Formats: - HTML - YAML - JSON - 2026-07-18T21:08:09.621841
  • lfunc_lfunctions • Show schema
    {'Lhash': 'dirichlet_L_55.48', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.9510565162951535, -0.30901699437494745], 'a3': [0.5877852522924731, -0.8090169943749475], 'a4': [0.8090169943749475, -0.5877852522924731], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.30901699437494745, -0.9510565162951535], 'a7': [0.5877852522924731, 0.8090169943749475], 'a8': [0.5877852522924731, -0.8090169943749475], 'a9': [-0.30901699437494745, -0.9510565162951535], 'algebraic': True, 'analytic_conductor': 5.910570863704376, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]]], 'bad_primes': [5, 11], 'central_character': '55.48', 'coeff_info': ['x^20 - 1', '0.951056516295154 + 0.309016994374947*I', '\\\\zeta_{20}'], 'conductor': 55, 'conductor_radical': 55, 'conjugate': 'dirichlet_L_55.47', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^19', 'a^17', 'a^18', 0, 'a^16', 'a^3', 'a^17', 'a^14', 0, 0, 'a^15', 'a^9', 'a^2', 0, 'a^16', 'a^11', 'a^13', 'a^2', 0, 'a^0', 0, 'a^5', 'a^14', 0, 'a^8', 'a^11', 'a^1', 'a^18', 0, 'a^4', 'a^15', 0, 'a^10', 0, 'a^12', 'a^3', 'a^1', 'a^6', 0, 'a^12', 'a^19', 'a^5', 0, 0, 'a^4', 'a^7', 'a^13', 'a^6', 0, 'a^8', 'a^7', 'a^9', 'a^10', 0, 'a^0', 'a^19', 'a^17', 'a^18', 0, 'a^16', 'a^3', 'a^17', 'a^14', 0, 0, 'a^15', 'a^9', 'a^2', 0, 'a^16', 'a^11', 'a^13', 'a^2', 0, 'a^0', 0, 'a^5', 'a^14', 0, 'a^8', 'a^11', 'a^1', 'a^18', 0, 'a^4', 'a^15', 0, 'a^10', 0, 'a^12', 'a^3', 'a^1', 'a^6', 0, 'a^12', 'a^19', 'a^5', 0, 0], 'euler_factors': [[1, 'a^19'], [1, 'a^17'], [0], [1, 'a^3'], [0], [1, 'a^9'], [1, 'a^11'], [1, 'a^2'], [1, 'a^5'], [1, 'a^18'], [1, 'a^4'], [1, 'a^3'], [1, 'a^12'], [1, 'a^5'], [1, 'a^7'], [1, 'a^9'], [1, 'a^18'], [1, 'a^16'], [1, 'a^15'], [1, 'a^16'], [1, 'a^13'], [1, 'a^14'], [1, 'a^1'], [1, 'a^10'], [1, 'a^19'], [1, 'a^4']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-55-55.48-r1-0-0', 'leading_term': '2.70797411856500314484605146004-1.77054130777280769719050882234*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/55/48', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [3.235419655832571, 2.8406872708365842, 2.351463429588502, 1.7492370981802696, 1.0523897403767977, 0.33689087610650365, -0.2732022625380498, -0.6401515738458128, -0.6606588442007344, -0.31252461598999093, 0.3175324705600688, 1.0397844831831455, 1.60709879192455, 1.7921295216349329, 1.4731817185780152, 0.6965928920958284, -0.31450857400638577, -1.2197377812045433, -1.6783869118079293, -1.4861264911900034, -0.6776921809604125, 0.45402642040045765, 1.444935707982469, 1.8326412468139206, 1.3537660426065365, 0.08317049661096813, -1.5543654143041894, -2.9223977693643137, -3.4188163192325987, -2.73299611040299, -1.0007648954169406, 1.2218540489465377, 3.169484355575418, 4.180648716063094, 3.9765647418950723, 2.7751884254035044, 1.1810993898849635, -0.10244348783851587, -0.6030492677169692, -0.28774121099571337, 0.45602484379886354, 1.0580948251584938, 1.0961532451454492, 0.5376857211224115, -0.24641021736470395, -0.7134469806978854, -0.5015444350207267, 0.3011744372867631, 1.1426981006633143, 1.2841711289336695, 0.23351113260649203, -1.9057907780615402, -4.387197092500307, -6.136893271200298, -6.289408798918308, -4.65993469671796, -1.8836876251012147, 0.8762657013748593, 2.511588599343755, 2.528553941363938, 1.2734449415576363, -0.30498966938878685, -1.2193391161555307, -1.0049727187952473, 0.04980758446905503, 1.1358095510416286, 1.4669781778622824, 0.793576814919486, -0.43959453772210333, -1.3900958184520715, -1.3780363643677493, -0.3439622562804374, 1.1000397635859123, 2.066930673965013, 1.9812949266646913, 0.9626210217105936, -0.2625010834486632, -0.8736960407730154, -0.5532724814190937, 0.2524260399066766, 0.6152609266287253, -0.2084071929039151, -2.1688338665246625, -4.308244819223815, -5.270164686781279, -4.144186878629049, -1.1077905991343227, 2.5738659202007788, 5.2287945549011665, 5.732935713451488, 4.1406027127151015, 