 7, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/49/32'], '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': '1-7e2-49.32-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': '1-7e2-49.32-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.22755504333857055, 'root_angle': 0.034013605442176874, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.87477066187', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_49.32', 'Lhash_array': ['dirichlet_L_49.32'], 'label': '1-7e2-49.32-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/49/32'}
Lfunction data - 1-7e2-49.32-r0-0-0