-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_151.29', 'a10': [-0.42577929156507266, 0.9048270524660196], 'a2': [0.30901699437494745, 0.9510565162951535], 'a3': [-0.9297764858882515, -0.368124552684678], 'a4': [-0.8090169943749475, 0.5877852522924731], 'a5': [0.7289686274214116, 0.6845471059286887], 'a6': [0.06279051952931337, -0.9980267284282716], 'a7': [0.8763066800438636, -0.48175367410171527], 'a8': [-0.8090169943749475, -0.5877852522924731], 'a9': [0.7289686274214116, 0.6845471059286887], 'algebraic': True, 'analytic_conductor': 0.701241051920901, 'analytic_normalization': 0, 'bad_lfactors': [[151, [1]]], 'bad_primes': [151], 'central_character': '151.29', 'coeff_info': ['x^25 - 1', '0.968583161128631 + 0.248689887164855*I', '\\\\zeta_{25}'], 'conductor': 151, 'conductor_radical': 151, 'conjugate': 'dirichlet_L_151.125', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^5', 'a^14', 'a^10', 'a^3', 'a^19', 'a^23', 'a^15', 'a^3', 'a^8', 'a^11', 'a^24', 'a^4', 'a^3', 'a^17', 'a^20', 'a^2', 'a^8', 'a^10', 'a^13', 'a^12', 'a^16', 'a^10', 'a^4', 'a^6', 'a^9', 'a^17', 'a^8', 'a^16', 'a^22', 'a^7', 'a^0', 'a^0', 'a^7', 'a^1', 'a^13', 'a^4', 'a^15', 'a^18', 'a^18', 'a^19', 'a^17', 'a^2', 'a^21', 'a^6', 'a^15', 'a^19', 'a^9', 'a^21', 'a^11', 'a^16', 'a^14', 'a^1', 'a^22', 'a^14', 'a^13', 'a^24', 'a^21', 'a^20', 'a^2', 'a^11', 'a^12', 'a^1', 'a^5', 'a^7', 'a^5', 'a^22', 'a^12', 'a^24', 'a^6', 'a^23', 'a^18', 'a^23', 'a^9', 'a^20', 'a^20', 'a^9', 'a^23', 'a^18', 'a^23', 'a^6', 'a^24', 'a^12', 'a^22', 'a^5', 'a^7', 'a^5', 'a^1', 'a^12', 'a^11', 'a^2', 'a^20', 'a^21', 'a^24', 'a^13', 'a^14', 'a^22', 'a^1', 'a^14', 'a^16'], 'euler_factors': [[1, 'a^5'], [1, 'a^14'], [1, 'a^3'], [1, 'a^23'], [1, 'a^11'], [1, 'a^4'], [1, 'a^2'], [1, 'a^10'], [1, 'a^10'], [1, 'a^16'], [1, 'a^7'], [1, 'a^4'], [1, 'a^19'], [1, 'a^2'], [1, 'a^19'], [1, 'a^1'], [1, 'a^20'], [1, 'a^11'], [1, 'a^22'], [1, 'a^23'], [1, 'a^23'], [1, 'a^18'], [1, 'a^12'], [1, 'a^12'], [1, 'a^22'], [1, 'a^11']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-151-151.29-r0-0-0', 'leading_term': '0.531946471883116943840543352094+0.835861789249637634368863845827*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/151/29', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.9907734249950901, 1.4032799502340558, 1.9821798015265222, 2.3622055564674516, 2.1988499880980896, 1.300687003019016, -0.2785045648932837, -2.2050565097761305, -3.93645772316325, -4.903030278827217, -4.743026813859339, -3.486870147827944, -1.586651792554544, 0.2522629173813745, 1.380499645338182, 1.5092678827027441, 0.8445919038723538, -0.03933969243888699, -0.5356548888916965, -0.36453412205155855, 0.26314330487009047, 0.7978237452028105, 0.7452055091989273, 0.05691620889211342, -0.7566453674497727, -0.91044038415815, 0.1167712610001942, 2.1339740827225113, 4.213481476161133, 5.176749454324082, 4.330860270500573, 1.9839347250555126, -0.6408928136398816, -2.102558778533889, -1.6385895275035183, 0.3276816362147709, 2.437707972911036, 3.275329629218543, 2.296162830687868, 0.16980571654516313, -1.7129622408879812, -2.2264087411576567, -1.2837698917839504, 0.16274644172587555, 0.8894705746898645, 0.3514208390094554, -0.9146351335955939, -1.7461812894730997, -1.3092868592914184, 0.21166968530945163, 1.7503142059815495, 2.217828957296745, 1.3836349391205498, 0.04138243379908873, -0.6898027910469903, -0.3403200525880224, 0.5131557311264001, 0.8174088955656111, 0.12505694664955508, -0.7711491278250616, -0.30905301182485956, 2.530146868077874, 7.115135201004679, 11.262417042051116, 12.62005059821186, 10.347377846399938, 5.778357880932579, 