Lfunction data - 1-483-483.383-r1-0-0

Formats: - HTML - YAML - JSON - 2024-10-06T15:20:41.830814

• 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
  instance_types	text[]
  instance_urls	text[]
  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_483.383', 'a10': [0.5800569095711982, 0.8145759520503357], 'a2': [-0.23575893550942723, -0.9718115683235417], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.8888354486549235, 0.4582265217274104], 'a5': [-0.9283679330160726, 0.3716624556603275], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.6548607339452851, 0.7557495743542583], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 51.90555867580389, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]], [23, [1]]], 'bad_primes': [3, 7, 23], 'central_character': '483.383', 'coeff_info': ['x^66 - 1', '0.995471922573085 + 0.0950560433041827*I', '\\\\zeta_{66}'], 'conductor': 483, 'conductor_radical': 483, 'conjugate': 'dirichlet_L_483.227', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^47', 0, 'a^28', 'a^29', 0, 0, 'a^9', 0, 'a^10', 'a^52', 0, 'a^21', 0, 0, 'a^56', 'a^49', 0, 'a^50', 'a^57', 0, 'a^33', 0, 0, 'a^58', 'a^2', 0, 0, 'a^27', 0, 'a^31', 'a^37', 0, 'a^30', 0, 0, 'a^59', 'a^31', 0, 'a^38', 'a^18', 0, 'a^57', 'a^14', 0, 0, 'a^44', 0, 0, 'a^39', 0, 'a^49', 'a^34', 0, 'a^15', 0, 0, 'a^8', 'a^10', 0, 'a^20', 'a^12', 0, 'a^18', 'a^50', 0, 'a^25', 'a^11', 0, 0, 'a^3', 0, 'a^61', 'a^40', 0, 'a^12', 0, 0, 'a^65', 'a^19', 0, 'a^65', 'a^15', 0, 'a^12', 'a^38', 0, 'a^61', 'a^35', 0, 0, 0, 0, 'a^25', 'a^13', 0, 'a^18', 0, 0, 'a^20'], 'euler_factors': [[1, 'a^47'], [0], [1, 'a^29'], [0], [1, 'a^52'], [1, 'a^21'], [1, 'a^49'], [1, 'a^50'], [0], [1, 'a^27'], [1, 'a^31'], [1, 'a^59'], [1, 'a^18'], [1, 'a^57'], [1, 'a^44'], [1, 'a^34'], [1, 'a^10'], [1, 'a^20'], [1, 'a^25'], [1, 'a^3'], [1, 'a^61'], [1, 'a^65'], [1, 'a^15'], [1, 'a^35'], [1, 'a^18'], [1, 'a^4']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-483-483.383-r1-0-0', 'leading_term': '0.526662667419021158432318081879+0.182971086889017333514880088447*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/483/383', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.5575410154331846, 0.8656120540114908, 0.5241839833880484, -0.33675449021380705, -1.3193544285592549, -1.879680577211359, -1.6320531659359638, -0.6545134409607203, 0.4708255215802494, 1.00268823952952, 0.5906736878131624, -0.38038185521545304, -0.9967530124489148, -0.5272358556944072, 0.8626218983739012, 2.023568161688389, 1.5894134120842591, -0.8793773970950935, -4.289617563730869, -6.577292210098839, -6.168118469263777, -3.2445689834609603, 0.26389094993892737, 2.0853208409272006, 1.3353227661206852, -0.8607198718892397, -2.407341522455108, -2.058635671041292, -0.41946805884235233, 0.7528879253654132, 0.2693666073222955, -1.3830563989878186, -2.5897556171365457, -2.2379771930698755, -0.7812956949398774, 0.330394079273394, 0.23556709243671387, -0.43875129906574195, -0.3567265801268795, 0.891398132095232, 2.1360765622633457, 1.8159624584165681, -0.1744577383648957, -2.05875441956015, -1.8797596149510933, 0.31017607819989745, 2.1797478290684147, 1.33265341856766, -2.11888283204187, -5.36937890962245, -5.545301192679316, -2.580791843697601, 0.6445189094002296, 1.1414087862211664, -1.261108187562828, -3.9053437582841175, -4.144089941514091, -1.9671201181629474, 0.30631843926636154, 0.7165381602206762, -0.3644382392905381, -1.073374830975902, -0.48482743849685733, 0.356450316355953, -0.0328501338513402, -1.486501665758089, -2.2340105181705128, -1.1009907837500403, 0.8823120402000537, 1.6018307580306017, 0.46854657647886216, -0.7383399486370906, -0.033496003940295754, 2.1396484100306634, 3.188386830319639, 1.544009026575945, -1.0150882162796369, -0.9888583525036015, 2.778610012581338, 7.280535078735278, 8.181048057256376, 