Lfunction data - 1-643-643.2-r1-0-0

Formats: - HTML - YAML - JSON - 2024-06-06T07:30:52.052534

• 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_643.2', 'a10': [-0.3588247492071359, -0.9334049492885904], 'a2': [-0.6365186386843249, -0.7712613192734703], 'a3': [0.9789540272387628, 0.204080897080074], 'a4': [-0.18968804521490776, 0.9818444100276515], 'a5': [0.9482977734962753, 0.3173819982009171], 'a6': [-0.4657227828320636, -0.8849306693471295], 'a7': [0.9845231970029772, -0.17525431396412755], 'a8': [0.8779985913140924, -0.4786632152677594], 'a9': [0.9167019748939845, 0.3995716321580758], 'algebraic': True, 'analytic_conductor': 69.09994664294389, 'analytic_normalization': 0, 'bad_lfactors': [[643, [1]]], 'bad_primes': [643], 'central_character': '643.2', 'coeff_info': ['x^214 - 1', '0.999569006226998 + 0.0293564607943608*I', '\\\\zeta_{214}'], 'conductor': 643, 'conductor_radical': 643, 'conjugate': 'dirichlet_L_643.322', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^137', 'a^7', 'a^60', 'a^11', 'a^144', 'a^208', 'a^197', 'a^14', 'a^148', 'a^151', 'a^67', 'a^49', 'a^131', 'a^18', 'a^120', 'a^15', 'a^151', 'a^69', 'a^71', 'a^1', 'a^74', 'a^160', 'a^204', 'a^22', 'a^186', 'a^21', 'a^54', 'a^44', 'a^155', 'a^196', 'a^43', 'a^158', 'a^152', 'a^5', 'a^74', 'a^9', 'a^206', 'a^56', 'a^208', 'a^143', 'a^138', 'a^119', 'a^211', 'a^25', 'a^83', 'a^101', 'a^127', 'a^202', 'a^159', 'a^22', 'a^109', 'a^34', 'a^158', 'a^162', 'a^191', 'a^76', 'a^181', 'a^207', 'a^78', 'a^117', 'a^119', 'a^8', 'a^180', 'a^60', 'a^81', 'a^87', 'a^75', 'a^167', 'a^142', 'a^153', 'a^211', 'a^117', 'a^146', 'a^29', 'a^129', 'a^145', 'a^193', 'a^61', 'a^131', 'a^28', 'a^66', 'a^18', 'a^61', 'a^26', 'a^42', 'a^51', 'a^134', 'a^184', 'a^162', 'a^43', 'a^6', 'a^203', 'a^24', 'a^80', 'a^50', 'a^80', 'a^125', 'a^165', 'a^82'], 'euler_factors': [[1, 'a^137'], [1, 'a^7'], [1, 'a^11'], [1, 'a^208'], [1, 'a^151'], [1, 'a^49'], [1, 'a^15'], [1, 'a^69'], [1, 'a^160'], [1, 'a^44'], [1, 'a^196'], [1, 'a^9'], [1, 'a^143'], [1, 'a^119'], [1, 'a^101'], [1, 'a^34'], [1, 'a^207'], [1, 'a^117'], [1, 'a^87'], [1, 'a^153'], [1, 'a^117'], [1, 'a^61'], [1, 'a^18'], [1, 'a^184'], [1, 'a^80'], [1, 'a^186']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-643-643.2-r1-0-0', 'leading_term': '3.29851943114395754806894261157-0.121753583094046123954425242021*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/643/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [3.300765725196275, 3.1242267262828385, 2.2386805386012414, 0.984797855765699, -0.08838751697063355, -0.4838300593008498, -0.11638159874025308, 0.5438539629790395, 0.7691862142137357, 0.17736647878496642, -0.8370798233986988, -1.3028001106913256, -0.4917186045319849, 1.2542708583470012, 2.4866911931626285, 1.6637667536450949, -1.4578560901781459, -5.247752591108691, -7.148370510405921, -5.592386231869467, -1.361532862644949, 2.8599691825055094, 4.510579556348015, 3.0992852471256778, 0.39752143359818376, -1.2679171633123762, -1.0305277845660763, 0.04342962646710562, 0.34904726262186236, -0.5168920252654052, -1.4765926976070185, -1.3599770071221038, -0.345610336115684, 0.2242487637162281, -0.5055842799279523, -1.6948085498394498, -1.5804908776145028, 0.45838453427177567, 2.8714344569927706, 3.3211735817099837, 1.1732652912800354, -1.6563326193748764, -2.6171281955366275, -1.2300679635781766, 0.4553242324620952, 0.29878609053608085, -1.2890013720026618, -1.6238071956018902, 1.1484064405441057, 5.567183642994823, 7.985409905115283, 6.308672064363716, 2.2701730722472937, -0.3512864866565574, 0.349822598504146, 2.6706021685816537, 3.542515811056771, 2.0074109486841767, -0.06617059491055696, -0.5784718007816272, 0.265591306538457, 0.5338991653290441, -0.7158900747036556, -2.1855839042929253, -2.1151445123235963, -0.6412290258152129, 0.44740217211404254, 0.20035653699672668, -0.2474047725662079, 0.4306631955169458, 