-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_161.44', 'a10': [0.7860530947427875, 0.6181589862206052], 'a2': [0.5800569095711982, -0.8145759520503357], 'a3': [0.23575893550942723, -0.9718115683235417], 'a4': [-0.32706796331742166, -0.9450008187146685], 'a5': [-0.0475819158237423, 0.998867339183008], 'a6': [-0.6548607339452851, -0.7557495743542583], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.9594929736144974, -0.28173255684142967], 'a9': [-0.8888354486549235, -0.4582265217274104], 'algebraic': True, 'analytic_conductor': 17.30185289193463, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [23, [1]]], 'bad_primes': [7, 23], 'central_character': '161.44', 'coeff_info': ['x^66 - 1', '0.995471922573085 + 0.0950560433041827*I', '\\\\zeta_{66}'], 'conductor': 161, 'conductor_radical': 161, 'conjugate': 'dirichlet_L_161.11', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^56', 'a^52', 'a^46', 'a^17', 'a^42', 0, 'a^36', 'a^38', 'a^7', 'a^43', 'a^32', 'a^18', 0, 'a^3', 'a^26', 'a^31', 'a^28', 'a^35', 'a^63', 0, 'a^33', 0, 'a^22', 'a^34', 'a^8', 'a^24', 0, 'a^42', 'a^59', 'a^58', 'a^16', 'a^29', 'a^21', 0, 'a^18', 'a^5', 'a^25', 'a^4', 'a^53', 'a^6', 0, 'a^63', 'a^23', 'a^55', 0, 'a^44', 'a^12', 0, 'a^24', 'a^17', 'a^64', 'a^37', 'a^14', 'a^60', 0, 'a^21', 'a^32', 'a^40', 'a^49', 'a^47', 'a^48', 0, 'a^6', 'a^35', 'a^19', 'a^1', 'a^11', 0, 0, 'a^12', 'a^8', 'a^46', 'a^61', 'a^20', 'a^15', 0, 'a^60', 'a^29', 'a^43', 'a^10', 'a^62', 'a^27', 0, 'a^48', 'a^53', 'a^28', 'a^13', 'a^41', 'a^45', 0, 0, 'a^44', 'a^34', 'a^52', 'a^2', 'a^39', 0, 'a^15', 'a^14'], 'euler_factors': [[1, 'a^56'], [1, 'a^52'], [1, 'a^17'], [0], [1, 'a^43'], [1, 'a^18'], [1, 'a^31'], [1, 'a^35'], [0], [1, 'a^42'], [1, 'a^58'], [1, 'a^5'], [1, 'a^6'], [1, 'a^63'], [1, 'a^44'], [1, 'a^37'], [1, 'a^40'], [1, 'a^47'], [1, 'a^1'], [1, 'a^12'], [1, 'a^46'], [1, 'a^29'], [1, 'a^27'], [1, 'a^41'], [1, 'a^39'], [1, 'a^16']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-161-161.44-r1-0-0', 'leading_term': '-0.348762102846527393354114113713-0.514093912824271885152123107322*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/161/44', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [-0.6212306782386894, 0.47452406608443987, 1.2547592817823336, 1.619466375089105, 1.5109225484406643, 0.9934156931496427, 0.2906429497807801, -0.26960157129633233, -0.39643491700050854, 0.000655809272343714, 0.7191344782455189, 1.3167102393255723, 1.3168849707752441, 0.48123299901381594, -0.9999871244048095, -2.5327509737850393, -3.3903790173184136, -3.114207483030839, -1.8213895965741234, -0.2122040941003935, 0.7784860643951959, 0.5232537918280068, -0.8762075358166537, -2.573095978574357, -3.4292562358245506, -2.705191582980107, -0.5682666909334727, 1.9285733801287495, 3.4329048096347345, 3.1081995418782267, 1.1623069896998528, -1.2718821141301921, -2.8491875984235415, -2.8578891721132247, -1.6302110368800282, -0.2378795665440557, 0.30603833776347283, -0.2398531434381638, -1.2371845576054592, -1.7326962674584183, -1.2474579268649841, -0.15983675765660083, 0.6340452503807393, 0.5129222678546079, -0.2887937917876697, -0.8404408785946382, -0.3459628867163782, 1.0179962927622088, 2.0088626342427776, 1.174277553576281, -1.9254842638740328, -6.100565952368112, -9.112686987432893, -9.13844645093447, -6.06294440596519, -1.6074942032604738, 1.8470919900536897, 2.871982561153161, 1.8215350130234977, 0.29019022575308884, -0.2986333641390758, 0.21267105808644787, 0.8099194730445873, 0.4231793083418042, -0.9783669696117564, -2.308266379123612, -2.364516301889662, -0.9834690804235231, 0.735771363615388, 1.3777180487197758, 