Lfunction data - 1-140-140.27-r1-0-0

Formats: - HTML - YAML - JSON - 2026-01-12T00:08:19.161653

• lfunc_lfunctions •

  Column	Type
  A10	numeric
  A2	numeric
  A3	numeric
  A4	numeric
  A5	numeric
  A6	numeric
  A7	numeric
  A8	numeric
  A9	numeric
  Lhash	text
  a10	jsonb
  a2	jsonb
  a3	jsonb
  a4	jsonb
  a5	jsonb
  a6	jsonb
  a7	jsonb
  a8	jsonb
  a9	jsonb
  accuracy	smallint
  algebraic	boolean
  analytic_conductor	double precision
  analytic_normalization	numeric
  bad_lfactors	jsonb
  bad_primes	bigint[]
  central_character	text
  coeff_info	jsonb
  coefficient_field	text
  conductor	numeric
  conductor_radical	integer
  conjugate	text
  credit	text
  degree	smallint
  dirichlet_coefficients	jsonb
  euler_factors	jsonb
  euler_factors_factorization	jsonb
  gamma_factors	jsonb
  group	text
  index	smallint
  label	text
  leading_term	text
  load_key	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  origin	text
  plot_delta	numeric
  plot_values	jsonb
  positive_zeros	jsonb
  precision	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  root_number	text
  self_dual	boolean
  sign_arg	numeric
  spectral_label	text
  st_group	text
  symmetry_type	text
  trace_hash	bigint
  types	jsonb
  values	jsonb
  z1	numeric
  z2	numeric
  z3	numeric

  
  {'Lhash': 'dirichlet_L_140.27', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [2.9010907910729803e-30, -1.0], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-1.0, -1.4081532572346456e-30], 'algebraic': True, 'analytic_conductor': 15.045089471247502, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [7, [1]]], 'bad_primes': [2, 5, 7], 'central_character': '140.27', 'coeff_info': ['x^4 - 1', '6.12323399573677e-17 + 1.00000000000000*I', '\\\\zeta_{4}'], 'conductor': 140, 'conductor_radical': 70, 'conjugate': 'dirichlet_L_140.83', 'degree': 1, 'dirichlet_coefficients': [1, 0, '-I', 0, 0, 0, 0, 0, -1, 0, -1, 0, 'I', 0, 0, 0, '-I', 0, -1, 0, 0, 0, 'I', 0, 0, 0, 'I', 0, -1, 0, 1, 0, 'I', 0, 0, 0, 'I', 0, 1, 0, -1, 0, 'I', 0, 0, 0, 'I', 0, 0, 0, -1, 0, '-I', 0, 0, 0, 'I', 0, -1, 0, -1, 0, 0, 0, 0, 0, '-I', 0, 1, 0, -1, 0, 'I', 0, 0, 0, 0, 0, 1, 0, 1, 0, '-I', 0, 0, 0, 'I', 0, 1, 0, 0, 0, '-I', 0, 0, 0, '-I', 0, 1, 0], 'euler_factors': [[0], [1, 1], [0], [0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, -1], [1, 0], [1, -1], [1, 0], [1, 'I'], [1, 0], [1, 0], [1, 0], [1, '-I'], [1, 0], [1, -1], [1, 0], [1, 0], [1, 0], [1, 'I'], [1, 0], [1, 0]], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-140-140.27-r1-0-0', 'leading_term': '0.0821650796928880079095510697201+0.147371656132379237335868467130*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/140/27', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.16872908863660385, 0.9047089932991264, 1.3658531682051527, 1.4508286879202832, 1.1015856469687977, 0.38172370096905833, -0.480352900448472, -1.130930242785537, -1.21744494182542, -0.5575982603617962, 0.7289355165777712, 2.2079264032182713, 3.275019381742152, 3.4174504691376715, 2.4781473035122703, 0.7801891946116916, -0.9808558398834286, -2.0545589289246005, -2.0164915290208727, -1.0054244533880823, 0.3357423312335403, 1.2115884497031413, 1.136586802178205, 0.2365017760712585, -0.8132950254608879, -1.2059661413298997, -0.5400870354208447, 0.8660498041495593, 2.1135114625124953, 2.267749890359399, 0.9839719794756293, -1.2004262187378805, -3.1339910717289876, -3.746508237831878, -2.734675517816998, -0.7743629364683642, 0.9093816655660958, 1.347171859781589, 0.4604364864393045, -0.9228575572455766, -1.695845074235659, -1.2999081792290483, -0.14200463049969037, 0.7254792476234043, 0.44389303572369015, -0.9234776951969024, -2.3547623365152575, -2.6005982941410113, -1.1611411482705782, 1.2421582555282258, 3.105354615844094, 3.2092560679531554, 1.5252423137940627, -0.744310480314808, -2.049026577755416, -1.634121724404312, -0.05972807211129472, 1.3107981833183016, 