-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_77.9', 'a10': [-0.5, 0.8660254037844386], 'a2': [-0.10452846326765347, 0.9945218953682733], 'a3': [0.6691306063588582, 0.7431448254773942], 'a4': [-0.9781476007338057, -0.20791169081775934], 'a5': [0.9135454576426009, 0.4067366430758002], 'a6': [-0.8090169943749475, 0.5877852522924731], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.30901699437494745, -0.9510565162951535], 'a9': [-0.10452846326765347, 0.9945218953682733], 'algebraic': True, 'analytic_conductor': 0.35758649667489656, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [11, [1]]], 'bad_primes': [7, 11], 'central_character': '77.9', 'coeff_info': ['x^15 - 1', '0.913545457642601 + 0.406736643075800*I', '\\\\zeta_{15}'], 'conductor': 77, 'conductor_radical': 77, 'conjugate': 'dirichlet_L_77.60', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^4', 'a^2', 'a^8', 'a^1', 'a^6', 0, 'a^12', 'a^4', 'a^5', 0, 'a^10', 'a^9', 0, 'a^3', 'a^1', 'a^11', 'a^8', 'a^7', 'a^9', 0, 0, 'a^10', 'a^14', 'a^2', 'a^13', 'a^6', 0, 'a^3', 'a^7', 'a^14', 'a^5', 0, 'a^0', 0, 'a^12', 'a^13', 'a^11', 'a^11', 'a^13', 'a^12', 0, 'a^0', 0, 'a^5', 'a^14', 'a^7', 'a^3', 0, 'a^6', 'a^13', 'a^2', 'a^14', 'a^10', 0, 0, 'a^9', 'a^7', 'a^8', 'a^11', 'a^1', 'a^3', 0, 'a^9', 'a^10', 0, 'a^5', 'a^4', 'a^12', 0, 'a^6', 'a^1', 'a^8', 'a^2', 'a^4', 'a^0', 0, 'a^0', 'a^4', 'a^2', 'a^8', 'a^1', 'a^6', 0, 'a^12', 'a^4', 'a^5', 0, 'a^10', 'a^9', 0, 'a^3', 'a^1', 'a^11', 'a^8', 'a^7', 'a^9', 0, 0, 'a^10'], 'euler_factors': [[1, 'a^4'], [1, 'a^2'], [1, 'a^1'], [0], [0], [1, 'a^9'], [1, 'a^11'], [1, 'a^7'], [1, 'a^10'], [1, 'a^3'], [1, 'a^14'], [1, 'a^13'], [1, 'a^12'], [1, 'a^0'], [1, 'a^7'], [1, 'a^14'], [1, 'a^8'], [1, 'a^1'], [1, 'a^5'], [1, 'a^6'], [1, 'a^8'], [1, 'a^4'], [1, 'a^6'], [1, 'a^10'], [1, 'a^9'], [1, 'a^14']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-77-77.9-r0-0-0', 'leading_term': '0.595633476223034422065389332960+0.921642953839939101229133561610*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/77/9', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.097362735088241, 1.489308506983753, 2.167884530907182, 2.876474728363056, 3.3683538357918175, 3.4417047942786274, 2.976599058620417, 1.9815075097634107, 0.6190988758932953, -0.8130759221662214, -1.9555401524374862, -2.4993780519503113, -2.3021670729146466, -1.4601883188576588, -0.2977861855271857, 0.7368892838326359, 1.2404617505080058, 1.0229953003359793, 0.20117713811680885, -0.8364538334136619, -1.5916363200946901, -1.6833321534749266, -1.0363276892990687, 0.06596259977575337, 1.1048681090242798, 1.5797322175093733, 1.2704547681161131, 0.36910176051095445, -0.6051760015559157, -1.084258947934816, -0.7874010901355326, 0.06924344747801847, 0.8268457723050675, 0.7060163414197498, -0.751806654561712, -3.3594449938535975, -6.273839790033233, -8.343234188819235, -8.656871894871218, -7.013819415309924, -4.049812268180834, -0.9352862216085539, 1.205540719735602, 1.8406609120550954, 1.2387241468770933, 0.22769457514068475, -0.3448036083959929, -0.11909203779892583, 0.6105564141104638, 1.1654388341319875, 1.0009699668391163, 0.121924468501469, -0.8948568768050185, -1.2986431248667725, -0.7196077463905601, 0.5099585799983057, 1.519665845795596, 1.4765493806293548, 0.19941218411097023, -1.6217633869873667, -2.796160410503693, -2.391188688629087, -0.39103127402833504, 2.2049393877819066, 3.9525772290320766, 3.8602801883806914, 2.0281654675582588, -0.4093476997688102, -2.0197426836293864, -2.0060368902440673, -0.70914884103963, 