0.48255456503191646, -1.033092173383867, -1.7242238520088422, -0.9705144866067743, 0.43698217358247227, 1.0672830312535662, 0.29057241122581007, -0.989798331774414, -1.0951187345326867, 0.7956432341409351, 3.657778844629429, 5.309262706537888, 4.2911015990183214, 1.2828493784820123, -1.2981009228624871, -1.2767872710927906, 1.4129196003091318, 4.634333568106461, 5.835544593189953, 4.151525300647699, 0.9895800982998764, -1.3370770161215444, -1.6044320335587259, -0.4908568985369611, 0.3972627110587259, 0.1865732456796787, -0.5756737413161197, -0.7787589271405393, -0.1169226473197127, 0.5512184206701818, 0.2525767073119237, -0.8014879184297623, -1.1779131016417068, 0.3338333642543737, 3.2173436829353195, 5.335245972898752, 4.788138989312147, 1.8279679871424792, -1.1215765460936542, -1.550442311385345, 0.8236176341317414, 3.7360692291796873, 4.432423054870426, 2.190176000878551, -1.0822611703974176, -2.7068263041754324, -1.7169218326798685, 0.4340291702902126, 1.5177950796393351, 0.7730713812328128, -0.5224701033737719, -0.6193261706869477, 0.743774583972825, 2.0743284873598724, 1.7906388992217521, -0.011812295357608792, -1.607683678087171, -1.4506386281338388, 0.2110665663741862, 1.6510622498809548, 1.5461870056967773, 0.347915998183406, -0.3585445957964046, 0.2427266119048175, 1.2361933375285783, 1.142911972724462, -0.03445137776111195, -0.31090471608759557, 2.3513896381718435, 7.516198904534046, 11.925764493980653, 12.07271244563282, 7.395856134250956, 0.9641321426451264, -3.120948577540066, -3.1487623874995556, -0.8211973874463083, 0.8850302039977778, 0.6463264145143275, -0.4162739960560477, -0.5476715431089181, 0.5003279311135608, 1.366569761658189, 0.9042210857611988, -0.3632984729159142, -0.8952312253104369, -0.07344291055312327, 0.9519149480519743, 0.6122912562843116, -1.0801680316775037, -2.3273811420512636, -1.5681173528674948, 0.5148134337521898, 1.4452723102859215, -0.3850567748058418, -3.715631856082962, -5.441024068910499, -3.7652101175098247, -0.13976281268702068, 2.1811144486207423, 1.4927890693726154, -0.6924246003553348, -1.4466615852018783, 0.3110045801332263, 2.683815415745216, 3.0003489694576952, 0.8497621002362915, -1.4368470524907888, -1.3509347444594364, 1.0800610810589457, 3.4119692698879676, 3.4792608810982677, 1.579070890079468, -0.1920185216556059, -0.44303179648520175, 0.17195642296838848, 0.1959654268081008, -0.5612234547412418, -0.794901084649786, 0.4156566891992267, 2.096063537300521, 2.3536704346511765, 0.8350928533287878, -0.43294758200715266, 0.773389257729504, 3.9482813523332747, 5.742797986334049, 3.2753678372989845, -2.5287531412533326, -7.355624302072595, -7.526338130785829, -3.4943368323307364, 0.8287861972742766, 2.080352659302234, 0.45974556777270825, -1.234588783175043, -1.025873767379226, 0.3645181405338364, 0.9973922166011908, 0.3290488672130216, -0.3395954167573406, 0.08339386328442859, 0.775934828796569, -0.024070858343283992, -2.542302869199291, -4.716570045982015, -4.352043849503116, -1.699557996160808, 0.7243632436284083, 0.9853718560081943, -0.1398677321858206, -0.34446131959375037, 1.1701537234377077, 2.6081254915845546, 1.9162376504047036, -0.2886732399542924, -0.9934863763673962, 1.7156953848745964, 5.984608165298244, 7.737829893982234, 4.9855702818605305, 0.07121041940884856, -2.7531961189080687, -1.733057043792243, 0.9002385492739257, 1.812367245475813, 0.28788998800925886, -1.4307715193407011, -1.1932513467085, 0.5293389364009882, 1.5541000369721174, 0.8594748802052937, -0.3098492333923126, -0.3179512378697733, 0.6747170932267811, 1.122990628301767, 0.43028199168483244, -0.11418988423230853, 0.7461543854933221, 1.9950613144252345, 