Lfunction data - 1-171-171.31-r1-0-0

Formats: - HTML - YAML - JSON - 2024-07-27T05:21:12.731504

• 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_171.31', 'a10': [0.5, 0.8660254037844386], 'a2': [0.5, 0.8660254037844386], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.5, 0.8660254037844386], 'a5': [1.0, 0.0], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.5, 0.8660254037844386], 'a8': [-1.0, -1.4081532572346456e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 18.376502139880877, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [19, [1]]], 'bad_primes': [3, 19], 'central_character': '171.31', 'coeff_info': ['x^6 - 1', '0.500000000000000 + 0.866025403784439*I', '\\\\zeta_{6}'], 'conductor': 171, 'conductor_radical': 57, 'conjugate': 'dirichlet_L_171.160', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1', 0, 'a^2', 'a^0', 0, 'a^2', 'a^3', 0, 'a^1', 'a^2', 0, 'a^5', 'a^3', 0, 'a^4', 'a^2', 0, 0, 'a^2', 0, 'a^3', 'a^2', 0, 'a^0', 'a^0', 0, 'a^4', 'a^3', 0, 'a^1', 'a^5', 0, 'a^3', 'a^2', 0, 'a^3', 0, 0, 'a^3', 'a^3', 0, 'a^4', 'a^4', 0, 'a^3', 'a^0', 0, 'a^4', 'a^1', 0, 'a^1', 'a^1', 0, 'a^2', 'a^5', 0, 'a^4', 'a^3', 0, 'a^0', 'a^2', 0, 'a^0', 'a^5', 0, 'a^5', 'a^4', 0, 'a^3', 'a^5', 0, 'a^2', 'a^4', 0, 0, 'a^4', 0, 'a^1', 'a^4', 0, 'a^4', 'a^2', 0, 'a^2', 'a^5', 0, 'a^5', 'a^1', 0, 'a^1', 'a^4', 0, 'a^1', 0, 0, 'a^1', 'a^5', 0, 'a^2'], 'euler_factors': [[1, 'a^1'], [0], [1, 'a^0'], [1, 'a^2'], [1, 'a^2'], [1, 'a^5'], [1, 'a^2'], [0], [1, 'a^2'], [1, 'a^3'], [1, 'a^1'], [1, 'a^3'], [1, 'a^3'], [1, 'a^4'], [1, 'a^0'], [1, 'a^1'], [1, 'a^3'], [1, 'a^0'], [1, 'a^5'], [1, 'a^5'], [1, 'a^2'], [1, 'a^1'], [1, 'a^2'], [1, 'a^1'], [1, 'a^1'], [1, 'a^0']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-171-171.31-r1-0-0', 'leading_term': '-0.0670969960408078636333516554039+1.75009428673174178920963553085*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/171/31', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [-1.7513800328109215, -2.839578407217216, -3.727028719952533, -4.1823437934266146, -3.9775916406182295, -3.0173651841913203, -1.4544816759721115, 0.29157141185143215, 1.6528991797776234, 2.138879183166279, 1.5728692407798543, 0.21432097954414672, -1.3226511916947843, -2.344812222131268, -2.4251779257164197, -1.6310417398708614, -0.48837614772432736, 0.3234191013814625, 0.3846322772684523, -0.19516002733662016, -0.839629137574127, -0.8901797471425006, -0.08142598868195924, 1.215641953102251, 2.184171140415904, 2.103829255532642, 0.8975867229580867, -0.7169149742364358, -1.6390964105602608, -1.1389325879677155, 0.5511848322106032, 2.2604189148525426, 2.5832999255623355, 0.840220888004441, -2.3632344311456954, -5.414081197119435, -6.679402613430563, -5.556389555381782, -2.853166271239029, -0.21660089387719245, 0.9958810794815396, 0.5904774649513121, -0.47011777918521447, -0.9194112511099956, -0.2044620223974846, 1.1320659020653834, 1.9885293859173496, 1.6922088878716952, 0.596750913495382, -0.2269155819326197, 0.05172084842363306, 1.2504497807569948, 2.290218626917527, 2.141083303279749, 0.7857506855016755, -0.685780782394855, -1.0138905847218223, 0.029490837884941282, 1.2623695499698597, 0.9846865096038036, -1.516068610631786, -5.123403865042938, -7.532091073245894, -6.965952287135332, -3.6071966914642695, 0.4678062176675797, 2.843555121381849, 2.5567972937414463, 0.6620059596317738, -0.847674663324283, -0.7799457565949497, 0.3729488299152595, 1.1140151928202873, 0.4737797699243798, -1.0570000499851284, -2.038625102722424, -1.5016179119072353, 0.11483825767725966, 1.409125766991966, 1.3928005964276335, 