Lfunction data - 1-77-77.76-r0-0-0

Formats: - HTML - YAML - JSON - 2026-05-26T05:31:59.254465

• 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_77.76', 'a10': [1.0, 0.0], 'a2': [-1.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [1.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [1.0, 0.0], 'a7': [1.0, 0.0], 'a8': [-1.0, 0.0], 'a9': [1.0, 0.0], 'algebraic': True, 'analytic_conductor': 0.35758649667489656, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [11, [1]]], 'bad_primes': [7, 11], 'central_character': '77.76', 'coeff_info': ['x^2 - 1', -1, '\\\\zeta_{2}'], 'conductor': 77, 'conductor_radical': 77, 'conjugate': 'dirichlet_L_77.76', 'degree': 1, 'dirichlet_coefficients': [1, -1, -1, 1, -1, 1, 0, -1, 1, 1, 0, -1, 1, 0, 1, 1, 1, -1, 1, -1, 0, 0, 1, 1, 1, -1, -1, 0, -1, -1, -1, -1, 0, -1, 0, 1, 1, -1, -1, 1, 1, 0, -1, 0, -1, -1, -1, -1, 0, -1, -1, 1, 1, 1, 0, 0, -1, 1, -1, 1, 1, 1, 0, 1, -1, 0, 1, 1, -1, 0, 1, -1, 1, -1, -1, 1, 0, 1, -1, -1, 1, -1, 1, 0, -1, 1, 1, 0, -1, 1, 0, 1, 1, 1, -1, 1, -1, 0, 0, 1], 'euler_factors': [[1, -1], [1, -1], [1, -1], [0], [0], [1, 1], [1, 1], [1, 1], [1, 1], [1, -1], [1, -1], [1, 1], [1, 1], [1, -1], [1, -1], [1, 1], [1, -1], [1, 1], [1, 1], [1, 1], [1, 1], [1, -1], [1, 1], [1, -1], [1, -1], [1, 1]], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-77-77.76-r0-0-0', 'leading_term': '0.418240022243393811647805958766', '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/77/76', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.41824002224339385, 0.44700724185048724, 0.4251842044837673, 0.19307268217314888, -0.328651016676501, -1.1155358848249701, -2.030683825153707, -2.8399514658763265, -3.2648129597641518, -3.069034068008148, -2.15587954014831, -0.6389546330550421, 1.1503619632447086, 2.7386135323443215, 3.6572589944619276, 3.614604776371277, 2.6247730174491495, 1.031069067251602, -0.6029435724703582, -1.7054817523057308, -1.9301733145356383, -1.3077897509722793, -0.23775663000300643, 0.6910730900949226, 0.9782174788423718, 0.4588668029291392, -0.6057368344461374, -1.652037307315089, -2.101698240896837, -1.6705168723621804, -0.5324952777162364, 0.7609844941215553, 1.5775369654689284, 1.560547773357472, 0.8424510184099132, -0.023470933810927047, -0.39590644133223307, 0.03542518126388092, 0.9944810761695582, 1.705162950528964, 1.3080979272832707, -0.6066236003289753, -3.660535352323214, -6.768220160256086, -8.636156684533816, -8.4266680965542, -6.216365701577017, -2.9749962470133093, -0.059024434913100485, 1.4991569914522407, 1.4971319251868718, 0.5721505978186843, -0.27568779172057795, -0.33682961704760694, 0.3946039924153899, 1.303384531766853, 1.6561607660635191, 1.1660068421651797, 0.21703322064552757, -0.41682675115816675, -0.16466327988722584, 0.8667945705887186, 1.9032642297044398, 2.02984912026382, 0.8861842450705488, -0.9728323641541812, -2.3517721319181124, -2.188395018836265, -0.31610417252354034, 2.3293671901320736, 4.24850221119201, 4.335662659630475, 2.6141493542632905, 0.23036236018125245, -1.3129522657118375, -1.1702239835841408, 0.2885341385701518, 1.76890341201327, 1.9898180213974384, 0.6016075128137361, -1.5709722573108504, -3.1292437345350126, -3.100406842354902, -1.6046848877574722, 0.2878333856921857, 1.3789608819039616, 1.2054597893655163, 0.2901461451461684, -0.3842728120477106, -0.22995190222999484, 0.46810233828684866, 0.8453919495802557, 0.2781156045912087, -0.9694487587308404, -1.8585621705124304, -1.424839724317397, 0.2992830058972221, 2.080205693192702, 2.268641600909535, 