1.5926310727215207, -0.4282704689667071, -1.001348180684907, -0.24431472940288035, 0.9208069781709762, 1.5054703665543279, 1.1527774110924112, 0.30591687882433893, -0.24131779611741455, -0.04123190229302512, 0.6141979298008842, 0.9182331661676535, 0.22865512459901668, -1.3286881117972518, -2.8308944682538018, -3.180669676799896, -1.9501736725267667, 0.19246830628058553, 1.8435514471489136, 1.8104692993954743, -0.012830591165301148, -2.4909517281660483, -3.968875264648949, -3.392229564325336, -1.0379014507787292, 1.675199002686897, 3.1712209913459426, 2.7966843179710517, 1.2206548516450835, -0.12156822078423903, -0.11646755734149009, 1.2191067764419032, 2.7998987958390886, 3.3345525195901207, 2.316663948491754, 0.3892471722088034, -1.1771402782065004, -1.463345918725544, -0.5630726433878401, 0.5801119489404488, 1.0002942936999326, 0.5080968129014539, -0.20108565560780228, -0.2155477022619742, 0.7183093616527181, 1.881710067034058, 2.1500066410797567, 1.0181662735865993, -0.7700343338927864, -1.5881368565104932, -0.10973121340119533, 3.5634040770362416, 7.73484806551235, 10.126325603893735, 9.385125521826566, 5.992498777071323, 1.9026005998161242, -0.8136578492421298, -1.3082028605311875, -0.31157395509436164, 0.6771910491894552, 0.6501869059956866, -0.21625996204931672, -0.9297170157895093, -0.7089449687182536, 0.2585777550034508, 0.986244656698905, 0.6155768946410857, -0.7394264015237612, -2.008043425442005, -2.0656109865163588, -0.7553304947294237, 0.882903569913122, 1.4327560695825317, 0.313999494971413, -1.6519975683683665, -2.857439746084962, -2.2415016926422675, -0.23314634293223044, 1.5279276658296594, 1.5191574473567937, -0.3631798507317278, -2.6289838363193097, -3.3415026994434887, -1.6818862366976917, 1.3462753307917883, 3.664591678592335, 3.72471308759793, 1.6735759919882467, -0.8460706581288533, -2.052958853947646, -1.396606686341559, 0.16887657904332604, 1.1516470575165465, 0.8282329242789168, -0.24600463524951321, -0.9000710881486255, -0.5053586249113695, 0.46341300385868367, 0.9667233953532375, 0.4951306404215364, -0.36088678516207856, -0.46920022055573446, 0.6303185823744152, 2.0147625904839814, 1.955156743245261, -0.5828357996514838, -4.790696705724143, -8.315587680307573, -8.913271723855178, -6.171931877212753, -1.8822998986736408, 1.291163162158672, 1.7793923589632001, 0.13317226399294685, -1.6723064260370566, -1.979618742004861, -0.7282500341707306, 0.756693226267193, 1.1478472128995412, 0.3491638596019519, -0.5268607039304107, -0.3423987225663264, 0.8904808582763708, 1.97414870505972, 1.66623267604693, -0.08918653864000399, -2.02409212911113, -2.6623383674827528, -1.6576827790463748, -0.09133929409633736, 0.5683507234428715, -0.130025828447992, -1.2018572253986344, -1.23330717339875, 0.11309322812776937, 1.5596640179976529, 1.2634842506034083, -1.4140480980309555, -5.045487386991514, -7.084431308331826, -5.914540030310961, -2.2509878269240704, 1.3560168033573867, 2.5328389627541723, 0.9080435102059692, -1.7704797419240432, -3.238953986115768, -2.5761587301879176, -0.7227493150576746, 0.6443794369841742, 0.7054744296583476, 0.06495828166528357, -0.11747315543006914, 0.5608719332320449, 1.3517699937903247, 1.2539254415826575, 0.2313710442344676, -0.5733516775504629, 0.0499581027774894, 2.010704228145266, 3.727470820456029, 3.474022823160753, 1.0877766484421116, -1.6167496801333194, -2.2741648291778205, -0.05345277316284405, 3.4856275066333495, 5.614096718318633, 4.706977616419979, 1.562796528559831, -1.3865624251740454, -2.2212617652427284, -1.0765087733838163, 0.26064781647253893, 0.209237051674399, -1.1055165694292584, -2.1022438096327947, -1.4156981600525311, 0.6878648584218692, 2.5289018456087895, 2.6174510944543696, 1.0473850484378726, -0.6694885099399853, -1.1184887223073845, -0.3125008778592563, 0.4714093877011329, 0.12704524701916586, -1.0865712562116032, -1.8444628651549442, -1.2439663740114062, 0.09813281167222385, 0.582305095455432, -0.6293524098331463, -2.424665320124426, -2.472837500630785, 0.6054896470505582, 5.628402561288445, 9.447761438516192, 