4.36116457322085, -0.8983929824188742, -3.4223105677531658, -2.3323244027899266, -0.29488998458479, 0.05436956518475913, -0.9818230628772746, -1.2160616024328756, 0.17807216641093218, 1.5456282163365123, 1.0636371175161572, -0.7316388005024201, -1.6065971328191162, -0.5816736201564019, 0.7960349698670454, 0.5814553067904419, -0.907835908113537, -1.5416914934454697, -0.3813014712515598, 0.9142933336541383, 0.42097757525328966, -1.0087073759460778, -0.38679562482349056, 3.3843188731707197, 7.230375173693892, 6.8401157893677755, 1.7404406327234871, -3.705280976087266, -4.92610549583036, -2.034846790000894, 0.8002133928070377, 0.5239759385248718, -1.5344419963904379, -2.0380943019730062, -0.18591307967299012, 1.4984228878341053, 0.8058567998792359, -1.2062649413117617, -1.8143668335546401, -0.34861916783260327, 1.1047251923528465, 0.772719496037779, -0.4296854745653583, -0.5066097876932398, 0.5228099435472906, 0.6559280290364359, -0.9162235379846917, -2.2263647015663315, -1.2014030935777593, 1.0028772312834275, 1.0508902708597916, -2.009646539061353, -4.857202623490809, -3.790176661734635, 0.33965473455921563, 2.823277613294977, 0.9227940650617843, -2.618578033873889, -3.057652049129674, 0.31918243749146286, 3.4127295890931273, 2.6336061120824423, -0.7465783377551417, -2.683220079755439, -1.654147325583705, -0.03100333885249659, -0.2360444476100594, -1.4801156700103986, -1.4639357420136587, -0.051110685851085004, 0.6553390021393208, -0.2543397930038585, -0.9505184027662215, 0.3121333214923875, 2.260211423309827, 2.211673988310658, 0.10486209463625473, -1.1059961870686812, 0.36872552942916137, 2.403809841904269, 1.9783108216460539, -0.12065295724851244, 0.01731433303076777, 3.692616166729498, 6.799125967668956, 4.53509209275573, -2.177401772506616, -7.246075025069086, -6.53272072469215, -2.3650234529338627, 0.13100229320016646, -0.4977977407514821, -1.3084790609126045, -0.03908448875059658, 1.7443149578423032, 1.5336991506243254, -0.1381036221371882, -0.6859887958530421, 0.3845379987746259, 0.7313372496896313, -1.0299126793583548, -2.926486868646716, -2.435245465501272, -0.24621144187560834, 0.829996929564305, 0.1431863606853815, -0.051417136864881655, 1.3123172592453807, 1.6992339886645451, -1.34304479435758, -5.512573366511729, -5.6875381254263235, -0.7996459107668181, 3.9069801208483845, 3.1159785181158712, -1.8405032398846433, -4.8821342705799555, -3.064248081689733, 0.26526726100275944, 0.793375112389767, -0.9909513269495808, -1.4799920484107376, 0.23159313130354978, 1.254147914964182, -0.30930179094633903, -2.358493230592815, -2.045596990641216, -0.017885491851892043, 0.8391514624898854, -0.10329307440993193, -0.6119439698549898, 0.44678634364952524, 1.228646031799015, 0.2644013782666569, -0.5481698702407203, 1.3146079603827896, 4.471807698702101, 4.889026790938715, 1.8613466790057427, -0.3014527248426292, 1.770619928948887, 5.2332307783656855, 4.575477149311816, -0.5787476459445395, -4.628362276090711, -3.55804336989152, -0.18909886021528885, 0.21961598416467454, -2.607464808833985, -4.140016681246157, -1.9508917086643052, 1.06280669241841, 1.3560708997675068, -0.3113411395082937, -0.8458809834241742, 0.1596086935486995, 0.38802367918599645, -0.818158956721399, -1.253932591556744, 0.21157465662150904, 1.3436161375597853, 0.05962425721404631, -1.8632472289220767, -1.2821938883069373, 1.233232544133651, 2.0305049659164496, 0.15337599606564026, -0.9302081516885327, 1.0664930606546017, 2.9334708491456825, 0.3912729525051766, -4.786756272636353, -6.1036280094773, -1.13547568608738, 4.739497701862327, 5.335763694415241, 1.5317090560314566, -0.8783469953165824, 0.5034743505695973, 2.370227367512433, 1.6651956581172684, -0.1001875307472008, -0.2368536486881283, 0.47863801447257714, -0.44636775142399554, -2.500556874458101, -2.6908005533620947, -0.5172769522866912, 