0.4216466591363255, -0.25820597622275476, 0.09911041094253926, 0.8427420413407309, 0.5177995179637018, -1.5474558724045404, -4.246491934859474, -5.42864018413639, -3.843990509568957, -0.49461867349287475, 2.0073487807861317, 1.6501565085673144, -1.168650517920991, -3.9419258419952152, -4.255778411834882, -1.9028063427013873, 1.0273139145772903, 2.1238264816830137, 0.8129792733654432, -1.3037416420709576, -2.1399054011889094, -1.111807145081396, 0.5001394521441869, 1.0403839977024991, 0.19219478801629186, -0.8437381714279606, -0.7943552570426025, 0.2408262046765147, 0.9264927325115986, 0.2500101971822033, -1.236582111729361, -1.927046529632702, -0.9523105749059766, 0.6985555200113489, 1.0746205305622576, -0.6259204566661025, -2.964472821749867, -3.5158366238966443, -1.3583290195681, 1.745925509197879, 2.8525070063485356, 0.680113286224537, -3.0157540527489965, -4.993118328226467, -3.5448007217024635, -0.04032866571492464, 2.4893036724317343, 2.246717257590718, 0.154207535535729, -1.4085835164049287, -1.1135222242928897, 0.2142829696688159, 0.8841310739119104, 0.39088549293997676, -0.10778854434862192, 0.662411472938897, 2.3983535429227305, 3.4013831175625366, 2.477784677673215, 0.3749975867199058, -0.9605353980085829, -0.5312519823699183, 0.6169893197063911, 0.6987549878625596, -0.5231177283327575, -1.1607419027184736, 0.7599045223168308, 4.743767845001281, 7.69553689536922, 6.702468530738128, 2.011844430924899, -2.9483031319950896, -4.682753479967329, -2.777504537839396, 0.06518957267842762, 0.9867482669855514, -0.26765861800571344, -1.5845902846072466, -1.1630224619304943, 0.47927770754471943, 1.3185006250065776, 0.31715869674862607, -1.370802401110128, -1.8159348125797725, -0.583198117149013, 0.8508788663449255, 0.9708368512634192, 0.07010054768056395, -0.19134474176388797, 1.0179915149145238, 2.4880942728774067, 2.3586873183328607, 0.5443429614772697, -0.8264686686586981, 0.21693573091149537, 2.8980935698958668, 4.051963015615426, 1.4025810992782368, -3.71624740335051, -7.334517672577528, -6.687925613098172, -2.885297750912245, 0.43352947357482774, 0.9237384214060493, -0.3272914326657679, -0.5139348546637996, 1.4893608047195372, 3.9373429455979334, 4.395417808564759, 2.562408247313612, 0.45251424106121285, -0.07327743508680201, 0.6609005472837084, 0.9133218789994575, -0.06699925104485023, -1.1074788417813857, -0.8026265207022583, 0.4168770344330795, 0.6261685156612694, -1.1039212897285788, -3.2012544958011544, -3.195630763114533, -0.7204591474997248, 1.7674751938061868, 1.702404753311227, -0.478219988496305, -1.6183243212408753, 0.5266714430313697, 4.415256494302573, 6.070017175428836, 3.3371790060716298, -1.6833561436872477, -4.781422012697971, -3.9392602834885557, -1.033204117348474, 0.701928958507827, 0.2519639970732023, -0.6350225828569936, -0.14889407293504164, 1.2439321175295905, 1.6423395020446674, 0.39592326586959786, -0.9516647376060844, -0.6661999704715053, 0.8841588461188444, 1.6837626496182472, 0.7280756608556601, -0.5852933518534331, -0.24318094589550826, 1.6520578211454449, 2.8298909795382334, 1.7701220168218312, -0.06785101969138946, 0.2019790239212331, 3.1453720447477136, 5.701198611426584, 4.321474538863629, -0.8263094663899392, -5.572179425731343, -5.966683046582299, -2.334171805851284, 1.3699788912700257, 1.9824375568577992, 0.17692324670132814, -1.096929083261546, -0.437532772580571, 0.6693090988272359, 0.2861804736617301, -1.227158173362104, -1.7277637323253705, -0.23108029570997785, 1.686345772373292, 1.8692891754763563, 0.31280516842911454, -0.9532031408924717, -0.6162058933289551, 0.25256446910804387, -0.11765622238345651, -1.4622391541862487, -1.5829799381328185, 