1.5041258345812503, -0.4427247988563498, 0.1020880536804931, 1.614328047449623, 2.308382160004834, 1.569126916513888, 0.2182712728181198, -0.4887514942608183, -0.12755427776691564, 0.548420170851988, 0.45301516343757264, -0.6609278921514325, -1.877367654849587, -1.9938642631880323, -0.767880375694674, 0.7118928495964423, 0.9784671180870809, -0.3761612989356595, -2.1694983569825697, -2.616721366172538, -1.0151612961277048, 1.4456251614722189, 2.603788398513426, 1.2418559016014141, -1.7288693202417438, -3.961223593774063, -3.6916673000390468, -1.279717804744064, 1.150150670667053, 1.6552314944110469, 0.22462181242048532, -1.2820309264343586, -0.936118712924762, 1.4151356262280674, 3.984903551808366, 4.688212220300519, 3.014775977373909, 0.3861529616814659, -1.2536892166825289, -1.1766627151391598, -0.267245063942404, 0.17784201285906226, -0.10855398797747655, -0.20895579453430535, 0.7409963457610813, 2.3400418265386085, 3.1590183805508096, 2.2905716618500276, 0.5617399637967921, -0.04750840074741137, 1.5834825981843312, 4.258431578630366, 5.2144239964096695, 2.6191100995537893, -2.4909328204419743, -6.79139999372058, -7.399574283711408, -4.2926251579049515, -0.19407347272495987, 1.9084114747494763, 1.240165653951363, -0.5387274960047369, -1.3309641146788023, -0.6580799547821623, 0.24068235761886816, 0.11975203550906206, -0.7675737542347792, -1.0265811272268424, 0.13137454685498387, 1.784124796588899, 2.1606764394197002, 0.5900640092073203, -1.6184905508233252, -2.423723799368603, -1.1645809746592635, 0.7407170848101492, 1.3150457731904859, 0.14864559539283928, -1.2049655889012527, -1.053380670264743, 0.3747489538370722, 0.9954222888831472, -0.8296861590360851, -4.170172195882056, -6.008197799735719, -4.087926234665903, 0.6874068528137249, 4.838501977486033, 5.421111813317644, 2.619531491870647, -0.6997480030922767, -1.8908701344461978, -0.8753933138107233, 0.32134756772627143, 0.05855825848311052, -1.2161508923453868, -1.7670467925667879, -0.7337749950273071, 0.8965505390586986, 1.5351385293231787, 0.8622906395533122, 0.06057282773780597, 0.17222996541764277, 0.6560486357059693, 0.045937432252044816, -1.932537038949861, -3.3836158005303445, -1.9248896314618649, 2.5174338429396066, 6.942295498810647, 7.760885844100738, 4.234900671521387, -0.6898329342743788, -3.138917614528133, -1.893865882577681, 0.8224368489875984, 1.998263583268579, 0.9535156400927542, -0.36020061397119746, 0.0645172239117407, 1.9152232025068758, 3.0396272800893542, 2.066394966946517, 0.03506950023097811, -0.8409155265734095, 0.231497212061234, 1.736262088615296, 1.6763409497733162, -0.0748945652984374, -1.6739273906355479, -1.5297878442067636, -0.15709771234976844, 0.5579358257432131, -0.25377230412914076, -1.3698195627492713, -1.1041948844682716, 0.3344558700995712, 0.7835290616708324, -1.2855079062584147, -4.5230899606884885, -5.714650254835365, -3.288896395682092, 0.5503460764860932, 1.7218490061000797, -1.5649705922837522, -6.801424219258386, -9.558839375563688, -7.7675327815910125, -3.4222768111935604, -0.15857986596985352, 0.3980381586650362, -0.4004701741788093, -0.5059817679563585, 0.3605468729268393, 0.8923827039220238, 0.3576653425028376, -0.2953410354360787, 0.16425364289938887, 1.286415553243949, 1.1828455583897541, -1.0755621408961171, -3.892584623893737, -4.626296538689497, -2.600939807897531, -0.023035172640633927, 0.5203055036808911, -0.84070632879781, -1.3263483921150765, 1.127259583872673, 5.087662295178802, 6.840965372748134, 4.414340820216888, -0.15042160242841449, -2.917125214533075, -2.1761181344845384, 0.09098900933718902, 0.8980165633917936, -0.2322235272266066, -1.0392161441112509, 0.37476248478624274, 