9.40333439181181, 5.518475279617727, 0.47795439033428216, -2.5862713499434156, -2.5148238537344487, -0.6573696327670386, 0.7509777392264898, 0.6838209207411958, -0.06647903138570556, -0.12218497340963601, 0.8566548166845148, 1.8598168661074492, 1.7470326914700292, 0.5942664010285903, -0.33669611278682693, -0.0016172292513860582, 1.166692793627098, 1.5695309135974855, 0.11210048083127083, -2.4764826714260497, -4.136860677646415, -3.434807566353391, -1.0634631588732975, 0.687964291097164, 0.09461339207571137, -2.2955801839659906, -4.1303116474369395, -3.514060070205354, -0.8816465481596182, 1.3682426996701254, 1.1580913015620091, -1.2748463445421427, -3.6123011110984424, -3.6745278725673756, -1.4551043844751075, 0.9784788948735923, 1.542646445551652, 0.08223484356602738, -1.6678659097710433, -1.9361314713316304, -0.6351280975273252, 0.7463357991152484, 0.8263132730845748, -0.2574717860591594, -1.1588275837559103, -0.9113320324091383, 0.014523269200862998, 0.3652845080484377, -0.28143953168804914, -0.8256330148362616, 0.18742760266056754, 2.6799946353133945, 4.549510003641555, 3.3997341237890306, -1.0080235181338038, -6.0482821536463005, -8.202855659201491, -6.037660424060638, -1.4301611111270836, 2.1156873633098643, 2.4818766728686326, 0.483371270320055, -1.341129275662452, -1.307248689826292, 0.041437027542934615, 0.9307280717307383, 0.43189276071898275, -0.6461622236261735, -0.8833016901989728, -0.008781401649646496, 0.7209316215554039, -0.038019502854802906, -2.0676311570692643, -3.608915835170608, -3.1245054212375445, -0.9415959469815224, 1.026219808731008, 1.2420935632805565, 0.11461581391740211, -0.5386646714149128, 0.4054066394993565, 1.985683963809161, 2.077845658600103, -0.23997184596237459, -3.3917377317331656, -4.603587483017326, -2.6355490070462864, 0.8164447273687949, 2.5791940628502465, 0.9811352165894361, -2.5657895641496524, -4.934845911656446, -4.226196700243528, -1.390825625022917, 0.9411567311999632, 1.0779549222288336, -0.3446396378094255, -1.422179766392055, -1.1211463863579763, -0.158938736124582, 0.1514477010323271, -0.4154620271297653, -0.7777399094301161, 0.0017738609656801677, 1.371715340515322, 1.756787368565762, 0.4333179908302728, -1.3363481779246045, -1.414066051068241, 0.827300857167546, 3.413372637411217, 3.397521116604732, -0.20886338534644458, -5.162930239033354, -7.818864469457776, -6.390226033069412, -2.4771142606192433, 0.5982619821448466, 0.9168369507563315, -0.5599271042663821, -1.4554966115693129, -0.6342785598406636, 0.7870650333005044, 0.9803767001972821, -0.3701913191112202, -1.6640175061369051, -1.1947014245009577, 0.8980266002981127, 2.7274868641155767, 2.6907842372667368, 1.1651249840886808, 0.0016337584144063054, 0.42349260206801087, 1.709260886562125, 2.128757200066215, 1.0269136472319764, -0.3724271137516114, -0.4179266388462346, 0.912812650846989, 1.8109619525123977, 0.721756344226834, -1.5286319427109214, -2.1043440963613373, 1.0249495036035203, 6.641002708364218, 10.894178412518734, 10.620658034468086, 6.1768785507020425, 1.0143734522222092, -1.5232360656897983, -0.9772327510544777, 0.4667189034505535, 0.633403977087627, -0.5225819865464013, -1.393780083244513, -0.8921055617094167, 0.3039324581395885, 0.7443600257137747, 0.07857242758290275, -0.520897684317065, 0.104693777537809, 1.4955672522075396, 1.9480472967409972, 0.584821618211377, -1.2875488944130435, -1.312857500401709, 1.319465036164135, 4.682334815633527, 5.843334659497212, 3.855416627973239, 0.818005679901325, -0.23694618428326256, 1.5218229012183049, 3.887182559495132, 3.973658942587859, 1.2617765080239538, -1.90412433857126, -2.834360184630974, -1.269405377571848, 0.5422874500698299, 0.4240075580021012, -1.392049093100847, -2.684724672311601, -1.822933698562986, 0.4311797049990226, 1.8426972781159627, 1.1945430950981795, -0.4926871693653631, -1.288559538824186, -0.5694776161438231, 0.45757343250055754, 0.4171908975973275, -0.49576322871463546, -0.8563071645358993, -0.016594988388827857, 0.7616767151411501, -0.32433117994380867, -3.142792116333749, -5.037828371240048, -3.2460859043818098, 