-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_837.355', 'a10': [0.9135454576426009, -0.4067366430758002], 'a2': [-0.24192189559966773, -0.9702957262759965], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.882947592858927, 0.46947156278589075], 'a5': [0.17364817766693036, 0.984807753012208], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.374606593415912, 0.9271838545667874], 'a8': [0.6691306063588582, 0.7431448254773942], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 3.8870116586608887, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [31, [1]]], 'bad_primes': [3, 31], 'central_character': '837.355', 'coeff_info': ['x^45 - 1', '0.990268068741570 + 0.139173100960065*I', '\\\\zeta_{45}'], 'conductor': 837, 'conductor_radical': 93, 'conjugate': 'dirichlet_L_837.547', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^32', 0, 'a^19', 'a^10', 0, 'a^14', 'a^6', 0, 'a^42', 'a^14', 0, 'a^43', 'a^1', 0, 'a^38', 'a^36', 0, 'a^12', 'a^29', 0, 'a^1', 'a^1', 0, 'a^20', 'a^30', 0, 'a^33', 'a^32', 0, 0, 'a^25', 0, 'a^23', 'a^24', 0, 'a^0', 'a^44', 0, 'a^16', 'a^7', 0, 'a^17', 'a^33', 0, 'a^33', 'a^8', 0, 'a^28', 'a^7', 0, 'a^17', 'a^21', 0, 'a^24', 'a^20', 0, 'a^19', 'a^13', 0, 'a^35', 0, 0, 'a^12', 'a^8', 0, 'a^25', 'a^10', 0, 'a^11', 'a^6', 0, 'a^9', 'a^32', 0, 'a^31', 'a^28', 0, 'a^11', 'a^3', 0, 'a^39', 'a^17', 0, 'a^1', 'a^4', 0, 'a^20', 'a^24', 0, 'a^12', 'a^20', 0, 'a^40', 'a^22', 0, 'a^29', 'a^15', 0, 'a^39'], 'euler_factors': [[1, 'a^32'], [0], [1, 'a^10'], [1, 'a^14'], [1, 'a^14'], [1, 'a^43'], [1, 'a^36'], [1, 'a^12'], [1, 'a^1'], [1, 'a^32'], [0], [1, 'a^0'], [1, 'a^7'], [1, 'a^17'], [1, 'a^8'], [1, 'a^21'], [1, 'a^13'], [1, 'a^35'], [1, 'a^25'], [1, 'a^6'], [1, 'a^9'], [1, 'a^11'], [1, 'a^17'], [1, 'a^24'], [1, 'a^29'], [1, 'a^26']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-837-837.355-r0-0-0', 'leading_term': '0.820120302536862837240397198586+0.554716305324511578509789726282*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/837/355', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.990104787396785, 1.5139530128352277, 1.9182597621556523, 1.6781739336479196, 0.6907675087430053, -0.5313750812850727, -1.2182211100141884, -0.9730392455535002, -0.1729505223812832, 0.28213364031303634, -0.2222008308796108, -1.321135627033962, -1.8224324371267087, -0.7580262316374575, 1.524571045315957, 3.3474559955724574, 3.038429956442779, 0.5652259640116221, -2.11687125846636, -2.593745917316771, -0.1949764771128291, 3.201109444046309, 4.7150125187414265, 3.079479772219579, -0.1557211827300815, -2.0762036129403927, -1.1603632251282439, 1.3754555606866887, 2.9690273364794675, 2.348837004847933, 0.6425765922028824, -0.12340985676067348, 0.6508076048905813, 1.6297596612038843, 1.3375313597863496, 0.03432315953161779, -0.6262164789406681, 0.25527089290422084, 1.5684048303166915, 1.5167771994980663, -0.01989759556055249, -1.1146046383439314, -0.1295894976178728, 2.0065855407772943, 2.605294598114629, 0.47370483399698393, -2.286996135868664, -2.464284554659684, 0.3664514790368013, 2.9331184000049717, 1.8123879566135312, -2.4834924683710007, -5.758891092129184, -4.6589226908512344, -0.3055368402451304, 3.125196977890624, 3.0643329007749136, 0.9145678944682011, -0.35317536514133696, 0.052244547067890994, 0.37647128875686325, -0.6560727450728054, -1.832212242067027, -1.2049866433192382, 0.9557985037114776, 2.2708806372292525, 1.3984455133346563, -0.13087153997264755, -0.036360417401774967, 1.5180444768346886, 2.178518566520166, 0.8407788634326376, -0.6622126969546479, -0.3264146305674319, 0.5341182223972332, -1.595071650139674, -7.4677170025142, -12.839587833836578, -12.662255995992323, -7.000926069558228, -1.1765575197042022, 