0.5264548392281619, 2.6193053259943704, 1.3509572285181368, -3.5365443983477474, -8.19513572285453, -8.525485829616684, -4.642459010789077, -0.6718221331953668, -0.051137971260973344, -1.8684591979194283, -2.4514209444489694, -0.0420411489477426, 3.1847564461057467, 3.988570622055281, 2.000929094096485, -0.12237929544322573, -0.1895056465865726, 1.0297728583866173, 1.300657007351234, 0.09643686284790648, -0.8505719075818133, -0.15749700742859313, 1.197427171655061, 1.2804818816285013, 0.041736311157892454, -0.46996256504227935, 0.9997976128944686, 2.853714948407935, 2.5000334161207802, -0.07138276430805342, -1.8457778060318595, -0.4875947999024043, 2.3813012160957214, 2.795446805614577, -0.6717628162808412, -4.7909339568826255, -5.210477671190009, -1.5238911856651025, 2.2796750663868304, 2.507714240521707, -0.14195454679854586, -1.9045888354699785, -0.7031669646896266, 1.666068100769609, 2.2751513123117624, 0.794939981838639, -0.555552420793071, -0.29668421032435666, 0.4929950014610423, 0.14783620505130107, -0.8777837811145909, -0.5483730874861588, 1.6751766443998255, 3.6414046709660255, 3.1134695031317756, 0.7440155079650882, -0.7413720365409965, -0.1921421708550539, 0.49584845408782274, -0.6925409656845003, -2.470987315019173, -1.3354992710187394, 3.7066383478846223, 8.864558466835632, 9.235110992114933, 4.374495169214668, -1.0287755247390413, -2.337217678044207, 0.2017404019590025, 2.5743415307000648, 2.1813530799222236, 0.4508696977025856, 0.08809142727971422, 1.1856173822293028, 1.414699158489676, -0.37409829987398185, -2.3660414014096434, -2.244348723612784, -0.34422551491235287, 0.9082178430508758, 0.38150598546206627, -0.374080812845552, 0.36444062066202976, 1.7944011240808841, 1.7113181141344314, -0.06507163938274817, -1.029833495500228, 0.545635119237246, 2.7126322366460895, 1.9561056585181078, -1.9580898433403173, -4.8896338572078895, -3.0190594178060017, 2.2941659326052903, 5.770796624868604, 4.26121468150484, 0.14568439871160846, -1.963986108260228, -0.7850110617540417, 0.798176329955736, 0.13967355623400507, -1.7010919977207657, -1.8370776861305458, 0.2314269431834564, 1.9557338121361783, 1.2983802394203785, -0.6170572354075275, -1.3246411044689936, -0.460949378280174, 0.10431917545261606, -0.6033040105416548, -1.091287090119855, 0.16793268972216496, 1.921602015012153, 1.4240131369129856, -1.577769016112295, -3.8760696004562525, -2.7701218671660186, 0.1382347126001822, 0.7464093366363729, -2.126989372270679, -4.89872884621885, -3.7335625346255363, 0.30829819930384017, 2.3330330361049776, -0.3082460107165087, -4.721989914916403, -6.117579109542195, -3.5497826694778105, -0.4853907417629518, -0.006961773320098712, -1.2945537451326532, -1.6432641159802763, -0.5227168022519266, 0.1185335564861473, -0.7481875570282075, -1.475726067049703, -0.25945859199071003, 1.9124144185892522, 2.4119767732076496, 0.6846640679046402, -0.9301313362132061, -0.6048709460832479, 0.2832896103003245, -0.7180876260734289, -3.12199211301933, -3.650799194363646, -0.8635358216325852, 2.166863820453411, 1.4375783225990997, -2.466580417526126, -4.489501849578819, -1.2606630568321855, 4.495606892854283, 7.089271399595411, 4.562672039333122, 0.47968318974411295, -1.014592898979735, -0.014490500221774479, 0.4422020280357359, -0.8392679614880095, -1.8506462468692402, -0.8652291085835986, 0.7702850025702046, 0.6487239300676086, -1.0433031671317625, -1.7496340205218044, -0.3210731623140608, 1.2776746983175136, 0.8742408137406013, -0.7257646941513233, -1.0528624917362106, 0.1903496429139153, 0.6964451756542909, -0.5387256155614313, -0.8457137496859146, 