0.6649558817518728, 0.9056854991318075, -0.3522891564163705, -2.3826133452418885, -3.891200606578753, -3.9291236663016904, -2.5373063234650846, -0.6671561513199487, 0.5436594410583989, 0.5864710868232572, -0.12359714364432753, -0.6776710413485498, -0.4671091776706791, 0.3064041050163234, 0.8289481580300289, 0.4327040094603194, -0.7090713560797129, -1.5637776393037766, -0.99445728987257, 1.253082760674722, 4.122678286382359, 5.803139452229366, 4.950191598052058, 1.7074650403470968, -2.2567461209938573, -4.786842677081925, -4.643756082680211, -2.2758514345806633, 0.5881088432167364, 2.199894163057771, 1.9599910303773647, 0.6495910176414923, -0.3720150838020281, -0.3049235296717231, 0.5398867152775757, 1.1740957192784527, 0.9201702882692566, 0.0718918331637396, -0.3557193651150977, 0.42740543140146037, 2.1785356267516836, 3.693142870622066, 3.74978663300096, 2.1520267369132142, -0.03777080229914573, -1.3227251240793394, -0.9978805105814698, 0.25968433895175663, 0.9769938602271375, 0.19525122499632888, -1.6010971041289856, -2.7733170112395094, -1.8681266952463, 1.0730875722314044, 4.353747717399015, 5.817522567941608, 4.483376568739683, 1.309309064698835, -1.5398875979842883, -2.3326557176830502, -0.999496495516339, 1.0049438482999267, 2.015227232843956, 1.4970801062073458, 0.3112226523670885, -0.2307704386758983, 0.3976144425783098, 1.5272603574988466, 2.025817747186977, 1.429572899223293, 0.37802723847468706, -0.06816771103449673, 0.437116572707931, 1.0722529311101978, 0.6046743121565036, -1.2761137771111923, -3.321298538649295, -3.523808532233683, -0.8146849775352805, 3.786547216829308, 7.661815483515243, 8.457752705912966, 5.844861103923508, 1.7205056921030288, -1.3130506589789945, -1.9186203778096307, -0.8179882118595572, 0.16048991834191423, -0.16656904314853746, -1.3704478619458034, -2.022719762366328, -1.2133913021534708, 0.49927724476158175, 1.5964453828109453, 1.0530902752063995, -0.6658327753924514, -2.024495602333512, -1.8499552701704607, -0.4074654147908429, 0.9110417674572556, 0.9750129131186624, 0.02065565270051263, -0.6214394816369786, 0.07421354247432203, 1.6875271941941223, 2.6571116957809613, 1.8222348536259525, -0.2700543354963939, -1.6475272400677232, -0.6743065787994634, 2.282380529130055, 4.8954165937011105, 4.744905152842115, 1.4272424610970846, -2.977653122919718, -5.542943294109474, -4.827006946269653, -1.8878842770754813, 0.8211269980612219, 1.5791303750704342, 0.6234777211399247, -0.49053623100803756, -0.5795989449685265, 0.1360034473882031, 0.568552617904578, 0.14616557129391933, -0.49535840058651703, -0.25996836056836864, 1.0376502708779622, 2.2077742343817066, 1.7572405464742913, -0.5024652095440005, -2.989752398846779, -3.669800040508088, -2.0004228505498416, 0.39832997051117375, 1.1307549740592446, -0.7371038706561363, -3.7048682225747678, -5.1251257670514505, -3.6096411152585914, -0.3134100428116935, 2.1134845819099617, 1.9156215142847426, -0.28326974221773504, -2.248214538082417, -2.327761085629174, -0.9224158898120332, 0.13600365248399118, -0.43336688227829473, -2.050273959422272, -2.920210210502189, -1.9159341331661373, 0.2535801038183977, 1.7587303722380603, 1.4730221280218228, 0.017039716847567214, -1.011945003744216, -0.7504280742066638, 0.11841962737728731, 0.2935405572009901, -0.5329320925373783, -1.2245141726537665, -0.5295558557934957, 1.1761778781506724, 1.7305288026917882, -0.9057376141739811, -6.385488503921168, -11.67673097912925, -13.300498710223199, -10.207832950376874, -4.662478455098622, -0.29687542730614136, 