1.236719998976441, -0.4783146686095595, -5.353330635968956, -9.958105510095917, -9.662105974560788, -3.762725525469553, 3.145455961422641, 5.622179978200087, 2.847140778026994, -1.0622317448563872, -2.002902561372961, -0.11677306679987143, 1.404230160015846, 0.7734328639465685, -0.5308903927101851, -0.4368440878764934, 0.6349910026637247, 0.5666760877536403, -1.110961563655854, -2.2315986219750714, -0.9130505924169839, 1.6526867632655065, 2.5490327472454717, 0.9262798386462462, -0.9433092107825798, -0.8168806180784078, 0.5405722302690421, 0.7086213916443385, -0.6801390529194693, -1.2994818356482014, 0.33117867880136637, 2.200386694103581, 1.2482536531614012, -2.085182420984308, -3.699203673263306, -0.9440913663650041, 3.5735512464058803, 4.907561880838726, 2.003704425342602, -0.8767653609450106, 0.4245884008366842, 4.671891090193816, 6.87787869655639, 4.554896205750618, 0.42437901523998134, -1.469302209755091, -0.5834896348157386, 0.5299086579067436, 0.3416800533229031, -0.04374084369726102, 0.4983582632568784, 0.9804233247322092, 0.12832537886873793, -0.9740897756902875, -0.13143609344083526, 2.263827304133321, 2.9582918348116203, 0.22911995889442166, -3.162551043582136, -3.303763783029239, -0.6409201861658168, 0.24792157800139084, -3.090530209680865, -7.1829102665843845, -6.884117662020003, -2.189574478110697, 1.6756946551268461, 1.0205501123166119, -1.9302472085436653, -2.7047830002291735, -0.706204864511554, 0.7407904743885227, -0.21588482122118482, -1.390264866692128, -0.3208616937219548, 1.7340123045562539, 1.7229140541943888, -0.40877678346711144, -1.484152842450611, 0.18121988394432362, 2.271472270770976, 1.9403341436562347, -0.08027759200874214, -0.897738785724954, 0.04386051668424048, 0.47229863354384066, -0.6359524615923036, -1.215529822810543, 0.29728471952946195, 1.8522528344970985, 0.9253352664407754, -0.36625912812556893, 3.1545301165715687, 12.12405913407706, 19.640439047485714, 18.394499659795265, 9.367841916501622, 0.6448465810044589, -2.028000353664884, -0.5355921083539238, 0.3280007273961222, -0.36403879461412303, -0.13691125784843766, 1.5969713260878846, 2.3575020121391947, 0.8478662533485413, -0.7924946485901357, -0.42008376382324075, 0.7826822590611648, 0.5519487706545657, -0.5152707102271322, -0.07542925869481347, 1.5327655852797366, 1.2216566857043718, -1.7433944481018544, -3.647587504179179, -1.4480808787099146, 2.2477169958283376, 2.4525320502900994, -0.934398469273031, -2.782318441995902, -0.18324015280822498, 3.3303124389453718, 3.1443122958435548, 0.3345548178543697, -0.40325666405499183, 1.7275633341853487, 2.3905315465553607, -0.948706433335841, -4.73644097542382, -4.373743873760577, -0.8627332899202731, 0.9554028232980357, -0.46789477875775565, -1.7855166421850552, -0.4682430255861929, 1.5284638579920184, 1.4158553331749626, -0.03738381109930104, -0.36529834554344837, 0.3009409830309637, -0.00027173823083762413, -0.9453668098988023, -0.1924496212317758, 1.9873483839518549, 2.0755118647382047, -1.0721971834432809, -3.350869767778162, -1.2205836523052291, 1.9997469711435145, -0.03258242758288799, -7.168695116440939, -11.78688921250287, -8.733538930858213, -2.199916333297607, 0.2683165215371269, -2.3081309525259757, -4.4719137545969385, -2.930722851875626, -0.3012097639233993, 0.2416043203021271, -0.37835398508575496, -0.03388047797552038, 0.46939071539322835, -0.5528832190573079, -1.6361656231680828, -0.08180874661640547, 2.934630630403192, 3.201767151847076, -0.15553265861665436, -2.9459811883638856, -2.0202029699604886, 0.3465609045364667, 0.6305682885276748, -0.4015300522312726, 0.024885120429812786, 0.9372397821798, -1.064759691969311, -5.037052187482064, -5.393846171152573, -0.14816848145554393, 5.018442681584842, 4.285363190181778, 0.0016930491529328203, -1.0187004555358439, 2.342183661871657, 4.364939245786336, 1.617369161246448, -2.1032228860535156, -2.093558494514906, 0.3503646947509934, 