1.4403787893107802, 0.44651451105017015, -0.5541935924924453, -0.4577663404070726, 0.8140770090626847, 2.1813075085943483, 2.3084973025180324, 0.8052372050083836, -1.31304037931576, -2.357310758239784, -1.3359675641246698, 1.1714349204818018, 3.4043247559423007, 3.7957204590123785, 2.2051377341852505, -0.022531469057111505, -1.2193014885671296, -0.7794403161802235, 0.4228575076050766, 0.9254160668644608, 0.06155144379340376, -1.4245988134842649, -2.0998118694582284, -1.2451715702189416, 0.36748714841953606, 1.0962752037880166, -0.059720737455243436, -2.4277082203984555, -4.103971798189732, -3.5548088921273835, -0.977788336845474, 1.8120213937368945, 2.9050507383759356, 1.8875922121283863, 0.08456350114321284, -0.737029823838665, 0.011999467772740998, 1.2990297686463128, 1.5817965744362072, 0.3773377457604797, -1.2473656542382359, -1.7558248894881974, -0.7454328122234184, 0.5258705952552598, 0.28223520680788977, -1.9977057980157955, -4.897203738002715, -6.207082094368274, -4.897558029363557, -2.0756990645582127, -0.0018800380227886337, -0.06711987089148383, -1.6256497667094163, -2.7574357126248836, -2.1782861374617175, -0.4231531968168706, 0.8247905339550455, 0.5315109154319076, -0.6143627196616384, -0.9599648006239787, 0.2923484777842843, 2.098261562831654, 2.510081947763475, 0.6730101116104639, -2.1334757601181886, -3.545992270481553, -2.3201498513241487, 0.4560705202608032, 2.3603477147481144, 1.8976370079192157, -0.17803599642313034, -1.7468506028595834, -1.4724827028710927, -0.034326640106759176, 0.7588897178290485, -0.02313973898577334, -1.4465422913864414, -1.792170606677559, -0.5349808799848776, 0.9345145881480084, 0.7063619802125498, -1.5412147047791773, -3.9719506800152558, -4.279933485047719, -1.9956171824030884, 0.9535010127753631, 2.060135668828746, 0.6314571993529707, -1.6474802746659285, -2.510511142657885, -1.3743814875092968, 0.25838017766662397, 0.5837125297225073, -0.519935819574362, -1.457171301535068, -0.8245530663382772, 0.8871884456688487, 1.7414679997215758, 0.5339401982389393, -1.6852179485600909, -2.5147628395370143, -0.6984715534218461, 2.4174932343965194, 4.093576399724162, 2.896423508138785, 0.09771221043261838, -1.6794252576528834, -1.1217858266676166, 0.6030306840596151, 1.3205821697853475, 0.2682692820897393, -1.2024539196824402, -1.3376729760983683, -0.09918183564951094, 0.7567356694721672, -0.23914234630627482, -2.4013126038963044, -3.4498048895158973, -2.0099639532797275, 0.6917631153817732, 1.9170659041751739, 0.24426322110431647, -2.8817444976013458, -4.584591839273258, -3.4693281175864046, -0.9098148394551122, 0.6008328287048026, 0.14279404127109133, -0.8602569485819637, -0.5296687422123032, 1.1846429716045328, 2.4737386207907406, 1.891975708117093, 0.19066104876460513, -0.4612249862099965, 0.9430517841316403, 2.857016471236515, 2.722711701273483, -0.14715851708698408, -3.575595359242409, -4.6400691065193875, -2.665405925199602, 0.164851607050652, 1.2161338107196804, 0.13620579092321344, -1.0712145560492454, -0.5620583185852148, 1.217999678632231, 2.209054883382217, 1.3105796018201241, -0.2677189190496856, -0.5149944236360551, 0.8139038950213877, 1.7102374785955297, 0.23498097842917348, -2.9882549775377143, -5.11178785131085, -4.043211678531371, -0.7734877925345824, 1.613478128470978, 1.1978475674971103, -0.8713143837629828, -1.889024547410593, -0.6990784090301448, 1.174503753088332, 1.5402778787556308, 0.18321453838161084, -1.0202762332761655, -0.5660597813353831, 0.7149192464750039, 0.6649010837891961, -1.389337560632581, -3.483115373324159, -3.0989901769081274, -0.17321529138891276, 2.552719872901419, 2.419438816263459, -0.24089784482384796, -2.503348489612328, -2.1063295783667684, 0.16194757013974878, 1.60537383884341, 0.8112461729713449, -0.9011298857010981, -1.3585805980021586, -0.29953797528544135, 0.40100437817189793, -0.7276711196974512, -2.6802110943946693, -3.0672331496394127, -1.1406509213263123, 