3.0280378517135347, 4.1728927802176035, 2.586120929975903, -0.008377716010030555, -1.0349616447318295, -0.01602596440766475, 1.1910303837782614, 0.9403532350743351, -0.22187817297894571, -0.5731422951273233, 0.3093209411712797, 1.0092869332558436, 0.4110752423831215, -0.45229209674750404, 0.3671855106878204, 2.6994021859066337, 3.483391036335011, -0.08172614038924064, -6.76978706694425, -11.61076355382065, -10.528347544817015, -4.474953733950943, 1.5262918511945747, 3.4037450411854087, 1.6192255921839023, -0.32687412727764525, -0.22255059993516083, 0.8465235126939742, 0.6892132822523196, -0.8579411650433855, -1.851953671776057, -0.9910669341772517, 0.6321056028528556, 1.060998240989827, 0.1343103403879742, -0.35282980841183614, 0.7771976050118308, 2.2751516011981616, 2.0043633064946493, -0.054600428464831804, -1.3699198181536354, 0.13491012504136818, 3.311162891174739, 4.901574711891127, 3.3705113715120825, 0.7095758430096567, -0.12977252139622927, 0.9925217294635686, 1.255018660581677, -1.319328373939692, -4.87037987748789, -5.491185662952451, -1.8709516604024068, 2.8359969139711696, 4.326215548913167, 1.807202723891505, -1.4341262673930233, -2.0091689568064894, -0.055224523365447385, 1.5995122090003735, 1.1939297317320456, -0.14246873709629365, -0.425615480121897, 0.4096640525914828, 0.7221038696932874, -0.226243468333276, -1.1001359714634193, -0.4472703157879405, 1.030517487175299, 1.2834295335180308, -0.08989109259020762, -0.8767033944316447, 0.8882506197035211, 3.7283852997898173, 3.733508373383504, -0.8038514169848077, -6.6727404424243675, -8.695329129870856, -5.295534609712939, -0.21585321627665413, 1.6667009371052188, -0.4949917885383815, -3.270144007710861, -3.419120857271309, -1.389196437246406, 0.0809925991040608, -0.20577307566873315, -0.79583015586222, -0.2591811997699831, 0.4298194857830916, -0.7583175518750778, -3.7139616077389004, -5.705430480608813, -4.54611097390817, -1.346070759668152, 0.8051207793823048, 0.5347792007934203, -0.5403582770777041, -0.4528798007149438, 0.34968360786783304, -0.039201445990941844, -1.7316437734790509, -2.3059488961998484, -0.05921168127069816, 3.0075120937731468, 2.9482897013883993, -1.2362009441020196, -5.728087659586333, -5.877871083117892, -1.5392414632433111, 2.732779764913321, 2.9373558361254806, -0.003993277732259843, -1.8729249745947032, -0.41233427712046616, 2.347671111892686, 3.1316309793060224, 1.4754101930479018, -0.2901086143417348, -0.47328284378499813, 0.0562083988044491, -0.2515644325978355, -1.099935404125427, -0.9495476191843276, 0.2879743283941298, 0.7134390241898789, -0.7944416301588646, -2.425155908140048, -1.4301783404672281, 1.9406502784106094, 4.002248187817022, 1.9307022039354629, -2.4259674357037047, -4.362889216696904, -1.8654051351311887, 1.9819686823578726, 2.802189474968049, 0.16149788973043178, -2.3043918272144643, -1.7687873753154322, 0.35476973063956, 0.7097220441001596, -1.3253518165048856, -2.868185955632266, -1.5195913789735924, 1.392632291925759, 2.6054462354552133, 1.1644824391576534, -0.6099424101630297, -0.501565375211062, 0.6954383676698384, 0.6420438126584584, -1.0150709999477174, -2.1216865150909623, -1.1597339771264854, 0.5335899605501774, 0.6955283204726184, -0.5750241570021568, -1.0027096304908378, 0.37719724490054674, 1.5922328094931704, 0.7445767755111093, -0.36839174966644295, 2.3487045359026566, 9.767891748120164, 16.946491995906563, 17.58827286525079, 10.824659591309302, 2.2470290427062984, -2.0669404986809288, -1.3901818728000461, 0.4522239720090456, 0.5165765078845073, -0.38531593351151594, -0.2245465414481008, 0.7829239934741534, 