0.29884981609903305, -1.5099051352859512, -2.253997802589174, -0.22918514143132387, 1.8987008628517177, 1.3399013646201368, -0.8692596857281045, -1.5633246106511511, 0.015689466321352027, 1.408149529940276, 0.7382220821504971, -0.6310718295936152, -0.3843540753300654, 1.1515370043756024, 1.5706789119112925, 0.1740693548194067, -0.9035211643270944, -0.04464301549065533, 1.215097966373885, 0.6061532012707215, -0.8932376472181469, 0.041417227557931945, 3.910086541791373, 6.551761791288219, 4.208645356726614, -1.0237655868153384, -3.301371466517075, -0.4419402545947243, 3.315063911346415, 3.043161576118064, -0.5006554137189558, -2.47972925227134, -0.8898478491754064, 1.0758058955815686, 0.10978594970034213, -2.4467772337210274, -2.900547451977806, -0.676636479905407, 1.1881486828750745, 0.7438223774741383, -0.4140918064697616, -0.3002150449883949, 0.21551485825196717, -0.6675775182068953, -2.016336424925144, -1.194799780793583, 1.665141435271243, 3.094158907438023, 1.2022962836383413, -1.3091613162729079, -1.0972329392318996, 0.6719230977125427, 0.1732592574999121, -2.6309157913553367, -3.055199472147151, 1.4291912545584835, 6.439132065184705, 5.771709260312725, -0.24427911597179014, -4.977495601513125, -4.075172796338304, -0.3737543187749637, 1.1250077870687851, 0.11588440924675501, -0.03199983995257434, 1.6581102333390614, 2.5128553052399867, 1.054598448026123, -0.46658952679484955, 0.10482504263628539, 1.2525697011446786, 0.46789626370662507, -1.3529313654013166, -1.260465737392358, 0.7846540813663789, 1.6835686779255292, 0.30218031966427733, -0.59166386384444, 0.9166575424706229, 2.281100879241283, 0.6009647800331552, -1.8046856132421398, -0.09282764747830072, 5.206101753526844, 7.485315120433212, 2.911571274561127, -3.745026874860896, -5.23704121073159, -1.3166257198726474, 1.905148794691792, 0.9874982662777635, -1.0348989341248507, -0.6131227945649298, 0.957246063609219, 0.7789212387539318, -0.2528184319038078, 0.860627189199056, 3.6660224663580143, 4.497367697115827, 2.2115225687156768, -0.12341745667637767, -0.21581565042713566, 0.28546775503740096, -0.5380696072100605, -1.2596012742742264, -0.14910003999184074, 0.6457597784317606, -1.9694379641405133, -6.079982101371604, -6.412863838094918, -2.4033919837050406, 0.08370836777789636, -2.777626009897209, -6.745821713057886, -5.680042695638182, -0.7709567821969958, 1.379608025496662, -1.2579585069350834, -3.596567885822582, -1.7695907159820763, 1.1737136616824597, 0.7299537243894691, -1.9253807673787502, -2.3960755431299443, -0.2232727784816842, 1.0768013157894993, 0.2074590907605529, -0.3861052823998698, 0.4257323608676761, 0.37743681375938115, -1.6177035306630336, -2.808283828927001, -1.11110373274268, 1.0442297439498254, 0.727961087405202, -0.343182940939885, 1.0867939157972075, 3.389728085929092, 1.9542734433539515, -2.768995487461761, -4.768367927787126, -1.5964090621321556, 1.3705719214683185, -0.8146012053964304, -4.643841211357979, -3.4449774105995115, 2.123181413270985, 4.94930698859849, 2.1288442733963753, -1.404462308810129, -1.1010167002406068, 0.9768733213402663, 0.9694634749946291, -0.3851544935478498, -0.2429095714060801, 0.7501847425797764, 0.0826073630454465, -1.344694731201271, -0.5020130414130187, 1.9982686054018053, 2.353797851994116, -0.012900194956055459, -1.3630430736169399, -0.03361445821685375, 0.9496898528649864, -0.28459802021395275, -0.8832319500959913, 1.0041898246484142, 1.4428519375484004, -3.1351041824774524, -8.182423297138717, -6.010377661939223, 2.527475073054786, 8.128927963568898, 5.712231882243839, 0.5330919097599082, -0.8155922311370127, 0.5650010851692502, 