Lfunction data - 1-847-847.164-r0-0-0

Formats: - HTML - YAML - JSON - 2024-12-21T17:54:43.072549

• 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_847.164', 'a10': [0.23575893550942723, 0.9718115683235417], 'a2': [-0.9283679330160726, -0.3716624556603275], 'a3': [0.5, 0.8660254037844386], 'a4': [0.7237340381050702, 0.690079011482112], 'a5': [-0.5800569095711982, -0.8145759520503357], 'a6': [-0.14231483827328514, -0.9898214418809327], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.41541501300188644, -0.9096319953545183], 'a9': [-0.5, 0.8660254037844386], 'algebraic': True, 'analytic_conductor': 3.933451463423862, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [11, [1]]], 'bad_primes': [7, 11], 'central_character': '847.164', 'coeff_info': ['x^66 - 1', '0.995471922573085 + 0.0950560433041827*I', '\\\\zeta_{66}'], 'conductor': 847, 'conductor_radical': 77, 'conjugate': 'dirichlet_L_847.439', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^37', 'a^11', 'a^8', 'a^43', 'a^48', 0, 'a^45', 'a^22', 'a^14', 0, 'a^19', 'a^30', 0, 'a^54', 'a^16', 'a^20', 'a^59', 'a^46', 'a^51', 0, 0, 'a^16', 'a^56', 'a^20', 'a^1', 'a^33', 0, 'a^57', 'a^25', 'a^47', 'a^53', 0, 'a^57', 0, 'a^30', 'a^58', 'a^17', 'a^41', 'a^22', 'a^48', 0, 'a^45', 0, 'a^65', 'a^53', 'a^7', 'a^27', 0, 'a^57', 'a^31', 'a^38', 'a^50', 'a^4', 0, 0, 'a^57', 'a^28', 'a^29', 'a^62', 'a^40', 'a^18', 0, 'a^24', 'a^7', 0, 'a^26', 'a^28', 'a^27', 0, 'a^24', 'a^1', 'a^38', 'a^29', 'a^31', 'a^54', 0, 'a^12', 'a^43', 'a^59', 'a^44', 'a^19', 'a^6', 0, 'a^63', 'a^16', 'a^2', 0, 'a^31', 'a^36', 0, 'a^24', 'a^58', 'a^44', 'a^23', 'a^64', 'a^45', 0, 0, 'a^28'], 'euler_factors': [[1, 'a^37'], [1, 'a^11'], [1, 'a^43'], [0], [0], [1, 'a^30'], [1, 'a^20'], [1, 'a^46'], [1, 'a^16'], [1, 'a^57'], [1, 'a^47'], [1, 'a^58'], [1, 'a^48'], [1, 'a^45'], [1, 'a^7'], [1, 'a^50'], [1, 'a^29'], [1, 'a^40'], [1, 'a^26'], [1, 'a^24'], [1, 'a^38'], [1, 'a^43'], [1, 'a^6'], [1, 'a^31'], [1, 'a^45'], [1, 'a^62']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-847-847.164-r0-0-0', 'leading_term': '0.107818837099220130553513026866-0.233026399783353385979521806411*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/847/164', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.25676098735870967, -0.3489015585937852, -1.2152734481160008, -1.977718641147138, -2.011173328273799, -1.0603154484389647, 0.3964948248993948, 1.359867872805256, 1.0461100556553546, -0.3884971762106586, -1.817868996444204, -2.0132484518375366, -0.7853628599425995, 0.6512381392442399, 0.6272066498290423, -1.372206135410435, -3.8979218454676525, -4.496382089551374, -1.8350705017180338, 2.866825284017927, 6.569090414504963, 6.855948560797403, 3.9490385989873964, 0.4052805344943389, -1.230705227608974, -0.5651798169336792, 0.733976920842614, 0.9752741225426624, 0.1671970717913294, -0.3664700796432811, 0.15443071209425568, 0.9331926286209199, 0.6521866297485226, -0.699187196730504, -1.5922515825881907, -0.8080008640347595, 0.8296980514530932, 1.173770527480193, -0.6162001732602191, -2.661897037835674, -2.2336916480866176, 0.9045376231520038, 3.6260122145563827, 2.510954680688196, -2.2875605930501512, -6.820653591621192, -7.29329790465118, -3.910752886948462, -0.34752460441341504, 0.4306918688793246, -0.8955222827596114, -1.5220768586502806, -0.2755357722648141, 1.1669775349447713, 0.909655224445628, -0.3479457734600126, -0.1258852565565317, 2.4334783080148017, 5.113700364857028, 5.169878837751847, 2.656909772395145, 0.2502318954574755, -0.1334360705087358, 0.5696599154846871, 0.3907230107328519, -0.6887817492800303, -0.8661004772251627, 0.48588625551026937, 1.4870567320780403, 0.4345390233936795, -1.0927880187755945, 0.41043252180893014, 5.537729430999373, 9.997864396669346, 8.921670845341632, 2.713019922785887, -2.942978733096001, -3.3433736707674946, 0.20111395917895825, 2.5815047576295873, 1.2345162689726126, -1.410942933386734, -1.8774657603870581, -0.1699355935932387, 