Lfunction data - 1-6003-6003.1049-r0-0-0

Formats: - HTML - YAML - JSON - 2024-06-05T16:13:27.183155

• 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_6003.1049', 'a10': [0.9179165852537594, -0.3967734145782425], 'a2': [-0.9844116218848333, -0.17587995536180925], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.938132482603856, 0.3462765442295015], 'a5': [-0.8338232639998672, 0.5520314886060467], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.8025741491979327, -0.5965523740956988], 'a8': [-0.8626054156009807, -0.5058773536894683], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 27.87781479921304, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [23, [1]], [29, [1]]], 'bad_primes': [3, 23, 29], 'central_character': '6003.1049', 'coeff_info': ['x^462 - 1', '0.999907521857918 + 0.0135995489615099*I', '\\\\zeta_{462}'], 'conductor': 6003, 'conductor_radical': 2001, 'conjugate': 'dirichlet_L_6003.2558', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^244', 0, 'a^26', 'a^188', 0, 'a^415', 'a^270', 0, 'a^432', 'a^31', 0, 'a^80', 'a^197', 0, 'a^52', 'a^315', 0, 'a^180', 'a^214', 0, 'a^275', 0, 0, 'a^376', 'a^324', 0, 'a^441', 0, 0, 'a^83', 'a^296', 0, 'a^97', 'a^141', 0, 'a^186', 'a^424', 0, 'a^458', 'a^56', 0, 'a^148', 'a^57', 0, 0, 'a^220', 0, 'a^368', 'a^158', 0, 'a^106', 'a^426', 0, 'a^219', 'a^223', 0, 0, 'a^245', 0, 'a^226', 'a^327', 0, 'a^78', 'a^268', 0, 'a^431', 'a^341', 0, 'a^385', 'a^255', 0, 'a^15', 'a^430', 0, 'a^206', 'a^446', 0, 'a^256', 'a^240', 0, 'a^300', 'a^208', 0, 'a^41', 'a^392', 0, 'a^301', 'a^27', 0, 'a^33', 0, 0, 'a^2', 'a^368', 0, 'a^166', 'a^150', 0, 'a^402'], 'euler_factors': [[1, 'a^244'], [0], [1, 'a^188'], [1, 'a^415'], [1, 'a^31'], [1, 'a^80'], [1, 'a^315'], [1, 'a^180'], [0], [0], [1, 'a^83'], [1, 'a^186'], [1, 'a^56'], [1, 'a^148'], [1, 'a^220'], [1, 'a^426'], [1, 'a^245'], [1, 'a^226'], [1, 'a^431'], [1, 'a^255'], [1, 'a^15'], [1, 'a^256'], [1, 'a^208'], [1, 'a^27'], [1, 'a^166'], [1, 'a^274']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-6003-6003.1049-r0-0-0', 'leading_term': '0.0663458418621518499328745190587+0.362998885051715645035530690615*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/6003/1049', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.36901214245765157, 1.1786330822256597, 1.6188512903526204, 0.9856723711510134, -0.22429754095849885, -0.4271735146248435, 0.9798175724294791, 2.330276054416035, 1.4532932006890538, -1.2438240811601238, -2.693140593208461, -1.0347214191702858, 1.4616823378266033, 1.119709730857699, -1.6727031640308996, -2.0555003338013047, 2.937686485956231, 9.490497028084704, 11.00242019081382, 6.292230834521069, 0.8553799745855709, -0.5275300337702378, 0.7042236773745313, 0.5928570406119885, -1.0040637949281326, -1.216317034321012, 0.2335205282532219, 0.5038353914191998, -1.1264224572457542, -1.6987253140756002, 0.26462655936490914, 1.8563247070047562, 0.5412732011273405, -1.5061744538320827, -1.1723398652995358, 0.3147028882193656, 0.05163004776917808, -0.9253524570975449, 0.0700268226009233, 0.9844737189298817, -2.579592575318824, -8.471083592313473, -8.736876992243488, -1.5052562112574572, 4.903864387933531, 3.7886314834221144, -0.49208735174790763, -0.5409690008168915, 2.349498215058464, 1.9546324464637475, -1.5203007723418207, -2.457609185493855, -0.15325006227956472, 0.5692450793153763, -1.4018589251695701, -1.9333034111882523, 0.0954259664301889, 0.8986253820291688, -0.6503463479989036, -1.0790890063052982, 0.5422077399738146, 0.845331236720234, -0.8410492691965995, -1.1364310691727453, 0.1747476078002358, -0.6188098439332037, -3.122264058358091, -2.656490761050707, 0.01649158717664961, -1.5185000403059121, -7.109464215733965, -8.233985098259998, -2.3965071729370715, 