Lfunction data - 1-4033-4033.204-r0-0-0

Formats: - HTML - YAML - JSON - 2024-05-01T13:47:23.479701

• 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_4033.204', 'a10': [-0.23061587074244017, 0.9730448705798238], 'a2': [-0.5, -0.8660254037844386], 'a3': [0.993238357741943, -0.11609291412523023], 'a4': [-0.5, 0.8660254037844386], 'a5': [-0.7273736415730487, -0.6862416378687336], 'a6': [-0.5971585917027862, -0.8021231927550437], 'a7': [0.9730448705798238, 0.23061587074244017], 'a8': [1.0, 0.0], 'a9': [0.9730448705798238, -0.23061587074244017], 'algebraic': True, 'analytic_conductor': 18.729173260907245, 'analytic_normalization': 0, 'bad_lfactors': [[37, [1]], [109, [1]]], 'bad_primes': [37, 109], 'central_character': '4033.204', 'coeff_info': ['x^108 - 1', '0.998308158271268 + 0.0581448289104758*I', '\\\\zeta_{108}'], 'conductor': 4033, 'conductor_radical': 4033, 'conjugate': 'dirichlet_L_4033.3776', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^72', 'a^106', 'a^36', 'a^67', 'a^70', 'a^4', 'a^0', 'a^104', 'a^31', 'a^23', 'a^34', 'a^40', 'a^76', 'a^65', 'a^72', 'a^90', 'a^68', 'a^96', 'a^103', 'a^2', 'a^95', 'a^78', 'a^106', 'a^26', 'a^4', 'a^102', 'a^40', 'a^103', 'a^29', 'a^35', 'a^36', 'a^21', 'a^54', 'a^71', 'a^32', 0, 'a^60', 'a^38', 'a^67', 'a^93', 'a^74', 'a^21', 'a^59', 'a^63', 'a^42', 'a^11', 'a^70', 'a^8', 'a^98', 'a^88', 'a^76', 'a^43', 'a^66', 'a^90', 'a^4', 'a^94', 'a^67', 'a^92', 'a^101', 'a^19', 'a^107', 'a^0', 'a^0', 'a^107', 'a^93', 'a^47', 'a^18', 'a^76', 'a^35', 'a^90', 'a^104', 'a^86', 0, 'a^24', 'a^24', 'a^27', 'a^2', 'a^56', 'a^31', 'a^100', 'a^57', 'a^46', 'a^38', 'a^49', 'a^93', 'a^101', 'a^23', 'a^85', 'a^27', 'a^44', 'a^6', 'a^33', 'a^83', 'a^55', 'a^34', 'a^19', 'a^80', 'a^19', 'a^62'], 'euler_factors': [[1, 'a^72'], [1, 'a^106'], [1, 'a^67'], [1, 'a^4'], [1, 'a^23'], [1, 'a^40'], [1, 'a^90'], [1, 'a^96'], [1, 'a^78'], [1, 'a^103'], [1, 'a^35'], [0], [1, 'a^93'], [1, 'a^21'], [1, 'a^11'], [1, 'a^43'], [1, 'a^92'], [1, 'a^19'], [1, 'a^47'], [1, 'a^90'], [1, 'a^86'], [1, 'a^56'], [1, 'a^46'], [1, 'a^85'], [1, 'a^19'], [1, 'a^45']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-4033-4033.204-r0-0-0', 'leading_term': '1.77328822336119516144813045112-1.06271988148577343235704721831*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/4033/204', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [2.0673472542407194, 1.7990832130578474, 0.9393963651023437, -0.2500771869844925, -0.6761064688448599, 0.047720457449677116, 0.9121436170781106, 0.6963557009594548, -0.3449863126585877, -0.6048085329178997, 0.7444158718108184, 2.325155154928542, 2.130559479392171, 0.3822592455008241, -0.46860868853082016, 0.6181256927745666, 0.7178445666538131, -4.076504403943013, -12.881913588451665, -19.15170941343807, -17.17468767111526, -8.631954022482734, -0.8455905413492097, 1.355673050260034, -0.027041349488196805, -0.4859642703824511, 0.8104726279225294, 1.3603097758263893, 0.3113519979844901, -0.26778950613153824, 0.614270871959249, 0.8382514931850401, -1.1138753138481152, -2.911618470185107, -1.571452645250898, 1.6129807660781545, 2.628238018012303, 0.7272071193652095, -0.7597086434517194, -0.13298412359982878, 0.036523313392013396, -2.092822582597159, -3.649595793041449, -1.5369352125991376, 1.8048167128121158, 1.7644690756507033, -0.7063727507772841, -0.19789367283349785, 4.070996580893722, 6.17129117740171, 2.7631578378084027, -1.0377936120280367, 0.6265302735142475, 5.091853143250382, 5.388002158973885, 1.104639521489972, -1.5625556644148804, 0.08908081979907131, 1.8861662139298747, 0.5952182338267176, -1.1836368699168687, -0.5196275465183413, 0.8504039841141768, 