0.9918962706593399, 0.6462034952178818, -2.2286155756206543, -4.756572243733652, -4.256747867976102, -1.2247287542721585, 1.2770294125572217, 1.074277839200568, -0.864994585057436, -1.9031483069710124, -0.9854380796741158, 0.2942311297848106, -0.034458617742228546, -1.6920651266424827, -2.5153863881487415, -1.3376024474025203, 0.32630249707715586, 0.0651575720116345, -2.2751160112798687, -4.049652346869654, -2.785067914375027, 0.7893649591067924, 3.351628323736115, 2.65000470213642, -0.04831886829551549, -1.566970281587512, -0.49795840679950304, 1.4321858857541994, 1.7676746619498949, 0.3678526682338177, -0.6668501199699625, 0.07913588056969885, 1.412109327009934, 1.1150183707763284, -1.0003855145154403, -2.5907429065230447, -1.6621590239838921, 0.7124333598212499, 1.3906178838188192, -1.116103216625453, -4.673387051879234, -5.805587614444539, -3.5915678074989676, -0.558624594431454, 0.4019422515406045, -0.7135023719640367, -1.4657471676305802, -0.31217604716514497, 1.477607569481467, 1.6658232700454965, 0.11374066600473536, -0.9958643744622275, -0.1029861772972792, 1.4915990924375269, 1.1645976103453992, -1.5157799176289333, -3.8208696067385968, -2.919878929107673, 0.6466363860818133, 3.392934291412882, 2.818000132136046, 0.13283823628143562, -1.437248590900701, -0.5586348826520684, 0.9156078123760276, 0.6549584074589688, -1.0819823730314047, -1.943136054787004, -0.7316056143148244, 0.9722822128635891, 0.9960424401681991, -0.3367035719514588, -0.4240588549559381, 2.155559482639639, 5.377005592312234, 5.833273523527738, 2.794136529734658, -0.7713633734770691, -1.5874970093103793, 0.22272063084605445, 1.6059330831410552, 0.4907955223619256, -1.8020347887385566, -2.520667773529338, -1.0696451086004937, 0.44434190598102996, 0.2419006956279816, -0.7011871497706756, -0.12107592715300265, 2.1554142157856417, 3.573719542079679, 2.055313597062211, -1.044957928481573, -2.2559390681911973, -0.18092180050421366, 2.675790562888063, 2.856272030104555, 0.07792171689586645, -2.5556604582472793, -2.4154197832863664, -0.3595703037146875, 0.7601776590913945, -0.09844101803572236, -1.0759567027898262, -0.27277615784241965, 1.4733042785794321, 1.721256356030218, -0.0682794565918476, -1.5139454180865086, -0.3850526020378503, 2.204796052231706, 2.8719054906168484, 0.20083884986308992, -3.2390640623981124, -3.827255771972135, -1.1997262767511383, 1.4451598150170109, 1.3371681855040893, -0.6904740134921443, -1.7224117375001826, -0.7098935933967233, 0.40841202603961985, -0.31198232275903537, -1.9831804090030145, -2.1193352086218784, -0.22202492418820233, 1.3108266639081734, 0.3994354738200223, -1.6394204026267334, -1.4835463119912442, 1.869512152066995, 5.456442025329774, 5.722539622365142, 2.7655198797254825, 0.09225378668596519, 0.26490645277458846, 2.0220596362028207, 2.3769073307739452, 0.6618367884163588, -0.8542414574164486, -0.3456581417426595, 0.9996708320021062, 0.7574667625059829, -1.1539918634537407, -2.18677995254036, -0.7389646411317373, 1.2927057850480954, 0.71839678501462, -2.650414862227235, -5.344493290983121, -4.35124444807097, -0.8337137983825023, 1.3263448825602808, 0.2727997852496794, -1.8700575258525358, -2.129877210059612, -0.548574200354647, 0.2844935803360798, -0.9191842615531115, -2.36006773084793, -1.828571969181124, 0.02467473789201361, 0.5334115641258517, -1.0964113403929296, -2.335282425350876, -0.6196948673666003, 2.8901873476895057, 4.310123515459018, 1.7970074455596634, -2.0492898784388416, -3.3351655130803133, -1.5329978590980966, 0.30101368025458647, -0.21984105460415992, -1.857907359484547, -1.8468413826254046, 0.128903555034525, 1.6090982303304715, 0.9635068955773864, -0.295744837578629, 0.17130911858102185, 1.8735991193308976, 1.8307686727494346, -1.2526810384695382, -4.685590133391326, -4.821963849757817, -1.6796511524320406, 0.9743705722596051, 