1.7921725260552566, -0.7670177881074138, -3.2877799102455856, -0.014823069723679314, 3.6483881810160015, 1.9622184096524318, -0.5932956087953606, 1.528604790863418, 4.543061971302413, 3.0974830210751163, 0.09972254742180496, 0.2653807903042828, 1.55297540543726, 0.6730358777957993, -0.3781559750980001, 0.20170896276153613, -0.18204657887811673, -1.9385678004255398, -1.032945043711945, 2.441528226489978, 2.890195583427946, -0.28470680491286116, -1.275765801431216, 0.7482566026429208, 0.5269715588548838, -1.7377783758835033, -0.8929214158010905, 0.6079470279564625, -4.363569906632594, -11.760515013923943, -9.904520020507686, 0.31645157850678374, 5.7428808509227265, 2.3069663393330746, -0.9170836073290657, 0.37198581191299246, 0.7530570799798098, -1.298096772257624, -0.895116035665733, 1.8431266267123847, 1.9946236933523531, 0.1817869487201053, 0.3716824947785964, 0.9074887802599451, -1.1358503087729996, -2.3657035331220557, 0.19476061670629416, 2.347562325956287, 1.0297147520365137, -0.05708626541336504, 0.5376671377381154, -1.0916276449029259, -3.9889169146714254, -2.5500600178169686, 0.9511885705917388, -0.4913753485434547, -3.3079504907907653, 1.1048262619445564, 7.807499070770822, 5.0018819846295965, -3.991145024102435, -5.885480661831695, -0.3549388743659034, 2.166085448267466, 0.14348546375482865, -0.35386674779820126, 0.12892857988404133, -1.8184584195043019, -2.6157763385024775, 0.700865550093907, 2.8076762420900008, 0.3926682490187824, -1.4229492930815577, 0.059520683420571235, 0.7004398029558454, -0.5059035136318425, -0.35207400043054693, 0.009749113605668627, -1.593695296579059, -1.1380533710868521, 3.1968458506603965, 4.563457296070477, 0.5349121486033154, -0.7918236405183301, 2.6574919443571723, 1.7548212913435177, -4.591470445188182, -5.589538704379349, 0.13898246102890013, 1.7709515800399542, -2.0005831606951974, -1.6793072529376103, 2.410366667390479, 1.3072938535033551, -3.4414960289134595, -3.2755016807982704, 0.34504927556883125, 0.8460872274729669, -0.21361422146244627, 0.5767373548238242, 0.3482815430129982, -1.747839780049618, -1.3651589075225208, 0.9013076131130838, 0.409793925456038, -1.0234691899388508, 0.27405639603369364, 0.7086148816624255, -2.0486534207341767, -2.4106722479744027, 0.7213049693562267, 0.37126127529229536, -2.966743663350476, -1.5071126842093512, 2.0104780060993166, -1.040501297360402, -5.5665941090126605, -1.7760758479847185, 3.8581429932015627, 0.8125936562854686, -4.297492566259766, -1.4079735995435807, 3.5010755323136755, 2.046024641519439, -0.9955324296516097, -0.29306316949276895, 0.38489522617105765, -0.505542853718618, 0.4868863099782969, 1.6816680334628138, -0.037397704258817804, -0.5702994080683914, 2.525345511446893, 3.4543859675570667, 0.35347591108708204, -0.9493872272666226, 0.0663399654992347, -1.0691307474567717, -2.2185106513436206, -0.36657817096157325, -0.28003848295826833, -2.661715061020555, 0.27192906460483257, 6.089464358253674, 1.9718856531703688, -9.381416515940494, -11.206529459977991, -2.766454441648877, 1.2775118099350462, -1.207634056320575, -1.1239764291857888, 0.7521728752661173, -0.775471979161666, -1.4111473378169708, 1.8746496503750096, 2.6521131280614076, -0.7186167646080215, -1.5878941292285749, 0.3707852961949226, 0.15886245430990112, -0.5284291473135302, 1.0579633432186277, 1.0893333877781548, -1.1041387021796272, -0.4754750112937871, 1.7279797556879264, 0.7465927599750184, -0.20724425876695865, 1.472105619284183, -0.38075524456701393, -5.572660149642691, -4.127528240572181, 1.9986384939363524, -0.08755165443727356, -7.765951735111276, -7.19669219046692, -0.6789151032339129, 0.3944484866821099, -0.7452146457533845, 3.055155734541482, 