0.8621794691356494, -0.29869189884641933, -1.3526123083775028, -0.833634346554558, 0.6071186901543524, 1.3168743648034869, 0.6144893659803671, -0.5253032682926752, -0.6926487539548212, 0.30141657235100566, 1.2145814747348067, 0.8347330226094887, -0.5476008261306093, -1.3625216601024515, -0.517740849301269, 1.2288146636725847, 1.8872792524448825, 0.3271975684401396, -2.3560504953036356, -3.764017576367472, -2.590748790210616, -0.036088458570103184, 1.3125698266621437, 0.07927804579670127, -2.4719313960816685, -3.6994375892240186, -2.2976856517080306, 0.31600933592582997, 1.399733098777271, -0.32494246816712624, -3.332037246039463, -4.762036944317503, -3.203038930014842, 0.01720147765481692, 2.2461903770668004, 2.0774111880414288, 0.4553325252689734, -0.6395664043415883, -0.3311979852808438, 0.4959949240786481, 0.5516499066227242, -0.2084112101335017, -0.5713808204514834, 0.34059747103888127, 1.8206767145037916, 2.259107145649289, 1.0888204343767875, -0.2761895335538775, 0.18389969029436334, 2.6980913525201693, 4.946545670067422, 4.072035849397969, -0.3622774484891533, -5.515960601144734, -7.602987017169364, -5.2727205627420926, -0.7602890159345485, 2.283126006929435, 2.080554048968712, -0.06064519405230144, -1.5605637630236846, -1.2644282018405513, -0.21237314022805773, 0.039011787155485304, -0.5974301924061298, -0.7339392974184412, 0.6268803082467571, 2.6380017647376746, 3.351876719544582, 1.8861505807061254, -0.45898704139201263, -1.4762197682476812, -0.3658871229981431, 1.476164439354045, 2.0786808271745927, 1.086577498799958, 0.020924866555269355, 0.3002288536835675, 1.3297639703175315, 0.9946132380567633, -1.8109011684023406, -5.43650600350907, -6.693611317762234, -4.0298767723851014, 0.6369130954195168, 3.5072852911259647, 2.445297252099051, -1.0861516563267264, -3.629653232690532, -3.151281311670288, -0.7618605835719714, 0.8377494638066907, 0.2901759524030153, -1.2685189218425834, -1.8308836889940001, -0.8397917462685556, 0.41697341926595555, 0.5636316360841868, -0.20999919383189458, -0.5687337563171395, 0.10744403982846311, 0.8339228740791595, 0.3243659855856121, -1.0552803243887159, -1.2251905287571148, 1.3387060576049497, 5.442960922095816, 7.791928050374958, 6.1167050734469655, 1.628031575062787, -1.9396116587549406, -1.882905442567368, 0.9494241471516099, 3.2616578658679396, 2.792609217681627, 0.45269798526883254, -1.0290190829314585, -0.25788580289071006, 1.4126340736800316, 1.6421202830007327, -0.12009162268165381, -2.033530057791625, -2.0339080586574254, -0.19061621593992206, 1.449615263097763, 1.2627726086289859, -0.15237562599630858, -0.8303330041705008, 0.15090284342715735, 1.6015621577616086, 1.7326042849154888, 0.37708086301602856, -0.8001855324798426, -0.38165078541597863, 0.9833570363689305, 1.341716317523113, -0.010457485550417497, -1.3072907939198122, -0.18441433481061537, 3.2584210155045144, 5.810619648494925, 4.083330498990765, -1.8504824594126905, -8.04461118401057, -10.153198007304287, -7.324205575383027, -2.6099428368305606, 0.29077593342887603, 0.3819383848956603, -0.5154417908880162, -0.45421323799529634, 0.489073869305876, 0.8767970322979464, 0.13863663167925394, -0.6002478280498229, -0.08013616413985541, 1.2510531427451603, 1.5994783310585947, 0.08460387445958373, -1.9081069287274965, -2.1335101200501945, -0.14391537032153207, 2.0082758793001623, 2.0568061318883277, 0.235427382922976, -0.8489057851785056, 0.7578479493266819, 3.8510296559717068, 