0.4764944261929536, -0.3395140671319182, 0.1876922585016881, 0.5918110131131901, -0.299099836104542, -0.053408406335168496, 2.503583172041763, 3.187872540742231, -0.9556515413863742, -4.675098066113488, -1.4290657945894498, 5.34842726580127, 6.4076081339291875, 0.9947451177334354, -2.300698418846224, 0.349432974540676, 2.81935930725996, 0.6797339435445925, -1.4549933640819857, 0.9314465959839039, 4.064517698068501, 2.983186250192271, 0.017454653956479264, -0.41217022829850825, 0.31889808434126377, -0.9301699429636454, -2.2970623610074536, -1.056055731616428, 0.12624527279518918, -1.9179819707982046, -4.024434561011828, -1.928786032009446, 1.708777641934351, 1.8258813659012925, -0.36535625236134384, -0.6149222005481729, 0.417116626677855, 0.05635691749861113, 0.1787457949511499, 2.774726022646269, 3.686507425356618, -0.1168400857002509, -2.0432850276683343, 4.631181900171029, 13.299796067536201, 12.296761617190306, 3.391018587788886, -1.0833594581086912, 2.261420316391142, 4.755960948300167, 1.7946954681725087, -1.2780567528886633, -0.7249474304859602, 0.2683291778843913, -0.14908698365047326, 0.5095559520978166, 2.1595008557692745, 1.607715731523276, -0.4110624170977792, -0.3276513861826563, 0.8711250770539722, -0.04727839015426781, -1.0541617545677617, 1.1925386200344525, 3.241208171060622, 0.5892665571904562, -2.750319171803419, -1.1625886264283096, 1.293556534430391, -1.5288964544433359, -4.734381299408694, -0.25487011962258516, 7.501543595356613, 8.070201196432617, 2.30313462454925, -0.7531501474100741, 0.25941953863434103, 0.12371327496186439, -0.7128394108297772, 1.2674240098417477, 2.5531320673763633, -1.722792776328249, -6.853181350586156, -5.561003652927476, -0.6125757474260046, 0.8327609546997548, -0.598725675517661, -0.37082296514093194, 0.6169295352791722, -0.06790950160296277, -0.2761880169283117, 1.2431584013662822, 1.2028782260054074, -0.7580022037538284, -0.3853012966501877, 1.790406915456059, 0.7256205983368738, -1.5896247712705804, 1.4231831597579874, 6.236282260554255, 3.1573483268873486, -4.652057116226641, -4.237514430664677, 4.389024314261434, 7.672576998640857, 1.7848083326157642, -2.6805278230128495, -0.5848403324733469, 1.4997390798422987, 0.0957047548474694, -0.6895635607853209, 0.17845561766568357, -0.29707063201565537, -0.9548073434306553, 0.8375679413496075, 2.323273206267815, 0.9349905602877762, -0.06137976843164626, 0.5662507477449605, -1.8112639257612786, -7.014251991110744, -7.5819476271572475, -2.430049564357796, 0.5115067528812149, -1.0332971124844144, -1.1411170287067256, 0.7058589932169927, -0.5733145132556335, -2.893737900692539, -0.7012746091816167, 1.672649187855853, -2.423916715804442, -6.6836328265555505, -2.0037127347668076, 5.596002157216672, 5.145393676570261, -0.12509429602123964, -0.9231889881941748, 1.0354665715170663, -0.1360575288870556, -1.6419925891811256, 0.36217840852304367, 1.7486517681651743, -0.43355244557338024, -1.7468549471601504, -0.2263246068820669, 0.03388728802994104, -1.5222904124321157, -1.2537939177803652, 0.06867691643422062, -0.23525636385498028, -0.004541276423226086, 1.6486632515298878, 0.48804077873466456, -1.709243483649728, 3.7206837944212796, 13.935846221451047, 13.796511526838735, 1.3699591174439603, -6.870646633466783, -3.3486505138495266, 0.7555521931049454, -1.4646859246045065, -2.9857975542027813, -0.48650232182193076, 0.2617008331243829, -1.3673679401504202, -0.3674180029403758, 1.7872302208363253, 0.7273091677388498, -0.81857854175623, 0.169233734234881, -0.27376914972015964, -3.3842699216147745, -3.2830410053947174, 0.7107552521971687, 1.8765480732495337, -0.5008787810040444, -0.8470225925978672, 