5.410367562093487, 1.3943481006154204, -1.214453210736746, 0.7311226944048904, 0.5087218791262198, -1.926457273988238, -0.9965812646745, 0.8770735644827665, -0.3136131052604897, -1.0796441792886935, 0.06403206128246684, -0.32650007931033376, -0.6328191228479582, 1.3581834384553733, 0.12373976829184949, -5.465842152784023, -6.449632000501112, -1.5667710867479427, 0.3069954432487314, -0.9484833562097245, 0.11169777600820738, -1.208462901149954, -7.228337669150503, -6.163494404635827, 4.715747063531191, 9.252441818741845, 2.2879001835171104, -1.5893015699848971, 2.1875096050952094, 2.9452459696358377, -0.44831770922751374, -0.5210169144601319, 0.8777265466227345, -0.35598642540079417, -0.32391934048285675, 1.6657078622302213, 0.7443658718382418, -0.9713837287837275, 0.8409914748926799, 1.9584149843891563, -0.1629769013957701, -0.2098856415789978, 1.7656642923286494, 0.545815353064093, -1.08256540600496, 0.5745372574331213, 0.37235295249242295, -2.363669791029398, -0.7570699831640962, 1.542667638605077, -3.6633462771631975, -7.7973627241542935, -0.834714202039619, 5.8124563722395335, 1.397267901152072, -2.6992674431609616, 2.109726447438878, 5.379686246002471, 1.851566197526929, -0.18729488489621643, 0.70489714509865, -0.4269103938407937, -0.842079148549317, 1.3196135595600635, 0.27713226902769017, -3.2919951511091106, -2.4729700871938003, 0.43674235435048253, -0.11800200253271165, -0.7797364421576025, 0.7722855672780653, 0.46440344517611615, -0.6506370044399981, 0.6752735809244492, 0.4652996408294543, -1.0739020979816323, 3.8359677073268856, 10.841074521812358, 7.653143233992724, -0.027272251848499785, 0.9209356319162927, 4.427754930366179, 1.1321559899544391, -0.5597249809941912, 4.293695191361905, 4.776766724963442, -0.9040428644272386, -1.837908397508673, 1.004113709958641, -0.7347595289233784, -3.025757498725094, -0.5877426857594015, 0.8018684971672262, -1.0419350192252863, -0.7648345040387595, 0.6603084771649455, -0.16619011320962615, -0.10035114984722186, 0.7732885764509144, -1.9974138702831254, -4.512591548333067, -1.8004850603572538, 0.2879377729380015, -1.2856161589250692, -0.45497202148601146, 1.0690643054198592, -2.6375151577149483, -4.431547649803904, 0.9394539543389859, 1.9208338832972316, -5.177424287369656, -6.311602162094096, 0.13639767815941586, 0.7764878116721788, -2.6175880479016214, 0.6915876779006261, 4.69242348305528, 0.9011041704371355, -2.9183634293695224, -1.0713300654052254, 0.14437247876042938, -0.5885767274125481, 0.5272460127061325, 0.8702184248522074, -0.4189957560177312, 1.1872587066346794, 2.8922443606275414, -0.2977011460853765, -2.8196930192064977, -0.7644319113779168, -0.16391391044864176, -1.5152690484197602, 0.23645387660892034, 1.3581703129441398, -1.069852906657583, -0.4488454212354269, 1.806767756590543, -2.042395594820725, -3.203170445524519, 8.52041018146787, 17.98404759649482, 10.484389316830827, -0.41446519286436695, -1.12491038208936, 0.33780357138962397, -1.4152286812194328, -0.7957196622958325, 0.3301293086245266, -1.8274770211238538, -1.2665759160621564, 2.959053979797699, 2.9576437149775394, -0.07837981398280743, 0.20341765348056826, 0.7971562359767612, -0.8279999222635698, -0.4135068848662232, 0.5794600261095778, -1.5247874078838648, -1.96092835318058, 0.6919278417591491, 0.38119799903850293, -0.48669107094680775, 2.8454757438245606, 2.6531910322700867, -3.2896410163607106, -2.3806844022939737, 4.705281396508365, 2.893698185304307, -4.1335661820317195, -1.8855092807515028, 3.4809405735069965, 0.9999150641085247, -1.7395711853550055, 0.7169299148319179, 0.6586030429832344, -1.3969805194373213, 1.184656584295538, 3.295562227505304, 0.35997231172399097, -0.8266538595191346, 1.2001519045402909, 