0.7358694196724151, -0.7231192156561879, -1.626780570681227, -0.5721922218705842, 1.083273003204249, 1.1376354695919737, -0.11335380503369104, -0.11123928725758274, 2.2017372902418146, 4.43573076711472, 3.7074382175870646, 0.6257481001875846, -1.361540120229977, -0.6519177262351559, 0.21687194913448793, -1.9107983833310525, -6.076060421191952, -7.868492432072778, -4.956800622281971, -0.2315496316821262, 1.7197907993817347, 0.23281146129577482, -1.0720056604131412, 0.5381574609267944, 3.2621267505150477, 3.4238864137862404, 0.6007105187810363, -1.7801300932762107, -1.000840849671557, 1.5463797855539765, 2.5288963725292746, 1.0974588453437815, -0.47918730181036, -0.3382970838200709, 0.616353974443835, 0.6200391482948141, -0.12801872525406782, -0.1606675327319028, 0.29949990829097595, -0.852122419914898, -4.11056369676345, -6.362848744210355, -4.23384973399901, 1.0230854587251461, 4.034360922900716, 1.503646657025957, -3.548297970916934, -5.242230165075098, -1.8973121634341144, 2.1970240615841217, 2.360275274983433, -0.8961762985941981, -3.2030432775296687, -2.1759686384264545, 0.13873731122539762, 0.8154804000239356, 0.013648747942834478, -0.03323225094551559, 1.1699876335751744, 1.708204099025286, 0.5486424540859792, -0.468928565165089, 0.7709747227140682, 3.221849223255754, 3.6965114141836084, 1.2263251391104957, -1.428549720250333, -1.4306960603195138, 0.41646030430815545, 1.1524972223562866, 0.11440526503476832, -0.22677304504780857, 1.6498928545667346, 3.4240477538665663, 1.9420682975598167, -1.7990280341977574, -3.0887473866522326, 0.45152459657283583, 5.179953448793787, 5.485029402415151, 0.677147838909418, -4.171956715320554, -4.44296529448584, -1.1216881712966587, 1.3581118979531417, 0.9642248099838816, -0.26851964265390577, -0.0859461237787838, 0.8035411094052327, 0.5099341128460029, -0.6814774238732856, -0.7359445555389568, 0.7513157338063791, 1.6878020292458698, 0.6414624671620865, -0.8633611300890718, -0.6847578826120956, 0.3965578543879936, -0.3273636098562573, -2.8812955342808286, -3.337195458120127, 1.2464230574127289, 7.93382720700863, 10.298568767296619, 5.8439482438099635, -0.9478475770326609, -3.9633993071612337, -2.298975139127149, -0.0471491253132516, -0.17072059691770194, -1.129734691079674, -0.24957497982716156, 1.8385686097852103, 2.2623194699869256, 0.5310957433764768, -0.43897380879080367, 1.4656784211033176, 4.316950333520884, 4.6749539186552935, 2.243536300074598, 0.0013949451310783438, -0.12806952934603663, 0.38834468970297714, -0.46747856875199817, -1.8992030946606775, -1.6384017308748486, 0.18915328962441152, 0.9025827637288595, -0.634235908953445, -1.9806615463235009, -0.7928565399620962, 0.9512662423785141, -1.0090684798321454, -6.904695999558758, -11.233992711055967, -8.96178229258893, -1.9399901586653332, 3.04823445716767, 2.28228480702962, -1.133884008772664, -2.112503504462337, -0.012724338337276861, 1.6473493465649947, 0.7070561532790751, -1.0526753205792865, -1.1926112699405829, -0.13085951472600613, 0.19461115778933905, -0.29078271921462595, -0.01110770161995071, 1.0063694924340747, 0.5403832475247589, -2.23061042769461, -4.502293165221634, -3.148776882393225, 0.6765923755119652, 2.5775627317978995, 0.7203460643564841, -1.6829597983896099, -0.9475023719345662, 1.8588448133292754, 2.600006860310381, 0.32496925808691735, -1.024058449727101, 1.8277614624785203, 6.481484385508111, 7.671888967297662, 4.125742312019609, 0.0025206286434534585, -0.8265052631480921, 0.5410960830966066, 0.6239864265483825, -0.9663678985495552, -1.2530453594665865, 1.194552117457709, 3.778872065839327, 3.479440231907749, 1.0456432150083628, -0.35322424778765266, 0.2962896955729831, 0.9365533409858595, 