0.18014117439204594, -1.4300782041976263, -0.5200225979476684, 2.3704413674526044, 3.065524104336478, 1.0063814458962728, -0.02431404381084991, 1.3243976153546257, 1.993575827174554, 0.4558895341493219, -0.5983682992197433, 0.45263012060839775, 1.0646932605485808, -0.4494442370930668, -1.3291027880480994, 0.5218276063650593, 1.9926376197091784, 0.03974985984370023, -2.0899012295055837, 0.13063687630063547, 3.7390306941643114, 1.6733596800588555, -5.6188777711534215, -9.503335661482197, -5.614185650723415, 0.14908512713383554, 1.299484492263631, -0.09627686546847848, 1.0539610314279135, 3.5287767307425018, 2.5712064381612345, -1.2095970787976087, -2.72492456278378, -0.9156698398252086, 0.2362104731909016, -0.8735774420621666, -1.30123019065394, 0.29119208316999856, 1.1887350041810354, 0.058511968598065026, -0.6277800976547891, 0.09060723793685797, -0.7486152100377476, -4.045647463075404, -5.432446299384862, -2.184304036266879, 1.3876103099352077, 0.558118010564048, -1.9949374015210313, -1.230088128871655, 0.8428475115026421, -1.4811735212481223, -6.537784492281698, -6.286366733716004, 0.8586633958441077, 6.5631296256216105, 4.742596958948159, -0.2209317341402124, -1.6014184989759799, -0.14654524059927992, -0.25254951073002, -1.5326224901693946, -0.7581332987530908, 1.195198062190135, 0.9744924985246654, -0.7339753752924628, -0.5895628074028783, 0.863471811131173, 0.2205785131771572, -2.03375844808853, -2.1000619280403234, 0.0006597463217360502, 0.31286826619899244, -1.5968760227677354, -1.8049523046062355, 0.15755921489791197, -0.12346991171276474, -3.137235226059168, -2.761750253678972, 3.3635968722099903, 7.9015623243836615, 4.355887764152441, -2.363841346410445, -3.3478628999499223, 0.7848793206366576, 2.179384705950388, -1.1396102987360257, -3.4275588918937783, -1.8161772780287584, -0.005659644743985377, -0.3233503319218407, -0.08774853291510201, 1.8665532348547436, 2.178934178641156, -0.5028267459374668, -2.2613935932108626, -0.5810659423386768, 1.3805999484474152, 0.7359751290663585, -0.3758141085659642, 0.17959497991014214, 0.22095824489981822, -1.5847782335821752, -1.764553855737601, 1.3787522501299696, 2.6112197249607, -2.1467726935528235, -7.329489199304949, -5.2860886556374975, 1.2311547732510175, 3.084608702585462, -0.8609181695632913, -3.0396709455537687, -0.5002957623217956, 1.1142628274450819, -1.3523559058288934, -3.059517566256292, -0.40061840478677235, 2.5385222661652493, 1.5182864158835612, -0.7850186517785162, -0.4404181948836119, 0.9222702931991857, 0.3449647726018418, -0.574967083454285, 0.47682835419237174, 1.410582129445108, -0.04669482018966044, -1.3393392661368289, 0.0813376870685962, 1.214043803771651, -1.1238408452996964, -3.649034740719909, -2.1499668744539813, 0.4153193280698968, -0.7855857082605768, -2.6585463960190263, 1.1220419337176977, 7.9210459549537315, 8.824084659190142, 3.031509468358377, -0.8090516671446757, 1.1624224613233103, 2.7684910465373234, -0.32048074624116146, -3.2796786007364487, -1.3872999219493398, 1.901480927728336, 1.7937508497225658, 0.05479548246084538, 0.22717220069266847, 0.9699057124806095, -0.011799533424694532, -0.7257517183084709, 0.7034864085572222, 1.3625830028487333, -1.0541050781395813, -3.017826400879123, -1.1192012111888006, 1.5667040717679845, 1.0873373146611336, -0.3919614673691485, 0.23947880743982317, 0.11075731268171238, -3.66304842040105, -6.125948509201779, -1.8210255301273635, 4.020487399053069, 2.0448935285884215, -5.8921140520780515, -8.918883494083815, -3.8803143570077623, 1.165577705817641, 0.9119372902648722, -0.6001010794031175, 0.3619084705073006, 1.1628303534541415, 0.03183679833442861, 0.370953781821015, 3.5608688985617327, 