0.6979346555922724, -0.4941302184177825, 0.6047494270324627, 0.38672778912224703, -0.1363168109072545, 2.350043175255138, 2.694876835442995, -0.37776762907160544, 0.8147161709235056, 3.731769805096193, 0.05104687757855921, -3.5261725319238337, -0.011687947494982821, 1.7392033779808966, -0.5466446231063675, 2.40666119594841, 5.133527039240984, -2.4899115354450716, -8.348120243408516, -1.2201246712264755, 5.375842341277249, 2.0355242165442142, -0.7404600305236149, 0.950645548018591, 0.49301373926196207, -0.43724656529628314, 0.9634591961749224, 0.19699794152107067, -1.5103424735586888, 0.21704872073943055, 0.7278941590709036, -2.0239867781740504, -1.6077325509473257, 0.92665562145295, 0.14036652066424743, -6.113256294832485e-05, 2.3179266055566483, 1.0710521244974123, -1.1556617218172105, 1.1904983955174613, 1.5733238805185916, -1.6876331118248573, 1.0152021592826268, 4.587811917963076, -3.6213965887687327, -12.314560674137656, -6.191562185893954, 2.6919723027727773, 1.4456097865250113, -0.7667790161347458, 0.8139777387276714, -1.253430779374439, -4.121270530174437, -1.497963267915939, 0.8915730435025169, -0.018036424638357737, 0.3713060992587361, -0.10043910419903755, -3.4019069142085154, -2.719894579230995, 1.6274332151137505, 1.6791596358458085, -0.45931675260854343, 0.2563476705328634, 0.35576056577877035, -0.3893493649069023, 0.7315842341126755, -1.3750062531079494, -5.665726177765582, -1.4697323805285964, 5.786375640240788, 1.9724994895933716, -4.320654610986381, -0.18746492537694703, 3.2551959722203865, -2.2621078072366143, -4.416115845913578, -0.38356951810409085, -0.24290054026232466, -0.7028096386251835, 4.061128016405553, 5.462370437637437, 1.0474076392291731, 0.050035250539265844, 1.474669209294601, -0.643201613228248, -1.8814032241025485, -0.04942677268140774, 0.030120925067770928, -0.21554599297276997, 1.0383140043702346, -0.6589671116200251, -2.8925682935456694, -0.5374127262486376, 0.0908692470373592, -3.8902205017629146, -3.7839929234098673, -0.29745207231339255, -0.3550389325933003, 1.96948188553427, 8.022423223051524, 4.617770450812043, -5.474757747345881, -5.286926957828714, 0.4553008198942431, -1.7471666727761972, -3.9126642491196737, 1.0295914079501436, 2.2144960270496568, -1.82202184255921, -0.9387622392543741, 1.8556415556828156, 0.07782139549871656, -0.9954492569022287, 0.26329141254292016, -0.7157380257441315, -1.1601376889926802, 0.5675297217365198, -0.2629169256460983, -1.0624371135334028, 1.8818798044050624, 1.9497246617560147, -1.7006261827067128, -0.8378884615930279, 1.9924357832824533, 0.6821808310773401, 0.2509731384311382, 1.0362396842684836, -2.3712257518847917, -1.9267212016505018, 6.395717825392044, 5.940700289682875, -5.90092520274908, -7.8161619515182235, 1.8438892837830372, 4.1877411363341, -0.2261986517243905, -0.06261305487318415, 0.6932569297446503, -1.3679895554794277, -0.6797450624389834, 0.4033042708278949, -1.4263248079264659, -0.20884881071163489, 2.9511424923745864, 0.8469075183374948, -2.007545768241986, -0.32006006508914653, 0.5259579180469632, -0.4706873756825698, 0.21615205721054995, -0.7200853535556914, -2.4937280562702417, 0.6925768241873779, 3.090061492463924, -0.13275336133292595, 0.5562568776994375, 5.130716285594449, 2.327206252254438, -0.8454172571835921, 5.981320715033561, 8.910580897114446, -0.3662977738892961, -5.320473361350451, -0.8964368863130527, 0.08078629607137641, -1.7286095409564377, 0.007756082210884442, -0.7875553931357228, -4.300100166074039, -2.4401971841172037, 0.733411574430241, -0.6411741536930554, -0.7369191293429642, 1.456094327860608, 0.6608910218849302, -0.061232601057431876, 1.3892196325454838, 0.4719781478652106, -0.4169694091145263, 1.5944924481691491, 