2.742324609969916, 8.547337838835046, 11.017510990322918, 7.14649478424258, 0.42537558062760356, -3.095722982007125, -1.771260475206115, 0.5024582933108026, 0.016267277923561484, -2.0821301060752044, -2.132362501125083, 0.5238054430921862, 2.659403045116777, 1.7725682848254731, -0.5905598559879849, -1.2978562087825183, 0.025843498789921447, 0.9962867985473739, 0.34977591216206294, -0.31218101961809624, 0.6489303844449964, 2.1108940561211638, 1.8810531173145522, 0.29798034605020796, -0.0013158509588504855, 1.8407614127713086, 3.1239910096896986, 1.2715702041166361, -2.0786038157088385, -2.862237878441884, -0.3100647523976442, 1.465438553828264, -1.1968690890169742, -6.250908127509963, -8.155342379263757, -4.898082980800826, -0.49100143828626985, 0.3276792026449529, -2.046141246194071, -3.3289591782588426, -1.4487655508667816, 1.0450697762706909, 1.0567228302117264, -0.7872870018445732, -1.565454188767105, -0.4820630081141757, 0.39569919584795543, -0.2504688240255107, -0.9098792763744843, 0.10825785668711516, 1.6131032078011356, 1.0992298395312246, -1.244255192527196, -2.3546943476122966, -0.6320191711865423, 1.5674470900338173, 1.262876999191315, -0.7265247531362742, -1.0358669383025245, 0.7870780824766052, 0.7724266119343639, -4.061806294266196, -10.594482277779655, -12.400020558470118, -7.427027962692284, -0.537850014765515, 2.4230713169499576, 1.1413496253397077, -0.25359836499436056, 0.5815810493905277, 1.726886313751784, 0.9196624992232987, -0.6934387802728454, -0.5011893307594095, 1.3503394663432222, 2.10494060626368, 0.6143325123323747, -0.9156142289977914, -0.30414104068404124, 1.3351252120627275, 1.4363394590482257, -0.012420836289770698, -0.6218837105799004, 0.2882971925394919, 0.24474066250114257, -2.4168033468878996, -5.095546122439186, -3.902279976252031, 0.4928478317943115, 2.781815871087944, -0.26751940253766093, -5.2306428044358375, -6.180247351152946, -2.239010456975622, 1.5967123912695529, 1.2274971845876643, -1.5964855811053793, -2.5006338589796133, -0.6601293862688945, 0.810224669497261, 0.029747259355967354, -0.9781743949072541, 0.21612515141895203, 2.5137802798535116, 2.9196211730969064, 1.0280385508837004, -0.538474511994186, -0.17177407955174964, 0.6267001790049976, 0.210419308610517, -0.20414674213794726, 1.4147003276713086, 3.949766533366101, 3.9682862990327825, 0.84417176127856, -1.560166362936309, 0.030076686859499595, 3.365571198898617, 3.37934835897094, -0.7460607911206968, -4.1394332598203585, -2.7783223087535247, 1.040184954019496, 1.9825309114476317, -0.95501030110964, -3.3162283692885444, -1.5730509297463384, 2.191123154572901, 3.561128091620525, 1.7643259216331029, -0.12354862960250884, -0.15394051464731262, 0.19094740740281585, -0.7104335237560607, -1.5946142476919227, -0.4901550932176042, 1.619702109993177, 1.855370348630949, -0.16197260992185167, -1.5420405461714093, -0.4708205170270945, 1.0073283435073472, 0.29771054653640283, -1.3777837395611496, -0.6644169607834385, 2.322870645621887, 3.2515671449041132, -0.3048889515876072, -4.531940297917835, -3.780747458034438, 1.8019390422955945, 6.103030689615388, 4.845244623985893, 0.7314245974524899, -0.8104290727964469, 1.1507382870069844, 2.7993540810844646, 1.6628727452236507, -0.2857246193384703, -0.41411950896288247, 0.4539340403322082, -0.13120483164004268, -1.9088306242652773, -2.21124247904581, -0.3521927756434108, 1.0578472810475685, 0.10084269298810784, -1.45594689037674, -0.9759800945839796, 0.8583483083972837, 1.221963849042017, -0.13216861002064068, -0.37882144490670294, 1.391396554395874, 1.6340866532960168, -2.7784329224463615, -8.858330154801275, -10.021359995778493, -4.417085409683937, 