0.055679889737644345, -3.755249992900352, -7.116515873827694, -8.058648287727978, -6.034143002868422, -2.29270130915912, 0.9975116011626072, 2.230777903200296, 1.3524861871054568, -0.3378223374526319, -1.3342302064373228, -1.0706994636842981, -0.17389275457382092, 0.2958934556087636, -0.10572579585596753, -0.7984657613315149, -0.7540838770252968, 0.4733619846512451, 2.20640127532951, 3.1174717853727354, 2.346730099833144, 0.29722338887602456, -1.6211547219264888, -2.1313535299440725, -1.1550741928572839, 0.13371308706048907, 0.3575257853716475, -0.7938255079234715, -2.1932906649093815, -2.1956169018924894, -0.11719954237769961, 2.99047896963914, 5.003690618789802, 4.357965678180116, 1.3299283804286293, -2.107782197078559, -3.7747036769885822, -2.9163972210189186, -0.6670371409644179, 0.9930941137759219, 0.8690142769495128, -0.5965386827902132, -1.8985886035894526, -1.8769064718108686, -0.6799234284735854, 0.5228457623751627, 0.7249444326955892, 0.012464392425631063, -0.6242050164604032, -0.36966594852040396, 0.5380855649941445, 1.0382611687725025, 0.4146722976547742, -0.7376535209114685, -0.791079765055744, 1.4763353928750875, 5.521970736720056, 9.075524933590449, 9.732051614417161, 6.858329975557162, 2.1926072447016156, -1.433545665298048, -2.2270020049242487, -0.6559350830320837, 1.209810889251373, 1.585582891134496, 0.4061858528822979, -0.8914527594953616, -0.9100645859316225, 0.3403657388516548, 1.5093617329324702, 1.2756145786267594, -0.3369133940270449, -1.9668496688826957, -2.2236193621550453, -1.0173461208672667, 0.38090820386627616, 0.6008933757078193, -0.4826683648754522, -1.649103825714127, -1.581884180848657, -0.2332883077024166, 1.077711343606687, 0.9833604976526513, -0.48056549003843746, -1.7791181558909583, -1.3511862642321926, 0.7103930695231924, 2.456530270103225, 1.721350732987801, -1.8031505791880038, -5.992534551783384, -7.86624307834528, -6.009629944885617, -1.7261662039599315, 2.0806511179831206, 3.2719048629640843, 1.997210357519707, 0.14910724765538855, -0.5513982416382042, 0.030229293461695058, 0.7455461626994162, 0.6519181090193563, 0.048461916973794164, 0.01573853236134992, 1.0438749650730887, 2.3040792618019115, 2.4310977453525515, 1.0489183160634774, -0.6038612802593675, -0.7482559187883856, 1.1234856475812587, 3.5394425993889507, 4.301663959191857, 2.6120022695229714, 0.002165467222425352, -0.9525371759441704, 0.9757727730944473, 4.424656352222026, 6.578183237738349, 5.66388451790957, 2.4814094677472895, -0.4435715816322861, -1.2170556581602228, -0.17293392867650562, 0.7537526778415337, 0.1332917025679824, -1.5237140938133846, -2.3961878112473904, -1.3231463659311078, 0.9365292860399457, 2.4278417928970586, 1.9296171357523804, 0.10377548008105329, -1.2722516126419745, -1.128870043032991, -0.06493663875263371, 0.5026090055498492, -0.005558579273980528, -0.7300842607997806, -0.514568226316035, 0.48523006917627887, 0.6278683571010643, -1.518277452043981, -5.267734926548203, -7.828360885875541, -6.566603735467053, -1.5295720843607663, 4.24773692863101, 7.123202564876171, 5.814673626117537, 2.251661876392513, -0.3859635931176744, -0.4930200904877928, 0.9154270932446824, 1.7016211448438814, 0.9093299941599602, -0.4759253828373906, -0.8823783647698958, 0.02878382664158333, 1.0810644522936195, 1.0415295996276148, 0.09119863801426761, -0.3943558935374649, 0.4750311600692102, 1.8840348777397882, 2.0306239180683034, 0.12159914568035735, -2.526985989224075, -3.618784289496492, -2.1919546197418063, 0.3021203288365819, 1.3940849840197078, 0.11421616329533327, -1.9827228934189338, -2.4224931410614867, -0.4367948409719644, 