Lfunction data - 1-4033-4033.182-r0-0-0

Formats: - HTML - YAML - JSON - 2024-06-06T17:43:00.796254

• 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_4033.182', 'a10': [-0.28680323271109026, 0.9579895123154889], 'a2': [0.17364817766693036, -0.984807753012208], 'a3': [-0.05814482891047583, -0.9983081582712682], 'a4': [-0.9396926207859084, -0.3420201433256687], 'a5': [-0.993238357741943, -0.11609291412523023], 'a6': [-0.993238357741943, -0.11609291412523023], 'a7': [0.5971585917027862, -0.8021231927550437], 'a8': [-0.5, 0.8660254037844386], 'a9': [-0.993238357741943, 0.11609291412523023], 'algebraic': True, 'analytic_conductor': 18.729173260907245, 'analytic_normalization': 0, 'bad_lfactors': [[37, [1]], [109, [1]]], 'bad_primes': [37, 109], 'central_character': '4033.182', 'coeff_info': ['x^27 - 1', '0.973044870579824 + 0.230615870742440*I', '\\\\zeta_{27}'], 'conductor': 4033, 'conductor_radical': 4033, 'conjugate': 'dirichlet_L_4033.1529', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^21', 'a^20', 'a^15', 'a^14', 'a^14', 'a^23', 'a^9', 'a^13', 'a^8', 'a^19', 'a^8', 'a^5', 'a^17', 'a^7', 'a^3', 'a^21', 'a^7', 'a^18', 'a^2', 'a^16', 'a^13', 'a^12', 'a^2', 'a^1', 'a^26', 'a^6', 'a^11', 'a^8', 'a^1', 'a^7', 'a^24', 'a^12', 'a^15', 'a^10', 'a^1', 0, 'a^12', 'a^25', 'a^23', 'a^21', 'a^10', 'a^15', 'a^7', 'a^0', 'a^6', 'a^4', 'a^23', 'a^19', 'a^22', 'a^14', 'a^20', 'a^8', 'a^0', 'a^6', 'a^5', 'a^11', 'a^2', 'a^7', 'a^22', 'a^17', 'a^1', 'a^9', 'a^18', 'a^19', 'a^6', 'a^10', 'a^9', 'a^5', 'a^4', 'a^6', 'a^22', 'a^1', 0, 'a^21', 'a^6', 'a^15', 'a^19', 'a^1', 'a^17', 'a^26', 'a^15', 'a^23', 'a^4', 'a^8', 'a^9', 'a^1', 'a^1', 'a^11', 'a^21', 'a^1', 'a^0', 'a^0', 'a^25', 'a^5', 'a^17', 'a^11', 'a^13', 'a^5', 'a^16'], 'euler_factors': [[1, 'a^21'], [1, 'a^20'], [1, 'a^14'], [1, 'a^23'], [1, 'a^19'], [1, 'a^5'], [1, 'a^21'], [1, 'a^18'], [1, 'a^12'], [1, 'a^8'], [1, 'a^7'], [0], [1, 'a^21'], [1, 'a^15'], [1, 'a^4'], [1, 'a^8'], [1, 'a^7'], [1, 'a^17'], [1, 'a^10'], [1, 'a^6'], [1, 'a^1'], [1, 'a^1'], [1, 'a^23'], [1, 'a^11'], [1, 'a^11'], [1, 'a^0']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-4033-4033.182-r0-0-0', 'leading_term': '0.522707928443027599256416343085-0.339226683686393207263941368173*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/4033/182', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.6231358771424331, 0.8087126580339459, 0.3641069337894083, -0.32505735914659645, -0.3057350053430905, 0.6516000073921865, 1.4489962649419321, 0.8714629470680935, -0.7215926839199573, -1.5443244217945487, -0.58772915773532, 0.8464947157565419, 0.6511303122477415, -1.1353529413628234, -2.026285690282552, -0.4324848821134162, 1.6426341735163774, 0.7938749695063136, -2.969071201085078, -5.43233359076076, -3.303475379733941, 1.2411106837753192, 3.1016886538508635, 0.8725475395318876, -1.5476690180313304, -0.6743656520658584, 1.7410319681655326, 1.8175980707674229, -0.16439914608891948, 0.019924616301806072, 3.908049863954777, 7.39544988976082, 6.2365107274876035, 1.9198032315211546, -0.7436617165073331, -0.3093582808285087, 0.44187179024544987, -0.1892292610843028, -0.5259879951419179, 0.5623728194562226, 1.115559319126332, -0.3626784543686288, -1.8111832944797484, -1.0499370340752088, 0.16586459988647184, -0.6281541625229056, -1.2211093288938992, 2.312698986132807, 7.712087765707513, 7.6145093768229515, 0.3680081520094856, -5.971676893884037, -4.3019500319092465, 1.555030114999806, 2.8964918990435655, -1.204578015070347, -3.9344855496925764, -1.9818580249734319, 0.5170351286481644, 0.050663723300188285, -1.098767316730145, -0.29678518120527, 0.6826428065851736, -0.11647594249170727, -0.741225062448973, 