2.3032632296723596, 3.9291061204618507, 0.9972732597412265, -1.1814505937446333, -0.20355192568704855, 1.0825829975391192, -0.0021224295556676164, -1.653458644197594, -0.6909630564208519, 2.239971004735624, 3.5030051252382046, 1.8154189913793715, -0.1919193954366322, -0.23241786229993133, 0.5102347817155503, 0.033239603017434456, -0.8501105717531741, -0.02494612618538086, 1.8550698257280414, 1.8278481928740489, -0.6115221442706935, -2.152034688614594, -0.5671977430503796, 1.4497563504570603, 0.020052590896372218, -3.6591562638746784], 'positive_zeros': ['2.1333093069018148031464879702', '3.47992597698358830008471598107', '5.15787981251878808921833779659', '5.85190542658668669453190244298', '6.8964999465729207764800272782', '8.295046421674184885624754346150', '9.285282959345058722789234853890', '10.40338715407853728251804832342', '12.22159079234832991829898399126', '12.9846135078315301408467235892', '13.80134637046592971199559211585', '15.18721419647709204236668368124', '15.605609783988243154885361093355', '17.025985334186635097198183212100', '17.80602849617710485237281544837', '18.59196613918984780073594026118', '20.27262269128305951832249203011', '21.35875522873052971632305819094', '22.094144338886617016713382085661', '22.91637616308359973968175471549', '24.04156943341056918160357332225', '25.143616140251543525567108596674', '25.582924720104071381934767988691', '26.355140751607763713331193918019', '27.85910590968082727935709932538', '28.63719642529366080751690307917', '29.878901186312532247959656513083', '30.74048285364111299561685599863', '31.76787251377005420458796893762', '32.54924786991080883868212989163', '33.37180148567784451942002353652', '34.11889458459897749914730637759', '35.17212803869191026027225834048', '35.85206581401170712493667335970', '37.00583654701915420988028678310', '37.871780437203765311645519941040', '39.06609503656958835103392867739', '40.02201149136391428228392820549', '40.8857639864851252627338333463', '41.742270877610931420841071918900', '41.98944688567393571791946216416', '43.49785678946737798643879120891', '44.19960496458213191080163516545', '44.882927975203795170569810449831', '45.54555988305840242350695710275', '46.989592000844575956197309659646', '48.11584648260269663893250236180', '48.70084228101047051500034018919', '49.5981741772700284795764884897', '50.36939518155396937616693631567', '51.35984450358766868355139284568', '52.2137504029691009746548039458', '52.58249708072027047272732050465', '53.83752598489428886986575782798', '54.343752987453802139920536145921', '55.40425201749791677461893734163', '56.81630732241938208400465687369', '57.41972723408343223899976144049', '57.925934301942357227169308599', '59.50700269587413921771433762404', '59.73771972929564932311960662159', '60.60901731719352960584084667856', '61.45330087469519264641411950369', '62.02433234985161791135060616034', '63.20004910548187910331157482205', '63.998732757805295011104944385', '64.63955343698583880786771725030', '65.83204178709770950166306043196', '67.010485048505952326790188543749', '67.571103457804135946190667858163', '68.16142190332320160443633242101', '69.13694370002918163903270267601', '69.83118345115658193954644245205', '70.77402278741151308387374185579', '71.30015280676482968335547756852', '72.48305130152113400859393252913', '72.774548923608959583731349479600', '74.01811380144213148696262157963', '75.17430883516423460532311892454', '75.96538563993690290552527023962', '76.665901684673367828307902059511', '77.25315385072006877633400288778', '78.15860732792900577817964770702', '79.11841105491508382821582898332', '79.88324