0.9571542361046923, 0.208210563826113, -0.7885306432730665, -0.40423347280690825, 0.4929940446279521, 0.2187565042196049, -0.7556486629487302, -0.4635626978947126, 1.0799312501225558, 1.1770494422690376, -1.7223486164071837, -5.05057256903677, -4.924541383047009, -1.4152759338638745, 1.1845936244117543, -0.046626672811474645, -2.7984749308338053, -2.9151314714767365, -0.35127242028905437, 0.8045250915802388, -1.640329625676003, -4.563192314984753, -3.784493033178881, -0.028637828955705068, 1.9607406746777416, -0.052091347808318686, -2.878461202580575, -2.58251676489199, 0.11991553710893924, 1.3189043556773425, -0.3427678742495815, -2.117894669595911, -1.5928700151820405, -0.06845039775137135, -0.012968556523813603, -1.0320918760597, -0.7542012182254402, 1.053687375889223, 1.9587858461220138, 0.8094105597659467, -0.371063732542583, 0.1660885021949453, 0.773376928588631, -0.7137395917418698, -2.2550255296939365, 0.6563601201075804, 7.88205690807995, 12.619619143879513, 9.010312313290276, -0.07925160799461677, -5.984492506312193, -4.439115593625139, 0.3287235264389441, 2.2424246704042656, 0.7975421062355413, -0.36223311565063865, 0.2085095811329064, 0.48737094481310006, -0.516792080803022, -0.7959060005082375, 0.9110828791765909, 2.4022827385626426, 1.3400461435947781, -0.6903932183844648, -0.35417531863705026, 2.151042146640839, 3.2270735918439617, 1.4520293428642759, -0.26942396001308666, 0.5053186202691096, 1.8089352102073826, 0.7223903008812144, -1.3849681744091296, -0.7970099550143344, 2.07074175457727, 2.366583205384743, -1.8960700681102507, -6.070558208303787, -5.151647832328685, -1.0456433812892032, 0.3255222776798835, -2.117362194719616, -3.236755996195641, 0.21343949277340774, 4.490759260323964, 4.398821812361957, 0.7341981289765787, -1.4495415342906761, -0.328813167421227, 1.045586380636791, 0.37007810934685204, -0.7352143776902554, -0.3794733429084205, 0.2984459362365071, -0.2521427209433187, -0.8292187031227289, 0.08484385565713615, 0.7452122552775411, -1.2698354722043024, -3.9342012984356725, -2.6450239759437246, 2.314690982793318, 4.723423411933472, 1.0287534031851722, -3.9071902623796166, -3.3874863086376603, 1.5015087082767589, 3.712184989974855, 0.6786278444781465, -2.46787979179082, -1.1878816570786255, 2.013152049095532, 2.395292540421507, 0.3792914458030846, -0.1575260600437761, 1.2731546527281818, 1.5191455045894435, -0.19566505972812326, -0.8736408787365895, 0.7319949643940794, 1.636573623500577, -0.19833859987419034, -1.9675026844319785, -0.44527122595041313, 2.540058085215572, 2.902604873811392, 0.7129088622750664, -0.49464557503450585, 0.07432142002196661, -0.2705729947636352, -1.9760092137638101, -1.8755698223904815, 0.6233102176936021, 0.9771453389725807, -3.1768174073716366, -6.1963596657528255, -1.3568013644080084, 8.484050338944266, 13.265652616191838, 8.809770066788367, 1.6764551457617356, -0.6698238756538939, 0.9705746356232294, 1.5302331990979696, 0.21395992912290543, -0.02211381276939815, 1.106814984367784, 0.8952491015495813, -0.9369085017087968, -1.5994419016767374, -0.4010950585544135, 0.06909886232421915, -0.9991684666598121, -0.9001360021673369, 1.3794068365426055, 2.6082134933365264, 0.8939630533637702, -0.2760652668635197, 2.2402158265238685, 4.85179863897254, 2.1108502849918507, -3.9425417508905687, -5.7239226513230275, -1.3781200515899994, 2.413140636965713, 0.7150411645019952, -2.7214965071668047, -2.392337592383029, 0.3671966475009379, 0.9362698849448466, -0.222390227540599, 0.913666805870476, 3.870081278860016, 3.827809251824405, -0.04605075505748993, -2.6653463470223966, -1.0126009679926786, 1.4553070971983333, 0.9802558082908054, -0.7668049151315879, -0.6125772995460279, 0.5336671337043989, 0.22541873350024147, -0.5986731647210888, 0.09625700814030637, 0.719750819746891, -1.2333798586643536, -3.561771402416155, -2.2288868189559197, 1.0804149367279767, 