-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_6001.4807', 'a10': [-1.0, -1.4081532572346456e-30], 'a2': [0.6548607339452851, -0.7557495743542583], 'a3': [-0.6548607339452851, -0.7557495743542583], 'a4': [-0.14231483827328514, -0.9898214418809327], 'a5': [-0.6548607339452851, -0.7557495743542583], 'a6': [-1.0, -1.4081532572346456e-30], 'a7': [1.0, 0.0], 'a8': [-0.8412535328311812, -0.5406408174555976], 'a9': [-0.14231483827328514, 0.9898214418809327], 'algebraic': True, 'analytic_conductor': 27.868526838260447, 'analytic_normalization': 0, 'bad_lfactors': [[17, [1]], [353, [1]]], 'bad_primes': [17, 353], 'central_character': '6001.4807', 'coeff_info': ['x^44 - 1', '0.989821441880933 + 0.142314838273285*I', '\\\\zeta_{44}'], 'conductor': 6001, 'conductor_radical': 6001, 'conjugate': 'dirichlet_L_6001.5614', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^38', 'a^28', 'a^32', 'a^28', 'a^22', 'a^0', 'a^26', 'a^12', 'a^22', 'a^41', 'a^16', 'a^9', 'a^38', 'a^12', 'a^20', 0, 'a^6', 'a^24', 'a^16', 'a^28', 'a^35', 'a^3', 'a^10', 'a^12', 'a^3', 'a^40', 'a^32', 'a^23', 'a^6', 'a^8', 'a^14', 'a^25', 0, 'a^28', 'a^0', 'a^26', 'a^18', 'a^37', 'a^10', 'a^19', 'a^22', 'a^8', 'a^29', 'a^40', 'a^41', 'a^10', 'a^4', 'a^0', 'a^6', 0, 'a^41', 'a^17', 'a^34', 'a^25', 'a^26', 'a^8', 'a^17', 'a^33', 'a^0', 'a^9', 'a^2', 'a^12', 'a^8', 'a^37', 'a^19', 'a^33', 0, 'a^31', 'a^22', 'a^10', 'a^38', 'a^43', 'a^20', 'a^40', 'a^12', 'a^41', 'a^31', 'a^16', 'a^4', 'a^24', 'a^13', 'a^18', 'a^16', 0, 'a^2', 'a^7', 'a^23', 'a^29', 'a^34', 'a^9', 'a^35', 'a^36', 'a^4', 'a^8', 'a^42', 'a^7', 'a^38', 'a^9', 'a^0'], 'euler_factors': [[1, 'a^38'], [1, 'a^28'], [1, 'a^28'], [1, 'a^0'], [1, 'a^41'], [1, 'a^9'], [0], [1, 'a^24'], [1, 'a^3'], [1, 'a^23'], [1, 'a^8'], [1, 'a^26'], [1, 'a^19'], [1, 'a^8'], [1, 'a^10'], [1, 'a^17'], [1, 'a^33'], [1, 'a^9'], [1, 'a^33'], [1, 'a^10'], [1, 'a^43'], [1, 'a^16'], [1, 'a^18'], [1, 'a^29'], [1, 'a^7'], [1, 'a^33']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-6001-6001.4807-r0-0-0', 'leading_term': '1.32133343220746069834863243198-0.952370821100856045022272316580*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/6001/4807', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.6287824348124174, 1.634743727977921, 0.851414148473739, -0.2289191719592862, -0.44409541578954614, 0.18823650548153004, 0.16146687927776937, -1.4394257268632393, -3.1875543852163872, -2.713527045864325, 0.08708426183143818, 2.443643297946479, 2.0669220937690214, 0.1213351928000633, -0.5396110026293262, 0.4736097032819298, 0.7529239823888496, -0.7526301081209184, -1.652945935619124, 0.09748683522952875, 2.295746243856207, 1.3794377929445674, -1.581818867292435, -1.6050521824493393, 2.6524823382335483, 5.984623191176504, 3.921505467867866, -0.33076266192638154, -0.5001925194647194, 3.050436569662975, 3.6479073674456712, -1.4479396811623066, -6.679799631960712, -6.330910717177378, -2.259317598824217, 0.14750996291750013, -0.028110523358730415, 0.05794617264044614, 0.9246052688746951, 0.7038395104931793, -0.14949424671758682, 0.5658053483739608, 1.9922647507282683, 1.2949730803274282, -0.5656754289428245, 0.08964445184304996, 2.4008509463953462, 1.393590863171441, -2.8049934048548635, -3.5032815182358066, 1.560203976414357, 5.218558217101202, 1.9670212650291332, -2.9660378520666546, -2.454781029932747, 0.7995258488276208, -0.1793024888876636, -4.146141437890675, -4.288939736285966, -0.40426317349615193, 1.4597463214362423, 0.034603922846962135, -0.20406583368260853, 1.4192360762587986, 0.8104615636243071, -2.0384074219935164, -2.4396466346136423, -0.0090066009083998, 0.6085355193875268, -1.154580956086928, -0.8262038303568601, 2.040086771875573, 2.7639479788887558, 