5.101662282348488, 2.659974764305025, -1.6779954775890198, -4.24650111428803, -3.3173863683718574, -0.7314156378034586, 0.37923128850463783, -0.8990151504645253, -2.486983584484503, -1.9963932864639558, 0.3721922996983729, 2.072676881392179, 1.199088035519409, -1.3403933186708108, -2.9308470784500233, -2.203827397170583, -0.34790935121257377, 0.5817149279513032, 0.1045667564107031, -0.4584744697105246, -0.021575611530807393, 0.7599497619997992, 0.5263248845314519, -0.5935320421910278, -0.7005368231382039, 1.4884328046995272, 4.400441980718308, 4.619686047275556, 0.5627541788817494, -5.2159395735059055, -8.022115471032883, -5.549146796192508, -0.16488596231557268, 3.5261018489827785, 3.2149834252693648, 0.7022085210645419, -0.6548922630199723, 0.31003270020271384, 1.7966797782213844, 1.6767657108832912, 0.09175171145817695, -1.016765706386993, -0.5284947091990078, 0.5301198791632779, 0.5503948300822279, -0.3629758240599507, -0.4315882359141512, 1.3940038382815827, 3.758849631373373, 4.255530332605332, 2.3076662363529383, 0.023131551500300204, -0.187140662819689, 1.5606072290367, 2.8064591945975765, 1.7938930663078225, -0.33115767736274504, -0.9537346839669447, 0.5974703366127321, 1.8889202700120498, 0.1411562084632321, -4.197071322690943, -7.392316481705003, -6.254305895949008, -1.6351809993882098, 2.3722098001666074, 2.6560050820634755, 0.0298582265708811, -2.1788445203792834, -1.9516551209658506, -0.36763582091807584, 0.3274773790001633, -0.39284761230894766, -1.041359429020964, -0.4232422757892121, 0.6878818212653457, 0.6811725190479225, -0.5784107278972521, -1.4486447459142915, -0.7190928421456309, 0.6098521315079559, 0.5374404412771564, -1.0752489710720778, -1.7778701764642155, 0.6597842920925322, 5.031137924784451, 7.196677191614282, 4.2887277985133005, -1.9403602256435044, -6.5603409904707135, -6.307363074520147, -2.571960075973136, 0.5867371720077315, 0.881971491712054, -0.35241712504283174, -0.5770955434324545, 0.6419489603555951, 1.4705091863078, 0.6244759452111394, -0.6983102708285591, -0.30824852819970083, 2.0219471131925473, 3.9992327572263946, 3.4551464284920668, 0.9200480099407022, -1.0702087597699788, -1.0177005758250504, -0.023876478669494827, -0.01016865779781832, -1.0475247711712796, -1.346057355455609, 0.0885571561120904, 1.744814765385008, 1.368482927314476, -0.8453893924616906, -1.8758743501615105, 0.7007743197134746, 5.396733042647622, 7.84855599523329, 5.443016979081374, 0.3341034203017997, -2.7298023460116574, -1.4072198200276411, 2.0162632778391902, 3.5061157875990165, 1.71398544164899, -1.0603913357717272, -2.013083828696211, -0.9698862560257495, 0.07417893555196226, -0.13402125768105158, -0.7088602597576676, -0.3012032498217935, 0.7774930110530133, 1.033409460439846, 0.18075026951863038, -0.03927547097744237, 1.914288979326374, 4.885943794238158, 5.810782616899332, 3.286487179322565, -0.3943347858386642, -1.563655280646096, 0.6439428201342436, 3.2721560817323647, 3.058612558397142, 0.3396569781583966, -1.3774230723678216, 0.31974899707654597, 3.807155218480447, 5.344478292595621, 3.470043028567258, 0.5474755228799411, -0.26228053255744077, 1.2561363225294486, 2.4531950150808757, 1.3610262753156235, -0.8797822281407074, -1.6514040152178648, -0.26087160686783745, 1.2813830341557544, 0.9608328557039704, -0.683684660439308, -1.4216351282459152, -0.33238116853463784, 1.0713495370565513, 1.0018317566428618, -0.18204002503280353, -0.6229303161577923, 0.22550245745344127, 0.6440022843528355, -0.801359517251362, -2.4735529935519724, -0.791424059129672, 