5.206645358977605, 2.7879941638105397, 0.08791547953269037, 0.1339948364056495, 0.543650743114634, -0.403419945443204, -0.04741384792795701, 2.428971536880188, 3.128739732431386, 0.8112928920393874, -0.13892465968227927, 1.7398135797520486, 1.4630415181535807, -2.4264313429077378, -3.02749446891705, 3.2020213090116703, 8.352975207164413, 4.875553903492271, -2.0350451639980793, -3.1278276425207228, 0.31701084357948656, 0.7642828711949238, -1.934591271097228, -2.0423649319893564, 0.44397102960610313, 0.445259383610404, -1.9475998656336422, -1.904892289450391, 0.6387548132420875, 1.1304363435164588, -0.809119094233572, -1.3141273413545989, -0.14283655288658714, -0.46008516565210245, -1.7930029787942248, -1.1829412156203594, 0.013558995265785488, -1.3852580087194628, -2.8905831886451874, -0.10723428677516011, 3.8944801829629676, 2.6033187428753886, -2.1189709016923977, -2.7050593430316123, 0.7260850308726321, 1.0656594535255448, -1.8483499107860297, -0.37163311753158584, 6.274754473105192, 8.944291241877377, 3.6099315680121955, -2.110135446209574, -1.9472064195993313, 0.1447660657994384, -0.7662335895045888, -2.2567784982002905, -1.1369779099647468, 0.21204283784679348, -0.3491738486147304, -0.18604901774626492, 1.920388017759509, 2.3715828344009764, -0.11342620487051389, -1.3262120536672404, 0.5616893800468213, 1.6133805436554052, 0.1868337762284365, 0.13481720096931976, 2.3912785134346777, 2.3107151485904045, -0.7534485698954109, -0.9313684227319351, 2.6654274778908933, 2.4523837727236004, -3.9659597152854813, -7.4909220370376834, -2.105361552946015, 4.598061384277242, 3.897179250592518, -0.5301213624368744, -0.8218517259936117, 1.7710015423277978, 1.6527379109048277, -0.13700117517996235, 0.5115188767982956, 2.0300771573652483, 0.9727624969173154, -0.6100439343097267, 0.3627714476758688, 1.3544496082854458, -0.5841166348015224, -2.402984897177138, -0.8296248290168561, 1.1703660421510236, 0.3042807515694234, -0.8668977154819987, 0.10787779080161924, 0.48029505282904095, -0.5828041812101495, 1.9569331221840933, 8.74557388895095, 10.827552498518191, 3.2092383954501997, -5.218173847555419, -4.815327298938558, 0.26775071450812543, 1.0030099353461668, -1.2725003129711323, -0.002499776139101998, 3.2391948611182606, 2.6053482536107606, -0.22474735410773586, 0.38756287462708044, 3.058154156981385, 2.54211712851594, -0.12200938916010015, -0.3481889065691658, 1.0438895134442983, 0.5132071711871715, -0.6872831780542236, 0.18358272263029674, 1.14049365060248, 0.05147556651834809, 0.005188284856420561, 2.9168027711979168, 4.155590911351889, 0.8261130900007243, -1.8509628339289035, 0.03671185524374421, 1.5385472343416924, -1.0567933294902385, -1.6869904851174529, 4.290687898398368, 9.489437229313689, 6.006602568610111, -0.7938090163414186, -1.5119109076583384, 1.9183010133006304, 1.9439799200363774, -0.4331564406193684, 0.6473489737456545, 3.7347288951412345, 3.271765920415388, 0.33811806230857133, -0.2346714153772463, 0.9010137103128253, 0.4065093252220819, -0.485054714677438, 0.29864656852666793, 0.08278936571158182, -2.910003672270614, -4.451957127622392, -1.7883291382539284, 0.7295369085514607, -0.03838630196111395, -0.12214533143090035, 2.7709631086261446, 3.761085702488713, 0.7115947185604147, -0.5858456857740301, 1.7196944890487738, -0.22937612119473116, -9.520208466065956, -15.783137383348516, -10.745303286017846, -1.7028980638805014, 0.7570052388568445, -1.5944978826148197, -1.6114144349347632, 0.0779237710721346, -0.5459970282913602, -1.6029431764716968, -0.18801290545970625, 0.7594613682191601, -1.257274297672408, -2.4239832625935636, -0.025593392540312634, 1.942472320434515, 0.547270516791101, -0.8056832778392825, 