0.5112188884706151, -0.46246401018502653, 0.7310115821743101, 0.7775319276234735, -0.18718231663234935, 0.5518336392485623, 0.7310487844915035, -2.815171453101623, -4.071816094526165, 5.113803350622016, 18.51380261010237, 20.648297249713977, 9.497889964450994, -0.6937201443758898, -1.2578894143161472, 1.2984020320211158, 0.4135328691868214, -0.8742238926552398, 0.23932934620387591, 0.3320605571331319, -1.8267828476904435, -2.2716556335559877, -0.3293629876695167, 0.1371539468667506, -0.9672751161518518, -0.3148540999202085, 1.0825611607134225, 0.28460300585868104, -0.23594062586329292, 2.3854529454805498, 3.8450487043659103, 0.4097642459786431, -2.4484351027596127, 0.18213677532238426, 2.69110516252143, -0.15957574603528293, -2.4516927385595126, 1.1635587656009208, 4.221069873157721, 0.8146140879699821, -2.8170438084335685, -0.6582405772041054, 1.870042905249031, -0.1154610995830658, -1.2879758883461614, 1.72157695288519, 2.627048736997006, -1.337312003839711, -3.0160336942074584, 0.6790944739517228, 2.911755429379217, 0.45436396094004544, -1.2377709693853947, 0.15611182023234868, 0.613585140264942, -0.56962250133764, -0.39092816363456473, 0.3398546701807651, -0.04464419980233392, 1.2088388721638912, 4.321313185086843, 3.632468865273204, -0.9897026543292815, -1.7479530637584033, 2.015375291674056, 2.230722915299261, -0.12128701155869923, 4.791665442965995, 14.227253790346676, 13.782015344074846, 2.8560399785656925, -3.5477046119727413, -0.4517443740397021, 2.0417911855313853, -0.3766794712667164, -1.5540979018035652, 0.09730555235394205, 0.3849954216710437, -0.1788977492256776, 0.7934665888887343, 0.7863943929271278, -1.0739410675691572, -0.6869355292248988, 1.1757652951076076, -1.2180561349870787, -5.7495292740336925, -4.7838088704418835, 0.029868561418487472, 1.2182276139729824, -0.30193978628821594, 0.14874825991504687, 0.19421300285385548, -1.9298803789478924, -0.8234870462833472, 3.6770094334740437, 3.2931329012819424, -1.5917449732514122, -1.0087669055717847, 4.174493726231817, 3.3592282165939915, -1.5151834873597037, 0.8329766585501425, 7.888472982201647, 7.819984677009381, 1.862403529743975, -0.30002848395807225, 0.8137908551802658, -0.2323240328408717, -0.9842643465562861, 1.3070348828618918, 2.2638428362992173, 0.2808096052016299, -0.21555897008515865, 0.8852095907474065, 0.03906155269481635, -1.041892059064815, -0.023388274424596338, 0.09190913898694913, -0.8062092259416908, 1.1598433777299213, 1.8738457421293488, -5.257031741626491, -11.894626512548365, -6.017184692801146, 4.083833313847816, 2.7014858614984774, -5.3861214944322375, -5.853255536597156, -0.8042355698197146, 0.2092034407495798, -0.6458250471012476, 0.988598970171684, 0.8160926452449779, -2.048321517447588, -1.3449885218576498, 1.9705121828789227, 1.2096075683869318, -1.451058215408407, -0.39481740504493107, 1.0426362307170436, -0.724201789434967, -1.1436886838415155, 1.1645453697694799, 0.8939308524033278, -1.216095786925075, 0.0812706300746976, 2.0305203089149266, 0.12467303050805478, -1.4835632841343211, -0.019706426796112366, -0.21183339768468418, -1.5470417377719712, 1.2732533674001734, 3.4640815155785214, -1.2113016325396688, -3.288213272574097, 5.6472900035469396, 12.868079135760219, 6.492306302921264, -2.2325084324804148, -1.3100988367103583, 1.4383332343382356, -1.7753422000126668, -4.166580545555551, -1.5764456324213416, 0.22607290620290615, -0.3651761897623694, -0.005358427199615953, 0.08141932780680813, -1.1324393439395666, -0.48443543065462336, 0.7882538329650797, -0.9733388441489514, -1.8861245743221335, 1.260370768189841, 1.960254734827172, -1.9513251485061769, -1.968300914381073, 2.655777488601779, 2.685228237236023, -0.8799873968993736, -0.16635602081567857, 