5.373564691024297, 12.263470399467792, 14.277460728910093, 9.600366667925803, 2.1559725056428536, -2.3819015702391573, -2.0532676289883924, 0.3743786158328067, 1.357672534456622, 0.4185723953806183, -0.3735867841969124, 0.19521864461634816, 0.9283499129273723, 0.2589559729839829, -1.2777518120968159, -1.6661176040432948, -0.24506463976851586, 1.2249815031712843, 0.8572883195267087, -0.745537148461308, -1.1804775323689396, 0.5188240006677522, 2.400879637625101, 2.0256271567536936, -0.23936721604726768, -1.4763688935273822, 0.04710043327240563, 2.4085211206825474, 2.209346042922259, -1.1181952708242942, -4.31954943828535, -4.087072161250746, -1.0209042558714385, 1.1605653522997381, 0.22188112534475646, -1.890017991200963, -1.5879028997429625, 1.7784566027839384, 5.0012239573562765, 4.81218915659327, 1.6414568683133668, -1.1602090718741922, -1.3607685505771459, -0.03450366155452363, 0.46082976499065686, -0.3646401314924336, -0.97317079919958, -0.3885349603332217, 0.3720953884919386, 0.024213133825878856, -0.7478574898406293, -0.03389329437187585, 2.339240022899853, 3.867773072683356, 2.329559272746559], 'positive_zeros': ['2.63246400368537343570482040109', '4.45567490399429252483318831660', '5.686059566119153231509162336737', '7.1698320186905603412186746685', '8.54836105599322430033443532328', '9.664570789924731707619360331147', '10.49924691379127745090794619333', '12.92604332417501172100032129097', '14.148151928713256942027800453695', '14.7473388718454776197515841696', '15.9726447285893869301126831207', '17.06511523540811457951726690824', '18.16043402447972433584158880230', '19.42249536671613540438134301046', '20.88210281599245899490332384987', '22.01920516348369056300930124870', '22.74958518257749446903451692194', '24.51290079164217201935190843174', '25.26393789369063848316239544004', '26.134314163992792849642907900017', '27.005888576444419094454476543482', '27.974643805291777989564889177501', '29.50633087787813592264414110859', '30.86687288234043900866547074907', '32.03973890832587879666578490375', '32.62873323975561132201168226628', '33.7779686246022541255257361641', '34.26403708569727204120454169844', '35.931500661026406138271810179391', '36.81182475603646032465403484376', '37.538984247437432025999876212278', '38.65106985393971582341883739033', '40.12558588632854819551839897317', '41.08821029717730620476485741862', '42.29487651442683583461058954405', '42.67660795091591511097731156241', '44.24052902994745304164871399735', '44.4684266623319779957854705930', '45.43495390662820731775089744943', '46.62326825547711407871554750850', '48.27483080336997866538090274163', '49.28963636360454452790206298557', '49.62727476037919243960180245369', '50.847840731402184577757852896507', '51.76251833483337308792651440508', '52.891739088063333351929204187054', '53.75617584273477561958410417618', '54.35754260048856831959863788391', '55.58570434964423357995945777349', '56.33432583194814988906175972171', '57.59929774174176618640757317603', '58.94778052670768036896169327570', '59.83958997353743061816457439395', '60.570561521989735000486951888985', '61.3116704153229052572819979153', '61.95555861773845314367069146871', '63.06694003135875094633861387642', '64.31487819228646273463016693228', '64.91268043748415889104964854374', '66.28004933276082704320204443221', '67.15200625460448477139865013654', '68.3585822829859624054842131510', '68.62346383791999193685074656873', '69.96370306779019212854233873149', '70.94105158984226237813914129791', '71