0.7281969410432161, -1.1585693303493354, 2.6657019715864676, 4.514747554928528, -0.2633511347492478, 0.3785343600240584, 6.344273360181667, 4.304745264153613, -0.5540232283613625, 1.5561660572020242, 1.3199171260423053, -2.917070803049377, 2.159120337670687, 10.676674314353024, 7.222692311137611, -0.3121968083653501, -0.40150811959041727, 0.6476914673071628, -0.545303336834618, 0.2005716424318185, 0.1265633920198932, -1.2653446622727065, 0.9780739392950848, 2.897193984711186, 0.5215962173789185], 'positive_zeros': ['1.18460364279483691012247383809', '1.69011083302607466287998889175', '2.67479182584273120616834827452', '3.551219167427332503507325739564', '4.19559050053784943860743700258', '4.8527692509446810768615532336', '6.33788736924215840140200479885', '6.70942097693572609118577178042', '7.30844882917243711487950970376', '8.07445651518573760286924060276', '8.55496241893950729778076779025', '9.34177401424240748551496157121', '10.06979787064284265014706821074', '10.851690219783494592512448128688', '11.26353198977035674350330140803', '11.86269350193136087806027695115', '12.33085824932022514033864619467', '13.49304383684406972912075938058', '14.32760738267837144862266996472', '14.74877215317626743710093575470', '15.48961555129795265180265756345', '16.27143803786026941165095224940', '16.67447866064802695122419417644', '17.486030448497027298464652280327', '18.01070268974190476405310324897', '18.65254142855226986309461751736', '19.22889525435201061358398432008', '19.94559132713933165029496471446', '20.21066372425538790370733333', '21.24664475786333580625912047060', '21.41589611218623700295498027997', '22.62269453831621896000838548873', '23.06769058715365850364254522242', '23.75092485581053377531648989613', '24.56339067216057152823206875829', '24.85576793431253862993074678705', '25.95729700886990363254122621657', '26.19072325458576595872961740131', '27.01631535142487674568518930681', '27.41748257255270472206114313269', '27.77237785571486960362168963031', '28.53437834107412366119555501649', '29.34663068391433577994044671707', '29.88723814280459509899804483754', '30.383083313401679417967666747046', '31.04787628350044432959069470762', '31.33682202617936150175786993756', '32.49014923916147688372175279756', '33.28946729657390848750620280023', '33.69135543125668415997228037472', '34.18456539544748266527393971951', '34.790486395958426090466746973391', '35.69219912175967558915198449602', '35.80640350005663335769621414525', '36.42474485997943833612033938338', '37.16968974402243166592971638218', '38.03313370269060381486621753632', '38.174374143562111459166499645267', '38.62160123000588588122363740251', '39.57529326526956988546809952458', '39.95817653167555266062933044423', '40.57885110541757860418357761067', '41.418431962738371678010377349843', '42.20815438507085719685701509034', '42.83589940699669367389772550387', '43.24606599784157622707350139097', '43.481883422267782141248582671112', '44.32082622250265023944057538901', '45.03872230926569569432426105887', '45.6150460187975396063607145158', '46.11868619333930496779234521714', '46.689946251827166085156808572339', '46.87891205692677047054236228793', '47.597208405515039477986740473577', '48.47971562108323343101414030533', '48.83799116820125763252706044433', '49.46911588429014744809723236612', '50.30453816665300112166839096001', '50.779426285196880428830630879539', '51.37227052388537519810306294780', '51.958448257404385317372447097456', '52.77513721051412344895908765639', '53.32581736048504298403272424266', '53.58619566850465675551841508303', '54.11957547756542550232378103450', '54.859019182523423278219175792083', '55.37744402444013903868091628971', '55.893301379609161965221539483979', '56.35055456095636640633238421526', '