0.8503328487337503, -2.361702883460221, -1.154017040356125, 6.914213207046874, 13.618465207336964, 11.0761722293625, 3.06980318465946, -0.8889932913369473, 0.9669280729239418, 2.3345253527948406, 0.05548357009616878, -2.0969918417809335, -1.2195486928655916, 0.25087886805104626, -0.0802443898744294, -0.6372479724794176, -0.08627366359014423, -0.35139146473328814, -2.213165901927833, -2.565227941303777, 0.13957071547302838, 1.9605989936499675, -0.5215352285664647, -4.005264608974454, -3.5023662291848403, -0.46540313596044236, 0.1308909575993682, -1.4679790679478004, -0.8667289232796789, 1.7595561062587635, 1.652850463612517, -1.2297450790708624, -0.8072348152599272, 4.6940306292072, 8.365881368843961, 5.021977526546203, -0.4766725305649482, -1.0132385404584865, 1.9239159421269005, 2.037564112230235, -0.8863624606835064, -1.6119081623277403, 0.8624201076205952, 2.044663628102996, 0.29691980970797976, -0.7694877620566882, 0.6461050496035059, 1.590015973082897, 0.3319410696668374, -0.5997470827545602, 0.3364395141384051, 0.8867680661637016, -0.0007309109314951014, 0.19426932926872, 2.0175652352692754, 1.9411961054851696, -0.30803639767174396, 1.4662504041117017, 10.01952374199216, 17.060066972764673, 13.25142181687307, 2.1459900844709523, -4.360236910415166, -2.4782976422975054, 0.5306162752641659, -0.5379615708112473, -2.24164691406177, -0.9949227116368831, 0.5758758300941541, -0.25627915448329874, -0.9579759969753526, 0.8148915384707497, 2.235968522152996, 0.7023931723061035, -0.8530621530786382, 0.7766579480088597, 2.9857275064972293, 2.020553604846861, -0.25864552263194307, -0.1428241625168729, 0.9377058302380119, -0.45691352429907656, -2.6480201066076194, -1.719156886746577, 0.7913096365762071, 0.40951240076976025, -1.7375931920927403, -0.8243064545759033, 2.13810386052873, 1.392183111382917, -2.5510860524829555, -2.3533655281041677, 3.4572673499721795, 6.60704544654658, 2.157326914328482, -3.1446806446828046, -1.6055601892630245, 3.6102781652504747, 4.657707406644795, 1.3245163160840818, -0.7153390810367662, 0.03048740165782036, 0.4613326888937906, -0.00712778208100209, 0.659202987093712, 1.7352196658764956, 0.9669625148548024, -0.24368769692101194, 0.7989522135129268, 2.2261572051874188, 0.7392795359010581, -1.2164313512673346, 1.0813405775122167, 5.372434576746712, 5.0681932562461185, 0.6910674976762435, -0.6083081994392635, 2.2119425376804918, 1.7865497904789045, -4.486152176772263, -8.862095557518364, -5.61950548078707, -0.1427393159450362, 0.4904908362613126, -1.689126277557642, -1.2045445435643503, 0.9356301439827199, 0.7437285153187734, -0.48032565621566886, 0.6256574541650588, 2.017109537811634, -0.09803782424070465, -3.3284647743190945, -2.6294986244851333, 0.7654880453033861, 1.5957516389615956, -0.31507338919268013, -0.7871841300591738, 0.5778770981212413, 0.5833661079667368, -0.608239711570292, -0.24064726119350557, 0.6849745465220621, -0.3886829056756688, -0.6360871693014146, 3.979400281470844, 8.752136477589989, 4.829750763436449, -5.736413872702933, -10.526259627287889, -4.7651054153564445, 1.9983684700901894, 1.2755882200784985, -2.73380132994478, -2.7334596295392175, -0.15429146171439367, 0.026903955886329368, -1.193601481175653, -0.3737253448756758, 0.9925036382845799, -0.03730220167147678, -1.6008072881114181, -0.8054670503229292, 0.5781169731524838, 0.10517405191953827, -0.29051540796312436, 1.0014831004294416, 0.6685620135923828, -3.1885359093894206, -5.554172039938047, -2.3152010626544897, 1.833228951729181, 1.0529620175523753, -1.4012777198611286, 0.5827797668333661, 4.389166681794545, 3.2953801233315465, -1.1379857412368497, -1.961850178886483, 0.542667081503621, 0.18675976165392716, -2.760557401474267, -1.925885890646211, 2.6581094891295374, 3.7052024350975357, -0.5119161380725477, -3.206373716638199, -1.0057475846038793, 1.1752977122433794, -0.10516682972643875, -1.4921438056976961, -0.42086264211776125, 0.45441674980574753, -0.38913814580837824, -0.33994493286296945, 