0.48079345266731566, 0.9736591387191083, -1.3096896892571073, -3.060464558821871, -0.8221874196493119, 2.355645294419398, 1.4410662323790657, -2.0955514377867046, -2.870876528832827, -0.6400674195195553, 0.36312137202637607, -0.28040427606321033, 0.5035866832192267, 1.2007014236301887, -3.056166007737746, -10.048177481117564, -10.733999388221577, -3.0459527713552257, 3.6403405200897336, 2.376157873270359, -1.6283114764113191, -1.040310740579572, 1.9267287130111845, 1.4459639434416127, -1.0453465801991424, -0.5180950911854183, 1.9870647296255135, 1.9251910375785914, -0.10339237613353085, -0.2423382700667402, 1.0614383883334686, 0.7780072813156939, -0.2973967395441434, 0.21583643751536807, 0.8040605047674336, -0.518580770219872, -1.2305469625346583, 0.35789855977832186, -0.2372034273797884, -5.625144681281459, -8.739310478019714, -2.9151216153395056, 5.442074295072259, 5.599945152529417, -0.4172929032110132, -1.9245841408714028, 2.4720305053097986, 4.315857990944666, 1.0212566362623792, -1.1977106368963764, 0.09347250273370106, 0.6033109079913253, -0.6129681069008781, 0.21269769153398496, 2.4088453109021666, 1.3158023845722329, -1.9917593300488363, -1.9426001591607323, 0.9842845280078139, 1.2422157926913437, -1.2286806509948263, -1.6141578995928423, 0.12371588338756184, 0.2039938642375318, -0.6076414711781827, 0.601853242634838, 1.3687309788258712, -1.4589990393512116, -3.8690999466115663, -1.48639186753646, 1.4001944208365793, -0.09381683638131944, -1.5481342675159433, 1.292794527575388, 1.6998158881562424, -6.245473246605681, -13.672172699115839, -9.392293635909562, 1.3128571447122952, 5.231274644417981, 1.5848546204439857, -0.6621497094357984, 0.5958296394044116, 0.6922689361049772, -0.6119070978065069, -0.3078783814937232, 0.4810901621088842, -0.15044667458456737, -0.06214880002989161, 1.3867439698274056, 0.6214904563436032, -2.1426350136827446, -1.6708946021721824, 1.8107533290199747, 2.096117045951904, -0.7183989070878287, -0.2986895914215841, 2.506759741301406, 0.8366247573796106, -3.4806886950170988, -2.3171197847147607, 2.283475940240577, 0.9271943407312975, -5.0731148300525994, -5.819442835059917, -1.1076160324459936, 0.6948976594126611, -0.7392762623791147, 0.8780901135553963, 4.091738312376528, 2.8597123121117503, -0.5072832878151935, -0.1301218747215626, 1.7134523175896523, 0.5488735056309905, -0.34938160129205964, 2.529868678144303, 4.531013702979868, 1.7993231709811703, -1.2280246526316332, -0.8439224176230218, 0.07178462592969292, -0.0038003386912189374, 1.1513264045584717, 2.1898348191243455, 0.34799305213612397, -1.0283371868967979, 0.45127694240156124, -1.9872002153637778, -11.176527604556435, -14.697602527416025, -3.413667649006296, 10.271010832348146, 10.551070022054327, 2.198541482402102, -1.1885852881417058, 0.4718536014722773, 0.22238928261417645, -0.46402060594423195, 1.865042372285128, 3.1440426017363734, 0.6060291313438503, -1.0126704537997786, 0.47707550135030374, 0.9979242598447636, -0.18134742647431232, 0.0928044344993147, 0.44108221357074473, -1.4986546929465245, -1.7245646165390667, 2.0670160105385977, 3.4549191855986914, -0.8282779348447242, -3.6444587102044874, -1.2921125295468163, -0.1118767714647856, -2.224385295871512, -1.5253965662568563, 1.6062466032331741, 0.13910404967122453, -3.646912590262062, -1.5740572748193808, 3.0686046760775234, 1.6464780023188332, -1.8381835357131961, 0.9557102464102962, 4.975242020536884, 1.8896157735525134, -2.8902002810617655, -1.1541856221483764, 2.6134434361436676, 1.6974721537909945, -0.49973057337582183, 0.08019528556880458, 0.4319475332444099, -0.7741147233845117, -0.549442462220883, 0.2518459178235619, -0.9781511966947858, -1.4910838223206009, 