.826246141252013320912006080564', '72.32929366298796235504601077126', '73.227739111159333911572050022568', '73.99195833386264694316895062784', '75.97240367957592569108477075164', '76.500753977999033460534451704068', '77.369186995193902603705245166949', '78.28088326845631575483522430461', '78.98502112563689066556270409685', '79.882765442595251353508609139495', '80.71971690747280277631296801115', '81.60248920885283910955091839225', '82.8172821161990361689534998372', '83.44814740796219927641591411979', '84.64592207099303407450618113335', '85.27532588374434873415876495439', '86.56079008706966055033052104986', '87.59266577242330138094244772805', '88.24225455745845553744217982688', '88.984737130016237559152365551312', '89.60848077993553438058311194573', '90.84854140657411310647273399704', '91.21280848759289957920043129967', '92.4791745300385957705089768333', '93.8071889945804913947839901494', '94.67894558082796632721476639272', '95.72513928562331830173340177361', '95.968497921479526193716341212307', '96.76716221368768536643173673612', '98.058004625299518097984001902476', '98.81010779117784909408882805595', '100.01422146063593688729164205775', '100.17894404299957838018448600448', '101.07868416050899383828445440321', '102.45582325673735344213783814055', '103.346181043751759097180155268644', '104.4827162112272702172608590532', '105.06065132772697416380920615567', '106.12625078801652437146487049083', '106.79669890101881883196944854901', '107.46489167189657870792924769636', '108.20258368222260006429968665430', '108.938422018199028349476860763603', '110.42774514686789179630381701656', '111.15710011301331371577919230348', '112.25080234623221820843338882514', '112.86003287068374483566899355856', '113.73338167957584699914332273030', '114.71550677009615308522811110248', '115.59115273553631079784336451686', '116.2189570237535297149347331346', '117.26272181697354433370845175907', '117.903412759133134193943591007', '118.74816101413790589625174651619', '119.39640243532973466544540638878', '120.540039719077511506490603432192', '122.132166133335962548064691183444', '122.62543337251336436246132599650', '123.283985395516350889515851538335', '124.105296934586399999755602210768', '124.70833692792051046181141873439', '125.63725497871491364716998844582', '126.58016452707153510627899412956', '127.53875170072577541182484630458', '128.03147660601799045798280384405', '129.25325898255997894516806156574', '130.43347428218837313917569801332', '130.77186149945735468758715917368', '131.82961799041756818323725506372', '132.65389516263507309907185136676', '133.82128688484572762993344772087', '134.41572233335689279759884499413', '135.0078555518456933439136112955', '135.7763800340141496796074256082', '136.38765724526855054939213980627', '137.53059205478386163092634520788', '138.759872976680963129991252248242', '139.79043269581895100809611099822', '140.2519960428509781002280929737', '141.26710657958950866858656653899', '142.017944721404108363426017233561', '142.692243213340790559458905406571', '143.232469847168905828884901608715', '144.692380625926561413528037081692', '145.04805735732076320307276576667', '146.19520455345841360906370209982', '146.78046636908438353983761319768', '147.512495316478103538746168102', '148.85508238216556049317033588233', '149.6906279395808425642224486531', '150.71619235395870163902491952776', '151.12285911659455975246865540432', '151.98450270962055782120199639618', '152.68561626062420875074394035723', '153.59230830478738124787666173349', '154.1839255357