0.12092395315533289, -0.7758925515302719, -0.18527452623467583, 0.758969017809058, 0.1247142519110076, -0.9992803957559041, 0.5382944771288612, 4.62100050988446, 6.2233221667137455, 1.3135662709106688, -6.95960955582165, -10.803357334432249, -6.71468576521139, 0.5228856583007732, 3.8671454752002914, 2.0131071220626886, -0.6649017217656081, -0.8475934943763729, 0.10240280481676964, -0.3334888595101264, -1.5693654584074275, -1.3065776983165396, 0.3527034117221779, 0.940160259916609, -0.3120574978964519, -1.0304409085301418, 0.6139017223143923, 2.8152021865160215, 2.650496549951156, 0.4978069279794118, -0.518418865722156, 0.6397638912296016, 1.283303654996125, -0.6911829867266743, -3.078193232841671, -2.2793988531506804, 1.1427805210129476], 'positive_zeros': ['1.82665160496469263595539245247', '4.01400493597144898498473113443', '5.29682749127294158712361354324', '6.130205179558663880824552716157', '7.20773623999051276790918921975', '8.10196607054315876406772291284', '9.91660604899096266617755691363', '10.8927500525680363038724406008', '12.21121707231255449108182502929', '13.39858672978288463119441383939', '14.15611138900076446569296069903', '15.27448828153775438750150367805', '16.57340784628269560913679207182', '17.31244362884836021109072754238', '18.16261033738694960268056349529', '18.80325342434219830364801227517', '21.12475660642750843181188258965', '21.538375328793658487569728343824', '22.87310825122750594784094800508', '23.491480561606983823247136610138', '24.21550464393096115088095306060', '25.46049521891919573584675151986', '26.18510423635341686689729689078', '27.31433654653717668087015811919', '28.263243577562739461712469407809', '29.5207557773856896078974019850', '30.35024844157513095876437384718', '31.08494341621027927699968467513', '32.55245041218130295504030733280', '33.55442570463087604310029395815', '33.97895293483281729490928366813', '34.487434083617617256462391792200', '36.09446509591375931437589528015', '36.27484944643109437957430954679', '37.66796593040326529508147178340', '39.080312721217692177268578796755', '39.90078961195310206572431159172', '40.82762058527830665202847311697', '41.29968144526749287675295957773', '42.16286039902226222353722548056', '43.20491327692246467774870973321', '44.24304066282189849477718554416', '45.028641978959026064064241630663', '45.85990389005901725414321899839', '46.46567869388916408934470719671', '47.770806057782370975731539120972', '48.98436111565908391484741188865', '49.88456305899517235218465114976', '50.32994605789618245419387112770', '51.38488102601632413075592624722', '52.56453939266018349543209422973', '52.66696414628039948926514794652', '53.44729711233663201733515036968', '54.52753858233581389803755935787', '55.88855589439387763525134900454', '56.77482507378824192865862910128', '57.695507596383968125865645960228', '58.110338742694701437062134897483', '59.3811953325778635730440145710', '59.95569830831632752268976848845', '60.92611631356632378147527005733', '61.91270386584695616410292980777', '62.436378589684053537441275436028', '63.36576110241495162871452109074', '63.91405274149997755817868854528', '65.26113552946886719670194998258', '65.82950035991665760635705152040', '67.52810026611206178698759390692', '67.975261683761930724580599732969', '68.635198930922273377425489062419', '69.50891879268922248577949585984', '69.946982392600005550519308652273', '70.81723741069532875031792494046', '72.191453775788645305332436024692', '72.642724991870694464437101936973', '73.33404259075611765094072722838', '74.67655191831350168370546196249', '75.61039772751626039731484889911', '76.20025064770733540809804700773', '76.82451099136483585