57.11041735733170570358042199013', '57.53518709776693165065859274794', '58.23122395414564574481772092094', '58.69277038696404881253136639451', '59.45133955148969437455452819713', '60.03848011786625239460906039163', '60.69664393018958211289132899732', '61.42171982054779595616939880639', '61.934262842146390524270616429497', '62.31815128524622113639024398731', '62.72913885968832889274247106376', '63.43223520168665145157913722938', '63.82841532770502808840874521235', '64.72437751373063719102946035015', '65.273471811626350324999917580040', '65.41794855953964266823844291831', '66.31520495477352886407284628509', '66.51470681716214561667174053507', '67.17394861142817445790792126259', '67.86865897359993479332185149739', '68.87596133236493140225244383179', '69.24372915946468318603844740995', '69.83390871370853465405908879695', '70.210763884194179386837324576620', '70.77861822125313135739148238478', '71.49713038193078876828779177436', '72.1176108630289482884423964530', '72.536856042095146515088691967826', '72.94728449358898151334398266243', '73.58769146831682697093349611239', '74.12020310011845584366252282654', '74.81325919312527002473733139769', '75.05591200603399731044391462544', '75.599677610856624088824095560371', '76.44260825545895496160021682084', '76.87119828864014941473486571436', '77.86260678363616666517937550950', '78.18541196037611459111971862109', '78.53927170946745404898231284981', '79.472153673729740881142364948274', '79.89992360417121369470746158949', '80.374143471494668877680577318058', '81.06074448075640066010890360288', '81.5107373396091691648592466214', '82.16411829216703213918880413238', '82.40483494671164435749759255965', '82.927926700157122625864116112020', '83.44612089533199030463369491437', '84.51485630242557846726097695706', '84.76559282474432255124589227442', '85.288173749432134247628309185135', '85.51695876817146822701252743635', '86.4359141850758158856286788589', '87.288468935383529803333112627', '87.66017608494661872404368407262', '88.38815727004031785180809700553', '88.83323419040899769206970180062', '89.307302705780821439633610275011', '89.73935244016878247553791726646', '90.406560398079468600185825765614', '90.837817706079658118479070524122', '91.53834186592556710027270312139', '91.90732960772438799930320281019', '92.56564499035805575279393472356', '93.03883387442636024049103138870', '93.48051975116894146356744015159', '94.12336783877760798574037437121', '94.51906072550769314200750744613', '95.33860009211322276851693978385', '95.99964682148167689193307821779', '96.460523141903475591418899624669', '97.381735751420861743802945609926', '97.57980865932695082948068517407', '98.051477683215355096428176683405', '98.565744856408566141180407765149', '99.08650180431385385208973696318', '99.92845063639510773158692048125', '100.29028687255240343180593904708', '100.7901949281134715017117494005', '101.33750377410422487394644720224', '101.751316698863933608067692402285', '102.25324052268441014975021877494', '102.63144249808295562100185977706', '103.74803204653169226556261380253', '103.995943796407022023609884663251', '104.76927701648553946760313470119', '105.0540788745240654792198451695', '105.88391145624928485548975066719', '106.4264968229052954852062514998', '106.80927333093078174434677836495', '107.56050921477898631901026181930', '107.96169981183306145735125404620', '108.565740307943048516671999597433', '109.018831972418543612375399537988', '109.39862311151544250474285658398', '109.82789784700999797750298206382', '110.80882076150867957493790496157', '111.02691995232626677746158379404', '111.616314854182096081126050572548', '112.01077352315790799840121527038', '112.7634129355753803705349812672', '113.225075993946318678583248990056', '114