1.171936456611585, 0.9631238806543072, -1.1306957769138364, -1.3646711102628701, 0.26031371470454967, -0.29697326162005366, -2.281368412718828, -0.500697131469365, 3.545238532800386, 1.791075031174668, -5.6872855387081875, -7.704744913401136, 0.7375678906932714, 9.339752830345843, 7.938269586966064, 0.9773440730907905, -1.780696784217024, -0.07668545477186733, 0.522575508844891, -0.25655750384397735, 0.5862679771875359, 1.7729884049382325, 0.736191293634085, -0.5587133594050914, -0.0010302778662468653, -0.48423249321286793, -3.9704386212004117, -6.015852048893574, -3.045735057375962, 0.6880537452198692, 0.31065700186779477, -1.5047626272470076, -0.5529936760134276, 1.036681503752835, 0.25429369633927096, -0.06425322779860254, 2.297604981243209, 2.6251463530803867, -2.1745307806227956, -5.757024249433144, -2.3727393432470723, 2.224611775401094, 0.18822392602974816, -4.6193448834924595, -3.567740806441631, 1.58553256474122, 2.574339087201985, -0.6013006263058238, -1.0446574303293545, 1.7925542903094844, 2.108290313651606, -0.7440060720959312, -1.704393187345087, 0.11991903312682416, 0.8009063261351294, -0.2836509441556235, -0.3865738485439128, 0.14765720920756903, -0.7069501642920678, -1.2847595406127126, 0.21496991301058302, 0.573892141021247, -2.2512375456402283, -2.8981657280370805, 2.455477794380452, 6.729930697573244, 2.1577777261973923, -5.672156975267352, -5.946718787236627, -0.0562181818256194, 1.9798663250112782, -1.241814267860009, -2.358073096232402, 0.05291930325386604, 0.14423082196943177, -2.7780648222307116, -3.187834457555904, -0.5005921162658538, 0.23878621843016262, -1.3884642702441732, -0.9723931680027049, 1.216560205151456, 0.8035624418814729, -1.4662609875545454, -1.0138640244451018, 1.3030238945679626, 0.8728584013651812, -1.4203020729800406, -1.160448682912829, 0.5802788655825512, -0.33816929105661553, -2.3876895973446715, -1.487850440736434, 0.5320070202134178, 0.08090394526709996, -0.023863660149769636, 3.285347200356111, 4.4473170734595175, -1.690261364452525, -7.435734440217314, -2.3013841458315185, 8.88362931335067, 12.12364523455707, 5.447893606938129, -0.30811764092534616, 0.11846644791401596, 1.3997813589103354, 0.2596193760339358, -0.12494018688035013, 1.2047550802139513, 1.1996860155766493, -0.08173942286383844, 0.01887198196826183, 0.2818126767923174, -1.787005404860284, -3.4798466979561193, -1.4110565427126087, 1.2904819468596165, 0.6869599339665158, -0.15966080718247194, 2.1694927525095786, 3.2969878746128476, -0.8183758654110311, -4.570349176057234, -2.1231936486229537, 1.1278044161093845, -1.980220965587029, -6.712528239085411, -4.640883244008738, 1.198356952262513, 2.1699618420466935, -0.9313739077086702, -1.3809378977045035, 0.5043162467078809, 0.23676565081115195, -0.2823945843155625, 2.9533657470631733, 6.20552592660535, 3.7919420077079042, -1.0785372827887019, -1.769136910338941, 0.507248654457907, 0.5909290243408504, -0.8145724025862152, -0.3141876141347623, 0.7312524147567354, -0.0035928428645524927, -0.5157954663537612, 0.33181649747905395, -0.5632546697047756, -3.145085499608128, -2.3399424977445324, 1.2502947864144434, -0.22547351324787043, -7.044132993116162, -8.193280540866393, 0.4313983403803526, 7.46139714724088, 4.159357767605773, -2.1160353684549933, -2.016743348920849, 0.8969586150722902, -0.3279311476923152, -3.047616879266413, -1.9913104581657786, 0.4607346330911201, 0.25153945461345995, -0.6219911111334435, 0.2176333042132986, 0.386469495868614, -1.1222850739580932, -1.1899087455172195], 