0.4507292670813859, 0.26961698509084453, -2.670717208237405, -2.2277505442554357, 0.9758097673391721, 0.027036996806397512, -1.8983610094324055, 3.623769776311616, 10.310532010903653, 5.869922158963462, -3.5801865773313337, -2.954636731257704, 4.813074948394336, 5.941787726528498, 0.7422259779582556, -1.2063475482979271, 0.1593407787646384, 0.026255068698254242, -0.2281254377022975, 0.46002794875011144, -0.982280172743095, -2.653833791302233, 0.12124363533518145, 3.2900074137310447, 0.6318025745499681, -3.323957064198721, -2.122780868347861, 0.45787458283233134, -0.024891461716918424, -0.07564300983315252, 1.564759454024106, 0.6324724264393532, -1.551941475956049, -0.2870186579871724, 1.1973917413362343, -0.5877181294702843, 0.7088978486623002, 7.2343589358348135, 8.042373821881682, -0.3495194374370589, -4.785778104564608, 0.14140395996436958, 2.5752768131228865, -2.055234559873792, -3.2646897999063182, 1.6287134166309805, 3.0380289585783764, -0.5806728640666624, -1.6839330888945792, -0.018061348777171353, -0.23373265276360006, -0.6334997534002802, 0.9320068453298467, 1.033174975328288, -0.7550301272218672, -0.5301878637383116, 0.6757480539905443, 0.017957184106517976, 0.15093335541462874, 1.138209524358421, -2.6812974006143557, -8.16856077853362, -4.506341729245962, 5.122235778777101, 6.470481016136127, 0.33494901773710817, -0.4652420480192979, 3.4629748179210287, 2.469781517458431, -0.9438571129723714, -0.1151152873682081, -0.06725192640382459, -4.885938865788891, -6.752036226583413, -2.2840038830253757, 0.5007932626374645, -0.6291232604518581, 0.36344421299394414, 2.320503858740234, 0.015522159697102729, -2.767378433032174, -1.2237398518661147, 0.41351443779023916, -0.41872636270392927, 0.7167670624979064, 3.201355685721367, 1.6798468657332277, -1.4380307172812081, -0.9751130426849526, 0.19482402552765432, -0.6220713154653476, 0.10565831464035756, 1.494183919562078, -0.09379989683930373, 1.9442816544050445, 12.780048780876474, 18.96612328308942, 9.143878623703003, -2.5075764664300584, -0.09758574403281765, 6.91713407234029, 4.790992662791954, -0.5043153262032717, -0.27162467428135206, 0.9071976261007273, -0.6565398041744477, -0.8218409906656327, 0.44523942435702735, -0.14294955708447643, -0.31876063221865947, 1.3064221463674999, 0.8563867900462363, -0.8389645953151685, 0.485877617467053, 1.079197491444418, -3.3501328284611738, -6.244823294908868, -2.88170405518487, -0.0002805968797602235, -0.529202424287085, 1.1336761262870239, 3.116009039938832, -0.5935811247786498, -3.362920577962251, 2.2599007868011403, 6.855693578829997, 1.9454384358398722, -2.9539682998324492, -0.49071154217712254, 1.3478540425229018, -0.9688716715488739, -0.4963511597725438, 1.8496128994984247, -0.17142951980476853, -1.6617262218584357, 3.0846215341404393, 6.276576473165618, 2.0489524068985365, -1.931064365553077, -0.7730531130610558, 0.3811502562703986, -0.1308869479046895, 0.5526010589440703, 0.8230130331651959, -0.3784749722745766, -0.03023528171471459, 0.1717357414904734, -2.7458985042211483, -2.9808250198129573, 2.3920430300696114, 3.8830993147123447, -1.0794669705675162, -1.159310316726183, 3.3950345560431017, -1.5273236558518377, -13.139460991888859, -13.678950535789228, -3.903507789566921, 0.3667788941959805, -1.7737084980679725, -1.2071221888876813, 0.2996312749997133, -1.3315026585187304, -1.4320826833476326, 1.1806049381537824, 1.2135678560916943, -0.29967651757667174, 0.45278155344603954, 0.40908112329470403, -1.4421014893355086, -0.23466235279141337, 1.9091343834030323, -1.0962642543946197, -4.553460186150557, -2.121153229748178, 0.4690769176868424, -1.283666930053999, -1.483213395576617, 