0.44979009703353184, -0.28115878187108895, -0.2651704571740907, 2.6568855507867326, 2.77812320416308, -1.64060338205422, -3.0001793509975663, 0.1217126144312327, -0.22791500619112157, -3.4961488923165147, -0.837492401726391, 4.602235754894432, 1.4736363346479466, -6.605263249100875, -6.461333708811316, 0.020183348272242687, 0.9105439673109638, -2.9896765046631044, -2.6884663296412428, 0.7253976451133147, 1.0677096414531704, -0.25786870872175816, -0.0713618418046709, -0.13173000722345696, -0.7052946047243038, 0.06818188578111452, -0.4115885053888958, -3.8513660628682183, -4.6647616297525145, -0.6262406398030069, 1.2332988713028517, -1.1088662096401354, -0.547698303893766, 2.8646691485392752, 1.600887894486942, -1.3430509707037939, 2.875075173045481, 8.654998572592818, 4.781986878031829, -3.1455952793762325, -3.150058315846558, 1.069144360816616, 0.44060134570255033, -1.506015565477588, 0.6205618348634903, 2.14283297373205, 0.3583305385520845, 0.3798606475063505, 2.170639266785924, 0.556559956149832, -1.6282056499653572, 1.139828848499933, 4.296453716722412, 2.223119563950592, -0.47585058001446423, 0.36017034227450123, 0.6406005950006667, -1.0294679743710209, -0.6051596784924662, 0.922956971635277, 0.1340185657071015, -0.16017438301535658, 1.4052410600799012, 0.024648149578797556, -2.1955527953497493, 2.6310574549127494, 8.08922781741046, 0.0410538751005643, -14.670116103416099, -15.683477269326243, -3.606154186630748, 3.339676575850359, 1.1665225720122978, -0.21053349330228024, 0.6313764527159961, -0.5668041047775674, -0.914592735060767, 1.6189732911283592, 1.9315775258194448, -0.7200313939527013, -1.1359034774932255, 0.09838165696612323, -0.7332130423511403, -1.2932948407071716, 0.07553188560521414, -0.3608014297469692, -1.4811706777324156, 1.529663118188167, 4.041184768479897, -0.5092156255914398, -5.113352707258618, -1.7418257673083617, 2.4440730014465983, 0.3578388966606771, -1.4751306880307347, 0.3472401003434327, -1.3892348716641172, -5.942638673179271, -4.132973399252048, 1.2732231667613851, 0.7755255452367834, -1.8144247209551359, 0.7685800735829533, 2.184317736359648, -3.1354171679368616, -6.652356967417512, -3.0524466568459743, 0.11990733949239839, -0.6700890711463456, -0.28533328236378097, 1.216931521178757, 0.11169807587408138, -0.8522957067804164, 0.7209786713645265, 1.008524116734444, -0.32609503411737584, 0.4371296163686597, 1.1880211527134787, -0.34408554533036967, 0.9470896801738125, 4.9783046255411945, 3.0747268505618366, -2.573348269582412, -0.30707739137067896, 5.897838590692423, 2.6404694919442973, -4.1885497819481845, 0.24382704322606086, 9.615657427249255, 8.757645653979191, 1.6869663164168907, -0.10599057717135735, 1.1341061009264721, 0.04920300572647518, -0.4811014402966935, 0.45767379446867207, -0.12625841199630353, -0.2921913104155183, 1.0733079027583727, -1.07554074461155, -5.690128270624294, -4.642957558528317, 0.5307948679981109, 1.3320930300515246, -0.4400948144528345, 1.130798289293929, 2.3994637783625716, 0.12471044692009567, -0.7560105496024846, 0.3245709951320681, -0.5448656817724633, 1.1115846086563508, 8.316497156174046, 9.919976304589815, 0.45625657365731065, -6.326703129527421, -2.7318234188144754, 0.5022108101716307, -0.6522227722056734, 2.571893949984985, 8.020425171967458, 5.223946266670564, -1.5788082065390774, -1.8950437896898968, 0.8220183824389131, -0.1263774110364667, -1.1613857909085024, 0.14171054172676198, -0.11611072626017645, -1.180692082502404, 0.11130445220707552, 0.9068710585886396, -0.2445994981316336, 0.03750304172242116, 0.23480835105795983, -2.275808381533074, -2.0322670404687404, 2.032823414734756, 0.2121653060733529, -6.481523022944464, -3.759682080222998, 