.05459760921589697134278823643', '114.43647871103477742135146346922', '114.96348417353549272362029877665', '115.67349691578785850212978835697', '116.410898940035682941280328022182', '116.62531239244225308062093260497', '117.08488838487641546362984465335', '117.68165836723853020234320037349', '117.97981296350543551980393705169', '118.728918675437577448777855065154', '119.51024158119844264260409328136', '119.64129923959848442047260243600', '120.28566759366564002822667392769', '120.80898874736447260514674792264', '121.29415831674826264029137633221', '121.75733017514140587882012360975', '122.3060876578528244862082921417', '123.41728182913198152006895948457', '123.8934879697377805878522593721', '124.146146382636193760958328336303', '124.81154494086446538499520771009', '125.07686798414371527285176634027', '125.721673130288753209793184775961', '126.549387394744768335411804236793', '126.83285433409584220765600662206', '127.34746719438518133733237455879', '127.88625210762481453349413817352', '128.25004258091972290193950279947', '128.973003543575099037530007899972', '129.43405325264803521435585775740', '129.7589990295763418971256757853', '130.45513026619734611018527822830', '131.03897028297392522363382035389', '131.67563732544226423958393393629', '132.2735054626446156775231896831', '132.87897308195981082810688734223', '133.35904910877771096769154291564', '133.82649004931619215757825562041', '134.28079475089703301143007904144', '135.03447058822746466323605645897', '135.443851290822173716049537117798', '136.056581729196814087959561970172', '136.42075739379626969464671653033', '136.96940123116627024890082962384', '137.21959980775771452450716489247', '138.07555320754877568730400133473', '138.36340029294692820769353002404', '139.065209434751308044558086496906', '139.68829421644950873416074891164', '140.21045890878463092538349180248', '140.45935148053868357713215275420', '141.17399622523596553977219073141', '141.91273428077514567936923189367', '142.64420453346898456098583899361', '142.97048554547148006569412446840', '143.5260244142554287296022689493', '143.8682414356776853923820156889', '144.40108889198044725607228686693', '144.97210970267273753093979598696', '145.40605055817018421187146548271', '146.10686608744486542943435160165', '146.58974141908966217795459272061', '146.8750103002952426376447406768', '147.60248105869242680169747057956', '148.00852036590783316182949149117', '148.576584259869336359812607072274', '149.00597168402223139841407945062', '149.59145010638217566877085860542', '150.49427518409602871879087312574', '151.05852860754371878984506677750', '151.40403890666687017125797324324', '151.76942931603101384953805643207', '152.630905550350796368039542076661', '153.11796542159735981950028795971', '153.31742466429153969096271396866', '153.73712115311334097468615532260', '154.56000010677801736861007525308', '155.209209968205480933675761650939', '155.56375672009004160217807455618', '156.032037129430089003120143180130', '156.380440863658462506050142417822', '156.76876523947572828952886435596', '157.55171507742990592273103107288', '158.19688048176294340031618335795', '158.758444533470259581357064214', '159.26967225738390399228791725044', '160.043501992330069272917682094259', '160.27321334387660296582449365614', '160.691966074929827489091568910763', '161.67279045977422075968560426495', '161.86510352275061023923784000274', '162.432828193988670739004425300651', '163.13539898295429951649287474293', '163.4473756566980040125015583311', '163.80730993636416820087552694428', '164.30920476103890526464475875125', '165.05812669625865519376449126377', '165.322938501331553834156437326215', '166.31883754604692247188087354086', '166.42556657120219758474505112453', '166.72