1.1099446114434952, -2.6056643193349682, -6.2425847340881635, -5.819653444654754, -0.7176539708149791, 5.117278251177616, 6.944227640148583, 3.9714353561470572, -0.17285821962843584, -1.6156115255538128, -0.17438513474493544, 1.2656594522636593, 0.6953489020151882, -0.7427189570451329, -0.6865701381396825, 1.1147938288967838, 2.42736216369164, 1.477467943118922, -0.700683317758741, -1.5643827226016378, -0.28910194868190525, 1.2616673503665616, 1.0281099939543812, -0.5884974071367464, -1.3623073064927382, -0.2748203545496603, 1.112982358900517, 0.7930403361940781, -0.9052638222475053, -1.687690220894358, -0.45905945542043175, 0.9616186043214561, 0.12840669396083373, -2.4974185888323888, -3.541945804666406, -0.777551796764389, 3.5913690806420826, 4.795869398713117, 0.7776147432389564, -5.228539700185532, -7.957315069770731, -5.5444972137261965, -1.0048599458722085, 1.5478691355542995, 1.1734544359301864, 0.08904140752858596, 0.19135361350777708, 0.9007894463658364, 0.7188408813179941, -0.2233930519848573, -0.34882964684479, 0.8564204189539546, 1.7986986251962127, 0.9325340628959384, -0.7943065762055299, -0.8392820090751055, 1.5206504923299282, 3.7936872338983214, 3.1223404343440424, -0.019405928916967935, -2.1693767112661555, -1.165240864491159, 0.9554411577932844, 0.3254123818215002, -3.8389356765442253, -7.908372546303067, -7.901525402521361, -4.030511627105998, -0.22667714232644917, 0.5808469758290874, -0.5060328217942051, -0.5319466347473452, 1.128282453932976, 2.0955703200044296, 0.4719487092417759, -2.345952119578111, -3.301673535031712, -1.5463420874316007, 0.5778914184787927, 0.6292266636397641, -0.94412665738704, -1.7528746100266193, -0.7935046179662125, 0.4593944697981572, 0.47177942387522165, -0.10711439969724443, 0.29847207142676024, 1.3059664259718538, 0.5897239592972157, -2.608710556785744, -5.220912331102802, -3.187954526512177, 3.3868984119492995, 9.282524343182107, 9.302474395362182, 3.834085082458747, -1.7249501904328441, -2.9622329346124143, -0.752394911570905, 0.8474656590802809, -0.13920296159098683, -1.8253919176174593, -1.7285465648241214, -0.18121737419048792, 0.5526612612434102, -0.2960580675511913, -1.0418931311395982, -0.22018897480723926, 1.1702677853191708, 1.1807309893902314, -0.03163366405095593, -0.18912176821598053, 1.785060096528083, 3.778484627470325, 2.973146162310046, -0.2696591667715051, -2.4891783503987415, -1.4028839412555554, 1.1851494343226265, 1.8307501225693479, 0.09625190655474003, -0.8654936702090784, 1.2970479851611234, 4.6412733090315745, 5.2113288033133855, 2.2837633109922164, -0.3774383683561362, 0.8735180817062704, 4.932634866303735, 7.239961456637566, 5.3026163813007114, 1.4219885748379344, -0.5351374595767157, 0.2134570393352612, 1.1878163640157706, 0.5064348308741518, -0.8002798740988506, -0.8552251666044578, 0.09601431470648339, 0.21635601911105007, -0.898279417344466, -1.4230091733463246, -0.07997566646762633, 1.659567683662257, 1.5115776167651371, -0.09251966389598922, -0.24342616518146284, 2.1332191301752177, 3.7734954985327045, 0.5702044088690946, -6.778671661076055, -12.419213252224381, -11.46199202559326, -5.387231989366286, -0.1564433849507369, 0.5199194048192909, -1.4823277332598994, -2.226226661383622, -0.8254040226966926, 0.37619272982387064, -0.156164246998598, -1.0523825678028575, -0.5845398432927171, 0.34786012979012126, -0.562392119934817, -3.3354964573381674, -5.073955079997348, -3.6258354595018734, -0.5252466371171409, 0.965282641133423, 0.043993004763322276, -0.9942295056784082, -0.37056698418335277, 0.6653085041282683, 0.07044065018522509, -1.4189068286201458, -0.9542029168639496, 2.0764544701077168, 4.346674598844304, 