0.9294717029408156, -0.7035929196776127, -1.330210414636035, -0.06579089641400773, 0.6575910095653351, -0.07314624475326137, -0.1424629950203087, 1.2893030312200995, 1.9223232447429761, 0.5635106050311409, -0.4533069655089265, 0.18332674178826308, -0.7588139932445954, -5.873632346158329, -10.824835909888114, -8.708196531268785, -0.33440190188134106, 5.471717636247157, 3.36988952982087, -1.782269939389959, -2.692402497952239, 0.331051588738672, 1.7349366560509574, 0.09353175738857311, -0.7761865002871713, 0.7270769197322918, 1.433329832788552, -0.399039394961544, -1.568064950693289, 0.6082607491317734, 3.422503830982865, 3.033713465366339, 0.5944397303307556, -0.0628181202861068, 1.1705049125886613, 1.258496146074826, 0.04288219597379454, 0.6448599312393636, 3.459397760795314, 4.684091608395222, 2.473134283312132, 0.054825844470386915, 0.16156525569555147, 0.5858248546303418, -1.007664245779649, -1.6624052852813662, 2.1126836076663396, 6.553115713903607, 4.2595750575126115, -4.36822756798023, -9.923040016714493, -6.40263427101351, 0.861586018832059, 3.3409580339159977, 0.654996953884369, -1.262020142819298, -0.060170500711453204, 1.095968958046314, 0.34394479625568664, -0.23727395420421687, 0.5041625422369409, 0.5812686328639942, -0.7728882310056651, -1.0983189192277716, 0.6512084872383098, 1.6165974348072145, 0.1063143275069202, -0.732523569472708, 1.8271988247742064, 4.551332827386402, 2.9205339265608936, -1.049565222277228, -1.5446047746027203, 1.5419402550457049, 2.399093574492745, -0.7071753357203423, -2.026819310161012, 2.2196483825540287, 7.026113424063289, 5.976557905148484, 0.9108039521390394, -1.573007443883462, -0.2847532708917635, 0.36185689094317053, -1.0821836468897028, -1.2548896140990524, 0.7491075668169944, 0.8736875753763947, -2.789382601401368, -5.9442985906055945, -4.567188116029832, -1.008549389512036, 0.30418158788979255, -0.3884195811897509, -0.1522657226952483, 0.8585003249091594, 0.5413789661611899, -0.33304289730764275, 0.2800660561331306, 0.7317354371862103, -1.8346560734391433, -4.659621196030901, -1.778417167568032, 5.696229425330461, 8.750442688617694, 3.0737656261304944, -3.9031633121117406, -3.482598943591944, 2.0541951093275883, 4.075538453813447, 0.7832800180410214, -1.8066325614361898, -0.5801992566784084, 0.8185213157744844, -0.3550833382664475, -1.5020922115222963, -0.3065650043694798, 1.040227587137477, 0.4041824517023761, -0.39520734305747346, 0.23297059467211859, -0.020548327518274064, -2.7926814693178, -4.751317323853454, -2.6338820736514084, 0.7109005930060165, 0.6905560633980878, -1.270035193593726, -0.45082065180740777, 2.4554217598722, 2.314101472931372, -1.1319753380669832, -2.294218546768281, 0.6463207055063198, 2.501077295174494, 0.31235455242386845, -1.2341904834802335, 1.7239204681586806, 4.5695972918844925, 1.4223448632617899, -4.5304108303935084, -5.366607438098207, -0.5343540310764682, 3.0132879273587885, 1.8774327036289749, -0.11187312056847773, 0.15405423449746083, 0.6007707231741123, -0.5518785623416409, -1.1613219566276713, 0.09450982905634948, 0.6924849999418806, -0.8221980832077145, -1.7089958111999233, -0.1978825744204187, 0.927415332535511, -0.26345703596162595, -0.6824332407561031, 1.7842101409163231, 2.976242577111461, -0.49321932502955745, -3.001856762922701, 3.081540003074168, 14.21269795428974, 18.440239778801814, 11.656513061521368, 2.5415250576214024, -0.5785567358487581, 0.4571844593334244, 0.49036344668829945, -0.038758133555002315, 1.4057048120988282, 2.930971509246295, 1.626836818376693, -0.4853310910463219, -0.04721644531797119, 1.2377501029803972, -0.11872422319223835, -2.3580044822723694, -1.179793460665707, 2.3449421734240703, 3.230112347948498, 0.9485223806753875, -0.3535577649024358, 0.35858472431578625, -0.06602602223438371, -1.9116799469663959, -1.7067861043041557, 0.34629006991125233, -0.4368995686532259, -4.1981103471923005, -4.439107570205355, 1.0863792304231694, 4.898934377919915, 