0.9620451605691848, -0.0950889561931854, -1.5166764583530918, -0.9013457429442906, 0.38288848916324575, -0.2015256494416879, -1.5263347407180943, -0.3142768494371045, 2.8667640587838052, 3.3164987137784743, -0.6127228879614003, -3.750681966308706, -0.7043163275960467, 6.093043218465092, 9.011309318411584, 5.259372753506952, 0.040729857481105386, -1.210512121302634, 0.33081515783032056, 0.38057182974322046, -1.288366393265153, -1.2746067677220063, 1.123944302238632, 2.476271878528532, 0.7706875097409936, -1.4161052577525812, -1.1661284593505048, 0.36390936370482757, 0.4463722202783837, -0.4809780541329018, 0.037719955004344684, 1.7268825853947571, 1.7953714382664194, -0.013466294096521812, -0.5020625019498807, 1.4768661738744322, 2.2916031835656643, -0.8745797617388933, -4.571801371925609, -3.3482859399981533, 1.8599890714539051, 4.342788618690366, 1.0863369225422488, -3.0131720373843556, -2.616595116969296, 0.3390006984137358, 0.2519435562664689, -3.279444344264936, -5.102768675723228, -2.6078113012088493, 0.6747021298725654, 0.9488262696330978, -0.49948973640980215, -0.5147698753675125, 0.48911214695053484, -0.05193269947884015, -1.8081484882807035, -2.0060199432339916, -0.4153267741372709, 0.1790331558978394, -0.9313796113065484, -0.7812747232406108, 2.0574751978729076, 4.287754892970982, 2.811600012379456, -0.0331311907747192, -0.08181775190187837, 1.6739601932236545, 0.6166795567209609, -3.2270239991041922, -3.869194634213252, 1.6751841666888982, 7.783909545757773, 7.418895506207942, 1.8149830118557149, -1.754551065758161, -0.3503742772297327, 1.7566340383837284, 0.7899032559641342, -1.2269097627449483, -1.0413054501160848, 0.2803699360095898, -0.03575351264629238, -1.193238281403933, -0.3923958531263358, 1.8107692705011718, 2.1096788648995277, 0.12295993014292142, -0.8509239771011278, 0.5164515020143536, 1.3514098677149762, -0.25820073181787195, -1.7891428438146013, -0.8342911046188024, 0.3165335113042049, -1.2165294543134737, -2.68190461043669, 0.9976376557038577, 8.277780705208254, 11.199008171278006, 6.152152072116542, -0.7108187492447864, -2.004966095182445, 1.1361153966756201, 2.314463022805183, -0.07058150333505364, -1.7153620330718065, -0.46683197244551483, 0.4988213446956881, -1.1596075422681473, -2.7861953113551223, -1.5344918692345761, 0.6356229971068625, 0.3971380352963454, -1.344586506774573, -1.3805004198243647, 0.1251969744390571, 0.3167271669674223, -0.8844513663386777, -0.6891466898326164, 1.0434758130252926, 1.0829305746753226, -1.0400292157417885, -1.07886865238781, 2.8994744649991016, 5.911463087527418, 2.8870412102901812, -3.057764301531299, -4.699212760075344, -1.4770070066999126, 0.025492547458585396, -3.306825451604303, -6.379367230270261, -4.2761397603892375, 0.0990148911482309, 1.0777010196443972, -1.0049289074820733, -1.4366515183224189, 0.6716797305294511, 1.5667591068235696, -0.20719996488009318, -1.5707538848901872, -0.5943687710969645, 0.4982654215812901, -0.05637127374761358, -0.3413843503404341, 1.0734832756972639, 1.6230101828627574, -0.9239059855600521, -3.7495528309703254, -3.014091190908373, -0.32359686312186836, -0.10845692249459794, -1.9051473998692339, -1.1560679499439137, 2.17220358775117, 2.237801588033541, -3.137462300431514, -7.559458820484785, -4.993097250856224, 0.9853825011612662, 2.4727619871772926, -1.1697807947878995, -3.423529856110928, -1.2029102794727256, 1.3777655686049335, 0.7466374425654462, -0.8387374964910949, -0.37400851981275285, 0.6806387796734011, 0.0020957904463882247, -0.7682985114556149, 0.8154087096895565, 2.886700656238797, 2.0437542523200873, -0.6474488934924896, -1.3294162097150928, 0.10088586664846155, 0.30617320539153564, -0.9873078974289705, -0.45181560235040175, 2.068464502559051, 2.2202217201594108, -1.0296478907267022, -2.0487158931031537, 2.737639094161698, 7.664001721582963, 