2.647921052933308, -1.3922353989669198, -2.6589562257888977, 1.15156956013844, 6.337406606403322, 7.47996525190165, 3.882461383940694, 0.019219745003481743, -0.27561281979753066, 1.8196267514857345, 2.4731643315525345, 0.4976723005087703, -1.5687487242575764, -1.3959940480849244, 0.1286810379688575, 0.724531813341239, 0.10554762379708378, -0.14275496157917358, 0.4432979081476929, 0.34815270900710826, -1.1614752794999905, -2.1239282968922844, -0.3921182999937785, 2.680333194071802, 3.1758198390971994, -0.2344520717415188, -3.8366393143892803, -3.094661750908093, 1.5387109771319192, 4.96985618130514, 3.7768969348848977, 0.28207695904436214, -0.8644410480971922, 1.1816965344231043, 2.8089995698425345, 1.2777266175831492, -1.5426333785414543, -2.000439740291582, 0.2374057763392559, 1.9827821203009257, 1.1858701946281973, -0.3623224380312328, 0.036952480777714625, 1.937684575923938, 2.481973214183654, 0.6736512803640091, -1.1564663143346277, -0.7679343561360241, 0.8110791348205115, 0.9907344419117837, -0.4601406546711591, -1.1920795285551218, -0.011348828290180392, 1.2282206682813834, 0.6282346581499811, -0.44415124766862263, 0.7438398486935546, 3.4255936259105138, 2.962426923872761, -3.2700873815119595, -11.218938633397974, -13.656344403560054, -8.264609471016312, -0.2856688736290663, 3.5709041042061243, 2.2128155314711218, -0.20093453364470726, -0.41071539128405765, 0.587347353362073, 0.5026672376723064, -0.39678401891044507, -0.19062940383432067, 1.1574818413993138, 1.5337417523856722, 0.09229791436636009, -1.1643414562747267, -0.3692212087059149, 1.1458955082533275, 0.6361364463860524, -1.8101562596194158, -3.0268939233287204, -1.2919401508174078, 0.9346048983036778, 0.4185782528952846, -1.940993225980008, -2.012781635505348, 1.6649162430384024, 5.273789710949357, 4.4605270380237485, 0.14659730009258412, -2.637679295120721, -1.3303672040273198, 1.2170678054175683, 1.2441160495799781, -0.6005958804242422, -0.6115792711658341, 2.1948375555337263, 4.3505836428097995, 2.70580241463938, -1.1836493383792352, -3.1812060685564267, -1.9557751837992599, -0.07853647599307624, 0.1238112635957164, -0.4736334557685543, 0.015324429305801936, 1.1757155394297114, 1.150054719290755, -0.01993373793214037, -0.32104095340033634, 0.6205387070378289, 0.21746342369757116, -3.1575137988504194, -6.516959540364348, -5.158425029743307, 0.8371986304455782, 5.603361336066475, 4.324277325126495, -0.7026935650820023, -2.958816302081148, 0.12184404496799207, 4.397868434761926, 4.873096426867274, 1.8656716243361116, -0.44426037441322175, -0.072811746686141, 0.8556798157411963, 0.18474667790303495, -1.0075415563444357, -0.641411774450521, 0.7288175057876854, 0.8260904900439239, -0.4414644009146266, -0.5292411474710035, 1.683739222065051, 3.5894125977450564, 2.264627260212158, -1.1692349358504133, -2.8374514166041025, -1.4053445465404615, 0.33862913127748884, -0.12280169562556631, -1.3722894544597697, -0.7311000206876558, 0.8970165383726321, -0.15648285538942225, -4.45134300610285, -7.303842876487492, -4.43982055009501, 1.9242579566032256, 5.3056044695719065, 2.9401756569600495, -1.1034878109967345, -1.6263170854844762, 1.2197097548598412, 3.1505454054594955, 2.0298197067975106, 0.10154681425386392, -0.14117768480567394, 0.44829508180108635, -0.254263922204744, -1.8436337406100012, -2.039994958060315, -0.5005135146456562, 0.5425634088523719, -0.12573329829455523, -0.808808786203634, 0.014764240414593255, 0.6260345668094441, -1.4386674862930589, -4.612794496356363, -4.125957738915629, 1.4256233595151637, 6.881848370928328, 6.192193790359818, 0.05559082876700897, -4.801991697345563, -3.9229725696758595, 0.03378376549848443, 