0.9656484105567129, -5.235200630738265, -5.092782415139055, -0.11447501669246472, 1.6291657471312606, -1.1475449272860685, -2.3021127135528765, 0.3918064158536054, 2.2980597357058854, 0.9008860123365823, -0.4008033973325429, 0.7170352835560251, 1.7423755615119472, 0.843910369066287, -0.007010293396022357, 0.28971551636418397, 0.00951898887526038, -0.49566551681611515, 1.8667806780594083, 6.066786381899044, 6.0840877443132415, 0.584731724504272, -3.2555522597037014, -0.47232570338225766, 3.6748912645468224, 2.6043216358959835, -0.770363592213599, 0.031479957728320525, 3.196862555758541, 1.9570961666397602, -3.0896072459284585, -4.740546198829787, -1.3982461913178967, 0.9298517243335152, -0.5562561785431651, -1.6415682042189608, 0.06637682215922017, 0.966825283332365, -0.9045023269566002, -1.7681202092276507, 0.6097308756619546, 2.372644952530095, 0.5423449859229255, -1.642515891817256, -0.8622458689560626, 0.5138162121154789, -0.4198049274917225, -1.531661839668758, -0.31849585223837745, 0.9221158340188778, -0.08841546997550406, -0.6721193096308682, 1.1585055187573006, 1.48582651839394, -2.1153025622777815, -3.2811985002006487, 4.155263190672784, 13.856233385330217, 13.94945195060944, 4.483598468912863, -2.6385778022645097, -1.1582341571738906, 2.620349030606343, 2.1561302067516754, -0.2369425625444992, -0.36603665032378246, 0.4995767960094965, 0.09450273256985786, -0.027593150756820548, 1.1099372317449485, 0.7124652220384544, -2.1838519321545946, -3.6021715940936434, -1.3389492423541027, 0.9042584712476013, 0.3345121364451849, -0.0183533197410198, 2.084104647404403, 2.935021431672982, 0.055573704642113406, -1.7765430929306456, 1.4882479126922785, 5.004871908543691, 2.7665962289910047, -1.6267248168825237, -0.8735581710915474, 3.454972661790146, 4.01960757004153, 0.5843042074048647, -0.5143793713919467, 1.6446097874202046, 1.6697447196970407, -0.9581633006373422, -0.2864392192619488, 4.822173683244204, 7.575601406342164, 4.325150210981847, 0.04917252517608809, -0.6184282160131531, 0.10910974402631465, -0.6562264689371069, -1.1717925759215895, 0.04678653277740013, 0.6498510729373991, -0.3954662065340705, -0.31803944656112937, 1.4347725065028538, 1.2830185620585068, -1.1909218567775872, -1.541067450190915, 0.21354270461900735, -2.8236988534479077, -12.063034292734107, -17.46268440624443, -11.460291944226265, -1.1024140564879106, 2.5353500498943684, 0.32300128215035867, 0.5590994710805439, 3.9498037884018977, 4.217730287325204, 0.5639858465705909, -1.4171209782468237, -0.0902761003552455, 0.6655034355859255, -0.2318112531516341, 0.032006218654987095, 1.284168022017644, 0.5992037901489822, -0.9681077898244999, 0.12073950290716222, 2.215753380801775, 0.5287359268321175, -3.593562857706585, -4.0077181893625475, -0.3021961452456931, 1.7381455215848232, 0.3768910535095158, -0.3484148401391236, 0.46657500642934985, -0.49193255160233584, -2.0654156313141923, 0.8763394313997497, 6.404306111435081, 5.816417603910188, -1.8089092009315852, -6.178288241516283, -1.5571986074437798, 4.449347273392401, 3.8061778404433424, -0.06672655612896398, -0.5003118847976296, 1.0441270987002047, -0.014669108350763573, -2.0452492118398284, -1.1901084231726895, 0.8140055901592965, 0.383892510652869, -1.0470490059374946, -0.5830299203617114, 0.34441212787539655, -0.2579947862969326, -0.35143929458958756, 1.3337999612532208, 1.5080971279617232, -1.0188600917388906, -1.3808216426673958, 2.351308830964374, 3.5393032253194696, -1.948207788716315, -6.507453899871463, -2.1182383279486365, 5.755406412637337, 6.376442254129613, 0.5292217946965436, -2.4012644787148236, -0.21120776050493761, 1.1066802406057406, -0.29984773196726644, -0.4187542283399372, 1.0989811951039812, 0.5101515061800569, -1.3318333820461201, 0.12367305005577393, 3.774292966512961, 3.939487646119817], 