0.4746979554429267, -4.70440159735797, -6.108693994829903, 2.417384860256099, 8.415640208030439, 4.112523021853723, -0.3740599283684358, 0.7678233924732512, 1.1617304144501523, -0.06168042314273453, 1.0901786076204998, 0.8345840028141699, -2.796360651816954, -1.9680237656357669, 4.375405453028586, 6.209153059662655, 1.898951429743672, -0.4551897909617511, 0.036064733260914854, -0.5847959040487171, -0.5384179241726099, 0.8587555711685371, -0.05367528760276925, -1.5086785083663834, -0.055310765408824465, 0.5112104103136923, -0.18802750500847693, 4.505549528264967, 9.522690348761632, 1.99483400795836, -10.627506797935546, -9.746086887373902, -0.2964831269892405, -0.07724612976301572, -5.661730418537472, -3.8291014306527167, 1.2232193876289719, 0.9548388883360979, 0.04486064668010613, 2.063947167152318, 1.963660230481898, -0.06548837973017649, 0.17923830620916584, 0.13956127482498693, -1.7801318649342697, -1.0337118275948245, 1.4409273515532919, 0.6989479542980139, -0.1464875837061661, 2.056609494599397, 1.8327297881395257, -1.1026657985925432, 0.5924864994882117, 3.927207442234235, 0.5071831047891654, -4.072745978294833, -1.7377595283458, 1.1125138854714203, -0.3158321570970081, 0.7550074165024091, 3.790275072462574, 1.1433888884935404, -1.79395810045854, 2.5645153219944827, 4.66482964851463, -2.378051308207525, -6.263750252437523, -0.6073777627890962, 3.004355927852014, 0.1447740622594166, -0.7316582281394882, 1.1582744268785594, 0.6005348960274307, -0.18079708203745276, 0.7466143982454454, -0.17162663036051998, -1.4092958897685082, 0.6008639360751701, 1.730188222805075, -0.32583096033336645, -0.665755612513806, 0.29384624969210144, -1.0604326506097221, -0.22486187087664694, 3.5919819219619775, 1.2008851112259185, -4.188889135717565, 2.0169202303159146, 13.631213385121558, 11.038894498974086, -0.8061024257292612, -2.790908606983735, 2.47134874538227, 2.2901222641804666, -0.23857835678026817, 0.4637275560234574, -0.11031628498889566, -2.0969039830032856, -0.7751137698409087, 0.655934533215176, -0.7617759854687817, -0.5610996724542651, 0.36586358248322653, -2.6453676423175754, -4.034702983090747, 1.1407004705801693, 4.626379563722712, 1.7997938357719792, -0.06837930954318816, 0.7804442843910144, -0.26824328749774135, -0.9485226486559006, 0.4139687543418157, -0.5883820512372435, -0.7690525374245769, 5.0970236239250815, 7.360521543161066, -0.6812214203090453, -5.295877454653323, 0.5214427336571902, 2.8196506244967527, -2.0318780091981727, -0.9408054982992236, 4.941579398937361, 3.6535899250746895, -0.5889126549971331, 1.0099866200591856, 2.537687235632863, -0.3184937173805603, -0.9799171712394501, 1.0398736049141897, 0.3341233804124628, -1.0247820573720783, -0.2050705336920233, 0.08789147806366669, 0.06573260470591394, 0.16701907413745867, -3.6503899362002965, -7.810362139776194, -3.9411321054662065, 1.6093083528022771, -1.0256331145520303, -3.626204410123367, 1.2938300317873255, 3.5263382888205475, 0.1444732518691343, 2.734522644675504, 8.758438608398706, 5.570822128543647, -1.265818386596503, -0.9195885543916342, 0.4805523478395525, -2.099850575167566, -1.6845600005454913, 0.9682618618871655, -0.9286095825910695, -2.653722869942949, 0.27782884805902425, 0.9922284518019958, -1.5453396802005275, -0.5043909535915453, 1.5100294575781568, -0.4657590810864469, -1.2777562381216963, 0.9391429808065388, 0.4442399479787742, -1.1558936327010048, 0.36648267652237065, 0.7343533727322901, -1.034458202641009, 0.2071372466508621, 1.371138095881913, -1.0583988070961143, -0.2621593658560974, 2.6037711258058636, -2.1069953356780493, -4.8369373014983, 9.354454754664866, 24.39410536407062, 17.839266034531647, 1.8687102643041857, -2.453540991099512, 