0.153438023286169, 0.5225921822159477, -0.3220049320386922, 1.2057401113491735, 4.189314636588899, 3.144267274692522, -0.7927967480147997, -0.45600188603293434, 3.340729436273131, 1.7399615421533103, -5.5259868724746255, -7.903393941169452, -2.117824875612261, 2.2069796238558226, -0.43602270065666743, -3.2781744042993806, -1.2525391609865737, 0.7626206446928345, -0.8343856576641149, -1.7503598153674789, 0.3567424790127329, 1.1409245890556672], 'positive_zeros': ['1.42116597998765100142594431829', '2.57380329542411331928399554192', '3.043989851694832276218355253774', '4.176235222115238240955849883525', '5.37086701602499372326134956958', '6.26786894855238165073542246140', '7.48415013192691640540532213572', '8.27353461535976922564443310657', '9.55324401441309429645440985090', '9.7918027118299024268841748795', '10.94599173340279854636572815318', '11.504024700936408012382393458927', '12.4963865848838522118164667922', '13.14532120497399316668965474486', '14.11077185718659265843769624477', '14.96662009561078486519027006320', '15.770326506144549027924699193422', '16.89588949542015339042899184963', '17.9791222134990614419672499875', '18.41545759283893504675819050612', '18.90888698053948344346427582344', '19.86912639187281741011933641768', '20.89947496252538888696687713662', '21.259891120593464290269067390945', '22.33132675368037901435108340327', '22.89772883312031139659173915070', '23.283051435351623669945778167642', '25.123192421362226460942460533061', '25.38952944537684004473701622222', '26.27625877542034228589180641587', '27.06256232041617875681415937633', '27.81005646313010625834941500722', '28.58660543035935763562135336682', '29.14797605232990340166469443709', '30.0324387941262975034655868395', '30.63404155306231771330137018864', '31.362286287977232960845538504913', '31.87028942527992091416816228097', '33.06056739573430431949553741682', '33.78141166565355145505513505232', '34.64480052877916899693657216730', '35.42273541671782793364542454763', '35.95169947292054961416618882952', '36.95862800635330984479147921287', '37.6767592031047035213664945237', '38.2559220765761978057074553635', '38.58475536542975951543711423687', '39.51446245970348491390576565378', '40.44027495401242577095008419735', '41.11836862043211724281170844607', '41.5862452631000338433606420951', '42.42278127953778874886361676968', '43.425999834465835246123846646396', '44.413984871212406281241106295402', '45.034378354811104138226471175045', '45.322038864926744280318664147574', '46.4255243969022191649147802020', '46.85076258073719413302006012148', '47.57659101980598654800305188021', '48.324734340757594172549634253093', '49.118845942741405680679034453065', '49.54456856874004380718482539107', '50.37588478564983140409747855484', '50.944194076350755605857125636715', '52.001040163836407090763483823795', '52.905404733204705485219520457393', '53.566758326874734465001293722562', '54.17340270595477460111290555322', '54.88805514982357495382740534007', '55.17133216264057414288194537936', '56.53429931568264733655214326636', '56.965508537910446337716124683340', '57.3523285381433931550859435742', '58.15401552926634873781895112160', '58.56887373419356538754853962621', '59.93634272470943784434398607867', '60.04156647443375820595827165896', '61.30695316007312469369982691971', '61.76311184739667988052697257012', '62.6636256432038236215062019011', '63.21390542891666451501982577975', '64.0931308582228319249827596890', '64.742833222994261852845132864189', '65.17581580925035637374286166843', '65.70413611247171848378925761158', '66.69654906618464337292186286413', '67.350406153286135966594540533388', '67.65390888773672570389689298235', '68.57325695637973913053834452973', '69.496986842046596223873716038515', '69.936349190483542524678206053249', '70.822952043029828664903611153174', '71.72145621113619377125448880951', '72.34071132866476184967514523180', '73.02179540056285415586992933969', '73.505250386692250400526692602119', '74.07869209863551545703359893651', '74.75274288108699901818875060462', '75.623423882599038446979444911031', '76.25575851866605146696615802527', '76.82090287343715625299217781453', '77.36141440148590506849921480802', '77.94888157553950320937289028441', '78.97535723143799568916913687286', '80.04837099704797575963099454832', '80.495483900439327665472401255190', '80.97065936862054619214308255670', '81.62231088223920941315093226005', '82.71021199640591023437291725253', '82.828049658455676977699171319828', '83.83034277674493166812797485775', '84.27732903824319023555114764959', '84.9266711653181340083200917440', '85.55947773606424011379411780835', '86.25406486437575503812165232627', '86.8650388197525815968542624802', '87.58121827697996947850440600870', '88.73836061050923432202904432525', '89.33726561891066376926151459027', '89.51786004099996153509144429791', '90.52437791090732028409128444766', '91.41119428412240641261934406447', '91.67386623384934583707806614555', '92.45115842132945495376305321559', '93.1379484303341380659047555427', '93.70586868095689859237583398272', '93.927280858426205914530153221076', '95.15760705135413258964023653359', '95.68565840394628878466876044454', '96.3988461967880737979582388809', '96.7614916357709363043895889685', '97.779845475870473988604319118662', '98.73239476357488360659096214145', '99.42070758633653244592783497872', '99.61222313757925198206479938842', '100.423851467102326194145289169996', '101.105823968595656377878599781264', '101.68034335064215237011988582050', '102.22002594930185401319840652478', '103.12488634265392336149417156248', '103.50113500517866797808986994354', '104.34606661994991556854895779168', '104.66996260753359619266582546275', '105.474998857422498717698274300499', '106.43875653324223094600548217962', '107.12955348993847607819124090842', '107.723370070720945184470102205326', '108.75294018788194033820106663887', '108.90727231328662891710292215162', '109.393933615339793740108581366252', '110.26224550998678594715014486833', '111.007038352114878777208103165476', '111.72113074703892528157587258445', '112.12556624665669446849706499090', '112.552736781191309001966009891195', '113.31773261838329491305125597892', '113.95564369473576599649839927221', '114.93530708524796955273891748852', '115.56600785033921912057667628661', '116.29988786783950098166001185953', '116.74247633037283691964011433889', '117.5320855660128639465901053553', '118.30499991853917332531243928691', '118.83413410461665290632282965524', '119.45440424486548847694656310649', '119.90589520833805440570356333108', '120.618076279755019122938805317039', '121.23812617853381030423229548631', '121.76719224221242157656900518611', '122.73000359057001354873347480597', '123.02593255418157405251593856376', '123.69454723242335779048841092572', '124.8727786154404687370309986856', '125.19426100864929141431566906038', '125.91419778110897598977750325283', '126.67637462614750387383258480610', '127.517949559640645419588633563243', '127.73577339782288834032309394272', '128.43496211219932605375776931919', '128.94213142650919143089355814737', '129.58047371017062674607918200038', '130.41953179021932622809209917417', '131.12818972463846471105200267366', '131.49847667109184704328838403345', '131.89085032363960287546912164860', '132.89394802248952139579544505840', '133.52458796492181348084111652655', '134.58140934443645350279774507537', '135.14290480392254393342917934917', '135