Lfunction data - 1-221-221.126-r1-0-0

Formats: - HTML - YAML - JSON - 2025-12-26T16:47:40.346032

• 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
  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_221.126', 'a10': [-0.1305261922200516, -0.9914448613738104], 'a2': [-0.25881904510252074, 0.9659258262890683], 'a3': [-0.6087614290087207, 0.7933533402912352], 'a4': [-0.8660254037844386, -0.5], 'a5': [-0.9238795325112867, 0.3826834323650898], 'a6': [-0.6087614290087207, -0.7933533402912352], 'a7': [0.7933533402912352, -0.6087614290087207], 'a8': [0.7071067811865476, -0.7071067811865476], 'a9': [-0.25881904510252074, -0.9659258262890683], 'algebraic': True, 'analytic_conductor': 23.74974837961213, 'analytic_normalization': 0, 'bad_lfactors': [[13, [1]], [17, [1]]], 'bad_primes': [13, 17], 'central_character': '221.126', 'coeff_info': ['x^48 - 1', '0.991444861373810 + 0.130526192220052*I', '\\\\zeta_{48}'], 'conductor': 221, 'conductor_radical': 221, 'conjugate': 'dirichlet_L_221.107', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^14', 'a^17', 'a^28', 'a^21', 'a^31', 'a^43', 'a^42', 'a^34', 'a^35', 'a^23', 'a^45', 0, 'a^9', 'a^38', 'a^8', 0, 'a^0', 'a^46', 'a^1', 'a^12', 'a^37', 'a^47', 'a^11', 'a^42', 0, 'a^3', 'a^23', 'a^29', 'a^4', 'a^9', 'a^22', 'a^40', 0, 'a^16', 'a^14', 'a^17', 'a^12', 0, 'a^15', 'a^11', 'a^26', 'a^34', 'a^3', 'a^7', 'a^13', 'a^36', 'a^25', 'a^38', 'a^8', 0, 0, 'a^30', 'a^17', 'a^44', 'a^37', 'a^15', 'a^43', 'a^10', 'a^18', 'a^19', 'a^23', 'a^29', 'a^36', 0, 'a^6', 'a^8', 0, 'a^16', 'a^30', 'a^1', 'a^28', 'a^21', 'a^31', 'a^11', 'a^26', 'a^18', 0, 'a^39', 'a^29', 'a^20', 'a^25', 'a^6', 'a^40', 0, 'a^0', 'a^46', 'a^17', 'a^44', 'a^21', 0, 'a^27', 'a^26', 'a^2', 'a^19', 'a^39', 'a^13', 'a^4', 'a^9', 'a^22'], 'euler_factors': [[1, 'a^14'], [1, 'a^17'], [1, 'a^21'], [1, 'a^43'], [1, 'a^23'], [0], [0], [1, 'a^46'], [1, 'a^47'], [1, 'a^29'], [1, 'a^9'], [1, 'a^17'], [1, 'a^11'], [1, 'a^34'], [1, 'a^36'], [1, 'a^30'], [1, 'a^10'], [1, 'a^19'], [1, 'a^8'], [1, 'a^1'], [1, 'a^21'], [1, 'a^39'], [1, 'a^6'], [1, 'a^44'], [1, 'a^13'], [1, 'a^8']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-221-221.126-r1-0-0', 'leading_term': '0.405359993523445322379048790514+0.724711692569124167141977083240*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/221/126', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.8303756750385529, 0.8840301999483942, 0.38958580153480216, -0.7814251770733441, -2.5826031898846487, -4.691707070444468, -6.528391728815441, -7.434432417127168, -6.962670717256963, -5.137128488251874, -2.52599609470887, -0.041645424586168926, 1.4724380268084472, 1.6647869588194375, 0.861805299053512, -0.12333703934221868, -0.478927567780178, 0.10281680656328367, 1.2343107418469932, 2.101696528339115, 2.040072786776407, 1.0286463993269404, -0.259530597932711, -0.925122753987083, -0.5175385998965123, 0.5822486645945457, 1.3965088245490427, 1.079375215264464, -0.3887567696794186, -2.0996500620264755, -2.851781834191539, -2.083883759719186, -0.3781115743379807, 0.9246497462679303, 0.7742577530802894, -0.6720405048727038, -2.041721633894281, -1.7554403742104052, 0.6700804417160493, 4.0624918455066, 6.303156252046843, 5.841159487777292, 2.864400140062925, -0.805936662997096, -3.0419726035436527, -2.921584905038638, -1.2413010666238962, 0.3262056997657269, 0.6617319509194421, -0.009879735465937782, -0.5853413222377518, -0.2834004652771788, 0.5850672132953451, 0.9996621096593372, 0.360976601865278, -0.7863105457035527, -1.2253500360570395, -0.3420627850729146, 1.0592971465052512, 1.328127925824577, -0.45654051875176505, -3.3613223455389902, -5.120211586718353, -4.027376130936133, -0.5664212717794054, 2.7750254945532515, 3.488502676259462, 