'positive_zeros': ['0.1478142974155387147168078399', '1.78921131731641096846332621', '2.73912364452291746019122152716', '3.90225320820250883127291839562', '4.50422234103927148569846586125', '5.753122642640357747220414219997', '7.23419036815125010949135403785', '7.93780240641522586729219143311', '8.81001450445389592410092090906', '9.31859291182684599568219048040', '10.1641345898354708579655702005', '11.08744028846659031055385007622', '11.79250205502490622493326037601', '12.734611455405207590298742409069', '13.61729137079524981513858670156', '15.05106852701194676702560690046', '15.43793930942507598519964287097', '16.29846991183088361490040864445', '17.09057541271000548382598038471', '17.52414422125967627815212717807', '19.12527083577754936327263016249', '19.44153071458233002595485598239', '20.11942260145236491547539496109', '20.84413661996493174298736021556', '21.63402628512394576044475157622', '22.149935893801827606961611770130', '23.56339946921381922433003815431', '24.35861605366342287615676189821', '25.13543756293829966178492904896', '25.966177177609997679031865194993', '26.61298908390606874291040457044', '27.3097903062217720378036874207', '27.88030555377228805502818770822', '28.53908245942933639439594889629', '29.222373555875895889374164349621', '30.43758614127773588215998222178', '30.93218255122733456429690048566', '31.919194617654410714101468495599', '32.33711173768596692306282131751', '33.43993623683275653856664746790', '34.057492230715875698684240718627', '34.98561567990817050694803490516', '35.578899975523646917822182291482', '36.58439476991837428717228281448', '36.870137528263238697764896704', '37.64246299096631798099277979935', '38.60563898297664851497140537674', '39.01349827091887600394121968137', '39.58246804012521445797389276912', '40.274868369249923408229761802383', '41.55972437099425841235420038536', '42.4752328931325400194896746151', '43.27707801211951711505644950673', '43.6751494662324830673926623704', '44.23669737621807801795169684905', '44.86418901579863151603676937372', '45.81156254184068694391097227575', '46.30318043884045773295725056229', '47.4106626175431415731766196971', '47.70632207522588928372420046432', '48.53306057299714073087780616971', '49.15538528257201954214756522916', '49.88616428638847460832217130154', '51.050907972848022146778463871', '51.3178295013306245574806737227', '52.17391788816167550691510625827', '53.190745895490720755137620209417', '53.803774769601176299673207811050', '54.45791873735650903263441162711', '55.13088449954646297062209838126', '55.53916366544264613445684653934', '56.23021590017456547572524281176', '56.72990629239666842427591312803', '57.6740204085840050445469372653', '58.49332271984031039448210896676', '59.28196442044038826949156068561', '60.05004540281371598951211854352', '60.73386873609049910595385739505', '61.63829024460115406449071071645', '61.923915269853986786844091018172', '62.77905039281199170667488698722', '63.32101970255647189915118851574', '64.03830158593652651818724661957', '64.73245567888783869085129602645', '65.74014727750015306167714356288', '66.213588031531506572628122887452', '66.48879345818279433380754810610', '67.42428472616956741676129595089', '67.9142300319595878918656033159', '68.796186044137255905612480075151', '70.12537611245857844477746005778', '70.4701971024498638477229538106', '71.31282476607672429911160598309', '71.57087800889714470181048937752', '72.34785298307253184383706094304', '73.24222960990492615895189678649', '73.47076236909984913466682954263', '74.205099416368252270897210328489', '75.13932308150878902550640367202', '75.386291131022589602853761024339', '76.359015193555244142981203493003', '77.26913380740453284245344451214', '77.870114016398374758400630168008', '78.70194486739446480763263328320', '79.29304180095301762388407341820', '79.55123379939467909043605298431', '80.62161859885469224674212008893', '81.355308734422132138754612306965', '82.03260100017539363378925492404', '82.64825763530712888275119286362', '83.19097936763051877379363574257', '83.72554930269101270469527687377', '84.22769844788677508714094817291', '85.19628804766721080483513281736', '85.71122885380511902667560163617', '86.31029577298646810413631026569', '87.672049862837198362826237732511', '88.015849632491233722131609810140', '88.75559457498484982418759166046', '89.60178344284255