0.31741562937261125, -2.1373681786127694, -2.784771736890451, -0.6659642768529058, 1.5794170549559028, 1.5239013683338478, 0.10935783651102879, -0.07077801162972358, 1.3312602582833737, 1.9858136968694555, 0.506756844187743, -1.1687927725974414, -0.28777816692560126, 2.6515927780276924, 4.0966378050824845, 2.0152741337429383, -1.214882264089711, -1.6677866911603016, 1.1384523146737244, 3.683133723990097, 3.00406187937258, 0.2927246881473281, -1.0797694534562954, -0.12525507204625255, 0.8643398921208795, -0.010297101264477712, -1.4620292830754522, -1.0724352584774182, 0.8987590117187287, 1.6169491321997502, -0.2585978717372466, -2.3423311335781496, -1.588970802287351, 1.347218593644174, 2.591062483557518, 0.03904183964951912, -3.7362266671309787, -4.630356408121237, -2.0709494813692797, 0.6393700076627791, 0.8823920772864366, -0.14119295766685086, 0.2648463852891186, 2.1573645028082864, 2.94758269462014, 1.3462570769460354, -0.6148258092771237, -0.5212707142295683, 0.7676453841378132, 0.21365142240661944, -2.8410684249836615, -5.135108391335967, -3.5161257050409453, 0.7268799265423322, 3.2170717062878307, 1.90648694819871, -0.6037587353041216, -0.7918158529759263, 1.212798706242938, 2.304397901939557, 0.9919200626032006, -0.6897174219624568, -0.4266419786484744, 0.91482340680634, 0.6968564139247972, -1.3490025488151238, -2.4670566692235236, -0.9007368797365775, 1.176291139740478, 0.3471074606131843, -3.1777196081001176, -5.354375103945569, -3.3838642246452486, 0.6623566608812305, 2.5607546582030247, 1.286133906600535, -0.17434605651141338, 0.690281110480383, 2.574595595277201, 2.6394344483901873, 0.7890501664856245, -0.31636092511584984, 0.6416728218859654, 1.6262156935065426, 0.40281468891219335, -1.7681911978799474, -1.5697277649535302, 1.5229323428113666, 3.931263742305372, 2.464243326280897, -1.3467707248049134, -3.0972734444235908, -1.1508944775463226, 1.5239474703911333, 1.6184841371724095, -0.20716970424512163, -0.7744044410193462, 0.8634082031406876, 2.2733979571542373, 1.4907637883668787, -0.029434956860164625, 0.2479827524110477, 1.8707343521592954, 1.8506402102706285, -0.7611653615973856, -2.8911682855631415, -1.3504335521263302, 2.587968766010494, 4.500452696154113, 2.497853927823574, -0.4241817509220306, -0.5409771981950757, 1.7289760573036146, 2.827851426824351, 1.18243053425418, -0.8859213963836617, -0.8574713610000126, 0.37753528331848873, 0.2503497857822255, -1.242204682662411, -1.3437025718464308, 1.1557761230962473, 3.58327626156359, 2.853008688716528, 0.0073901087654412775, -0.86886670909686, 1.7888300627470117, 4.6897935741237395, 3.9835851275031255, 0.34288647756351187, -2.1010815427199043, -1.2945992608875205, 0.47597302099141614, 0.38688103772594823, -0.8949193557596853, -0.7105559991758168, 1.168367289841497, 2.0211236004541466, 0.3666227272449646, -1.5500863094334225, -0.9691701479227901, 1.0675151788187873, 0.8796524214017569, -2.489099690504507, -5.379243264632047, -4.139269925550139, -0.036180881371871865, 2.374699338103976, 1.155926470618416, -0.9645057409974181, -0.8973734210290283, 0.5822214337342992, 0.5688523342464986, -1.2867053239827007, -2.255476692382693, -0.7977522585278533, 1.0040673840568046, 0.6547336305023218, -0.7371208110687686, 0.07526490173537055, 3.3782956445215295, 5.356912212249755, 3.065954901387689, -1.305829972641447, -3.0579298071715217, -1.0274932278610787, 1.2539577936597126, 0.6831216426797976, -1.386329552457818, -1.6628406360644097, 0.11296368684211228, 1.0683797011026421, -0.23032363604632922, -1.6348422918085515, -0.9020132774655749, 0.6531943290423196, 0.12193799795982811, -2.2273193163540204, -2.7533582525662172, 0.38369007491235857, 4.083196477529509, 4.092495367675172, 0.6833927177483354, -1.756572599906509, -0.6633126271723495, 1.5613600789368152, 1.3715190675282778, -0.9164569334948994, -2.037818364934969, -0.8099224760493683, 0.3700702496921566, -0.4452191785565019, -1.611977802322775, -0.5568525253088992, 