1.143795742361205, -2.2655328275819104, -4.057544133056259, -3.1200578382276327, -0.6703820354843806, 1.086748444081011, 1.0421240077820413, 0.011155764217296022, -0.38918225604349777, 0.42712247083881966, 1.377872934712581, 0.9083183741314365, -1.2476165557037873, -3.6034256815417782, -4.28096518957267, -2.8238362087547317, -0.6010040592711474, 0.6067595796385472, 0.34747417478942066, -0.26018777727619824, 0.006532012700239687, 0.960948018231735, 1.1998091612223791, -0.11202731622161236, -1.8436963358052434, -1.643285518753167, 1.652852254349839, 6.374064055850824, 9.054200854699534, 7.4417318276764695, 2.6466849341713625, -1.7423193400256638, -2.818696031740066, -0.7911163411667776, 1.582948728748692, 1.8428753268556788, 0.04014336171334211, -1.7589168739027028, -1.876538348709545, -0.6607681026400203, 0.2546323194630877, -0.020979344228342522, -0.7292755724292412, -0.6369256138433234, 0.24486279602737238, 0.5640556320732978, -0.6420734186117809, -2.4664940125056645, -2.8468938260561707, -0.8961913013018901, 1.7839852975300658, 2.530449175874713, 0.4655357555019773, -2.341839221817988, -2.8616898891235656, -0.2629650046639377, 3.149069839852337, 4.313562974437473, 2.5988015431835896, 0.35009132380765234, 0.22170337928870967, 2.2468556422726644, 3.874337926675191, 2.8888402535035818, -0.07065753548110901, -2.189011054695498, -1.5374457993400916, 0.9241138687632474, 2.560426743808967, 1.9776308757030807, 0.307610933766002, -0.43419939155296927, 0.21262990150969605, 0.8312014013732905, 0.14585662284166373, -1.2475835783716664, -1.6351667820980382, -0.4572100027918607, 0.8361097842458095, 0.5586054022637081, -0.9702789088850925, -1.6856342638984765, -0.5284485147421032, 0.610674775600544, -1.49745889468065, -7.603871527795364, -14.242708431567387, -16.44601880432687, -12.403223069298678, -5.210238840755353, 0.14147116010259284, 1.3080298210371932, -0.018262812606692616, -0.8597094373769568, -0.32063811467787673, 0.15502243766465332, -0.6566623813357937, -1.9354844612302524, -1.981806877567525, -0.6431631521152655, 0.3153001957532601, -0.5195051113057586, -2.2233925534740404, -2.5137812869507448, -0.6087708072409375, 1.6345623154485827, 1.8710849550606552, 0.1249529303188934, -1.2529872300440952, -0.5779711648887627, 0.9597241590064849, 0.7763946735417484, -1.635247972423413, -3.640885505754728, -2.4237389615619938, 1.435739988320223, 4.211372976610548, 3.10624744188027, -0.5406817754016277, -2.747856242346787, -1.3947251201816202, 1.5208584060183723, 2.4213583117353297, 0.3373291381603733, -2.207401467235346, -2.416794370680483, -0.45429770872944597, 1.119485133468535, 0.6527742644357415, -0.8179618068542783, -1.2991184603942527, -0.4852940638131146, 0.1912902135250012, -0.11645596228032383, -0.4449644756623512, 0.27070279328406655, 1.0046364172403786, -0.5709527382167744, -4.799904130851769, -8.55129121566095, -8.119053808250188, -3.5645349129974373, 0.8143262985450979, 0.9339378344702199, -2.64784790974421, -5.515053825183882, -4.485762636349116, -1.0207673933290446, 0.901237586884592, -0.4115586682000163, -2.729689964274536, -3.060988197791373, -1.2982920258438586, 0.15474945422356623, -0.1432978609342866, -0.8905797762098233, -0.1719371417696843, 1.6295949864914092, 2.2274817863898613, 0.621453584544769, -1.3106321999333208, -1.111767849250833, 1.0454426085384871, 2.5409241417036634, 1.6884571683772946, -0.18194806199624536, -0.7068629864308945, 0.2187044927759911, 0.43150950831487206, -1.1286976103376403, -2.4060205479872745, -0.7579395791572141, 3.0004806963364925, 4.647396969546422, 1.3722375723109224, -4.352305482312155, -6.948563304653454, -3.7828676313311007, 1.9891000126539975, 5.075615559279296, 3.709965311035522, 0.7420929089042251, -0.46110975638854435, 