144596409126680', '89.97195642779618791335447457409', '90.6800491291422990737371256438', '90.81278430699417274532717258943', '91.86147371635547111346983930848', '92.45848378507174660138233007242', '93.508618709748959104300791897630', '93.78171953080585069197823768472', '94.47874626314001118621439845906', '95.17830045103573526088020131376', '95.68651880803570253810585861563', '96.83777805488166665831754629903', '97.300367578904360135747934883283', '98.03115706064107803427886069938', '98.65352609319520439083601014291', '99.42015503619698817081443390978', '99.890590901131798183527109038785', '100.689951476958500573797879067264', '101.16744021419962453873912621237', '101.874729262317360692051652634103', '102.13694944039284267988405867558', '103.07117488461063898838052269589', '103.32924372077435775951722274506', '104.75514367902507056916581786935', '105.53101666709612365407829435764', '105.86271018173849206837253264444', '106.712840634910641871848165560089', '107.13304485269948280684201568930', '107.70274770993109876739597570146', '108.532905196717575770942419363018', '108.9685017728193616889631942567', '109.94984730388682427833099231419', '110.345430746711564608043662411593', '110.87878554626039023487882968380', '111.75786366742082316695038980478', '112.24444803383965210184043617939', '112.89561430424398324645741478020', '113.54987266985348152033332864768', '114.20652541798421555651000903817', '115.10189273506247237716110204416', '115.72009884282681519171733947581', '116.700973473948596342371026393352', '117.17884936899033467420732231346', '117.79948953834339916949541341124', '117.88089481517971812239654016695', '118.95388019999079776545247654333', '119.22306883546947081015582448185', '120.08593301168124248422612171261', '120.54016256572911861603486887232', '121.62368032600765553583781546456', '121.96157630597785109380523642401', '122.60995163120631341046717718462', '123.762869041637167829677176328334', '124.13409156712829622309127344467', '124.84806160851853946638167729949', '125.46450112845130419021248942466', '125.834211709793277561395606616590', '126.55404059641948081615961773572', '127.42353797094057967251689584769', '128.07396470795325612241710813361', '128.62016042943535278516647404725', '129.20469979191936189642503459193', '129.746712944258960899607042920974', '130.23822261562626797863139056795', '130.6980223261768748442623349652', '131.70924614600501000964810274515', '132.68873967363349015468905739220', '133.217993730387310122656071130332', '134.09074852635866887189523479112', '134.38174651203406735772089092154', '135.064721918943709479866858419101', '135.6191008497434975390619856461', '136.396427111030190280471850102010', '136.90754585308181411414216755842', '137.28377587792766488842069470928', '137.88530108555455899890053152455', '138.895258083443057859618470636112', '139.482357614318372706180755277080', '139.95392364599973969894002506743', '140.84948255870540517501161786765', '141.48821303774236108479265831857', '141.89676544703557042917403378709', '142.6362112263905138468324577802', '143.404499654266429058457010184381', '144.16223695797779611302660220415', '144.67240183766461544409141204084', '145.399842933090781458257771475645', '145.82038462975664489999377647631', '146.32802787195236199979845780147', '147.02152141722912987004097897958', '147.751195815884633086996790657979', '148.076211932111498322581661620530', '148.786832104314750530971473096060', '149.45827630196623305933263415230', '150.29153599943336653230591628888', '151.30621792428064916616184944905', '151.8881785946547733697231325373', '152.36937519708522869650382479933', '152.68258131168497166919882466616', '153.56974450306657016649688680130', '154.06290815900231634309011621353', '154.2840724466141622056428065505', '155.54091442198464735831623174057', '155.98223057830303993900044210850', '156.64440850845641645083932802257', '157.24946714023966565065661354888', '157.51491649727780