079787980520066192', '154.94481236303338255496804877825', '156.15615377633474723544762354718', '157.416980823109275966064043969405', '158.0333497562823882371206279003', '158.60794177638809360585276056273', '159.50371672145806360437914905119', '160.05462484183770159589381356246', '161.363826656917564104592697236985', '162.19797026416831135680496322997', '162.49551304005914272585341183303', '163.423417637713621146863699828576', '164.263306313234177458711368209146', '164.94549513268097541697275913380', '166.27197283835961337728766030633', '167.00427595011489654199469524899', '167.99447307719209744807289968289', '169.01946446317464862846045347738', '169.306437454327921074125346016454', '170.0891599872555348068044709142', '171.00548067179083657379246211429', '171.26449453718409397308402565016', '172.77262366044064741064305387808', '173.37091474151975202711033013502', '174.41295601421526945682750939833', '174.96747153859297501820180579748', '176.342970599182983889875681010584', '176.64696267749570580417488297168', '177.68439744826414795792542082211', '178.47984145135092703105937547904', '179.24884964340670372756411640136', '180.06303241781763266621888918769', '180.88868724544952857071976722602', '181.49545718726698844184253452147', '182.057794320156660532314881232071', '182.86661309970179054872439916536', '184.48557017060970761413990535043', '185.2603374302446067895740371511', '186.05049191277616451714471865445', '186.498631949255969098895680637516', '187.242259824860626013163378691630', '188.166133143814689896407575544142', '188.91847679173366871047277874982', '189.61491479246854458142061195436', '190.59297060145719086642271813250', '191.24416835201421084695554194010', '192.09886566885003124257150279461', '193.23008725101580609055772815594', '193.78137820170311120853581970238', '194.544292408032812539408435783083', '195.77932472231125633703031805667', '196.57143040397775426298559608045', '197.0769623072958512343810647249', '197.94013081715665052569315098571', '198.44618893016393706190735660771', '199.068395254309140668347460389352'], 'prelabel': '1-77-77.9-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.35758649667489656, 'root_angle': 0.3173693464573663, 'root_number': '-0.410766030467157742386273577323+0.911740790035333473087767928923*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.317369346457', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(15)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.867696106958955381003992300618+0.764174555267165118582782704273*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.63246400369', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.45567490399', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.68605956612', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.35758649667489656, 'bad_primes': [7, 11], 'central_character': '77.9', 'conductor': 77, 'conductor_radical': 77, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/77/9'], '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': '1-77-77.9-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': '1-77-77.9-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.35758649667489656, 'root_angle': 0.3173693464573663, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.63246400369', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_77.9', 'Lhash_array': ['dirichlet_L_77.9'], 'factors': ['1-77-77.9-r0-0-0'], 'label': '1-77-77.9-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/77/9'}
Lfunction data - 1-77-77.9-r0-0-0