0.25334607985749474, 0.7697033164268278, 0.1960593307689895, -0.1372575939704641, 0.8410938799245296, 1.983307026141682, 1.4870742945663133, -0.3150003185339965, -1.1641623883582397, -0.022503157703386786, 1.3205043502160132, 0.7401929248101623, -0.9356176254830876, -0.6922330441071367, 2.393886937112711, 5.105745414276301, 3.5843023806916614, -1.6503800224157903, -5.69583121764067, -4.723831165705824, -0.3026661391505872, 2.7203274864357994, 1.9772499005915314, -0.24344043704760923, -0.7077812347789891, 0.47856078162528415, 0.6261164367526953, -1.216155581802756, -2.5908377697694966, -0.9529584694519332, 2.6482171426073178, 4.638208273814882, 3.3249087175290053, 0.7543674757564186, -0.2582666590384727, 0.3437706687343412, 0.4709692359164097, -0.6741333490370083, -1.4821637678307003, -0.6343095504343035, 0.615085064992995, 0.20354173038803852, -1.4224227130568883, -1.6171251767106944, 0.41492273188327894, 1.5728662413404646, -1.5233172736292617, -7.450604026534293, -10.478265340082068, -6.898032721495747, 0.4067069736882142, 5.0234204344480045, 4.089368032468828, 0.7977265800828379, -0.26913359785838503, 1.3935133957411268, 2.6320481877225106, 1.4630845873391043, -0.5482995111314278, -1.0436660137335678, -0.20659385031511351, 0.0593775210051948, -0.6300611407502636, -0.6438640886212406, 0.7080669235078297, 1.5242901039934273, -0.08252447094306344, -2.7272538672641318, -2.956268512480735, 0.18405232566592372, 3.496824836128276, 3.5450276612406277, 1.0088760575724296, -0.5028282467311899, 0.4331372784505412, 1.2078184146239863, -0.7119799646927902, -3.535481392313968, -3.0564034274542737, 1.5222233744456366, 5.850035730725563, 5.515941204637221, 1.427816761919933, -1.5604686243866102, -0.8073165154899886, 1.3470686312118405, 1.4432688418894042, -0.3448018293837662, -0.9865528425544393, 0.7470716977400796, 2.5803370264874754, 2.1342170112830487, 0.22089604422848186, -0.6365384256857726, 0.07626247624708515, 0.5143283346940838, -0.27733702039236363, -0.7921235299255316, 0.2943914206045384, 1.5321207445823728, 0.7156505367092183, -1.0796048013383437, 0.050225586616281126, 5.362627866708993, 10.310513434381866, 9.008792192342293, 1.4489778502930644, -5.859527546647124, -7.081412516545932, -3.214597336962346, 0.18650384474871692, 0.10199071181831243, -1.3335175458445885, -1.106926259500195, 0.3485317791196385, 0.6177575575871738, -0.5032893912391145, -0.7279689670145221, 0.8791199762568638, 2.105357898004074, 0.8032375828270848, -1.6762767150619058, -2.140258674302838, -0.038912103956100896, 1.8012083578878157, 1.2792070853193274, -0.1411231323804605, -0.037076868558537396, 0.988997464210493, 0.19434076635603081, -2.693715450923982, -4.266824296667481, -2.024892700109085, 1.6717103868648573, 2.4187760336634496, -0.1690419244671587, -1.8080155905829083, 0.36738612028684925, 3.387528542582321, 2.166022687864667, -3.473648822804679, -8.08686595573582, -7.26776332110611, -2.775893257557562, 0.3435734194626987, 0.13004099608937167, -0.9840054992264422, -0.624122928606578, 0.4083280370615845, 0.34417284526193886, -0.3649013520400337, -0.06438736151298985, 0.9216188069201016, 0.5449112360959477, -1.3931434507018938, -2.2661724557582303, -0.4713043931882904, 1.5535842062396097, 0.36032236400198675, -3.2204427212463402, -4.507995565871283, -1.3338804006017202, 2.4356642825915347, 1.684560560383232, -3.0322025403742723, -6.000131384837912, -3.737062356842415, 0.7839823012666691, 2.5547546550968443, 1.0532176839306036, -0.0513506212494791, 1.2232878238394045, 2.589358913093326, 1.51160374841413, -0.7505790816356696, -1.1951406413332304, 0.2177761503067999, 0.5763790136318692, -1.318813022952849, -2.89914749394426, -1.616200309391746, 1.1677245051003644, 2.091531755146682, 