381467059474499239190538', '80.27803840779394398635489036024', '81.18847480731045515157262995495', '81.97904466421531231391144138290', '83.55211607877711435543141358673', '83.7348829643616389475921678584', '84.691328418085032645095261086185', '85.90895118090535194532405917928', '86.306193646072448678720620438050', '87.20850958467291927036323537731', '87.847492286990863814993339170837', '88.76038932864136708887490812181', '89.20801078302482085447139462080', '90.304507867091155716248681868295', '90.99087035709258332284811938542', '91.82879413818345983156390441776', '92.91840285995900887215502361919', '93.73456805352849686655119321601', '94.464176604968500903460588165708', '95.4586798628289380382208036648', '96.03795283541472156345671822460', '96.6071903901015226038628681416', '97.28491208428554042921831063116', '98.54629818347059608800442743383', '99.11741148892254027966041306059', '99.56550479124447159219454900691', '100.415926269495959007258070660537', '101.80054183995088391237261558515', '102.48024127454405344419963701145', '103.60051204596243666328886158227', '103.69295570077817216027099818306', '104.63746151788757674523839615651', '105.68154566445922852321729585045', '106.36609308935653665268769934538', '106.787230183317995002396966525155', '107.801748507340089401188477298140', '108.36538718307230247398921565762', '109.234056115601419677545951221904', '110.1836239871353942610017774120', '111.26230323670846133349238227676', '111.99803219199084011048357274421', '112.52456220340190234247322234125', '113.407874330628577018801344344119', '114.2696444537956971916510080503', '115.167020053239691423518320630640', '115.40499282564958531410948690032', '116.22283433436752077333694604908', '117.039886718746636454206619454183', '118.10731366886119494760308719439', '118.55062461013048825420170981342', '119.663173749717321747819748695616', '120.29015761198786840728130055729', '121.66495126362257766338320141084', '121.87241225453403411019958750907', '122.97515087187380520657645429312', '123.21218476599363168861632022302', '124.09978849040571042110702185143', '125.10266169118636235058752349929', '125.796577054866040510494832821021', '126.117882229796652766395003013', '127.26035166340821021021270985948', '127.939291971955672354186454831489', '128.819312857347846501898437843910', '130.05093148293572541656380892251', '130.62870628083768907616581902620', '131.08038976312541146724667625203', '132.02276456361279513952557858275', '132.63124420662574402648966720091', '133.48740875133661957218261608638', '134.229748865840939230436739637246', '134.95627549831531195069576815727', '135.51315074469141857134621783510', '136.054358718372738959492307883830', '137.5228816272922463506099325260', '138.340942080296813875716072776774', '138.75268511274424014902240408518', '139.634605284245715918496807989012', '140.539617169275927671943917703028', '141.244933056686858172043127977324', '141.98246032712273618313191931964', '142.35369539606133240808699492072', '143.51756347239426839259052129775', '143.75042533452905568915180767106', '144.801852224637280883189889164297', '145.6571859299817925524049355373', '146.16201496144869531543003183556', '147.55709212645363703648322119240', '147.8737109764087889146163874592', '148.90944543997783121399599721718', '149.559692732473257546832594707585', '150.42925346539891094482120365128', '150.86191682504131571387359427327', '151.54243234269338387712075374957', '152.34272470859041402396038569274', '153.20033259810223951100582267283', '153.94493818173299128121124985476', '154.56294307110136835526224737523', '155.07892293731958712148220859411', '156.59407616028