6.754211046128384, 8.051939260795676, 0.38223485963185516, -1.5799547905371416, 1.4953097462719964, -0.08502904545262434, -2.754647266893407, -0.8603602831658159, -0.013243724686460652, -2.0328845583941657, -0.5780444468334477, 2.4276315947490588, 0.6213996027629067, -1.7840557294077515, 0.04002081323337001, 0.8259446667720649, -1.3815959485455416, -1.0689710837252981, 0.6418918609660687, -0.8443999246808, -1.5771734028092659, 1.210524848382152, 1.5292047327025466, -1.2203939559148298, -0.5923027569899606, 1.74985025985543, 0.7680789112267741, -0.03219519033923259, 0.6500717172403424, -2.0985623309900454, -2.793387228498689, 6.914382543251215, 14.46992367508692, 4.589001245921585, -9.436949114142275, -8.016858806284592, 1.003241574280977, 2.1566809463832497, -0.590793642390104, 0.08887757474189678, 0.37873990658586926, -0.8200196378987119, 0.47477116350330834, 1.8221264403349147, 0.32888610699635806, -0.3591856383951604, 0.059608262752515316, -1.5796438285150756, -1.9536305461963563, 1.0713085044479251, 1.4039941004580145, -1.1434721193827002, 0.708363355325921, 4.077378091016362, 1.6055066338532682, -1.0752880234314015, 1.3167015545768805, 0.3965018105567483, -5.340369847411075, -4.088087481344886, 3.105890486411042, 3.0605310310932357, -1.7712813798923945, -0.38365463799655114, 2.693193715252186, 0.10367904581591494, -1.8224493046447408, 0.3557508745349137, 0.2094735297609215, -1.298045930125455, 0.9220331592191108, 1.1921417188502654, -4.243952620428525, -6.23715237816341, -1.357983210811782, 1.5326974215567413, 0.029627060041146805, -0.42231184263909205, 0.07439351514172927, 0.003275729858355242, 1.3794967459185825, 1.8195084570182947, -0.8208859623134936, -0.31464800946710697, 3.9858069771728175, 2.963405673949847, -0.6234491980142689, 4.279731817837057, 9.689984789035382, 1.589962451282046, -9.11021905940084, -6.444691100678253, 0.4478317592344363, -0.43996207960961264, -1.3310422070523542, 2.9939964733792164, 3.937431125191882, 0.3372980901182289, -0.5140203682655538, 0.13829600643370854, -1.262415260395092, -1.2981734897543966, 0.20646540538067132, -0.2492214569787025, -0.01787401321182379, 1.8317063699666287, -0.44113008564342926, -4.502797167211829, -2.092662472907461, 2.4975144512008858, 1.2304668677539574, -0.8369556748172723, 0.47738668209015045, -0.9918077948412944, -4.082068177647393, -1.285822177966564, 2.270218984137068, -0.20208864501334584, -1.3068329480035288, 1.7710851658458076, -0.35954620638114165, -4.864310923279051, 0.04215885250930633, 7.314636309752694, 3.7712839841554384, -2.749327755453297, -1.247320066943736, 1.4124133425424445, -0.5429288364249323, -1.044991615957733, 0.734735024349761, 0.259407463450695, -0.10588190786335316, 1.1510840858020701, -0.08265987558350915, -1.9407042755718096, -0.10814548348411507, 1.2860669064582788, -0.28814946502834926, -0.2004507797773537, 0.6021286860576636, -0.9064108908093296, 0.5600164177427753, 3.4800232430736155, -3.971506632473851, -15.684834038220563, -11.710254940981148, 2.584652350018806, 4.832087434703057, -2.6972084878712606, -3.1900544251793406, 0.9706883409231587, 0.5368518647394495, -0.5859529111724818, 0.4690957310571221, -0.11548681219553748, 0.17151165590062578, 3.474209315760617, 3.2960487520716804, -0.4374634175717348, -0.04258531935543042, 2.203744512549789, 0.29416752886510167, -0.9992231141348482, 1.1498561957427924, 0.4545005686794158, -2.3270517773672252, -1.0415574135707724, 0.957014056958516, 0.07675565963956088, 0.8443205546809616, 2.0266512344415784, -1.1034709655902875, -2.3295428037564108, 1.259295912325614, -1.0496549236014898, -8.410833027645621, -5.6933619288628154, 3.837754040757771, 4.0249480517173835, -0.5987493961682581, 