0.5765619957138949, -0.71317770228278, -0.14623636385506694, 0.6855974639418362, 0.13245014258176152, -0.450479303111179, 0.8100037352880404, 1.986554656996038, -1.1510963115123727, -8.598904222313177, -13.980913291061576, -11.313138207507649, -2.551689646212932, 4.288334559124745, 4.357434159260621, 0.6833029403418085, -1.0601012382581907, 0.1938722905581295, 1.1527468785869472, 0.048652244323544605, -1.053282286529214, -0.17280598974225195, 1.2910443701945449, 0.9570354766655212, -0.6892891152718802, -1.2260781012806847, -0.2609775770365594, 0.18679578817050288, -0.5062694148997896, -0.0740161206326709, 2.84185235818532, 5.509781103868262, 4.298270350872663, 0.1803926168672773, -1.9158363390075603, 0.2691058118545994, 3.143029269838566, 2.423579015717304, -0.6646798798111208, -1.2275083562388607, 2.066821043692897, 4.96931530034706, 3.762161019573883, 0.44312541168840364, -0.5381589592389472, 1.1053337750279326, 1.4150042035099386, -1.4816953712180687, -4.293197035033475, -3.294569655638765, 0.3072635699494391, 2.2167757235069523, 1.0137292030454563, -0.5886928080327305, -0.3617675484280143, 0.4815631253379064, 0.10735963148337731, -0.6150370651977075, 0.1322566083430905, 1.49763381101666, 0.9678892247843431, -1.2858286893811242, -2.1185375903146366, -0.43925579589935193, 0.31184235588650855, -2.9088219368165484, -7.226356597674878, -6.7470884423282795, -0.8773846803149185, 3.790016111787707, 1.5534863178289884, -5.028802397966309, -8.5206339535047, -5.924681167763726, -1.3693760530242072, 0.38736017337275297, -0.3506888248788886, -0.5646561750687114, 0.2821072195214184, 0.3866300616808701, -0.3398306409639731, 0.17218674075179113, 2.179316446369634, 2.794722401449439, 0.22696667277570615, -2.925559848312239, -2.981172151061073, -0.4166333372806552, 1.0119074455889885, -0.02850268111183459, -0.7807880640036092, 0.7309401939984831, 2.2302385458674134, 0.9101363397689038, -1.5261903931764504, -1.0037455625127485, 2.3167311313685537, 3.3777331279234133, -0.5977475227011302, -5.494454614164237, -5.563678982458761, -1.317245780230387, 1.348434586012892, -0.5464454416815073, -3.3818820452801, -2.7443110026044875, 0.31612376255658886, 1.5038811362620912, -0.1981845554826615, -1.670813368225409, -0.9374609900336365, 0.1502480054708979, -0.46708203224850026, -1.6403168170389308, -1.2908840297995678, -0.08408752735961614, -0.10753088584789772, -0.9940607925629913, -0.556255678441038, 0.7638490499616394, -0.36621334979389886, -4.457198860192436, -6.366306003273953, -1.3739182696670893, 7.460493099044513, 11.813963266407393, 8.116513985571935, 1.5476684224573751, -1.2735491649004371, -0.3252489690080045, -0.15296093907872432, -2.1477706928694125, -3.0443153256259325, -0.9493371866130379, 1.2998636554436984, 0.6005675043410287, -1.6295478027670334, -1.9520597319228437, -0.37354089836992477, 0.054125333436306954, -1.460374922703677, -2.0985495258623312, -0.21088846443164644, 1.7426151149247895, 1.0431194152824421, -0.8850433933231063, -0.768047500011926, 1.2104636335459993, 1.776073463183932, 0.013584942452224878, -1.158515104647031, -0.07044188116123738, 0.5984126706039812, -1.556238510562231, -3.533889781641095, -0.5071609205048473, 6.1764475955377405, 9.037076044865268, 3.9376050715275057, -4.046088987819363, -6.949254532842543, -3.698712517546187, -0.05927637871324047, -0.02898427411842156, -1.5042344715470626, -1.1491054053534506, 0.3974844081031592, 0.6080780844441409, -0.33183977035431794, -0.2937595771967899, 0.7090145569007946, 0.6740963448272399, -0.3178086575560981, 0.3247072058505607, 3.0776611890625905, 4.479205619710523, 2.0761890935465495, -1.3545709308393277, -1.6168931724082864, 0.4815944276749915, 0.4245819545876185, -2.504135302463366, -3.3627373108080927, 