0.779185956480182, -0.3265702112051816, -1.8402141718382055, 1.2662082330289095, 2.7921550856028636, -0.05199136376817857, 1.3537606937679216, 5.170451707061636, -1.4558474835966677, -13.430118858330562, -12.81844817837428, -2.1601514664980614, 1.9965267039197205, -0.6595810135511402, -0.7873397337471999, 0.3321976430078671, -0.5274810554318539, 0.25066758247349497, 2.022576567634109, 0.5133846679428634, -1.1092900851609626, 0.5392776607537487, 1.222256021020242, -0.2125412319818923, 0.21220689702618348, 0.8349809582536978, -0.5734484022022843, 0.4192088905203432, 2.593516859549149, -1.2753784102620673, -5.345943372609339, 0.9156392102990619, 7.866347180133503, 1.8346517585227, -6.6406023376418615, -3.250298071724454, 3.2183453349725846, 1.86066894155526, -0.5979381262289447, 0.7325865427774679, 0.01753937384152638, -2.16872684297909, -0.7965012773096648, 0.20401260988914582, -1.894894426694044, -1.1142259697528114, 2.13425197390127, 0.8476713374659842, -1.9440587015232924, 0.09396605993482683, 2.05159143810171, -0.36804073367743284, -1.437142166723135, 0.48896720678023997, 0.5231991922314764, -0.06433841516811747, 1.2230571854257624, 0.6035104652754643, -0.6217904487196914, 3.1778539123477496, 6.188388391109076, 1.7354125961637836, -0.34625153659914937, 6.1581054760728975, 8.0426363501565, 0.3709125607409234, -1.9720158871000892, 4.076915846797304, 4.388903757803467, -1.1794976336659828, -0.5873269871382871, 3.4974915484787528, 1.8575776191150426, -1.4072464732849075, -0.6320200660589366, 0.3282559354723475, -0.23384316772247568, 0.07629527674756537, -0.2683739616710323, -0.998950930148242, 1.4498626774670855, 3.4562648815608865, 0.7553197429217176, -0.14404244711800776, 3.5879905069919173, 2.7384151304495874, -3.155279478574492, -3.2057962982417396, 1.181723250983962, 0.6681236888662069, -0.9610672864809487, 0.8467940949531868, -2.209760478735989, -10.030571494891161, -8.991266451496745, 0.014292700341855178, 2.8213701168729446, 0.04567924630536403, 0.6201945502952445, 1.2009270052944827, -1.4459492506494858, -0.5790948632864084, 3.0787201840488336, 1.5258571544779043, -1.8025687435389486, -0.008754030057859576, 1.967294633654726, 0.06841425335229395, -0.6601266328045982, 0.07340470795237428, -1.6719161881908502, -2.600998606241921, -0.44255176010779596, -0.1004583398698424, -1.3299813931932551, -0.1098770940148695, 0.2542839501408301, -0.9656817669599136, 1.8393290367293815, 1.447828949531458, -13.685513103778952, -28.83884880243058, -21.75801603570818, -3.4299856617665645, 2.0940698246352407, -1.8726502243431982, -1.3574624004523612, 0.46719905316675514, -1.2827776686731909, -1.4141169189950709, 0.241891554913719, -0.42062069706942307, -0.5235080849322684, 0.7606872481223987, -1.465852797400749, -4.40951411239276, -2.331386799636234, 0.14342237386758244, -0.9162040966327507, -0.6295731018746062, 0.7346416690476804, -1.1452509901431016, -1.2771628206789842, 3.1355517007353337, 3.131696024378774, -2.187110720273637, -2.4002049483091557, 1.122187457563808, 0.06181318321147687, -0.7435969186691489, 2.718064841915289, 1.42141057949873, -4.515253229165333, -3.5831400018214055, 0.8105019675240132, -1.6669367722524147, -3.5039790543131764, 3.161232953600102, 7.300279563862828, 2.6392372860482674, -0.5550222031511491, 0.8668677741464889, 0.025169637825008438, -1.711916407205596, -0.3647092253955757, 0.3552033266424888, -0.5460751869798205, 0.16166366708196922, 0.3561327367400377, -0.8379367398380352, 0.7309356215067524, 2.385759622026622, -0.24350006365764384, -0.9743835314353306, 1.7842922377237305, -2.0362172733043407, -9.459958857624256, -6.070027519243317, 2.602733400092614, 1.5678389674632982, -1.8244209079217675, 