0.19149367407444323, -0.06618635430184486, -0.1061723388419054, 0.8369660135421628, -0.16495826828062726, -0.04525768017734727, 1.2280287173887912, -0.7224367155210714, -2.3999591447573927, -0.19582456914293322, 0.21628362645193075, -1.9522491403318016, -0.9026521503227776, 0.22086297063550284, -2.5043721958583616, -2.573686367495094, 0.2317528428448495, -2.098832346471298, -4.7245440819503255, 0.044857983491114466, 2.750445987716834, -2.264297418621382, -3.4237436747043066, 0.6921859081096607, -1.1783239153985787, -5.203217068206903, -2.012205404091561, 1.1792647532227407, -0.7375582742061382, 0.28987788766698336, 2.7892075016821742, -1.2980230134801582, -4.889409708622019, -0.7399172978240793, 2.2015572954736227, -0.44565490020852383, -1.1758487426687292, 0.06330579769677261, -1.27178308853153, -1.7526021731247952, -0.041674988853878624, -0.10221859348686846, -0.2918760526628283, 0.6769435439206966, -0.9728870921120918, -2.0059072761970484, 1.4394032005808846, 1.6551510674548657, -1.0607806024232131, 6.920148529149174, 19.744688224327973, 16.530394989476417, 2.8802100631239718, -0.9891599102447868, 0.9201998833600366, -2.008231869427766, -2.004997661529668, 3.5085248591917955, 3.3637214931721715, -1.3724332874493839, -1.303842002776278, 0.5792248064199218, -0.15951341369359023, -0.03303603019050468, 0.24530249693766012, -1.1412408519114101, -0.0001428864502496306, 1.5987002963903256, -2.006800296447312, -4.338503103266815, -0.24217568241760323, 1.294242496470656, -2.039081824603972, -1.2975936344084373, 1.869694142674422, 0.9267905605067652, 0.08340678686737028, 0.7117310110499875, -1.6067365850325077, -1.2554403781686827, 3.958618876546932, 0.9694040309592133, -9.414609575724128, -8.770588611964317, 0.4422305835062118, 0.5014077389738884, -4.2377408292549195, -1.9842666014870338, -0.03215178529795603, -3.226772869420546, -2.5702304087105543, 1.4431940895399524, 1.0559127627958327, -0.5326529791818237, 0.28738108776002724, -0.05361324224748831, -0.23997413180564967, 1.690441053182456, 1.0802231702071863, -1.1807039111605122, -0.2790282284102026, -0.11050960193178307, -2.2409487039937503, -0.8601068044225113, 0.5249750123134169, -2.1250968963286083, 2.2036202658505544, 13.710208516831377, 12.645474605656144, -0.31601815813277856, -2.98082991664105, 3.6409742856334533, 2.649056586983699, -2.0457036030784517, -0.9664833080230923, -0.09068639597842826, -1.7473793223984153, -0.7191703819129528, 0.09566681262266241, -0.43487569491846, 3.4867326247717774, 6.928283443332736, 2.307290144904903, -2.1655798598838265, -0.1943501656450904, 0.6133483116347249, -1.2474756500906823, -0.4444103536694542, 0.052541550175823425, -1.470652382098132, -0.5486055667157337, -0.07654574569261562, -2.6424050807962853, -1.065857900372834, 3.491168526447804, 2.207430164145792, -0.20664680090261475, 1.1702405816629957, -2.1721432605111812, -6.435065846610118, 2.288519035817788, 12.679494575073935, 6.847180203544784, -1.9887211671523417, 1.5921391338987014, 5.550971060513335, 1.622380043809794, -0.39865596837726497, 0.8944828104571814, -0.27601637698920034, -0.8768487069457552, 0.24339935466962173, -0.7508705749393378, -1.272607624348502, 0.14016295204984994, -0.4556038341472638, -0.7580536164718291, 0.9223750231918384, -1.4644630291943583, -4.532047505002367, 0.3145258748837734, 4.584104685653356, -0.17510635169021094, -3.238667971760166, -0.2995626252914445, -0.6078481236294132, -0.6312506913298137, 5.659838535991172, 6.917302557262675, 0.17371442822407485, -0.8039905450437458, 2.4592233755641315, -0.8451461158398187, -3.4223293309715244, 1.0614571430012956, 2.5722165353145265, -0.31870782297867506, 0.3375977622003804, 1.0061191479943759, -1.4145095294093248, -0.5672079322184707, 