1.0192144097068798, 6.417434520627077, 6.449914643481435, 1.3507349518098317, -2.5969894203108423, -1.8606237834509856, 0.4183801228987465, 0.34582538948097585, -0.9747953573111533, -0.470225071917307, 1.0174020378042155, 0.005328850148323242, -3.432000909052592, -4.995719196108882, -2.45205285470507, 1.0114054471746177, 1.5501734300801182, -0.0794618457467394, -0.6425575586407883, 0.2948255132693279, 0.5585977866973961, -0.20408051514009812, -0.09475885339155164, 0.8137059247750796, -0.28326831204823477], 'positive_zeros': ['0.75144511218907808715123670946', '3.44369582387785349158488888678', '4.64079134452126436754579336874', '5.27829612367562292396214143499', '6.80607871643649187455056804214', '7.65622954919830537507490444757', '8.680818233515473494717613372130', '10.070228540436274435196991784106', '10.81118306128469573909431929173', '11.80740823712949216603285580270', '13.36370351383114405410057426235', '14.603129252820837024622487126087', '15.30874718726258385397620526439', '16.04565614134231816973356395699', '16.97337083860282877307031919723', '17.88637926324249127360698574446', '18.693771302913230761836043820880', '20.04559809507008588323983709212', '21.04019836575447338981933675902', '22.27879291465328493237001284126', '23.12867824255195188587418060289', '23.62718470014718098988477791811', '24.52851965820076864354295545884', '26.046880934116053612710391565887', '26.71417990975474635255623291829', '27.184890468484867404145449566063', '28.10617801111127452730610045762', '28.93711554982116857880016586240', '30.480161586019079875704516388349', '31.34018566773329654040085973070', '32.193202730807861408552148525893', '33.305573946974560201334458318544', '33.74085558884710729654873351652', '34.604799304057092054964586019684', '35.18994195610873440536953079340', '36.34839395635427605920170014839', '37.23562404017177943228988883199', '38.14781031277969676025117817523', '39.47912926313846143216434518585', '39.611978435186157690602615504804', '40.93027445458372176007488616461', '41.7633434299084068382825853767', '42.88456268684981343892335950741', '43.36612302196231455223888229652', '44.09644238023279214531449430562', '45.09055801676606235568761626740', '45.74947052126739059738747028797', '46.6625525571131962640558992299', '47.04683305550950427635886405724', '49.049395861485955537130599288604', '49.683662605506828274487052995917', '50.44626169018999423784030235012', '50.74385261491200817071861671821', '52.02693822862441540755688415645', '52.382832492166566335477060451863', '53.51191754711702015387619673952', '54.39449815007320157101071222860', '55.10942734479951580357486654837', '55.748109824952488020767069601343', '56.76651542689149765257838762784', '57.766711425612083132684591513915', '58.5827194144243191474788212922', '59.411055207570190366110495341021', '60.37815577679600203061764732480', '61.07454483221032618757370438299', '62.04671091154805958409203967682', '62.435779148314678768040623865434', '63.0443866587270914405281065094', '63.6873516314229649251301330067', '65.23288408147941427655221170254', '65.7265942232841932745903571379', '66.984039534189641670438448892690', '67.44387333703008593992529671762', '68.68793718295190267021917489790', '69.01028162553997661501827465950', '69.720438346740301883492747622305', '70.71046293442457180795172599478', '71.42499560537905591262067762490', '72.463788341644675931998508106656', '73.058998183269950630958696200564', '73.55593985034592131391348345144', '74.44328156556518082169122010927', '75.38861690276431577394487233308', '76.45149511000988569596488722339', '77.61563504387175213568021279507', '78.044879995209653793606474487049', '78.83746415931256132572571597921', '79.14483917546449191504138861984', '80.25774274488503800736795752