1.9938932284917121, 7.063731061964374, 8.066648165620188, 4.445692379921093, -0.5398317218095773, -2.958979924165133, -1.7574831883991326, 0.7840822731447243, 1.8189048808757904, 0.7732325729716913, -0.634029725144846, -0.7748983684692753, 0.060607611399238495, 0.3884934956162781, -0.34108223009770505, -0.94698230695877, -0.044831614163963335, 2.011842674098152, 3.2556409187319826, 2.306361699918834, 0.0898773192224367, -1.0525368546347018, 0.03236365053967179, 1.9840518914067449, 2.49726035732349, 1.0493796031833487, -0.39764008738023837, 0.341156465565134, 2.9651326681894266, 4.715159259067335, 3.301086696926702, -0.4582870801588421, -3.3043073507243137, -2.9212006611423247, -0.38103026258411876, 1.0349337197545565, -0.6346655937876312, -3.9793131216465163, -5.795787905964309, -4.464721312665188, -1.4430806818599289, 0.5572422185810404, 0.45278339369959003, -0.472588875567608, -0.5032943888667998, 0.4247839153763936, 0.9374472521616998, 0.23588155057511911, -0.7568759910285627, -0.5969405777703872, 0.6820089871086521, 1.4286894343345207, 0.48438242653238606, -1.0011531657323727, -0.5340497292225319, 2.722318367540291, 6.330602763189319, 6.565605758648199, 2.2318803889342544, -3.7539734657754016, -6.910139373745052, -5.3579213192915445, -1.331467598492273, 1.3939038331778204, 1.248229170635502, -0.15198725843254887, -0.45804100466809283, 0.6168141869013496, 1.3134689134142075, 0.31353506116939217, -1.4893930179196628, -2.0678512332946637, -0.7866698044554159, 0.7614346187812344, 0.6560536083785387, -1.0145222074075941, -2.2271615317274303, -1.4454784495013902, 0.5254075757894857, 1.502647649100628, 0.5531617746645587, -0.9119293608161736, -0.9371076229701107, 0.47465784405502454, 1.303179298581119, 0.12865816673452318, -1.713709309937087, -1.28208940203897, 2.5137019944670165, 7.07874960969947, 8.31676563175541, 4.751895034972448, -0.8244273120799945, -4.028874636512408, -3.0658549490639095, -0.044176197207752795, 1.6924652281386643, 1.0440896349999718, -0.2899317487062318, -0.33412117257943275, 0.815772181117799, 1.4722074280683832, 0.7106254888419632, -0.5009357253509452, -0.7233438107948799, -0.026184377520161485, 0.1442117889748588, -0.9050392947019552, -1.805832456548324, -0.5934393573791898, 2.6230273790096494, 5.158265621727049, 4.44083606086317, 1.02468220846268, -1.6726662189553043, -0.9199256274381717, 2.3345009371145684, 4.434739336255225, 2.961007248768638, -0.7182403644365585, -3.0767995381391215, -2.307678899781154, -0.06173461920431603, 0.7457694086568761, -0.6770652747957404, -2.3538017566261558, -2.1788198557923737, -0.5199000144212853, 0.32265102397677164, -0.977169270231395, -3.0906085296353387, -3.591145473283662, -1.807031208408033, 0.4753148876493789, 1.2047591157440634, 0.38533461004228087, -0.27773763048489053, 0.21060123541870623, 0.8481816384741007, 0.15274766649588034, -1.5238347341695788, -2.0770764893076343, -0.3547889673716802, 1.8197047135048146, 1.187506019930491, -3.1562408266921267, -8.062620984723473, -9.064292813794076, -4.9002488659924195, 1.0560718033575545, 4.096460474400651], 'positive_zeros': ['1.723758198772869418505426868613', '2.97992395557419224278476627286', '4.90456119209350543290966291353', '6.44015500418437437421037453011', '7.82916659086975939655955205908', '9.51798462482897505199703962805', '11.52983950795412698090652758470', '12.31677251168010655885873954675', '13.64830915552557132050017113315', '14.58529741217483543797274575657', '15.666798026076328082553958688348', '17.70430554696065935721439631452', '18.99680973227963566327431523880', '19.98727178602226004683273893887', '21.14195925722907328762159607574', '22.26284032013705932237979761198', '23.67553876730457443048068877961', '24.58933108698170895767017536496', '25.26563782786901351305311302693', '26.968278032074018810557586885171', '28.66486936651011508887660184115', '29.43954117173196649041801666039', '30.7557184708851293766202306484', '31.27319866070328329500585726727', '32.24239574939017536368366603291', '33.72227913452511069