2.134457715986427, 2.674434800590052, 0.518028431839041, -2.2450682768241252, -2.771752578631002, -0.2687753468896266, 3.2308207349170504, 4.8629160654884345, 3.631350579748516, 1.1167430073483273, -0.3526435689224014, -0.01622937199776343, 0.9006644994351825, 0.876203032410363, -0.14781203231298665, -0.878734945199011, -0.37973509470298555, 0.7180590560877899, 0.9558405245706582, -0.12752601155235666, -1.2947334454282269, -1.0086201951077998, 0.5739283437949716, 1.4050328611370109, -0.32139256177970316, -3.8534603743232143, -6.028164815157442, -4.096919789993962, 1.4509977990094547, 6.980241083798983, 8.798591077485906, 6.303231211328793, 2.18311533216598, -0.346399098124968, -0.3909073277328243, 0.43076687631881955, 0.26505689388966264, -0.9172245770419079, -1.6470479899121304, -1.0247943864173843, 0.02369321422151116, -0.20568890199656276, -2.0875579764830103, -4.004138688396257, -3.99013282841328, -1.8829071184105424, 0.457685616963933, 1.1425105858666096, 0.22980077778486088, -0.5412698055419938, 0.07179288287500951, 1.2771278904506291, 1.2080028796763287, -0.6578038252062268, -2.470127690211272, -1.7895246033564638, 1.596526604303957, 4.98154708303435, 5.200787493376001, 1.8382432949783554, -2.1992922752886392, -3.452780636984261, -1.227609968680108, 1.9187881909780433, 2.9084585351783825, 1.1553310604044194, -1.2050886598612314, -1.8372272622140593, -0.5834710072118336, 0.7682476462101367, 0.7455788701219053, -0.25461356946248004, -0.7805006619436148, -0.28255623450233003, 0.2787436735726485, -0.11097094755671266, -0.9136991876140754, -0.46875866364422425, 1.842198583005981, 4.300158888627593, 4.285165290830115, 1.168974317914526, -2.556733494635168, -3.4667209393447975, -0.6254140016669986, 3.377018228543106, 4.986417772923246, 3.208432730804826, 0.40203998908728944, -0.4070275269723097, 1.2859890257898174, 3.182056596535717, 2.92225743561836, 0.6861083669616602, -1.196992502454955, -1.0015092473372436, 0.5088016949804673, 1.1517157521003978, -0.026970615223091774, -1.6653845156899036, -1.767663062466608, -0.09660300882342589, 1.5629403961347041, 1.5364048383346023, 0.2104759904306651, -0.5200285748184162, 0.39549352711129526, 1.8873003370212396, 2.132940013729495, 0.8885945681470141, -0.16084958362161886, 0.37050384227929956, 1.4174504126347016, 0.2393955775216688, -4.352469726215647, -9.891310494802761, -11.980700122015952, -8.433627673362555, -1.5783313933903356, 3.7699860090993393, 4.646877474880684, 2.1973282479036307, -0.1820304272814786, -0.4737911135480393, 0.47321705209198384, 0.7570024479541612, -0.036781999747676986, -0.5939538713205861, 0.10448987991422265, 1.2759462192887563, 1.3086133315852748, -0.0557619327660043, -1.1869968475408605, -0.5032513324738048, 1.4545254022629066, 2.480641738334017, 1.333507062620644, -0.6005647413808153, -0.7868755670289942, 1.3863523208203028, 3.583173215346479, 2.976766254673478, -0.457413125525539, -3.6262320694011403, -3.523175306277342, -0.4530358761101997, 2.3378094661266386, 2.20916867009984, -0.14229547804655246, -1.7750760137779011, -1.0250391305437234, 0.6498102684703259, 0.5494508231137939, -1.9725861085834253, -4.669237536465727, -4.921375664240539, -2.6143697476087473, -0.08520403865524874, 0.6038637988931082, -0.24608368439696462, -0.831549332278392, -0.30202370860422095, 0.34732828179967107, -0.07340834357959308, -1.094712235857486, -1.1181840454173082, 0.2446976299381139, 1.1641182231631788, -0.38566476749094425, -3.7460004211170403, -5.514353487651801, -2.949859702382288, 