313', '80.941616163361575654463664625780', '81.69449043794163489271537295471', '82.27994591319435725752412913482', '83.346888514324610331282667581622', '84.396287853957443358647251903566', '85.2706250087060461397267298893', '85.819813109081942449590259862756', '86.383378859043784304228231699605', '87.2751060838182736105321895404', '88.584060491750741471267069089218', '88.92335216779358212738857321519', '89.52974043384677156123897312664', '90.44711584978219965088027428603', '90.98076717765644105376649630762', '91.820630499457723750137146645551', '92.39750218818666851031214670387', '93.73193064065581017368505772821', '94.80307454773343148992306223248', '95.08195639287310059109306890997', '96.151709031898291630617583066318', '96.96685157844990503835643537263', '97.228525164834663429517849329531', '97.98336432108411381195122608469', '98.74024155678665090796049975240', '99.6730065591228634182320053558', '100.76799413923377510113252328907', '101.15663169064868174225228513949', '101.797352200934048066998384647868', '102.72405641600171686001933771130', '103.86077218249986738104370031170', '104.48402582220446516933857906088', '105.25358165974166389998460580894', '105.8338680982335730805284553943', '106.91695370805463772087208635193', '107.47476926920972096611301559170', '108.04121435222251713662518187534', '108.69161153122476950351060449009', '109.48672629249468260573105862891', '109.995486658307930186616900740302', '111.30203522795322970009492131624', '112.46896512031155392500079425327', '112.834546021882903321432224899849', '113.66930751557703277007509516781', '114.24588533009257402424269786528', '114.85643269537708260094251349868', '115.722483803633489455306969377569', '116.56726928161118216746578855194', '117.45647046851355744771377388958', '117.82408508210577751134453512735', '118.46411153561218024350417807138', '119.53550541457498576527675060186', '120.2948325248882020340202324287', '120.90427102109347436275846909283', '121.69900896600936083856544234169', '123.06218310523476154134089844242', '123.469077114943228758744665813263', '124.233698049470657961053415331020', '124.82545895640106991679679919027', '125.33333574183005688650086670659', '126.038211626228433854653255891724', '126.93147869108343775394019813499', '127.53570636556365599730229086159', '128.52997737343838172132167215035', '129.187696607752559152020574271372', '130.251807279606974788735085230358', '131.17133443561061845482477817584', '131.29509639682247785914727939250', '132.385757359398575487985641681935', '133.07890010096915794091812586244', '133.5641945127708573236307760292', '134.55111803043273700980225734821', '135.41180874315143407658233799377', '135.97745664039700559835711028787', '136.60345857263296870561693519128', '137.0408117516728570611897306409', '137.745344444254567696991227561910', '139.153694532407055303294897938740', '140.06830801853385179058639239029', '140.590281375783854030501998624', '141.25935552979916568657025145605', '141.90714415914194794922129772160', '142.68149335448386973051865363881', '143.52350089372907604973369843397', '143.85898376042424594996716377688', '144.387602298831354160835060562423', '145.639485727383419706803222708436', '146.22545393388597370959501357502', '147.11491229445306787711405811191', '147.64561500442536167928049552752', '148.806820048374542261471104880069', '149.18977938029332034007097085635', '149.869274432313258310148954202974', '150.909972587505141607131738511922', '151.72762565682771574925691607798', '152.2990574323588208439896624299', '152.84826462193411729698714346282', '153.40865911457590714267643048265', '154.20356165815483847332669270459', '155.07405333133820911857908188276', '155.37369074709985336772409822934', '156.60438406945565049171497171376