903811584909', '34.68584140373115002372169298384', '36.05123280393783315479018743200', '37.45650490348829329947833548840', '37.85414860350795857872982464809', '39.438585001038059073068096486972', '40.45579539662932997093701088463', '41.45697931605478276523529451455', '41.97624115914339699621458495719', '43.300353257170514334566523957957', '44.07480173403731586738523830261', '46.1269943989509946336966850086', '46.95500294467865038770389727885', '47.74383000738992680068717472713', '48.67353612051659475834084722721', '49.53327776578959843850671332162', '50.75988911713410551131137239067', '51.61540383977829269759284954969', '52.84585839118248281458248454199', '53.70218397523576374168463745588', '54.86533886911046557672589936221', '56.13589705310432559573966295119', '57.15298713689316584488884114967', '58.05466364127770907269516860142', '58.91492786057622595992481130033', '59.85877122453873693313509855621', '60.480910871062957178525535697771', '61.510698966362522560977056374432', '63.28243617873895157696540888121', '64.08238700045914896243704570144', '65.13889648250613213256950365784', '66.04038290582746465164783692787', '66.668211030258561908309268079111', '67.79935578312514490418171536898', '69.0848958331368210152273239179', '69.65088086269023372455875702537', '70.60430822377962301731416524999', '71.42621783770902487511397684086', '72.99102017068951462103342099302', '73.85534060238037180905817915515', '75.13309761444544307918024816035', '75.974833537185576837628140397249', '76.33748545539744603483142968749', '77.563981847663670140724922247720', '78.11406717409576768736964526087', '79.48929073886485251377178790339', '80.31753057661675998423353691393', '81.709131333498667037937375520726', '82.72966680628412932592680236670', '83.19014272115006989080639489866', '84.281985952806751869540552278158', '85.485727720759750665500490873772', '86.34583140163805136898337237898', '86.91439202445803876548779816701', '88.09976403588300621337479797867', '88.63217222214327370414020050908', '89.64365153996837328629451700615', '91.2843706766645152349335560964', '92.30066482278457508553542560802', '93.09188038549795415277074699502', '93.49666597719343404668649427412', '94.84712818700156856849218712318', '95.31302448178092507605304411855', '96.2649959243590652141499817344', '97.64968829558185287663964063801', '98.14106525699784243640777948414', '99.47370651657363798603496917313', '100.16877572453184916426185167697', '101.419431308571622684752281075110', '102.200483763418696179409571423762', '103.24818541716454374020178912541', '103.9983793888722762027715812082', '104.99456779651903184589569570727', '105.52193714875103080101385635283', '106.21870871509159119957735455174', '107.43995258210534467634214431287', '108.85193023045723593717376919684', '109.75320050922574025146246548547', '110.615853926293577511973841352932', '111.3704674245081722227933517749', '112.190026298708749302587413947091', '112.80497964351203675684227325461', '114.1889279682154092983264854087', '115.03028963780104405636538284721', '115.53821687219365990721490129570', '116.53864364412172827504070145612', '117.735212096710268209455923421396', '118.5301324259774592917509320461', '119.84453721950861562543342162046', '120.55730981001578233235301284549', '121.63212630053971332194941377814', '121.99334709669660533478871828705', '122.81207439872615824267339893', '123.819614211878020369160650313489', '124.59549497022217160631004713412', '125.6115282385957054472845236038', '127.10181954988843165276703038349', '127.705158081457311029990311977475', '128.56735497254168059382457547058', '129.30561186041446473725166187983', '130.19209839868018963368208594383', '131.563723637347100581406639445025', '131.70876379699620162519504240943', '133.022627907764891243937494839829', '133.55679563298499592506790523861', '134.47668661746904018001161717670', '135.24198374507722626211420035563', '136.95827462006416621687570166486', '137.69692138882994062370266807611', '138.31471846084062346250102985644', '139.29026194167516135129041710820', '140.027485