3.668492840789278, 7.516318954443639, 2.0867704372663267, -1.21885838181195, 1.6366315847305268, 1.7539290789703073, -0.41186176192553103, 0.6139103350657844, 1.3326265241619746, 0.044366051912929874, 0.482827967543854, 0.3163325334955605, -1.6317081396867474, 1.5219540751023912, 7.925262132011429, 6.910418970867571, 0.9670363006740783, -0.11867553793668438, 1.0537467044000333, -0.31410057604286934, -0.531399147266219, 0.3590542409120881, -0.34434010408819465, 1.66110374274119, 5.03263758709291, 1.0664173407249902, -4.056954794404979, 1.3350117759788684, 6.668978636169972, -0.46118609677138916, -6.719525408228289, -1.3644045343211544, 2.1598263066218215, -2.5447313079042777, -3.5345499771526345, 0.662589090372848, 1.0371344203105979], 'positive_zeros': ['0.7774840916316317216765688507', '1.37450368717135672829586417910', '2.36292764071058196950397283579', '3.23780145911094384166786586394', '3.878171977011452336496956341748', '4.74196358879451210970380132505', '5.391486647576448882144750749599', '6.472575492783705371118072681278', '7.27420108759488278935801654835', '7.89590543820084989391358656364', '8.72028650920006107825952075357', '9.05978241881022816256755302643', '10.48742055632223819856182881285', '11.02208811053772552771257907918', '11.49794079733282110446800616611', '12.054661719473984229806704540375', '12.755955827184246161098832985225', '13.668499126369119091338670722423', '13.90995157892633681070781511642', '14.53403835729436531202442179230', '15.63845775337061327079759858919', '16.472078067508083667933936043407', '17.108722696520725260857380718085', '18.026445501693844942265368006553', '18.44792943897439867922308129558', '19.12681533687746211850837636270', '19.65866943377666030536499257009', '20.21664433528363830385982478585', '20.79207708454392708416709274349', '21.63003933678982177257072786215', '22.31399902052919436178888530317', '23.23141851402092814654112462962', '23.60842155146006353428536312267', '23.95126609103156594098991251300', '24.51741111796127447356413388851', '25.73459181713173790143457904146', '26.41368038614546443828558042834', '26.97566729310288265571858593694', '27.66509618653349724861324522428', '28.18925342965419756000690721549', '29.04235579371973086346692992812', '29.434592592103271464879435052386', '30.19331816898727775156919201345', '30.56214281274193306209404153298', '31.15643331694537361124525106083', '31.81060850793060805107359249914', '32.163930967807520838335440015648', '33.22146842827961082070064507565', '34.03861228751206963139776776334', '34.530647535129249113653433861898', '35.40130880384439932749499316691', '35.92042113699450335163580379635', '36.40227946881633496679097169438', '36.84426115197132704962262277808', '37.6188069327400268679481929745', '38.32801463389789417582727968158', '38.91061985675073749360771769228', '39.66061296057109107240921321783', '40.05905860209518116894306083311', '40.52019136776704462348939560058', '41.12528118618352560815085171078', '41.996206583409839078046845181630', '42.48954955248958501167758126082', '43.01275029738117766534195465856', '43.53499947049584303020759984902', '44.64409456523269803998287928141', '45.452820376614015446589588282869', '45.81819812783612268594037112617', '46.4033723508236963402064276054', '46.960555510206265163114196680167', '47.44520255067508272047841651902', '47.82856400365076926990502050188', '48.50859730243742659496963581450', '49.21238923360934377840220937194', '49.911484374692574633558672084694', '50.34499390004360387115673616965', '50.99399724303590955816556667541', '51.7066532554713761266936405926', '52.23899884259850992197147391662', '53.21748394278821975960509885897', '53.58