', '157.2673472016705899247950126483', '158.59931220628248591948735810980', '158.949869588902350627987684429829', '159.58634826519225260237923525330', '160.15980659310563930208852213736', '160.58740189352756809122100955045', '161.58212133263058382896189238722', '162.55270231326560903296298097089', '163.11910016664403652099009066982', '163.63898596387421920382302162853', '164.4796439587343253880419856676', '165.10503703692208570007403181973', '165.90355495115570789734948357986', '166.976165514135637277087324793549', '167.44691343506730996838084913413', '168.40295905046331454993553199520', '169.03465328847541905875363105795', '169.920188866795165028296896841715', '170.18077086258872124523681099440', '171.28556751196534275266151380347', '171.51525119326137974373332655372', '172.305535432936510812027681794757', '172.77185090580126784739237723875', '173.80066992275844198833789827263', '175.1061360283031035770705300520', '175.72392895104154733053529653688', '175.88870198262363101475805117492', '176.979207083191502481154654537176', '177.583081614363695665867018221401', '178.53162663565568737022489234050', '178.76935636673011159911714494178', '179.71319225794360732882694849934', '180.46862027901850620027014844727', '181.06733719011711137719742235409', '181.877055612961288857878421790954', '182.5142488136600655161093017348', '182.94330902189308925259653578878', '183.77648340016895881208108972325', '184.83398969393825947022082467138', '185.94729831670108346940017695555', '186.24361470362408472766593336346', '187.097250509169235387851057333061', '187.69857734531489196010412880433', '188.22110832213219483935136838782', '188.94894716143132574144521496905', '189.31776301119621069852263322862', '190.48323934750820454154486279313', '191.17340695533570034696985545286', '191.62067610310801259486966318697', '192.446670338765770155003296487678', '193.515732107998349546163908129261', '194.29914309796869983807994878173', '194.76357211394080716879764067423', '195.39991327309148667261023750631', '195.9381092031514943655578510644', '197.07762165674380261404151012860', '197.796599685479277892817987608679', '198.34869723194354061507697696667', '198.9770729254379562342010695897', '199.40762017921065289225798743919', '199.965143435152416537491200777627'], 'prelabel': '1-221-221.126-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 23.74974837961213, 'root_angle': 0.33766657754469437, 'root_number': '-0.523390683606822454215977969766+0.852092830807525966646142559393*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.337666577545', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(48)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.513945680090153964369828384123+0.392164782311582080869589440120*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.751445112189', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '3.44369582388', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.64079134452', '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': 23.74974837961213, 'bad_primes': [13, 17], 'central_character': '221.126', 'conductor': 221, 'conductor_radical': 221, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/221/126'], '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': '1-221-221.126-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': '1-221-221.126-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 23.74974837961213, 'root_angle': 0.33766657754469437, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.751445112189', 'prec': 47}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_221.126', 'Lhash_array': ['dirichlet_L_221.126'], 'factors': ['1-221-221.126-r1-0-0'], 'label': '1-221-221.126-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/221/126'}