1.8276218890918763, 0.5466783297684722, -0.5170156888094783, 0.35837481094255197, 1.013998530092631, -0.48197438648885044, -2.3046521381473193, -1.5962856208174714, 0.8825743530203516, 1.5612832432244592, -0.7366341540788474, -3.0560124247821383, -2.6192137414702263, -0.619806589707268, 0.04639527906451024, -0.7377768380415188, -0.6245022578998861, 0.9056768227865183, 1.44871006651633, -0.25357979895236726, -1.7056079397377242, -0.24268800950421252, 2.4047770644093207, 2.1385217580644817, -1.1202613357684033, -2.324649210017176, 1.8958470447057298, 7.792534043611758, 8.639161511645115, 3.3470352861710473, -2.1466434160721577, -2.5283863614429634, 0.7108274141051089], 'positive_zeros': ['0.16769247617180531571146399579', '2.01598718694963179676158027921', '2.812167269016762669862730711020', '4.17461811688863519365028736229', '5.984998676380960591210374727401', '6.70280541304940321254779339431', '8.19395245743010051588302606069', '9.52079238937702789842041982643', '11.01422052840258371209996324038', '11.47440361367286017154448146753', '12.85927584379009640904849970619', '13.64711240088171473888151747981', '14.46585195481076893289332461178', '15.45575996593617507826002107273', '17.31159545693537825782218680221', '18.52347517281722582536495283945', '18.97293195855197599174673528338', '19.79910394936571503647591149909', '21.10582104622031704826895668421', '21.97369874663593291448260918294', '23.02380512337407414749092131760', '23.8176417864788880530479941774', '24.587679772447523693908868119944', '26.06763572021268370615945490693', '26.73734844833553837796774858400', '28.231813460183877405725587706749', '29.19626039515169113352918874263', '29.76660959073021358492087763207', '30.667163517495163915569179217319', '31.33345747560076331281165021509', '32.142995566216060165525444649472', '33.61076076755786811956361542865', '34.29030754451500071047067292967', '35.51540085388432472364601335610', '36.49599690103075696072506407303', '37.359446172277655769415237186220', '37.98059489203374875396694751139', '39.06069664125588036986573397083', '39.96503635879911721390087369305', '41.03636291418284999654468234516', '41.48634400891378505498348831193', '42.490802163885999238469268023978', '42.88363972014222452025017848750', '44.74134247706584066979592462060', '45.738905457753561944051934512628', '46.43157132262102536707475676168', '47.06053645760479100764563128143', '48.03349694210494986199776171730', '48.76863752274634531158859031633', '49.50413591511621300041057059775', '50.54740190206300232138705816756', '51.20871205452718314229438137728', '52.512603813799672545153541574665', '53.335054629836524106110732532867', '54.0237866323783362819208892362', '55.09807583748745355590233807039', '55.81785721643299150552629679348', '57.137802019076859850711217499846', '57.72222531398445774813725227023', '58.22256419142528784157890940926', '58.98475996432389456119452060024', '60.1551057064538743099026190797', '60.511024238986621959432734182877', '61.74773230557062320453720110322', '63.05055187324798998094595123194', '63.81697624313151625538837572966', '64.60522484509921747290250095685', '65.42516108468217503241062189505', '65.90613274998308696552033683187', '66.558386779777049102327499772847', '68.00580850187414482854243430737', '68.70958762235189717079997861339', '69.16326951972668258881967015463', '70.26960881635865591190178210287', '70.78601201601883802161314381688', '72.19246732672866369218055575005', '73.01210790672005660222694605053', '73.79250586391512342960509025478', '74.59645968759523780070874103124', '75.52311518365600439544644507845', '76.05104318817659358373894722778', '77.04472967854679917929268769678', '77.28652