509204168905852040108680361', '53.97575446980492678947176353604', '54.93472805961254371318003542423', '55.33073772547218088786149874025', '56.024226453771187751470297386454', '56.3178722395641688647502449447', '57.33614602288256879378111314981', '58.05773365145421382526432816744', '58.31393048736410897717974914103', '58.44189979876229627201779114713', '59.41786655717847804574032519033', '59.90805002259964984697201279881', '60.18568333763498883288316863252', '61.31622223422033686477349558075', '62.30210392235945056699099622278', '62.726441255197071132933677830497', '63.17273372829113642970768455329', '63.535664087061003006872250389600', '64.43987515771521327341334001006', '64.919881542734786079215772436179', '65.56599150048703194191327300630', '65.90826614027076772573341400350', '66.34994840522987381319950147971', '67.0364208304293591118819221069', '67.762639761458609603201739986845', '68.640021283446236833893609146004', '68.70911195753698437880779037843', '69.51230240023377764255919874005', '70.01038397073254858106380754096', '70.71628842442107873307210072026', '71.36512550227204587157700729561', '71.81677565557117543728995985875', '72.59890608833590190660283116020', '73.20411523764903350610307994370', '73.952917937742606002860447784847', '74.35464355479503043712837503630', '74.8078165366140997872865882419', '75.46008029284989944002643669805', '75.742047928181814124596813804020', '76.492504382497966465870700423121', '76.90843937169714855418334348729', '77.69941504230003445629832673159', '78.12768045078960826981175153591', '78.600266218987946306460379189417', '79.55127199342451927343936992934', '80.1194298311442057152037962643', '80.99146394314015426397420877773', '81.5185081062557328944468349946', '81.885066769199595346402431841376', '82.28005131970596924256296066861', '82.67329867165550521132843878376', '83.42893716524897026844188372126', '84.1023882210663945331493698164', '84.91080493895797381172968260962', '85.305727325131389332611894154186', '85.641912720063166121121181539884', '86.324106980444606841278428907500', '86.91014807445372732466446970528', '87.41155769450896666607622600081', '87.76145370883529200676537933010', '88.73796872889669251344935097334', '89.367713593502938285851996094073', '89.87982690771435142394563268768', '90.52769163135118735588991189763', '91.20035811104802254570393296065', '91.8802090209726625891288923265', '92.11505571668399455324558024623', '92.64749565485039225924480101916', '93.2989755688874038240106280232', '93.85729293833764497447019333627', '94.38098889830971508969439173815', '94.64885770014186222787144694851', '95.1561538440260793609706368437', '96.07822320360493571258092459008', '96.89657588622884879806194949425', '97.22777473287324039041429987368', '98.00775566767988017695691270064', '98.455733272906967573598815099262', '98.742486974972943968700687203663', '99.868659477322672848467417674596', '100.16658255137364837447178180060', '100.578585142574752705759672004120', '101.25124903968009227554801604781', '102.03719190739174178090836425173', '102.3650996024056873269358230565', '102.71783159039796716912361704541', '103.581389991920828478255653879428', '104.252162527653094146913927282314', '104.48898219594064985322446929391', '104.98275291249352672480827792355', '105.60836779879681744206653578629', '105.81205696030104102065721983759', '107.087921447894624457563373000', '107.50379676922584099355487427625', '108.39011546125069000339377724436', '108.79006250441906538533126082043', '109.26299439140443723053139718239', '109.8625294194294907917910234384', '110.27334462747434250041801610562', '110.69668535186185779432922483257', '111.37670482956420277577030700121', '111.80793