670079734731593608990958278', '167.6336406710642997190559426117', '168.39273799661485998035990037988', '168.62700855386712537489352628369', '169.31683661255849931684226968311', '169.85267996524063246604347275193', '170.390399675815456400970808342936', '170.94655693436599032797238065375', '171.47215824637504516985540347090', '171.73767425428233819541892522041', '172.38490700011746200969503841894', '172.77198978976619420304963919299', '173.26199255429521237486813344541', '173.90898038939130061459310739353', '174.44723585094052100000889065258', '175.14856277711832916288221245461', '175.23235744826195942285035547565', '175.75614179157298899484875641931', '176.33430153287592243124935124898', '177.03653807887152711172551779172', '177.750578232959113561452204748386', '178.41492798212639069884271387', '178.759481344848390371540409977422', '179.1755626507571331005703255329', '179.790922066055636831923586399027', '180.09126352858272984844238780913', '180.642749623752322538354428662392', '181.31361011755929443811075588438', '181.91927116506054856939607056829', '182.32664920639776509403776865673', '182.736657654923249841290639717326', '183.01619048112368606092979225457', '183.703920523528590302640946112611', '184.36204727798757520560591222609', '184.64563025846740912413875413686', '185.44389018150308506412035258225', '185.69820703141343919563660804107', '186.55154484838428750117625172418', '187.26328475223564930347842302346', '187.51162512359726956179837242267', '188.12370534122297637751372441842', '188.353319158541808428259954151879', '189.253756856365717437472824175299', '189.59500503371538142522081059436', '190.097169133144911380857601875286', '190.75447971278888401232156964105', '190.95614351505818591215437735985', '191.637138141558406950683388430455', '191.95928869979499604975348726814', '192.574975775012355109208050948947', '192.955524345837438867966880839805', '193.7313534433553395860714069559', '194.04002747410645671225861520337', '194.927473697322752827339001506720', '195.16800745029817823455646147756', '195.71066038079144778255404727032', '196.17772184292450918917426547788', '197.16528491242987879341832705198', '197.557434588756903019646529375013', '197.97135481789193447810837243565', '198.38932909850376216940703855835', '198.77388699189319321823329325550', '199.28580610356886458849637929557'], 'prelabel': '1-6003-6003.1049-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.87781479921304, 'root_angle': 0.8849143392884014, 'root_number': '-0.935348872967538643591879961694+0.353726569313580482224656346445*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(462)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.612754682051452959504854115001+0.0710252431513190619514552658186*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.18460364279', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.69011083303', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.67479182584', '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': 27.87781479921304, 'bad_primes': [3, 23, 29], 'central_character': '6003.1049', 'conductor': 6003, 'conductor_radical': 2001, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/6003/1049'], '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': '1-6003-6003.1049-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': '1-6003-6003.1049-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.87781479921304, 'root_angle': 0.4424571696442007, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.18460364279', 'prec': 44}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_6003.1049', 'Lhash_array': ['dirichlet_L_6003.1049'], 'label': '1-6003-6003.1049-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/6003/1049'}