2.0460452250569015, 4.374708829382891, -0.8457666644968282, -3.4036024311747424, 0.6121885225278998, 1.9547945617197695, -0.11668130582980124, 0.15875339809383937, 0.7292919208054622, -0.18893303287740287, 0.4596360906257599, 1.0052903065737075, -0.42226732294227093, -0.2123526731044828, 0.4410776006326035, -1.2288005419216674, 1.9309784008709714, 11.378338199342682, 13.123685753613012, 4.285280149829785, -0.6141136995883014, 0.48932993271895947, -1.7517423146223292, -3.17493996907534, 1.0907279959080018, 0.4989281504411084, -6.590162143518514, -6.112841789140807, 1.4309107727781984, 2.670151347997726, -0.6542474333484483, -0.3631587151982032, 0.011737556890440953, -1.0679032576333793, 1.4172977059241023, 3.349424021073039, -0.4694680780623941], 'positive_zeros': ['0.86447114974761521157526540198', '1.548178190927507253940739272917', '2.39678993174853444511680413910', '2.988896131687622046283852949048', '4.13759536296137936905230833922', '4.549230096564851443090788599519', '5.08377666962927410574382305817', '6.93193251351071060473747325916', '7.494394920368688860807299245091', '7.95154170472499584615929316092', '8.83721056616596039575747759967', '9.1952261104738337734304144530', '9.85470858271937819132548899472', '10.77668572646476643903409088071', '11.667801682190743275989664516173', '12.23081525805254379966736241343', '12.510232067342888707798263467824', '13.56604333361840454891405318833', '14.27667457366643767737660449225', '14.70724009961967343853585041483', '15.814125128765570245057304637262', '16.20066305710013934975778725180', '17.26926163870290667883889188296', '17.80210509199450581479583517337', '18.51848817068878203435864927808', '19.15997844418375649382770242826', '19.82678190622268144441126192585', '20.24692079293303341415904602429', '20.845633078027685235681024079270', '21.25965144616913112479108439378', '22.13175566028190694413056310777', '22.877228640095122722442266915324', '23.805410314338736368757712667562', '24.34742301042692089479214259436', '25.06401070245883713806748132900', '25.54716969722665227408981482752', '26.56518518816329458158605828802', '27.00480252759449897639622172227', '27.33240057672714557130689557229', '28.320618082680484360005886482795', '28.492426068766470102962632824318', '29.52384301167049846183217901528', '30.25187472905694872541258982017', '30.788807364635158872138133753655', '31.2731038079025304873408134219', '31.51949915773204756998056703067', '32.49209144896865690599732740871', '32.95568415356035655719576619326', '34.21859328652564445114428398116', '34.52870577642648017088511295763', '35.454514928484557806361846487490', '36.10187746028406648574344770833', '36.46653225746472228548665534689', '36.75215245471625704453070454157', '37.73462107507090684570088577227', '38.1971845474119496136952128137', '38.74167372315273103508637192882', '39.25442324706008330915190056757', '40.04222880693507523215071129636', '40.7295642856594193282673645331', '41.141316688058350909793373267111', '41.88485546741150564396799687612', '42.97499749490644474475563433881', '43.37377515788678240263194432501', '43.78011635930198978380646340414', '44.22617862058442180135710974135', '44.90961091813922019361276934691', '45.99152314175533864128988113786', '46.43077033944524054839942570263', '46.96401241608689941668641894228', '47.48008549741329139269582536686', '47.885204410838244390811525790071', '48.62344141236365650573625599593', '49.11574792659108338088693725146', '49.76225208997402940203046875506', '50.22619383456192192290446317446', '51.057066155046631474545424976245', '51.72434140420456219405714703988', '52.5823016385663437995126846220', '53.17888151771693217581058602