441502908053', '78.12377623271415214103085647505', '78.75331640588438261601523252506', '79.62396872931648521546920446220', '80.22471264519606940245334831554', '81.05530809933152601006338601606', '81.49419118927314135351607490857', '82.495535853807283773325974257537', '83.96606514483589222130932001303', '84.92121002974014998110108138062', '85.37710978896748993165980885435', '86.09204664771182776830946554774', '87.056334627572707531609879850024', '87.853683590660452222374914726756', '88.272580886805063784752507409398', '89.36729142793994996755587789641', '89.98479184728327986963890649915', '91.39250388653968171540977625454', '91.62422209654616222773338692646', '92.37727091150848108255272281254', '93.55288072187175238160310157546', '94.5320099492367988105410345897', '95.31997714619797187301106480067', '96.21006232780215788585924944065', '96.73813811143680198168225506825', '97.4429610384775504597568864392', '98.2184213464120464411269984505', '99.04477560224604366197758162550', '99.579909106273266668964986865797', '100.582926732622308659826182606601', '101.89196444722209434692452034219', '102.45072249454556578546429409839', '103.71132996004680030765274461207', '103.9741903869170840773334219554', '104.77021814103729285003683402015', '105.189646200891308765769404696198', '106.71543280532375447354034721155', '107.32737889930362673905757429796', '107.974838966657928161079426680985', '108.42780548224788981532058282999', '109.38058969917513421840924952218', '110.237496993724420205743427882572', '111.343790720852823929020619166114', '112.18709956913657764505156209385', '112.85838218709278239229250557209', '113.98985182684082199408557139497', '114.63613100604418475309575028768', '114.878846277515891328515230231314', '115.86734555040534405782048895884', '116.435351865100711647737484576536', '117.33108681912436732969715220359', '118.26409115964061978672454090574', '119.20294024515345424256686147715', '120.01540478344788244997901366782', '120.87831598517051154346960527381', '121.3856961794259112946022469741', '122.34856421487642454733535999156', '123.3027489180095523387110709573', '123.878797502006403697866470649754', '124.5152998103399501455503825666', '125.5112245827093133518907579022', '126.1189513888554056656284693638', '126.808538478652680975197309622048', '127.64696397989799641342159291943', '127.92531210820124395659094589829', '129.80143481017568024965418503711', '130.52704569202204371860282900220', '131.10471583787747997194101366603', '131.63550960706348672638264154437', '132.36187387233461494969900063070', '133.22208431005615818089742090165', '134.031178887561993042920356505063', '134.399937629853882012023917726876', '135.6910608739569722308584840991', '136.40179857790830965251861393383', '136.645406237703505712427566515096', '138.14396227426548144699582000865', '138.78451360934913181961844115023', '139.31151565877985209339894116417', '140.370654334693655629607993939841', '141.062261544877627800944519568710', '142.06116299631839239217473947548', '142.60584658664003451478815101906', '143.37672355914149713470623157684', '143.83985777295220546340118344914', '144.22970705807655223884199286819', '145.56462835977096656477068085243', '146.3422518570559513400393663253', '147.313421995949414835907471005314', '148.04782590498285056726997664054', '149.03921970652341303456146193996', '149.69315993418887686637260083108', '150.01304902767183406784896645669', '151.05373430838749596059099594992', '151.440462073659132952887731925149', '152.62208919900076988220613006242', '153.367201291967215356449562846035', '154.093549941578687804981023503783', '154.43957838268430859444293686342', '155.47568384