5.253911859965378, -2.349133205590171, -6.153322524648315, -3.190512045312902, 0.4717007917544611, 0.05981679348692785, -1.6534027021973239, -0.9367915208127597, 0.3626805681127407, -0.8199243543402142, -2.5810450028505527, -1.4105501629030657, 1.3506357168438825, 1.7386317414459092, -0.09276472603573505, -0.6672392601364003, 0.40475033317047515, 0.23768891349508292, -1.4053876135655017, -1.559571223304717, -0.024751791183156076, -0.22534649390298467, -2.532947468917171, -2.5247385597543364, 1.188657704337168, 3.039368755610642, -1.0508760991078518, -6.102200414104007, -4.986554485932949, 0.4716749550567604, 2.3813457828896385, -0.8740938509162139, -2.886952006871339, -0.230799233735884, 2.4682886400692987, 1.054503367017549, -1.3411950045567296, -0.3115504380826908, 2.2953866639183533, 2.113726712721191, -0.2386475720896706, -0.990712594314916, -0.02233757131736125, -0.16878637127348042, -1.2952839029725034, -0.7988236996358693, 0.6862467427340038, -0.12489651532620373, -2.777848957703594, -3.117835430390367, -0.6064162759808372, 0.39648565623668725, -1.486737248205565, -1.6994793456292303, 2.061057993803363, 4.752308303277379, 2.0580908348375497, -1.6420680995704586, 0.053889256669308515, 4.626225628524862, 4.1240018223883075, -2.0536623448741578, -6.036083124663494, -3.614024117595342, 0.30473637980222856, 0.6057183159356592, -0.740719192445155, -0.04923574403855104, 1.3789941188997956, 0.797074954571667, -0.2838836365225087, 0.7609257589369272, 2.1807735579388847, 0.8952488138537011, -1.533897654276163, -1.4772588676826794, 0.18014479013193746, -0.21300683987359023, -2.1322552134130355, -1.8705967002440156, 0.16931616705479838, -0.13710820199769047, -2.624979530129001, -2.453334030297147, 0.5148245442808874, -0.4551450271194362, -7.903604137537408, -13.90755658763512, -10.692338929083002, -2.1136709617090395, 2.3079997069659117, 0.851924923574227, -0.5622007842806306, 0.47691492641212574, 0.3458676498278472, -2.2005537212686854, -3.222603513263799, -0.9503801917257689, 0.9648453909864805, 0.1497608760727931, -0.5572580877462808, 1.0503606924710012, 2.265129285683827, 0.694014521378887, -1.1427551523397015, -0.5318473480453645, 0.5925114209572178, -0.0064352407881564195, -0.038986580848104926, 2.5283103869544394, 3.945299740852734, 0.3927785417187233, -4.000473032180407, -2.4178068804040116, 3.238591723171217, 4.521447658459539, -0.2185863102254349, -3.388236054707125, -0.7057564218694943, 2.422339465163016, 0.7784219312483331, -2.1936689816795396, -1.2772892464237264, 1.4354048608704757, 0.9433056042888089, -1.7372533640779986, -2.0153809848831794, -0.041802870883540386, 0.3108781210748688, -1.150928191438185, -1.230527688113171, 0.11071226817316993, -0.04051149050643843, -1.3955497513172979, -0.9510830324722833, 0.5262898003460148, -0.8273395215434804, -4.343687862531165, -4.838944515672787, -1.560616258678343, 0.1459977180036191, -1.5705165118878537, -1.4439452281367897, 3.0491840528122096, 5.758942837466865, 1.6851815513831956, -3.7538596834734914, -2.7523325169252937, 2.4429753632468554, 3.5431598102579196, -0.44798895681030093, -2.8263183577288604, -0.8515293054999928, 1.0389756960756906, 0.16433501336673637, -0.4909177917859854, 0.893010788364177, 1.5592865390476864, 0.15565490691876246, -0.3741027256358264, 1.2118100389142992, 1.5876909045331795, -0.7993288449954479, -2.309028142159077, -0.6373159014630171, 0.8818221147339789, -0.3965959478440362, -1.4373739245624855, 0.3206751655024491, 1.514257327125048, -0.43828826984294317, -0.6310706216254923, 5.664286045630313, 12.896457658811265, 11.79152457274234, 3.624934992981334, -1.468343975022636, 0.2910099501729759, 2.3914337309777034, 0.24392081288746692, -2.226580301698755, -1.1727172272542659, 0.5539458998320475, -0.2011363133927419, -0.9865047072584944], 