1.879869490387879, 2.3269087701852254, 0.020035213176329985, -1.5360287612809504, 0.6726873152703405, 4.61481264984063, 5.61286840474742, 2.568432832416497, -0.6999369193618648, -0.7864231085240496], 'positive_zeros': ['1.7003000440856520411801028682', '2.962013405674335888482472672290', '4.81906831047126270424878719672', '6.16838580120941914467066301067', '7.253062983615418294430564189041', '8.25546793246418115848227508292', '9.52282482429614426950055490158', '11.06227973309800953059738805119', '11.97855823764077818994494660054', '13.16254613335902274987357913570', '13.87184128600035893493995925144', '15.155394046424681172907188940682', '16.454926290257718422393752321', '17.51092979691676403023657779386', '18.55459108576250076056868534428', '19.19991809570454315614611201224', '20.42873927102153000711367381433', '21.42685224225089977238904525265', '22.80888008568049079738602624620', '23.63794279840082816392030849251', '24.388591952752209945783586035100', '25.5504188781249847889456145745', '26.24066042064482119688548467403', '27.60007362489503159840821926516', '28.76738169154380200076842074293', '29.37208521714546070242211620604', '30.38084845384829164504613536470', '31.41122204178576893114827433185', '31.93209749616117730849392723511', '33.75054783200751132662661602416', '34.04210633789471751727223462847', '35.39028066438839781625471880000', '36.08453731783668652640406946541', '36.82364743414823848265254924880', '37.88762344421126755440237308599', '39.01176440611574902617396258279', '39.974749646343030532907910685550', '40.945164689247553182130124402212', '41.55727588020778459118814891746', '42.59728633294548003260647127648', '43.247973777564219839180770158679', '44.575891725435568598208444580382', '45.39613101132384651785241428061', '46.50127075063396479535560834526', '47.065555418028932018460670094190', '47.967797498627164248857820710844', '48.82619389348149964307926375536', '49.759509919797767223979343596393', '50.94890729902329800817574555533', '51.76370739153898769927412070094', '52.55133887687365167824548310861', '53.45984359376823959496287542179', '54.02094841135386049754531593239', '55.22888442677432605328316370703', '55.96366797194867071027148902872', '57.32535685844947721404363771621', '57.85200007839047119145549294655', '58.55013071408712591993108719149', '59.72866812066038439197637414694', '60.15096020832461277009482737037', '61.23747573618499644120546696242', '62.47779343901643912242089191184', '63.15212755044076441729313532050', '63.85747226842749650494859532590', '64.93623615364676951196658823804', '65.459374818340230508680811363', '66.27631492252296342564278403889', '67.57538370922549452894095579727', '68.30949023372620405844696571227', '69.17055259847107057418202038956', '70.03475719510004485389987607419', '70.75725189375217083278591284275', '71.37873082139398035060166128927', '72.51593318643152113575086246560', '73.41268141575359477237927939732', '74.353303602504982269513656537036', '75.14186106808717317503830023676', '76.016249848765943390069026962445', '76.42279864951234337277052931161', '77.64288035650748654766702886459', '78.21361949391402053992321348618', '79.49767466802548398895311876019', '80.17972182711920361619240482395', '81.15151996511936459231684690064', '81.55388793376845650541722039644', '82.73133799122291225681121981745', '83.13766056326572985958074328655', '84.30936331536456374180953699545', '85.30672685830048773632105579240', '86.01320440565990604380307627100', '86.94931513638665647633237750719', '87.48246720169393939754685356202', '88.30538470400037983578417061792', '89.27718832525562898430342334966', '89.89664241567278616016668567653', '91.340194210647476700651921275', '91.71214178663275885732304981033', '92.55063134962754636686742131355', '93.45786094713495806334805347471', '94.08132185515741783739659938115', '94.843915351096871103908692391464', '95.885186566701