2.73105434534202, 7.057637888236405, 6.605530382894916, 2.3832714334181047, -1.3450070126759444, -1.4728721888084273, 1.094618264018727, 3.010256968479883, 2.3464322306086554, 0.32201045284263796, -0.6954033867360545, -0.12051782846761792, 0.525102523278206, -0.05574469827407433, -1.1597422526858823, -1.1456918040120416, 0.1516481024364875, 0.9264132182902736, -0.3663679988015157, -2.825272635493637, -3.8590453130222415, -2.1702469251346788, 0.6291577786765566, 1.8334642544267015, 0.7683021119550196, -0.5807932685682445, -0.2310223026215856, 1.1498560290949071, 1.0135821905767697, -1.663984938486218, -4.5447415628438215, -4.202023185128519, -0.11859228503432073, 4.282960101892137, 5.021527606077475, 1.6944440453310818, -2.229924049366383, -3.201487227456915, -1.1333055307345064, 1.1084499802206802, 1.2690271177938208, -0.006679764150966959, -0.5684899293141409, 0.3108964846003122, 1.2078397077660106, 0.677008233669799, -0.7526646752323274, -1.337367612599867, -0.519872530246734, 0.3200836958430038, -0.1611341030725688, -1.228264368211475, -0.8974375554851823, 1.1487670094128275, 2.3822870055373295, 0.017927825925330813, -5.328213082535311, -9.421772950153871, -8.44656030571162, -3.0447996249664917, 2.2073719432824, 3.413685818323927, 0.9950113689238718, -1.4772224765116209, -1.5269822210199677, -0.08378119203211143, 0.46238238869841, -0.4038369061305481, -0.8322562311756709, 0.6662350181877463, 2.9852853559254933, 3.627488786909076, 1.8151375770135594, -0.47361210964142886, -0.8775408749715372, 0.5513326706216215, 1.609757991531643, 0.8282721016609778, -0.7591244811327531, -1.1755453490414156, -0.2447509791267964, 0.17839023118039277, -1.1322175746361514, -2.7696949313427943, -2.23808027007687, 0.6636372163954867, 3.019040833567689, 2.0244953091093776, -1.3856505371849526, -3.0904540061189216, -0.28826110170845143, 5.1267854262588655, 8.339568563747005, 6.652315501897814, 2.1327699716233193, -0.9387463586039426, -0.6457480505484303, 1.1570481758164917, 1.702271191582927, 0.554170345285116, -0.5451533247127677, -0.4175406854223217, 0.10001754767104026, -0.2744814033625482, -1.1612015276471777, -0.9915288958349727, 0.5163622927190692, 1.4248530490301186, -0.151691250441408, -3.3055418311090143, -4.890781005421105, -3.125885579456585, 0.09497836000318421, 1.26837367547627, -0.5440117518452072, -2.519162651393322, -1.4776027798576756, 2.1440900369600358, 4.618668556850885, 3.2515142582585037, -0.47449282142078214, -2.6820884145268185, -1.5810141611851434, 0.753445298515018, 1.2453981916531673, -0.4177148688671405, -1.735135871569232, -0.837722005209559, 1.1088552157216194, 1.525894402434751, -0.18295205996963887, -1.8784238602227838, -1.4496757298793455, 0.5595057276380184, 1.7969810378557776, 1.151692681499831, -0.05144425754595218, -0.1447873267413159, 0.5205364486989027, 0.26198094851294734, -1.1664580580232884, -1.775711534408603, -0.08325178203012512, 2.0352387043143754, 0.613411679683168, -5.75933969563021, -13.336872533756338, -16.275959220369124, -12.403404547585197, -5.315475188533297, -0.4990819513663688, 0.04636126401123261, -1.2060737419472318, -1.1565279659080367, 0.3146908675260367, 1.068447811289791, 0.10504164566366428, -1.0821053220347723, -0.740559530006352, 0.6521895587162055, 1.1120853308914427, 0.014928042896508727, -0.9291311211988235, -0.02673434168837105, 1.9102788935517383, 2.4624332093961785, 0.8728285547139398, -0.6946521058977912, 0.169803737477924, 2.8395749628289404, 4.16162824213617, 2.380552964033205, -0.4679137168345616, -0.9221142638251791, 1.594614468712948, 