997391079349912130662397', '112.29471514159503555393435379313', '113.43766285699867340293529338155', '113.52133334459920583094078710190', '113.93317966197308695980962577586', '114.653037215638817812272576559295', '115.21969989891915764714337498033', '116.02285690581573512956705351878', '116.602364816285634494412377462482', '117.06662749188554621876154740831', '117.55402647873531723477699625415', '118.10961350112032155530600773962', '118.584203294606172530457907396771', '119.49129072631427871976498747452', '120.12690920216143181883429550912', '120.52347850178613423080802466882', '120.764593657557090048353198524288', '121.4564665564631865015353382897', '121.883173013250865598771181796899', '122.21823669491061023819300112127', '122.99836154374047005550427140856', '123.68207827818441764257961220394', '124.1364735585838387884111630627', '124.641446680090997987716702268846', '125.82515857293049888989607780567', '126.02001436601055963689660503142', '126.74018170721258911534833006580', '126.979561801073488062131334831833', '127.669726967999805263038613892424', '128.33848726658925129858425410469', '128.637817065181541326848156003515', '129.132285265404744222268154771870', '129.711881139430979846065949929369', '130.240228352007551917639129152452', '131.12716076943315320239507816809', '131.38881015413044985670789820253', '132.06118932335814225857612822342', '132.46136667591317788205478616762', '133.02670248888953131625592699047', '133.74258724991996343324541898858', '133.94839621120572478932668229502', '134.64927116377088173750467371233', '135.70763506674610465402185377228', '136.17403854554915821694392036205', '136.71778996481046722522403577122', '137.028766030958116948111248199214', '137.46152704230454348403199868681', '138.185847685827726776131109002223', '138.67320737113986144320801909659', '139.31751133460508962333331296004', '139.63693464192559350464961178790', '140.1898485205727407196507713070', '140.57589332067326482689185385340', '141.1852466445836144221772452744', '141.845882335558037624399112976228', '142.55248217825293172101839166114', '143.252300413704700536417872279272', '143.91956372712041166804870794711', '144.23834975352555875890178411539', '144.68964856048303597032446943663', '145.42945663329163555897271510442', '145.670999388530358120052779130199', '146.34721007282601250206259272958', '146.94673529387489049783041472261', '147.491648018154509572877457411', '148.087139539210193487746752633875', '148.66799562370798824293771409063', '149.21567153403966443565977425213', '149.40324170985754395855979648183', '150.088409597584157673556308235476', '150.40925345368895708436144973495', '151.35852281598990880381607549378', '151.59234732040244013852517979496', '152.515401275233616208797634327150', '152.929492387058676043098060299440', '153.67182870610028972418082087657', '154.10283742038455715458399330510', '154.82988537756969562654872753504', '155.43435778681869974577305687064', '155.80296671053989135772836791233', '156.203937474773485770063721112717', '156.479192789130518161781546834833', '157.05064952262647382713893353501', '157.890946563046371901190867347', '158.14308548031248155034499148197', '158.8931148416748540224642329863', '159.58618038354501228359760025047', '160.075179688609879621455715194560', '160.48652981675359116049222780705', '160.818728226383974145569604452601', '161.87441925050955232976451369987', '162.50843608054125291316299315207', '162.70498649160112216345808641678', '163.27531369704830194060037382031', '163.79631632497074318598472295067', '164.486801247521094662426578390690', '165.00080750499625703175291831613', '165.63463450626907218957730103897', '166.144003686451875000143831732171', '166.291039112529544443899599412015', '167.26950587380105065780851007221', '167.47429112079263756903839158454', '168.14499661143985895089672617024', '168.49073658466275818017416645333', '168.91398317933582814297831631589', '169.42586038639756036012407076837', '170.71669844110270832329299955891', '171.10378419697909359330979442552', '171.720860950837518594553348723252', '172.00135685867203222458565847861', '172.73965814032572116377632011731', '173.02102506513147067269528204960', '173.54266374431676337572485673285', '173.92959168507865042001651785079', '174.94434153130655018864192093528', '175.11365809906454528364158682569', '175.72704888422692610208262336809', '176.10958003050762570856521368860', '176.66670175552871835183032532093', '177.36889360614037261138393094102', '178.0015904716346581876632387648', '178.44475070097605400007944178490', '178.833132439819848872409079599564', '179.44898017450574670136585847', '180.219850767750699421153830928312', '180.50664650520568161974923759150', '181.1291832887168410822586092765', '182.05531708672413534449980651320', '182.3387788577457055712492235744', '182.81577657397614402605609821397', '183.50254011414020423900854563859', '183.86595896749779004718387092014', '184.33326190716441959991768916297', '184.77297465807432629783019981859', '185.22790776711754731751682465227', '185.914259857052389248027151733582', '186.355041952922025582220372223921', '186.78627769307655761847634856166', '187.69597339763086639611103979857', '188.21632425471564994730120157114', '188.59145034394802807804928829426', '189.486811295722185795730745245275', '189.8460636696551100737100701748', '190.532252160093413633187314307243', '190.83483533265220515112373817410', '191.582983136905240988335519141476', '191.71358226907932764635445497650', '192.23661547233123660141159670450', '192.73083502760616034977752748906', '193.83944406939212693173168262156', '194.08666045628256938091376946696', '194.629704769386920669390975151644', '195.13508030718564048355547874836', '195.4847972708962582266281288268', '195.77231305962613357128266583307', '196.6080571033639756173600351525', '197.13976750373618559085634236138', '197.79859359080500241782698295114', '198.497602773339039948768307510704', '198.91834218934045110289109144602', '199.63089546858162205857503159249'], 'prelabel': '1-4033-4033.182-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.729173260907245, 'root_angle': -0.36647489865811433, 'root_number': '0.407286941054584314379793054796-0.913300250545459755342691385951*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(27)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.466218846583931338934850506381-0.597446272555829826493198413223*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.777484091632', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.37450368717', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.36292764071', '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': 18.729173260907245, 'bad_primes': [37, 109], 'central_character': '4033.182', 'conductor': 4033, 'conductor_radical': 4033, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4033/182'], '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': '1-4033-4033.182-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': '1-4033-4033.182-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.729173260907245, 'root_angle': -0.18323744932905717, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.777484091632', 'prec': 47}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_4033.182', 'Lhash_array': ['dirichlet_L_4033.182'], 'label': '1-4033-4033.182-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4033/182'}