375', '53.766199571321833014410234261101', '54.29921681225284982554856991010', '54.604331525486874467575390450669', '55.20359553974408555168908789381', '56.14059231247878045526476352018', '56.29353986286327047743390975241', '56.71796659085124545806355617313', '57.99663908827248920493949091337', '58.276779575894605764917349645432', '58.922579297659768248677733338792', '59.31020760759904469717824525350', '60.05655634227014030715994906857', '60.49384802569876548885487087913', '61.322211976187701575998013006450', '62.1777480310107496805988991166', '62.6283416556865167257575154059', '63.10749626516012016806330514905', '63.70979382069725613476389650843', '64.326262484105740332506678556981', '65.04851285899208180689317548003', '65.32114311746130510298210779574', '66.21932844248765067272993080322', '66.45747920950442704736946051595', '66.87600678737284990143897880172', '67.54899467169735395869633876660', '67.981692110203604738957658319198', '69.095268295415659145147285179744', '69.88581147434092919829005533338', '70.175459130108547701904181011264', '71.00308176889163187067367265357', '71.30566244234540062733608145434', '71.918813905962562865021452493654', '72.601613547397661834647231761841', '73.08391622836391066976253429683', '73.39802882079392763190447265837', '74.31820911732742075538254000072', '74.933448945748961782648390641733', '75.48685468262571874045697863234', '75.87056956228405280053601736870', '76.28928874026167799975217296343', '77.078756525171643847629305881065', '77.79839920218160531189025500452', '78.10171061163722306305385187576', '78.791742850603626269664568154339', '79.43017170332318872184973063465', '80.31126889187599806130703006184', '80.70290915679943806991379552705', '81.48389030211346019685740417891', '82.10012694385732729207354300788', '82.54756633667397820330705363621', '82.74195253026210517906391491964', '83.41548682443597421857346076810', '83.68326626963647430145957200416', '84.73568331525837790250867180207', '85.17809980715236996275979831904', '85.67468917916698539733462583352', '86.37472127111157956151595847379', '86.733070042888041873293656717', '87.66975423514119607955844418110', '88.337611543428569486389492454463', '88.798067548071571832298796956529', '89.31220123145168205419904297174', '90.081258150030546283084327678160', '90.227689500046376847593018767824', '90.9913235656135215464927537068', '91.4793158728075119544898700734', '92.40146902936819899102316642720', '92.73912630180850248219647242555', '93.24824260060798604206346896155', '93.84958904267944502220873935208', '94.40638440933526157230972549287', '94.725445653179763274098070200992', '95.31487010734575754637427515884', '95.82266095585316092488877594297', '96.56336472849090662676447537652', '97.60485071259470431586869707660', '98.27166695388144250551419229630', '98.51310732941054953495649453425', '98.9622400655461394828803943640', '99.5044731784203836702359670891', '100.22491491304861010737457197336', '100.88743676987717918126713909906', '101.07141814723487480848740370117', '101.85435558247095310735508955620', '102.11431619973641955267878389941', '102.69918773435715005491827417375', '103.413790110564982173727701772697', '104.15644065101947531316158707318', '104.71895637414358169407795053565', '105.24722692202438154938684748856', '105.50712773852601776799309118971', '106.46953534761128023487730173254', '106.94351214161963101717181404830', '107.43912271512975421402947936586', '107.97235490615606903265021296840', '109.02442852999136666236862461106', '109.20135629581020428024042295044', '109.736393809061060260928608077391', '110.33053712933812391924153891334', '110.81664936446280855984483172744', '111.4622925939793713890