3.9775634683390457, 3.2968729154923624, 0.5148397757526862, -0.6728042278444544, 1.495647227300347, 4.507808900679555, 4.5390040313872895, 1.0794640432839613, -2.447751478076467, -2.7249885901130644, -0.20504687887812365, 1.8891635160120515, 1.5814633287243824, 0.049767209631445763, -0.5505089187088881, -0.006767950198582487, 0.15713407935591112, -0.6929306818371025], 'positive_zeros': ['1.07518664972339127935611675580', '3.55056670578384210285742013662', '5.50311450515315147546139640413', '6.94388387084431951400558554216', '7.95830051980204677705751716148', '9.49909710522210984532320433497', '10.927311664284949109442757075780', '11.54828713233477550133866120260', '12.73546900626758556607578222035', '15.0079111508592099644854016147', '16.12326360357351206788546607880', '16.73559968481142131010888879651', '18.20251946705130657171112613701', '18.81373089363854149644084108168', '20.152781805949400179553861939395', '21.288914672040234576373997068043', '22.84615655212071405648302769446', '23.69732075073176553842644583995', '24.77709810862174352592399878500', '26.19771598585890605169585061368', '27.28930991398002848192886678524', '27.925588437926485895454634834449', '28.8276077041774636962363391404', '29.95368946866670198730352592417', '30.94277776709996655356941385830', '32.70060415388670283336572634747', '33.684677802711719370476959899681', '34.75750351159989512131589587548', '35.2642397542445866352869897379', '36.15617461284183643064251111709', '37.54149189606601544023626205651', '38.70842979756147753854207773085', '39.19503106562643972239803325444', '40.32501787317474820744925645138', '41.67594286868841019955748779627', '42.91013316391711858976276690573', '43.63721107295381741224935043195', '44.8430899715055750732314012704', '45.629497405571692089587883444550', '46.386261751706854420583662911665', '47.29661818959481833975718330495', '47.96371171924832948218353798943', '49.85143176990713650977311119414', '50.72213833580891563546128414609', '51.64554165205792746194545099802', '52.42829012920836290640455401764', '53.38193992032069376607951158788', '54.58471863738294866016998581262', '55.19986478825930680982719826402', '56.295453453352975376600578050', '57.099216047944795030232233761', '58.029624833489335310007069476270', '58.92513655300826317629926812588', '60.43631206823557530726788798303', '61.59631841317120370630916725220', '62.17670385086221670645312588108', '63.15791020120866636092019722067', '63.4278140114668331218661836886', '64.86859000063216133675602248113', '65.470848969844978916080276425264', '66.87531115887690135896174690026', '67.38984735468033461252530596666', '69.00026305365848509674500741266', '69.72832545991765911899685341764', '70.341410336060703777483141368449', '71.436178412294691830956451276765', '72.5172253897089607243147093458', '73.45754771515421671612143643536', '74.060442554585061971782978067828', '74.85300543312444706687117268054', '75.44790840468333273676271217913', '76.95297035452692501514151649949', '78.36731400882558953107674214526', '78.87281156102692816958166513767', '79.88316852227143981692507653975', '80.617779967685318765169260404000', '81.592687627698244418574935471335', '82.069322803009534812635627051796', '83.13922382922715450631786789027', '84.33309275235502194123868791938', '85.01669582941787172761862305043', '85.98647541618025318583027524383', '86.928682428533488299798276962786', '87.83617683551394168615883766465', '89.252085344904065768323082805438', '89.69291160097811028265395846370', '90.58468395538794579830052286390', '91.35632680862767099926284849