'positive_zeros': ['1.216761271005851941682048818139', '1.93048012134960747028644803268', '2.86933621699144580155120726649', '3.8467346488439734209120020112', '4.87504030443867294744994210399', '6.34059763416136745542558134059', '7.55187875772665539443352455157', '8.42275890117818533951142524076', '8.912703316076978779871742606844', '10.118742756213689201855254339745', '10.47306296768302043428241280949', '11.50697293496855424409483868512', '12.62101884776769884201500715673', '13.64041359907075945229234763953', '14.13083598026273548617166472059', '14.90546559813701783525609746724', '16.48502419278224763903695564961', '16.815965695227379452354050643724', '18.11150124117498582438459718082', '18.66296325867192006471366164067', '19.23311232019632588934087720835', '20.45266937142691067601617610620', '21.03222497612249220290193568897', '21.42858475181834429150825103351', '22.1417993760302175252488629601', '23.59536482121834459616351259875', '24.58730218865585877684175069433', '25.32873760696785876341265543199', '26.1028990634668957683529438775', '26.69013345428604376603069745561', '27.314054926833279326320772974067', '28.23510167196024035655450555424', '29.19272387479388604997413288029', '29.87210237293918636594822143731', '30.48869236513013102193613165190', '31.20498020506568782210827987312', '32.001152479510602167150362003122', '32.87605441807798591743926681802', '33.92848412430462388373779028928', '34.33415845154333329118299653997', '35.66499687933735528631046392352', '36.37877505016466957672051601484', '37.08187296216533234909133686225', '37.25862208670577733916301211110', '38.153936208443339256154582313278', '38.76981761192911413893326442659', '39.706112172955637768763329872', '40.713984735139629864575297941633', '40.98385643475298932359171085774', '42.3284913808258431285024290756', '42.921398921101518278992248457772', '43.852021373511485364409106960203', '44.333385419695788020341089889821', '45.04631971322430050659820657086', '45.88138824115863046525451241749', '46.53962812750226416834386014549', '47.48652996715895845116314176349', '48.11283341656178737943935234036', '48.60172256651552321868286360824', '49.33078626306521461039658101823', '50.15467418181615796960721462829', '50.40618454442624223566971426060', '52.22336003645801445281085676801', '52.92119746009692415310098157421', '53.296072231894907434903487098799', '53.78244749658679809544010044576', '54.81767019760408309093341699270', '55.410726552937593582158883810586', '56.08395931591852762983312488939', '56.5785402227146146599373848157', '57.334845069115587150114657517307', '58.23747459121635983756063850384', '58.98423984201994388645714568895', '59.701608828734175733772282690448', '60.67144227944031537479831857149', '61.01910450893226281400965352760', '61.80803607408271592441059398550', '62.90052920360885713819594575323', '63.36720354058955962852886643005', '64.12576924675368971869381530336', '64.99025634727606678856485346263', '65.47869600884021652554393356960', '65.93741282851255273711455383963', '66.5928347917154484851433646143', '67.409440178969617949555212223466', '68.22276170760175889434069704698', '68.74812274053557529506913389911', '70.18076149414514075140541211594', '70.38013653002835867397410653479', '71.62333953261739070177115386172', '71.9901725806794462369874351895', '72.51306668620281000092311212072', '73.007200674402747443387511589638', '73.75870226645719338151877061954', '74.67524266282374172511648357279', '75.56685837199630706995170917652', '76.11284541276581134749368702546', '76.55621172012639087528492646855', '77.084659158231399626737099729300', '78.13206113953389367259639414945', '79.06264728845990956324292695915', '79.49599892054375990056931394148', '80.429553955372060165246355585226', '81.200797480560322798615298755114', '81.75323603692985715042172449637', '82.5143788187595247679692410003', '83.09820253866422539242428278101', '83.48221125802285284426504016088', '84.48742567713085614913974443981', '84.92605575626653315923398938217', '85.2090192211708561657438028575', '86.574568143169787635119768959027', '87.37948817447018683126043679360', '88.09220611840124776284040152319', '88.76501632029598124454920729017', '89.25208493482444948272890300416', '89.945923180047127072751031561112', '90.56584178312067813906638454328', '91.68319459539803577396969658824', '91.89947197838088053422685065025', '92.830459211707051487480432691177', '92.98661685868323948687837209110', '94.39032962021309671487138935204', '94.62963007622386466819117126924', '95.152589583022638151161086708174', '95.80377203957426033098436683994', '96.72731921062900304402369249187', '97.76909068470877178189692744162', '98.50335084467985932291085173607', '99.07269637993728947688694893400', '99.79138757482168449582599425350', '100.13665875103526777444499439266', '100.77511386047009997106541880211', '101.46341931578130094010316357075', '102.204664330792767004151448238887', '102.63408305820692317284349846221', '103.65673531031188254456310657123', '104.23002469316562249629073395280', '104.93821827535034203705302584176', '105.499802069924703030331704555027', '106.62862327264303335147841177311', '107.2424107411248901824068576412', '107.60256185158175107034322698679', '108.32726066708317758471041321985', '108.85077582817718778030997598401', '110.14465298672341448301844279581', '110.470523976076731215383252928540', '110.98243343817685835992884307227', '111.719646506100056094189740338', '112.10905891424131844227189708068', '112.63520735283495496861568593560', '113.517905840424527871327428130547', '114.49187704987874971241874748431', '115.19755639669529171315218606036', '115.99991134661228544713995361843', '116.6484984528400747298373704609', '117.12678564511354054937648164736', '117.86369443146810953038099654283', '118.543363460669200330019690031849', '118.97704202024739789302693501389', '119.3710804669592195312707608284', '120.538981143528860811050860848624', '121.04084086275796254776037146025', '121.61262088808458274355000795462', '122.40137354882495793673660367584', '123.06824231840643377609380463150', '123.78290356951168012914981815663', '124.23909943832526752939202208450', '125.07163959789457761924079919119', '125.96883313557819523521884847267', '126.84147329932304796475475266209', '127.13480364700320279572650720900', '127.6925321573145876589289428782', '128.418045998983323365614960933705', '128.923860509982336489091009553168', '129.719051424082269137588902280969', '130.26143283324716781127094525270', '130.74120890884866356772796954842', '131.52915862135214932445229221273', '132.08252060981446721199706650827', '133.60691586416100498692194284360', '133.948626008114498621879668173043', '134.57203187323851695482343186307', '134.71530980177927617001754437292', '135.83835384633469792477387242019', '136.259215769667299073759206479203', '136.860548892997801031998371045592', '137.60558839480712296314338839535', '138.585050396119861955358379700830', '138.93231584117637737645005688867', '139.36166168159006038310067716448', '140.24777525630055438875743001681', '140.57426785102385849132180340123', '141.50991940214312450067921359784', '142.23091828996391633285191860346', '143.13304843785522206960367520241', '143.63969198843714481867411329047', '144.337806836098575752627945343466', '145.14935587031401847388458946662', '145.483810109970548248051561811404', '146.54910345922626470556081727095', '146.63448162398500124394475208142', '147.19102262720189340371933067641', '147.625445068891833427531604819053', '148.7800782524533003233605837114', '149.40431162503715067889204652052', '150.21961783648366909717106910552', '150.62184223558484873029285184293', '151.37580527828827680031310003312', '152.31222747047117819386748318194', '152.73406064616513017191904792859', '153.42773162091031707379898449596', '153.93917788331488207730337407948', '154.62438198685963461699783326723', '155.371112591993583565537067346241', '156.08784803896662249530645462684', '156.48177808669760819306406198