386495715', '111.78651133083880946255467102424', '112.42725334008407512701844519570', '112.718852276796312835099041254821', '113.58887173052888085163733970602', '114.07650274290876707439064968607', '114.78581668496933284831595571790', '115.30477724200070678072420819369', '116.39391845283448711081156571740', '116.58897028748300135969869196337', '117.1973166727881193708666138777', '117.64756646989140818734792769507', '118.08943402302020976105447125053', '118.505511103727757943111167559835', '118.9803767934629537543841741826', '119.96079882025615680997406231736', '120.507131828128517973047463614144', '120.79168305703108226847557026921', '121.57823668058396925206543960416', '122.06235322075377834736202195562', '122.36636246757932137492515702935', '122.72979190802406764597214691255', '123.76295067181893663478724518690', '124.56646113528960635989955852984', '124.83613644927883013620528672404', '125.14788428165259159300450733761', '126.159803523814082809684434641446', '126.74887715109588614242903698964', '127.168579123060536179181606908906', '127.77631712176051053674210492619', '128.09849107300908930292569965384', '128.731271408183889916198742261071', '129.304037581321576398241707570576', '129.676703532093031386869630541456', '130.0440068184323640617246519590', '130.7773879201492158921245588014', '131.260367788200066523772910269306', '131.98698894107788807923053137801', '132.83109829141936882957878992909', '133.273425815417917797585807507198', '133.74295475394033968198367517167', '134.499170497325773510310911274901', '134.68455433523107917745974837703', '135.36100365827584763392074466898', '135.99145173702392374171764704412', '136.557592859177690193394823820430', '137.001886425101882399660430917745', '137.651620569259427191554895135326', '138.00944689255204672695629928208', '138.6270583297149020236438854672', '139.22928210174285760295300337791', '139.75278180376344180918088939984', '140.47175617732386850419226968964', '140.63895665697384365450191451005', '141.06456426936128909117177484067', '141.68727516987424160542149732148', '142.586099414764696629013494239730', '143.39215866028888528767586191300', '143.96507621335355326299790713010', '144.356561834710470209532352447736', '144.774746255717401091163739904186', '145.24580276970357304169789934778', '145.99909876191342009376058312160', '146.41418466533467452825246558179', '146.59222641217895694538340836989', '147.39578392228744953867323170138', '147.96810217613580833574096967095', '148.382446394698651434885188685459', '149.18321223960997831975140862056', '149.550496412228449330399469247', '150.02451290295537057134819175154', '150.79426608037847317908430588302', '151.42733917370813649153286281309', '151.902735736128998075102789920046', '152.50830379173348658656200909734', '153.07514967332419509220731355254', '153.4684654368096292071418452428', '153.96729784752002635370456400291', '154.46326021364788826518099544353', '155.398586418573515439469877923978', '155.94310208355080547683277674370', '156.4549119563490432668259530263', '156.69764868121795388858164250704', '156.87266148753965311174663142286', '157.71975397418879007493664169875', '158.1507228636377280879891176432', '158.956946588660982081451269951424', '159.172180722193202093912983220134', '160.037229941094165470157546382028', '160.90092992877844545005722346487', '161.20543982525569828052259831791', '161.67870100728655671973780925964', '162.53774451228025841480603169836', '162.96474530545269650354533063301', '163.18325377982971535660146794448', '163.997404483942967446762985464556', '164.29733340370934919589457995221', '164.69068458565796815228126878308', '165.28243859732862048726192076793', '166.05449755