317329960226474105856796', '78.23904530924823757639271962751', '79.40997456835393494632529212660', '80.60853520961543040677654929915', '81.27751999523105903771221822931', '82.01548660677175019336076213389', '82.63922867190445817530778067303', '83.64568033607188984539401751007', '84.42328303852182050230297773761', '85.203437897346712022602598082357', '85.98901100185111370597750389262', '86.71647399417708130010069626376', '87.57910000901597541948181281138', '88.14326667064852137387907696842', '89.11718435999030191349324510322', '90.04024534830113972276231817961', '91.33469817458595459925079372581', '92.24716598365678196263684878463', '92.3829414623935251816024661643', '93.35935747105787189652331421801', '93.86799275516101847919095736481', '94.84672035134618671845438351898', '95.45128047463891342226208763656', '96.56065331674561211268143220681', '97.341712453951042714263918160503', '97.8474101682827391186322016441', '99.405744697434194421439286201723', '99.86342633003740591505234111522', '100.43347661847339686130232920807', '101.302302320134465544821794301710', '102.39218995882816077737581786725', '102.95065136030564087567721730520', '103.92289644983894445011290465912', '104.60457176097463284539941075400', '104.88722286899674313874811963181', '105.69931259068629173422869560898', '106.72894680822056262443463432952', '108.0074235422735591818323175179', '108.84938915677500298334302924214', '109.35120212576212612716178463188', '110.352087557932521334266930725', '110.85843037023064334801053706371', '111.608243658512605769219186517972', '112.49109627415921913486513502846', '112.86201719675006126899831105360', '114.03785422462424210862833789965', '114.85046074217426518818204763928', '115.64026258629492942476681385891', '116.11464528403588791837257274556', '117.422257867216372390037939839460', '117.71190759632107456349929964994', '119.22678305452307572670919194656', '119.63790662478709724902408918055', '120.4227557563648726360893874506', '121.21548308997361346235535269829', '121.64307567382736895985667076463', '122.51252414624565719663265263716', '123.41722692052245978721259282001', '123.799474515882311955524512168018', '124.71644024192890379345630291731', '126.2665342762085283214281482131', '126.65719251396616391561651703577', '127.66518498648809978902360964908', '128.07954947385385158698028840760', '128.91226578469184159186727232216', '129.276356432558377707500867227425', '130.68973136410812722590961973622', '131.259356385812070175032573055774', '131.96537919532056839085470399113', '132.51481889837719937779663981359', '133.24281815319152354591349382210', '134.26390146364462737188284689502', '134.931928149069948206770784110452', '136.2525853865381513193386495555', '136.61317327231427006002670274943', '137.56036283474056716286961315786', '138.408809824065825812833534255940', '139.1127072726953102000346914955', '139.47366328679874123082603641982', '140.094270846088710721356623530925', '140.9773853370130585037285988649', '141.858409021469870083200393062', '142.71814687216598204472275914679', '143.78158707176448896325183931856', '144.22865815196942567843311153693', '145.132772654890915374418479341666', '145.90927315062157037903093017050', '146.777687319752967561134390204340', '147.179943476417113708936689935', '148.21596175775282743019958674594', '148.89721690154211739635412569306', '149.59811573575840665786632342665', '150.314607509605900875948967260950', '151.081522925286747140613593122080', '151.451877282815257878504253089266', '152.366172610406017747424445722730', '153.76350660772676842152776242334', '154.64948911255964245330592790735', '155.12530506330284762217364113654', '155.790283105232392