219', '92.15950756287891220535281040070', '93.0197220732544189115747799614', '93.71534322986669662273626460286', '94.927336219105031587337895068757', '96.490247161761935882337404854366', '97.01256341078597145445864444920', '97.58364409328104570456609936211', '98.73894561829534985138209816616', '98.997001933343549859925352663019', '100.5501730537476523454660241552', '101.312992315016025686429128977497', '101.85603646845625114528409667036', '102.72132775859615200038664636874', '103.62141974023161629711695394365', '104.818346665378900531743600626216', '105.738776354979144284881834754826', '106.70277300694199611086020354821', '107.61239469314854620898796249174', '108.36118414098847932734898700796', '109.18152088788983702077677727151', '109.64385708862914764207653457365', '110.3965926429164498503099738042', '111.65200967925643177969668370763', '112.54716090668139946336456220277', '113.81523044494561595858825223370', '114.1763542830448694633285203075', '115.40169739028416357995864462569', '116.14692616918652046029366743292', '116.870254511679407384902251634514', '117.827268705788940660522092204156', '118.80093407598852855334192522568', '119.28741207100470580241058235538', '120.536797381446665411668125214004', '120.82329426417662620501248271770', '121.58646038798083942191881036819', '123.199234510638718922977797365341', '124.33846802410997310900562286852', '124.85133975087227521293839338891', '125.61298886937306956518981795582', '126.22234233850083524342241915348', '127.176680746352858399178432677240', '127.90018074464337943673040860922', '128.952438837333547563948474071032', '129.51788789633480234609220081456', '130.58888154741093183628399085698', '131.60264638760557550811269471797', '132.48233495536091020038302287779', '133.30249193854686721674754708845', '133.84216823298661183001346478206', '135.32790032472286874261798093384', '135.86355261970131498048237716729', '136.67453621194005578323330299726', '137.162818539839701963683948090', '138.07701326027828900260532885920', '138.70545369422360948852960661353', '139.8571870482244012855249759198', '141.10877814032610229409062188724', '141.75561812308489857738842931805', '142.87116826272399109971098997598', '143.477653102001277871078841978537', '144.04671026281081569778815026984', '144.967118924468517369937468189708', '145.57108308238244241810137264397', '146.798335903207528546744889969645', '147.6483086102710945411292599119', '148.1796216950270736214243364375', '148.89696498968069600314543531248', '150.007370004140149620904842678417', '151.058659129537018412256274582527', '152.00975389909633546814204737316', '152.81082093751442106999446632830', '153.356382726895161627404950290244', '154.211704655741980663248763535198', '155.15098725433396256992325532044', '155.57566990710613050320809781958', '156.40391617433245000197483509833', '157.18878915950767671460977836544', '158.59830124121625729837039611975', '159.47827676326635510141470762056', '160.3328611263333757109439492419', '160.81955587432910375693684602908', '161.4641692234067907640988611828', '162.73246498230247267040214437026', '163.33504943808720319485843999250', '164.21822088894304123848835733826', '165.081003728491446360256291758090', '165.39233970565525561003016748671', '166.49942234770240070391746862478', '167.37776902422426893383712918673', '168.14338218914455576193215117382', '169.55168358968830953633293012213', '170.113038524859748811824324662065', '171.06244649721874409550907026909', '171.78126070130360761166455660223', '172.06574183853059702498238508271', '173.02955965784459447392