352996588324159375273', '156.22226607510461109342379118053', '157.22347016973181572203589996648', '158.22974632876269129716526396589', '158.97093197918449735502190523809', '159.40414810542911238015833420628', '160.13272858259303953445406569764', '160.79826868922567476799329941558', '161.67653338097637987756571472251', '162.364911714355230938385806678090', '162.756494370354658642788208428602', '163.68872167885578862524735529733', '164.950285951036062944354737276169', '165.95075794046461079124829317386', '166.19604849478152073627088163167', '166.91394061950334974427367662752', '167.9063343211995092041174357403', '168.25088864623254032191103180137', '169.68786162951481218866139803523', '170.05809754803412432630245167564', '170.51746924476692041626699003293', '171.52977451575998988492631377805', '172.088431344433677025876238333266', '172.92401346807181281413794406252', '173.35525386964181798647345893999', '174.77779841692004594532048897237', '175.51530379442157431963985520343', '176.251562978628978004880276323074', '176.98796623574261556359408418466', '177.85980065196038598876595447044', '178.25766872703221783989577686603', '178.753802296074819404073735596665', '179.45441880546253805023952861142', '180.5686840246085018146368399126', '181.32599343838102466849395812537', '181.98368145648266097371621857729', '182.85167251904143643212701621069', '183.29309914173366510502532569219', '184.687786558367072563609284181021', '185.192866314783690107119160944667', '185.76001214247198501102367099386', '186.43942208338065837448871486659', '187.67001760206395452988631917470', '188.0376727912021766833889367969', '188.78026641539470338637787046789', '189.42345554223515599454697802496', '190.027670129998640190457787845130', '190.5696102818578098236036552186', '191.61353636034574352400452189370', '192.78672728340907251516289557593', '193.64822976554532338703874456645', '194.323239036157116405236946442474', '194.58538181941522741408641715872', '195.55812689746704383222483602938', '196.186820063617098913873032395830', '196.79376164509888594637834827359', '197.89529685714986627544516823556', '198.304586913896334597120465627647', '198.98410077442182883198861498126', '199.89885130683517013604772618252'], 'prelabel': '1-151-151.29-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.701241051920901, 'root_angle': 0.6391903134312186, 'root_number': '-0.423476303120955697495386183495+0.905907181059410991012761964354*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.319595156716', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(25)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.799525670558903376821000724558+0.572502142432519637923136769625*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.82665160496', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.01400493597', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.29682749127', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.701241051920901, 'bad_primes': [151], 'central_character': '151.29', 'conductor': 151, 'conductor_radical': 151, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/151/29'], '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': '1-151-151.29-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': '1-151-151.29-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.701241051920901, 'root_angle': 0.3195951567156093, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.82665160496', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_151.29', 'Lhash_array': ['dirichlet_L_151.29'], 'label': '1-151-151.29-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/151/29'}
Lfunction data - 1-151-151.29-r0-0-0