1.1051394772710745, -2.2980557717461076, -3.7622929081046674, 0.2751185245009598, 1.7282028256814574, 0.07589110698315106, 0.3504973262471458, 0.41921591256808255, 0.07736795017145275, 1.250864307649382, -0.1881007183413195, -1.4780794065797742, 4.240986071354909, 5.878586282239759, -4.488729448386396, -6.9510706917093525, 6.560153326593664, 11.636596694556593, 1.2735197202862603, -3.1411908459566655, 1.3714994430831402, 1.3181202755922587, -0.7840228755587066], 'positive_zeros': ['0.8590508257290085055921276006', '1.47482112824286628031595511399', '1.92606589790405371102678825885', '3.11638194242241030721896652180', '4.08580369641840287782822928928', '4.562956798065476605743888077335', '5.18134623726898385428953190252', '5.92606043971255633132143148592', '6.70489025814209104256226427786', '7.329210943521570152854380529223', '8.40503554884149842932755025825', '8.804072927717947568262985476123', '9.61695669549164792847518381920', '10.89057397967971079892176028633', '11.23243772843716127705481881823', '11.536410810895459953928266461412', '12.41400053239712528075111561781', '12.67169296955954456630632082275', '13.63410033821459954610286645696', '14.0495923713465773016400189183', '14.79716167740812121066037460671', '15.54425963243932933118149310984', '16.356176867096872536254505961329', '17.090763144788097463776790830345', '17.48383126843157960642183727274', '18.47204005383264490042276878173', '19.06949859469836755956018765763', '19.42108792263059544812702888556', '20.09339438384743188261370577311', '20.93875076193517117788318451116', '21.36925349039081159702125355085', '21.97411015456063260969582741381', '22.88990743321111169296838690545', '23.26712314022849243819441503282', '23.9689251509832782440313605147', '24.2337640661310620498284236241', '24.78091088284032459124202897811', '25.49489276125501799334002675088', '26.83883486224760360185227271531', '27.31581167337113960944167129991', '27.87580748763410657131291930356', '28.38558449323901581996431160516', '28.810771557205171188367892478729', '29.75381091695088294601204356618', '30.04357692278759200296585178662', '30.68153418340105675378726385819', '31.31144300096202228097552454834', '31.61312745595232409175278319498', '32.52808263658336599693431068555', '33.111186549193208001208597349289', '33.738142656984296700784113736914', '34.302948917680937293969679679563', '35.04883346510911787344494765324', '35.67857890337419870231293044031', '36.23773984054332194589232684521', '36.72334873684123007196012350846', '37.40778318600705548816708439594', '38.07743917366568760154411882311', '38.796448422939401163478529617534', '39.346073335692435649885080534643', '39.84826248953842357413317430434', '40.43334942952648742316212382996', '40.89269406383615638780466406511', '41.02992172242318916308836813446', '42.11701571917220014923093420972', '42.65186530628141289963175464910', '43.38214249729547065131766951004', '43.48736513371400762666275993316', '44.775240193747087648154005503577', '45.34306438219796714875675316816', '45.89839400088545927754478846693', '46.54306165483024612361592530122', '47.01856064524122602924359848695', '47.28881998595668397279872558364', '47.94770073306329604375874283220', '48.53228812154863683016165663217', '48.973481026748698592782297978704', '49.99757033191957109963962792795', '50.54386729345391206073387855816', '50.89630304412833843942858787494', '51.28623286986820334400893159097', '51.93546280844656645033608815326', '52.701998586773780688480497816781', '53.18754120505734675793685585012', '53.943640480797419664305797116295', '54.33369322001306237940221680377', '55.47125149428517672202042916929', '55.715553137506406165153347765467', '56.21115567885760942940782506072', '56.72457982827047651214577126474', '57.549833697549542002951625721470', '57.87295575232438184314223587884', '58.44464870130132867725184764499', '59.06858579295161831212993137664', '59.400812877845524910963572438363', '59.87059732964948451597930275358', '60.43280005410432669226221261911', '61.4136104560113064588551715171', '61.97597083454882440425336222932', '62.8938864184101879931881240421', '63.17468280196047025792510868539', '63.59445515652926177944818068830', '64.154448801715077272205175300', '64.80418653806024184084483926469', '65.431029059623756112751822322769', '65.98856318276909387626078616099', '66.46263083003302500627309908764', '67.03331807278051915935876633807', '67.61385282953808595191169525951', '68.11591657214059359647642970962', '68.763424816131875942027343849145', '69.37924042947277578995209437843', '69.64696004662277894226184387736', '70.21605633759292500638175909520', '70.87591815031709091479295459035', '71.40101340755848253161249744109', '72.388145333508057764547343362182', '72.90960075900031674907545878621', '73.31211492843563522837427537780', '74.2665577102774885704107954036', '74.526079846402015902425893304038', '75.00210375839251150867880130001', '75.338223345958447812404755158884', '76.01914641131945140020672741805', '76.44066848105126351954053279818', '77.07970337001161385044386366620', '77.66580296218983294621671654682', '78.26029740591415648679921533455', '78.965875757993315016039018112884', '79.39613023623605407161830344384', '79.73446834101203867404027232374', '80.551425441384322455633378599649', '81.500952364802477819348955672989', '81.75570019123308368120898975969', '82.45510199140867426038162073749', '82.57788787137796047874319296977', '83.20627027325795595962766155901', '83.85616022744690828480351303976', '84.86353755692830101396665759252', '85.275293678518961268018926199960', '85.40825168088014043776307934502', '86.050093303429335559847438658266', '86.55450711704429218964251646325', '87.19643518335597707010736502462', '87.62541044788902119220692418586', '87.84861667960627767794735191521', '88.79479448514272121983980716974', '89.70201743002216505445961992616', '89.995433946212296372029191767455', '90.83613845516943854191623508755', '91.43261102328180619617301529345', '91.54684814808086724749782188766', '92.483149564773925468341840217', '92.75488137537929096894708809800', '93.152613128518582400799198069721', '93.86343869680465863730447844642', '94.49911632316407632674319940400', '94.72373878618402632320756061050', '95.48878333704372339965134101271', '95.89186826594509399524980112981', '96.58828599034520413548728609382', '97.31867654856464143535009311444', '97.75371981599619843479934842270', '98.04627698286742007874683812468', '98.82368031880113440362025539073', '99.23650153621007740672301703926', '99.91265408261175153432855216400', '100.65300312231873251380892239862', '101.26442943900987015781920535377', '101.67893137080649857085534281399', '102.32215446864278923375412516726', '102.577602575049327302529355379296', '103.09771468110465054561936640076', '103.68128863281253619224922613151', '104.32773266291586256454853932087', '104.84217596117358382158705032723', '105.11386078912757317684032356442', '105.64456858737161375074791567127', '106.30637045474048689221785091253', '106.821133413043799762165191930804', '107.78585382401620720518770481941', '108.2838874938001096138828075581', '109.00222178496375973538013618476', '109.25525120387568726795480239056', '109.67134859772847260235775614817', '110.41432231597316623108037028767', '110.796782182225623505915237574926', '111.354643224385927594517460788787', '111.63636882544814916676883882709', '112.444074769364922446741384616659', '113.35444791066186827003962203529', '113.48087862280510754524297023471', '114.01560