962093854630836227', '96.89102809698063694378849582357', '97.602218513497272921025867406891', '98.25374255576379585601102723360', '99.18092513868734307483556820950', '99.92020414083565030680808023091', '100.39201660503268935949139362181', '101.79210134365556708539049087075', '102.46819965812313387989560682637', '103.19195309671007733948565479779', '104.25087199829118251301982024288', '104.76047722634548567162080400609', '105.33410528377257942727257191081', '106.45331219112671115316996200766', '107.20546634418002999079953757397', '108.13229379814441593163222236536', '109.121547159721589696782023392251', '109.66485725929356753207476415741', '110.361642754764340261052335546768', '111.24009322657597279164242168091', '111.92364369425871897183328414581', '112.829200387656533484847878161676', '113.86735078531656664452389106594', '114.5856033332081787350447443160', '115.46731644065127790448574200026', '115.8704049009333519908950248426', '116.90637131156061600636850060579', '117.55946219505786132895447554594', '118.289675531068134479310058617444', '119.71048955746821738152241663787', '119.93409048054405722115081487277', '121.04080543354778020864668943069', '121.63726672276620004851989043899', '122.32534886762857645668891049253', '123.222637508828393911809210819462', '123.83276983305867747647082367358', '125.08077730381868982223377370046', '125.66290317809629935993338608897', '126.68275133735291347928268223508', '127.00123458287233245942601354253', '128.120212254824559660432387983146', '128.57280158871558869424779332897', '129.433041304443068738539600852274', '130.45047972155798185400764365384', '131.478718748629832249556411319947', '131.82767448899325661375720512001', '132.79441395050630436058002175241', '133.65002580539866345415955763168', '134.02370084149341143726906122319', '134.89726477916655658117508507857', '136.09704442416597622591863575185', '136.6061106760116918662482321749', '137.575808941030565030940766975244', '138.46950049192187239766573970388', '138.77394534157884791731521825419', '139.76201607858285934894700720105', '140.34864401186382448560086057688', '141.43109617951956710746209364501', '142.081952374004206584736843315222', '143.16265061180689517433623646241', '143.77655507702827326874406037562', '144.37300586711016435973559183651', '145.17511162229241258632171199896', '145.90626795432600965040201770440', '146.73640837931680757659834541759', '147.503113219945426764239594278035', '148.652003605478614135985048724951', '149.31839237550193579553870449812', '149.62176167260845596708771903606', '150.81415554809926605427221003841', '151.3710197994566799639898475093', '151.905162168050499369320314274099', '153.07130981494160785600587144714', '153.97159856773999093297638923992', '154.5150700046160164741975600876', '155.46902954528093898452018382765', '156.034149017691717614592645474801', '156.68469590354898307949087891473', '157.61304032690865419856267622615', '158.16338512135295523944806711270', '159.31983009940030364403813791823', '160.23822355901377397171760918609', '160.48171197960690746505006119408', '161.71335172904331001878804331567', '162.04005835291066138549460816959', '162.86693736817389882650878946782', '163.61495669583976827689291920581', '164.57614142114317727982452425599', '165.42964729666171933432228248278', '166.21326793024570496315577021889', '166.740803345353862402302520332125', '167.802506468569337766989673672369', '168.05861960996940006494157588933', '168.98590823895800194552540332275', '169.79940409982872423696149421467', '170.876755823681149484637276281675', '171.33907629132612016955143383223', '172.341740817023493394217876692719', '173.01883259821754238708146753365', '173.49830202385968191632245261689', '174.25611951272795982813391932626', '175.3134170067437696834753606883', '175.76601880538802559942798982887', '176.90419727259162304584212870764', '177.70757033517067651380404923846', '178.219565394