980749929271023414413040', '140.5977651109285944567223551958', '141.651344087924265697553498779901', '142.37318650350755301058533992077', '143.88342244558638177657133974653', '144.14508007204626019150292991867', '145.42557486264990521066686521328', '146.44354848559413937983680134394', '146.96433572645733199613070216462', '148.065825703144064187964710555489', '148.968656537101815940625440290071', '149.839576996156549610581403343554', '150.46521913324940496540561332525', '151.25451250446158710357359298022', '151.82573225120268224801671283595', '153.01858376343519380313680824294', '154.33638715064583722527649624288', '155.20933661054294227800649924132', '156.08932523575634022500241748368', '156.85241481666515792811873619332', '157.38642443586717070401377991853', '158.13304890307483200725328333278', '159.388826284213498368527737535320', '159.99470682593303608562395506781', '161.126679544029107522228030130178', '161.50276866334514798769151345440', '162.776190709523459508053740848043', '163.799135647855765866711941223805', '164.30318418933051203309995533155', '165.810910264629059171364080686716', '166.395039903092573013317970839767', '167.057909716295240346740418080374', '167.87706984162007817943378632421', '168.59702629871548661739156810693', '169.46581576159651372767797081160', '170.0712069029460400845582383035', '171.36360524451687589531855946915', '172.61675663223563430452308189703', '173.39822371011190443075349109930', '173.908296365113799121801077088990', '174.74204089409572879916643400610', '175.76246076386124309980101337164', '176.39068749511549036424593729235', '177.41543007014154181822080338697', '178.2307253315838406685408844022', '178.96817859307610070575609329782', '179.707705012957916116096987189685', '180.4460235832526359473854860161', '181.82558141739326792981077652952', '182.817390532423023207957686362192', '183.6653746444240898797390150279', '184.1700467543075744232519866569', '185.16940364789182736910261444210', '185.9495095750372920365087174784', '186.31928982350740875721101734629', '187.2555942922018688260257188810', '188.5278896872796442848227477646', '189.16233566159459103590851162794', '190.25196831240901260889601084910', '191.26016998535562551551296258971', '191.763637683421014524462324491790', '192.92553825499527291380576455673', '193.26116604415824880524996228313', '194.610229504428913950090740439748', '195.43872462494553785929461024769', '195.85651673550248890155523748724', '196.59415920518522961346513596707', '197.54402233569521043566246456657', '198.23478756846041525202356372992', '199.62665025587847073682225662927'], 'prelabel': '1-55-55.48-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.910570863704376, 'root_angle': -0.18432035848521997, 'root_number': '0.401063357659432515877325320030-0.916050316927483036117140637859*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.184320358485', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(20)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '2.01050937875845902252203600390-0.874052159200032193072854381541*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.72375819877', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.97992395557', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.90456119209', 'prec': 44}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 5.910570863704376, 'bad_primes': [5, 11], 'central_character': '55.48', 'conductor': 55, 'conductor_radical': 55, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/55/48'], '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': '1-55-55.48-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': '1-55-55.48-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.910570863704376, 'root_angle': -0.18432035848521997, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.72375819877', 'prec': 44}}
  • lfunc_instances • Show schema
    {'Lhash': 'dirichlet_L_55.48', 'Lhash_array': ['dirichlet_L_55.48'], 'factors': ['1-55-55.48-r1-0-0'], 'label': '1-55-55.48-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/55/48'}