'positive_zeros': ['0.829475363790983710137298944757', '2.3604034570851814697073197549', '3.31913678429134552828414438332', '4.1953073372760794485271411071', '5.22296897252082111929473164306', '6.84798122877792552301254819812', '7.69522490039201006933995976639', '8.83080586431498816525493539645', '9.43499184992007514836250310605', '10.8085738309761618324394778879', '11.35761157583025205514058557785', '11.99018074068477093057095226394', '13.101631345449350784001830874752', '14.02429671690845071811236952455', '14.82602108313471780718376724480', '16.170809442581239676169343739804', '16.740177372179079370524888599487', '18.068080303015830057153343119', '18.65848164372925298467266790483', '19.525679761439457690100271215', '19.99079553446585403732651017880', '21.105422861218439001278084504193', '21.96845601507967350438837234851', '22.50587075748131553798877014043', '23.6115710070119240578563383219', '24.173776169217627705461125048082', '25.56502825542683656121139082794', '26.641971356767805636020650191805', '26.89887980673938983980702290464', '27.78125715278297148460402214194', '28.62604986734198074235100224131', '29.4872502506020631783657376776', '30.131332761704441162006011194023', '31.009784213257027646309230978774', '31.64961614040251276820725137297', '32.23351061161462807729102740274', '33.5251895427116770152924959532', '34.56752389672172814232541022148', '35.08436002698401672438782121697', '35.96269082641938347045808334477', '36.68767325212726690073640543206', '37.557599871539733888914318020118', '38.31499418791848162538944156816', '38.91184427186728412264184311551', '39.53349623569358779031468535959', '40.47401574667468520934395505033', '41.07192355797160670669811892410', '42.16230645905083648225896515962', '42.889680972469610809154758282498', '43.72572343258522521032737915939', '44.61947422615309829076112201028', '45.63657768773024615748145014257', '45.859240526482931242193464307', '46.886241622811447330756330883748', '47.43626522563024904014074705043', '48.076094881334069918866514472080', '49.07739884766786196458701182847', '49.6374216804047791751972353569', '50.60291945635139901137026482432', '50.93499563889873770099724310962', '52.09272829997303832959550386889', '53.39425651761368706362709873315', '53.62206211760380070554268117392', '54.3809704329537541772875116859', '55.28459533130241614584188865511', '55.84157771867580567936416714595', '56.41613143810884548851594128570', '57.539297803372629504589541429239', '58.17973102462991787978439704053', '58.457783310618938960482677143876', '59.272780276132512016117883027132', '60.35451158312183174059275957421', '61.140733098199999388811194687758', '62.1544461223734060597108611593', '62.650869982747656725652364044164', '63.40129909765365311631776637057', '64.021549132073360994994159720', '65.003010883087451387452450542905', '65.597628153188507910744326136892', '66.14748156727275062207018846913', '66.93347070094961550146178936418', '67.3406639538373017970550459271', '68.647318155672640362874682483177', '68.869311090696301448864835643766', '69.96862448264268934199931171237', '70.96234143455760157807431608506', '71.28525371377362187101175680687', '72.36944022773266779886832421844', '73.065539928102557925035064864460', '73.70354585842894847438546235167', '74.18492999721743299935568485805', '74.964424432861157994887497433640', '75.633408914120305186154975571786', '76.411781216855626873454545078266', '77.20950517999186412399404651100', '77.68865283640395912514843841159', '78.4624139750320666539019852256', '79.42728790537869185639615972440', '80.4501567354246021927133626925', '80.86984095053928764768783974417', '81.85013794446289832348040580493', '82.27542700786468015872064612766', '82.73106930503321928263449923077', '83.82007350029963779776435920988', '84.35861607543273613825807378808', '85.188317140075623074437458460175', '85.58101294898074726641057427