390262899539974', '156.30233873552374904884245169772', '157.20337129303826750531858870128', '157.8799143322715642463890001178', '158.53012172913486613207031674909', '159.52916145921840954341382212216', '160.0594220203498370863574274477', '160.82027033872442100850385091146', '161.8854675342870937532598847275', '162.6465142228831885967697666452', '163.33218576106078573266285717671', '163.84007646550106100575140477919', '164.903259093809394754986011718902', '165.959837519424466344003414855495', '166.310267062291920879079992444798', '166.87072469218017107011757396492', '167.80671301636524125258422032230', '168.2476635906414421502800403739', '168.78171033053759908492651279227', '169.960574742588684447740287331874', '170.8923024877755550445613712056', '171.55441124044186223350739835037', '172.712721601267071270125758997479', '173.14387620320691395000333043237', '173.79177814556327303333263540855', '174.517134313545237495351118680740', '175.20701090026696657907192607770', '175.726820252919545077897891206976', '176.76815989347753883691437097824', '177.71914251636979204597249593842', '178.09635054592828242026554665040', '178.87473611203427282909805142088', '179.35865356879178931587662430460', '180.529685243424362242253903750406', '181.46139842739916178167093502325', '182.06926872363810714495102522368', '183.15233587939938988350321327934', '183.50453362370256522352913542738', '184.00468627301101527742091724889', '185.0989434158042108960188886029', '185.58924241497141921592968444518', '186.24630136647292307862387811064', '186.712272600330107012832783538704', '187.74589031158246725395664319429', '188.752581434146829200214182672417', '189.684529285842576058422761995838', '190.41584538326103198910166386722', '190.85081399387095340947217646736', '191.49266873114810590128309057562', '192.38660059559864581049680111392', '193.04673857898618517223311120011', '194.22760147682444158198646420531', '194.40715777361971815256407515672', '195.14138984326514678731709195835', '195.90174303482097014776183375251', '196.58958036155105895713157853389', '197.399164458121069274060730061958', '198.022431813877231714665657852533', '199.22791508697628745093611186801', '199.934596238594464385860852598979'], 'prelabel': '1-161-161.44-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 17.30185289193463, 'root_angle': 0.3102609493650968, 'root_number': '-0.369648512412725298060243612727+0.929171661896260841429667352316*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.310260949365', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(66)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.735270627386005196194785375694-0.700162304466718384291819261935*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.167692476172', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.01598718695', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.81216726902', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 17.30185289193463, 'bad_primes': [7, 23], 'central_character': '161.44', 'conductor': 161, 'conductor_radical': 161, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/161/44'], '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': '1-161-161.44-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-161-161.44-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 17.30185289193463, 'root_angle': 0.3102609493650968, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.167692476172', 'prec': 47}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_161.44', 'Lhash_array': ['dirichlet_L_161.44'], 'factors': ['1-161-161.44-r1-0-0'], 'label': '1-161-161.44-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/161/44'}