782640132', '173.732718856129040721390157708960', '174.98912646717256343119089800774', '175.55714823253748386717786364075', '176.38903211222489334472321133577', '177.45970587009466648944957845331', '178.32561674715313637427490631288', '178.99752197241365858965080497662', '179.81743635151126258203927242262', '180.598757165334402900587757626327', '181.47924091705068080304703404972', '182.48081872567466866223326068170', '182.884670494711887630812086028443', '183.507167285108397534725179300', '184.38528233954379645465653860748', '185.042925312452964987501436685349', '186.95331173352919012597444851994', '187.20159952600357008646221265053', '188.061669067002852906157365144349', '188.77238685892543391489079941623', '189.54258703719365271196763298320', '190.31578868778032642251362673295', '190.94215561259108798761432020974', '192.01189629256972795684088994092', '192.47467988122970146451005588130', '193.68784731158871170374876498199', '194.20658703543395665809946501465', '195.38019353926250629245087052220', '195.77292080709184376050124868877', '196.95561168782063025112509582403', '197.834975341310874442406085378683', '198.76194577255671839774991651923', '199.37840302740097537328962935977', '199.77196454005460364166317654877'], 'prelabel': '1-77-77.76-r0-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.35758649667489656, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(2)', 'symmetry_type': 'orthogonal', 'types': ['DIR'], 'values': [[1, '0.497926531700574692692609795549']], 'z1': {'__RealLiteral__': 0, 'data': '1.07518664972', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.55056670578', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.50311450515', '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': 0.35758649667489656, 'bad_primes': [7, 11], 'central_character': '77.76', 'conductor': 77, 'conductor_radical': 77, 'degree': 1, 'dirichlet_coefficients': [1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, -1, 0, 1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 1, 0, 1, 1, 1, 1, 0, -1, 0, 1, -1, -1, -1, 1, -1, 0, 1, 0, 1, -1, 1, 1, 0, 1, -1, -1, -1, 1, 0, 0, -1, 1, 1, 1, -1, 1, 0, 1, -1, 0, -1, -1, -1, 0, -1, 1, -1, -1, 1, -1, 0, -1, 1, 1, 1, -1, -1, 0, -1, 1, 1, 0, 1, 1, 0, -1, 1, 1, -1, 1, 1, 0, 0, 1], 'euler11': [1, 0], 'euler13': [1, 1], 'euler17': [1, 1], 'euler19': [1, 1], 'euler2': [1, -1], 'euler23': [1, 1], 'euler29': [1, -1], 'euler3': [1, -1], 'euler31': [1, -1], 'euler37': [1, 1], 'euler41': [1, 1], 'euler43': [1, -1], 'euler47': [1, -1], 'euler5': [1, -1], 'euler53': [1, 1], 'euler59': [1, -1], 'euler61': [1, 1], 'euler67': [1, 1], 'euler7': [1, 0], 'euler71': [1, 1], 'euler73': [1, 1], 'euler79': [1, -1], 'euler83': [1, 1], 'euler89': [1, -1], 'euler97': [1, -1], 'euler_factors': [[1, -1], [1, -1], [1, -1], [1, 0], [1, 0], [1, 1], [1, 1], [1, 1], [1, 1], [1, -1], [1, -1], [1, 1], [1, 1], [1, -1], [1, -1], [1, 1], [1, -1], [1, 1], [1, 1], [1, 1], [1, 1], [1, -1], [1, 1], [1, -1], [1, -1]], 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/77/76'], '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': '1-77-77.76-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': '1-77-77.76-r0-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.35758649667489656, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.07518664972', 'prec': 44}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_77.76', 'Lhash_array': ['dirichlet_L_77.76'], 'factors': ['1-77-77.76-r0-0-0'], 'label': '1-77-77.76-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/77/76'}