895', '157.24027696461059581252845331293', '157.79440911174055772671498248665', '158.26945074315487915737670900087', '158.90332844067192921171595564584', '159.55347623941421447293364172452', '160.77736705721903582174757000413', '161.331611380526056798411128008198', '162.144846634315307430462887229525', '162.60797012591029467356897138490', '163.16789922251226836932072936737', '163.44893665070229940762392462372', '164.15516501204640160051710337297', '165.14401325566984284593915508711', '165.71778082583672673817998199254', '165.94286519567460619846283839616', '166.879911664061356996630701503577', '167.39831761031934872334820566966', '168.300262191296379945882993463110', '168.816391573647978918274796172486', '169.750703292879674605406310584575', '170.09341400259605113465984890183', '170.81903123560806119971533228460', '171.27369412285461486550904066898', '172.5058934292469129049476457263', '173.02981175932382935257873245239', '173.237452053355453168567531241839', '174.052412936493737228601106544449', '174.58207947737967726902670036691', '175.0653895520135497824385056559', '175.791351092989281828350943653470', '176.49908503383342114961528634232', '176.67743553352520812617009949618', '178.17084367720401347842040897851', '178.807326563227551501557589310463', '178.97849431489383094155011466509', '180.049654630064260659252796100653', '180.641630747718913985764153997432', '181.16990734583794671197021647978', '181.55428660058104119015917269937', '182.28666916235590960560349500487', '182.796815966446770120240427336067', '183.47849130919954614526200449956', '184.400248352451863727041173363057', '185.074012511692965249522611045963', '185.446906506187514330016360657006', '185.8566662299036742717147490631', '186.509545950848324711951635097223', '187.43179970709590061703331258283', '188.19137769147191094893711529306', '189.05499966555123488932293162504', '189.465464712343446112444337673048', '189.99805646888011110999873200337', '190.78627325796545781204178789765', '191.32163103202273532787807161002', '192.0228874603845488729799120042', '192.4137143591608836414730303107', '192.89591761897727895522636449995', '193.63371640528933192408062491306', '194.19932298498444513806900361812', '194.91239695491816246770598390736', '195.70276859316534021794089521472', '196.59205994819270790310827166882', '197.21169236340532790643199637332', '197.75243185063129568166444260240', '198.21277068467330861422261227014', '198.82519724516751186955231480119', '199.363591741755361838983682850574'], 'prelabel': '1-643-643.2-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 69.09994664294389, 'root_angle': -0.023487982055787518, 'root_number': '0.997278777234287503386200170907-0.0737227270119897372910492155153*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0117439910279', 'prec': 54}, 'spectral_label': 'r1-0', 'st_group': 'mu(214)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.54070795508379989820070325992-0.193843353786826480073984718372*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.21676127101', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.93048012135', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.86933621699', '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': 69.09994664294389, 'bad_primes': [643], 'central_character': '643.2', 'conductor': 643, 'conductor_radical': 643, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/643/2'], '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': '1-643-643.2-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': '1-643-643.2-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 69.09994664294389, 'root_angle': -0.011743991027893759, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.21676127101', 'prec': 44}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_643.2', 'Lhash_array': ['dirichlet_L_643.2'], 'label': '1-643-643.2-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/643/2'}