530099852234979618', '157.39110061756450630334638338964', '157.67807290009182222696693866790', '158.5986229860486367986488348206', '159.15849531859036215256956597097', '160.09631165970833405322769610131', '160.68188506846979115597933749506', '161.559793054098329535612512978880', '162.10262835142577498794178324762', '162.54677178394683678451946574495', '163.71529851600798466746532122555', '164.35827817207007570864889904590', '165.463868352774113589652067736669', '166.07590937928874385317667435530', '166.97213153067419885384256475739', '167.50638640443623973146346926921', '168.09390586815126074137248688388', '169.22424702792505993952175233914', '169.73986740384890533462476851183', '170.39257716169569846800624098013', '170.70847735258532542646917354483', '171.95135632730298845391064148115', '172.49714762011941518665541085515', '173.38918100725180733786665440838', '174.28284087153944179488397805786', '174.917083710676203540108776488578', '175.75307805302616484356075830886', '176.839561878130748060959991069295', '177.26778788845609218811179595061', '177.615505399583971798787363771070', '178.50788464028897829101431520231', '179.35294275623558496617692167253', '180.07851420114041114978861853793', '180.67571514378178165717568355396', '181.32837760725894816409071250160', '182.16819086451951139489279827405', '183.0344714931681209761648118168', '184.13537303354576340994957688406', '184.54258246600124613997239562433', '185.563339634835378557889136222370', '186.07211137316028609624640876748', '186.53478567684052759558938539588', '187.55165621992138865163324663365', '188.14231506487570543992942386771', '188.91328434890225488647502906600', '189.6572683349635492177238431012', '190.08773244912165181963385896229', '190.78038905907478536014844073331', '192.063305854153058642049186096258', '192.91051945759820273580876265994', '193.472020995627907495648513784232', '194.06216768179987900693563563085', '194.767077007094901924320040614780', '195.89111262543014658004883877883', '196.33404172091155649599765898563', '196.88461719542026409991501915554', '197.50434717210222233887232540204', '198.367938515053549625096159507038', '199.130287991646056861452677871841', '199.689393705112695555436188856068'], 'prelabel': '1-171-171.31-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.376502139880877, 'root_angle': -0.9756045349865576, 'root_number': '-0.997064545442533900962031275924-0.0765656073016680876936988075942*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.487802267493', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(6)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.894433422819993143348746933574+0.903362843263929982370110317127*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.1333093069', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '3.47992597698', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.15787981252', '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': 18.376502139880877, 'bad_primes': [3, 19], 'central_character': '171.31', 'conductor': 171, 'conductor_radical': 57, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/171/31'], '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': '1-171-171.31-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-171-171.31-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.376502139880877, 'root_angle': -0.4878022674932788, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.1333093069', 'prec': 40}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_171.31', 'Lhash_array': ['dirichlet_L_171.31'], 'label': '1-171-171.31-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/171/31'}