564503352212279642642200', '114.57953200809336259298493634677', '114.90787978276556705157035174411', '115.37489230378012478173367916352', '116.22772444698835333311664150141', '116.851500302376393068385695009367', '117.37163813966254323507547278186', '117.86091633253740710950362277311', '118.67545103378041178656548533144', '118.96313162223582467156536355234', '119.65509013858656476367497837036', '120.141895692765548105535903043367', '120.677214099531862924236465774801', '121.32237193154601036457091745068', '121.64478625644667538860486890437', '121.829797517218404618619129415947', '122.22022227157915964115705981466', '123.305157429971412040951808031021', '123.68653394882896645335285591608', '124.3085237011473611570186800489', '125.02677722787014619781496833834', '125.11534436679982909527757947205', '126.16855324239412986082101014463', '126.66760924029632702141872504423', '126.95696459077512673668874748572', '127.66321680133028569172247439232', '128.03771293234975671881695527986', '128.72378535630177635925296045352', '129.18203732404770056588787843517', '129.740501492226741983970725725027', '130.25963409484882371975548318242', '130.80374020856847445778742286732', '131.31124172708979999980240588723', '131.8203235719058968852259942922', '132.30704626674947443686166466507', '132.78661598671559842204833764386', '133.31378186188344955124428472191', '133.77213337248465981859632242690', '134.28277921683361353229503611965', '134.836719408858613286979291623324', '135.9941196174704371501571200759', '136.52926211174995421625086378966', '136.85628399952524646585527672748', '137.215549694707169320094636047770', '137.77212015763693002451180174300', '138.13432274832214226928330752345', '138.67520025188727153774307384917', '139.40089341831849028051915231311', '139.72116537956786409758015859521', '140.43924800216495262603288666016', '140.669579756350695312817969990105', '141.51405895911373745738972421410', '141.69541404026589786209460460965', '142.49775284064523661476086111532', '143.00367790690763863071765536236', '143.6818010066069344080930100378', '143.984189048511571376896037721406', '144.81703210466842451362610464514', '145.21068489197325939756315185879', '145.59815038105514627806985590775', '146.1833321514495518747154447936', '146.91735151210390404545399739848', '147.454384415920124337983837696788', '148.072620214932983327269519288447', '148.18926292007120383499857027537', '149.07354493926701243060824316653', '149.33829962402146237492736049621', '149.7709406745137581775164887203', '150.19217591743452043682460470777', '150.82308874697943462298263818057', '151.38800892364870066686390550705', '151.6657578331177717971003386496', '152.92137077330530158883715090229', '153.24741939637678302337097017088', '153.58394673052534006704960015359', '154.18128118724893576254658919917', '154.89442476899841518564476487273', '155.48036782767526137801363687143', '155.88862061445532042831496737000', '156.26091335948705132633273850947', '156.62805741434936074711001741511', '157.18751661929776542054253885878', '157.68180300196319871495769900124', '158.45401382829092258134977152345', '158.87947275055606299224077450749', '159.48202267904367598720426237097', '160.21461210327672422265440012285', '160.25982159172580781461322384954', '160.76176206229017852839242663706', '161.33017951510857508558939848598', '161.90586555122590766424274943236', '162.79222687395184478424868041494', '163.15399386320967669138321387682', '163.94290020064386235862645404716', '164.05551369930521158595391782258', '164.86919234685887461626763967358', '165.460510391044030314798298832482', '165.84603960156486639701314654412', '166.234596613231656559692025699821', '166.612325398854558603616681013046', '167.31164259964