425329614339943465785', '166.684948926183559238329658503923', '167.08506855746742913401234827979', '167.40282171284457924082656064097', '168.20352794638795397303094242460', '168.73278562554201926417978860809', '169.196561717784261376619496226545', '169.66681844694658214791857571778', '170.311047602478299187615656687928', '171.08609944094082453643888469301', '171.658579968810838383718050183801', '172.12133838899772440232588589352', '172.6678638256280970418911883443', '173.192056236292745376879988856472', '173.46876677980033486066380553844', '174.0525571579681494721376380497', '174.699753466828968431047213718244', '175.2574414192594464234315926432', '175.66900224464207725315744958192', '176.08289085455751681889205026529', '176.51540977548638651516303205813', '177.08013011985455776749810890303', '178.0592962221072317363916345086', '178.63264133522824067529292064270', '179.28047469837820048730496920038', '179.769382973154557382047374230235', '180.17405625251160731686973692662', '180.59512755022720741283417019004', '180.91305483290769317098023597176', '181.82819233962124151924648907650', '182.1922583227461262445026438712', '182.843903843547245252686021812397', '183.28315665476731642710786976293', '183.79548272861393511509406641167', '184.48908032690756851748364796636', '185.034215970836828520839659505739', '185.1349954640258635154361548554', '185.85195106450281595225264482841', '186.44988461676647475316647678808', '186.82429858812048889426252252557', '187.673878096354138150559103373733', '188.365884774889085199181100468976', '188.60859534014877094051109579934', '189.332983254893026088910619594027', '189.95614028396061979156244039542', '190.60015301345012418400648432379', '190.89798321503807683766502878356', '191.48222689253051435610667613013', '191.75998753875547167485945875671', '192.40917516127186684288354566001', '192.86071096064234853546951045891', '193.2247824621912068650566189559', '193.65595420229249093800954061687', '194.89203307137257578673562668383', '195.17833483819565526223276500778', '195.45893786727189217629583781490', '196.17510839604303209942214546173', '196.58853700105030461425473868349', '197.43342787560617995434629206733', '198.04500622432227468222359461980', '198.520073137958739601895871554165', '198.75319771836624408627086533422', '199.25166828360017601942251222599', '199.97003890592985736682885354841'], 'prelabel': '1-4033-4033.204-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.729173260907245, 'root_angle': -0.3437108622792866, 'root_number': '0.471505169693859795320202208220-0.881863297201989509360567094757*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(108)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.10791404769758014537398743517-0.492794194239895755088698655000*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.864471149748', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.54817819093', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.39678993175', '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': '4033.204', 'conductor': 4033, 'conductor_radical': 4033, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4033/204'], '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': '1-4033-4033.204-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': '1-4033-4033.204-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.729173260907245, 'root_angle': -0.1718554311396433, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.864471149748', 'prec': 47}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_4033.204', 'Lhash_array': ['dirichlet_L_4033.204'], 'label': '1-4033-4033.204-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4033/204'}