157', '86.28362877471814194728457087440', '87.147586165975612862490861553757', '87.84749157835978496645999112740', '89.06600537332124716015808036573', '89.61932597348749710466023935525', '90.07970883601310492838715786588', '90.806072250796946184628225491222', '91.65368607010767132734359816817', '92.41335296690499602902739876251', '92.95169806155709349894936905457', '93.42953832721034206104895124681', '94.37258083689126957172485244306', '94.79368017231014210898566275193', '95.56238687580215691581144182515', '96.454425929245223818573517971211', '97.25618642911961710248878282746', '98.0808651745937999286808996628', '98.46780929983437543860121252995', '99.60273508822401278108129003298', '100.19611394521787400391873975476', '100.77111181021786200116244228641', '101.23940514005577926704978121488', '102.285078777813893612385607695933', '102.57314126002583402418015735351', '103.23522673514310146856977139606', '104.3695268002130474634345309912', '104.70325319029958427405694862446', '105.36888269247436159024370626166', '106.1765499387128390408983101132', '107.29707455058154105968449879852', '107.85190381689209160417964671024', '108.544392265417057314350526972444', '109.28914055507672040191881227281', '109.67828445356881260428188597441', '110.370040405385351486959300046759', '111.26884090518408870873085453886', '111.78368524211665779701336769046', '112.46376782037653553192731538939', '113.28557023603881428769796342443', '113.56682600890132786966347384326', '114.32435284156071196351620813467', '115.582113849955467224382442395051', '116.14538525580608338419208498028', '116.867277663422660917010707790419', '117.5840668045374061493147751750', '117.9559686343372230814950520491', '118.94799687850466203625863991914', '119.447501192888939493015605040085', '120.282907918947620040155698605785', '120.715650717821929195490633657372', '121.37884098957760587501253830955', '122.04232683541033889589686981446', '122.610548990867150104144211458146', '123.58317074148462102766615096781', '124.55388043238303263377759756655', '124.6939335678930208952028199775', '125.92827759515073808068781023892', '126.42293126261972021752585274726', '127.097329696586637122463332734951', '127.78362973353331757790783325718', '128.56080025480875404336423522247', '129.0435116476759720488268455725', '129.480212108847485760264633054461', '130.22756760226898987616436926072', '131.31075096387169217159446050366', '131.53741668242595785891153375181', '132.30052187274280215353251065883', '132.96778479294102007249906542258', '134.00314633036580505454478228881', '134.60160721322793635168322952725', '135.42665487409606546798742778378', '136.059831582962899034179543385013', '136.648212529312766986966369524226', '137.18800355112760562199250530457', '137.701671222781884490753568301928', '138.66793010700592481816258254736', '139.352059546706906036645693414720', '139.768461161105151874149543960868', '140.3748219013395199833215246990', '141.15959665419611896187197357769', '141.732608851140897997408965675', '142.716275871851875140587878637427', '143.68473438446702029122584272623', '144.071927946263321916268726125449', '144.863873534480054012475284950352', '145.17705503083511449271682114231', '146.08852773177410776907874929217', '146.858409303835867001509480264972', '147.38580426205754890852737021261', '147.86452564839019136200056886636', '148.75639751030208861298797041028', '149.01659962907583347417494859635', '149.911175854882846084328054673339', '150.56918439668528783261167872698', '151.53316704263479789694007809809', '152.11885782208855572712583830102', '152.83141186127034595391227501936', '153.548936235487128219682110882782', '154.0980198239047086103389648749', '154.96521349061696606483567232819', '155.634076382539811282780912644042', '155.87993565735824708318096366260', '156.71149920698881444249796785567', '157.17012872