806734290294106876', '178.88178122136255940553176236071', '179.73529893155012269095538571333', '180.45544340944168007505368155864', '181.04188875030541327024158758772', '182.190342974281935632906731713', '182.96217828873353591430559540256', '183.621272314170396320343787099597', '184.17566488454094693228719856050', '185.11432716383958108403564160293', '185.75676283399674270231257665337', '186.24017096409212008594675693867', '187.40090344561234575922617581093', '188.2373147211531247188053780209', '188.85167004233157659357888692487', '189.669101368253205923962947802306', '190.27424608356299937943715944084', '191.097617310154120347154319869947', '191.58204559276714419626366675088', '192.4715770606997280550215832094', '193.49716406530306509303932022163', '194.14607085640032431052207264311', '194.88123171369079138432224045417', '195.786165794986044903284971228', '196.149830548143260407745704538058', '196.9473687976954147283504632446', '197.81482063498029962057797170912', '198.379537077804399836952568225473', '199.59629372381728020136835190624'], 'prelabel': '1-140-140.27-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.045089471247502, 'root_angle': 0.3381040955873917, 'root_number': '-0.525731112119133606025669084848+0.850650808352039932181540497063*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.338104095587', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(4)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.730894695206520171955223812509-0.172540832462728452027504057854*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.70030004409', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.96201340567', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.81906831047', 'prec': 44}}
• lfunc_search •

  Column	Type
  algebraic	boolean
  analytic_conductor	double precision
  bad_primes	bigint[]
  central_character	text
  conductor	numeric
  conductor_radical	bigint
  degree	smallint
  dirichlet_coefficients	numeric[]
  euler11	numeric[]
  euler13	numeric[]
  euler17	numeric[]
  euler19	numeric[]
  euler2	numeric[]
  euler23	numeric[]
  euler29	numeric[]
  euler3	numeric[]
  euler31	numeric[]
  euler37	numeric[]
  euler41	numeric[]
  euler43	numeric[]
  euler47	numeric[]
  euler5	numeric[]
  euler53	numeric[]
  euler59	numeric[]
  euler61	numeric[]
  euler67	numeric[]
  euler7	numeric[]
  euler71	numeric[]
  euler73	numeric[]
  euler79	numeric[]
  euler83	numeric[]
  euler89	numeric[]
  euler97	numeric[]
  euler_factors	numeric[]
  index	smallint
  instance_types	text[]
  instance_urls	text[]
  is_instance_Artin	boolean
  is_instance_BMF	boolean
  is_instance_CMF	boolean
  is_instance_DIR	boolean
  is_instance_ECNF	boolean
  is_instance_ECQ	boolean
  is_instance_G2Q	boolean
  is_instance_HMF	boolean
  is_instance_MaassGL3	boolean
  is_instance_MaassGL4	boolean
  is_instance_MaassGSp4	boolean
  is_instance_NF	boolean
  label	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  self_dual	boolean
  spectral_label	text
  trace_hash	bigint
  z1	numeric

  
  {'algebraic': True, 'analytic_conductor': 15.045089471247502, 'bad_primes': [2, 5, 7], 'central_character': '140.27', 'conductor': 140, 'conductor_radical': 70, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/140/27'], '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': '1-140-140.27-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': '1-140-140.27-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.045089471247502, 'root_angle': 0.3381040955873917, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.70030004409', 'prec': 44}}
• lfunc_instances •

  Column	Type
  Lhash	text
  Lhash_array	text[]
  factors	text[]
  label	text
  type	text
  url	text

  
  {'Lhash': 'dirichlet_L_140.27', 'Lhash_array': ['dirichlet_L_140.27'], 'factors': ['1-140-140.27-r1-0-0'], 'label': '1-140-140.27-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/140/27'}