130320091946389', '158.31972958071337794545948376061', '159.19204907797617308507595316616', '159.69895792941910643894221483287', '160.52217486809052433000400483515', '161.18910966517882352865570671227', '161.687163977321542306225475013246', '162.42090149294525950483351419913', '163.10539373599230871056669489847', '163.6691778079692497459111573533', '164.23110350103991953387719142073', '164.48999596153024446333492400417', '165.27535421522841790407570032905', '165.711886090840110668980030017', '166.44628092233912911368473858946', '167.26600089786291497747958969328', '168.12828430643857041989038191704', '168.64389542287677143466967678898', '169.36754152857897071386692288539', '169.7075261610460938518986039569', '170.698099005232598244650570186393', '170.99447357316252180900328364851', '171.69395711697005355408628863995', '172.292701847885314493027377086429', '172.94030426704017010274365013356', '173.55002343343945143317188669362', '174.24492614471484496587503162691', '174.63890606495740384403063237331', '175.51264101125238094959362751257', '175.95831279522358142239103410318', '176.25417686272767580042278923167', '177.12230042271239656405776034100', '177.87745437499989778848008479535', '179.02797564366852020886481542123', '179.3566737979893154509274800172', '180.06318891123313605617834338879', '180.352381492178941777147379454356', '181.22242399689598152437096057306', '181.55491157119219115188420288850', '181.94913249633776340172513478812', '182.94468048912305646197695633507', '183.574631419819354108449179433400', '183.79574516490499873127880150411', '184.64074883121942332096277768545', '185.46527808676840256279223215358', '185.813180853746658038667923824714', '186.8002114956407043206529292726', '187.40377862165273263200200628862', '188.0274339973667484232206486568', '188.492818495520218579080383681033', '188.804799567494583722343452245570', '189.91666420680700839047781333788', '190.54726613798307842039824552535', '191.0555813667540330782602505690', '191.63145908647674171403330912222', '192.18655130342737414489623058579', '192.690321065243602626308294065879', '193.03797560763912802750343139838', '193.94048196327426475348788517559', '194.36158206295969398760470427383', '195.29953093946298553877453185630', '196.12115005174056277635959590986', '196.75085373725130407395356908465', '197.1538860786763704291564906853', '198.042690272927350227437871201248', '198.498255192678210748205632213691', '199.00302458995947485014531231972', '199.469252041686505840026972857410'], 'prelabel': '1-847-847.164-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.933451463423862, 'root_angle': -0.7241169038094631, 'root_number': '-0.647335935724697140962875284019-0.762204819139469080673250823988*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.362058451905', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(66)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.577059009767818733909778484715+0.0111318222262228870790843350001*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.147814297416', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.78921131732', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.73912364452', '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': 3.933451463423862, 'bad_primes': [7, 11], 'central_character': '847.164', 'conductor': 847, 'conductor_radical': 77, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/847/164'], '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': '1-847-847.164-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': '1-847-847.164-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.933451463423862, 'root_angle': -0.36205845190473157, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.147814297416', 'prec': 47}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_847.164', 'Lhash_array': ['dirichlet_L_847.164'], 'label': '1-847-847.164-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/847/164'}