270096918650845469', '167.86852250497076963407143440818', '168.104280520987058814104347622374', '168.84461850998042764228352273064', '169.14159370456547996481055257403', '169.611861821503325914653028574731', '170.615974198921459857282263017055', '171.07596703849959750231440517574', '171.70882828114642209390716872728', '172.344291909793795545279878891529', '172.474244734766924747229875744594', '173.26074753483929409693646920164', '173.47303487234451939055965972921', '173.82328560451602825807803470770', '174.799927952566045499560071672903', '175.33415834634267959315527347563', '175.72416896253198217686588111293', '176.34137925910822955865396565426', '176.57615450539012214032471079945', '177.28977722870961230221347949223', '177.48482784779014691941184861047', '178.19100293918876699538927621452', '178.97174922461720207907544492570', '179.1416913128941706464789566200', '179.5671400979188152599007504842', '180.25949328899628132295560924357', '181.13653634728944703298240446356', '181.48958473873804734144550158646', '182.32435276738831302203886862696', '182.59579536169657925237996869155', '183.07948980609445473583090782846', '183.651135475795861958420337677500', '183.91136606668522228710098352328', '184.64414023502921236003168376583', '184.89441676189776686662472851205', '185.441681370985796358343652170093', '185.826575596954147771431498140562', '186.54898547034104059064029811031', '187.17895547779293087318282845', '187.85825347202781122064981673175', '188.026593254109830542393746365693', '188.48303288540513118402384655332', '189.384513248399542798691649985122', '189.75222679323106954825012537500', '190.263465395930729349023989509134', '190.874013334522246991125252143923', '191.51583957321686943681314930682', '191.82436717890085797985420337655', '192.32340154749167861761828913518', '192.87397877757602249201813495905', '193.26902893642904430061474072401', '194.04189505885055292755793438983', '194.71643045853647797495926255135', '194.863236518027171696093326280203', '195.51236218259240278733527514868', '195.572359594621937405376750259584', '196.23034569072654941775157283590', '196.68000756706049541473365869946', '197.38103371478016078903203848021', '197.98954053121028215610523346474', '198.789015020153328933026946550890', '199.27922096525257157030575473047', '199.828626135833569993522672811790'], 'prelabel': '1-6001-6001.4807-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.868526838260447, 'root_angle': -0.3975860170095893, 'root_number': '0.316220615014259247438633675602-0.948685681688094014532385184019*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(44)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.862362795581697073866517136573-0.744058855183346472088140546504*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.859050825729', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.47482112824', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '1.9260658979', 'prec': 40}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 27.868526838260447, 'bad_primes': [17, 353], 'central_character': '6001.4807', 'conductor': 6001, 'conductor_radical': 6001, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/6001/4807'], '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': '1-6001-6001.4807-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': '1-6001-6001.4807-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.868526838260447, 'root_angle': -0.19879300850479464, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.859050825729', 'prec': 47}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_6001.4807', 'Lhash_array': ['dirichlet_L_6001.4807'], 'label': '1-6001-6001.4807-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/6001/4807'}