015952366682244724853', '158.20997923620634155259760015302', '158.53128574312209619687330978330', '159.2289545902423065059515459474', '160.142167234851572740510822418352', '160.62117788926090098581910422865', '161.46785897842856681558906546761', '162.4639814742922212114138472819', '162.93504774890814464485656913360', '163.44663922549698934028849412444', '164.24278328861643119676939576819', '164.54022227134156612295298073830', '165.41659250623588054241459139400', '166.20450656309619144732895348054', '166.52102486846835728931512317403', '167.46671054355234052608593053449', '167.79050783815614736762519693421', '168.68840309346146758122258608153', '169.02975248390193714272095289226', '170.40857864833506128258122908819', '171.056363579745447445800484023614', '171.44998661563132481502668294275', '171.9302822505351160918573788103', '172.92253963457980605796866703873', '173.46973590982850660175967472878', '173.89988565335942879749586275858', '174.77822814294859471095873991037', '175.423578733542031826983020224162', '175.93544654606049074131751711655', '176.25851270052944534421722722387', '177.2104321582393843795606724053', '177.94671651431478453162063010742', '178.73753022644051586406844760549', '179.426598074232137352539176980013', '180.06812591212401944282662412698', '180.75702665657835017604171583172', '181.359231989496187224716507889', '182.195320384774724576284211997667', '182.577689913831945747831768833707', '183.405376717492751618097438340042', '183.73948381651204269435382754034', '184.54696734403907950465077213633', '184.90341964086106149219326198728', '186.13298393404595698096071797026', '186.30628895183841228013085548542', '186.998395565318209640116768096854', '187.89369752039996663049069986668', '188.60095280052820429613518166648', '189.34354794173730198966174320535', '190.097493085044098094574202353830', '190.6609342057712443658147659412', '191.082379798056177227755248004595', '191.90705493676352370038805708498', '192.28671409900080556357599965971', '193.03658757282083893625433591411', '193.83586547743929471840211698218', '194.31168363623772362774451547770', '194.95792666261589485153933308702', '195.56941321270938923979943200817', '195.99152789639186110329330243430', '197.35310404266096171024502136523', '197.78523556922302860710712707060', '198.46002219665013323694999065717', '199.232387707924981789067255309347', '199.645413614956166814359041243889'], 'prelabel': '1-483-483.383-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 51.90555867580389, 'root_angle': 0.2128672197394271, 'root_number': '0.784602187714095631803661090850+0.619999521801634167687406646287*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.10643360987', 'prec': 44}, 'spectral_label': 'r1-0', 'st_group': 'mu(66)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.611828472556510379903559964697-0.238020218977124896289676611582*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.829475363791', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.36040345709', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.31913678429', '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': 51.90555867580389, 'bad_primes': [3, 7, 23], 'central_character': '483.383', 'conductor': 483, 'conductor_radical': 483, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/483/383'], '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': '1-483-483.383-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': '1-483-483.383-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 51.90555867580389, 'root_angle': 0.10643360986971355, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.829475363791', 'prec': 47}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_483.383', 'Lhash_array': ['dirichlet_L_483.383'], 'label': '1-483-483.383-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/483/383'}