.55382998840495486038371990854', '136.25904403061303121131188994321', '136.49562915685547333725922814061', '137.83539487982281550873570206571', '138.074428942035776171358023244093', '138.63091891550020667411980353818', '139.0706015898914182284764075301', '140.12688682190218061651691394767', '140.35085086108323319015697130306', '141.0680961334913037721693553860', '141.74116424138583085111304361712', '142.70609022360639804902160996069', '143.40541763065908705383139319545', '143.846692839579616348577581668646', '144.62484360565145303992652838902', '145.06410658773081657884565862344', '145.85627307746204412256336122897', '146.43890935037312132720687420859', '147.266922214498564267886379936603', '147.33456275649614789635138659656', '148.41669032224000291702335892321', '148.476374527143367127132230160', '149.382217649529312925014289323406', '150.166247478706823029831450833198', '150.868449288451156592169625867794', '151.36549073421328225217320829913', '151.89692884602823578084799606108', '152.97795438656682874117523635797', '153.70755116701848213602141840963', '153.924608914315663614002654620472', '154.90300985213702060576626974885', '155.18905580405764555013880428728', '155.66174257934003646177342259542', '156.54946330539566309672567321605', '157.11293291287704138758298200141', '157.85581239398503732091230580499', '158.09617963215670016398924931292', '158.98375327038354877433635449535', '159.46776181484880051443316873949', '160.13881327189526050847667842861', '161.01831834790904601086772794843', '161.8274656171130789019615486170', '162.28639855119094830661914622306', '163.08617541431210045032780617833', '163.3371379156328554155171243991', '164.21109913982423302429139397933', '164.62257639977863266162586213669', '165.24578517679489509635635878540', '166.03543332969770608120940362190', '166.61577452907945412270647155125', '167.16277017353708961316009630889', '167.62842051116677900665994774872', '167.97657650021986429017719089660', '169.160791744995061787184163933312', '169.97898839797658912156295776207', '170.43992957237647366578709811387', '170.93773327510824950341333579392', '171.83844366266753404788906894058', '172.13622927659030039405519838696', '173.10614354216792122901759873283', '173.5123707282902058040686316117', '174.16508368671212997223839803399', '174.65075095466309925806934449624', '175.32460662808965202085315156486', '175.624052658680485454711903550598', '176.62501145474871388300815309085', '177.18363687279808347868558325720', '177.71210807263356078570212232111', '178.245780339499250460607159900881', '179.32699995126759759414516538266', '179.82450029272799389534615032677', '180.54751179408270416893209308750', '180.86373977634947511211386316421', '181.9277458041351222017830875660', '182.25313864071301748741709616699', '182.91102252112688621947067474872', '183.351394687028142767642701613921', '183.76339126722578731145919392898', '184.86082563574512115104209881001', '185.30392093748959538951147451371', '185.64548146501190249807880461267', '186.63609666708297480159729200166', '186.97322114798030626272007782324', '187.48847082286299920212421335495', '188.849950197356651985121969843567', '189.17785932363026036051651660409', '189.97416996094137421218130876208', '190.18893878997394135482747422640', '190.96709598293963420505343825806', '191.40585016757507618284578366734', '192.190038012745667872636449904411', '192.89324618965389841730052754500', '193.40095442853399969284551779925', '193.91793960267438699321572927490', '194.21774561972720720657217838849', '195.23773843798055011036481950238', '195.66484938284091082738413323800', '196.33333167211237307426382255920', '197.28974854457832027389275355588', '197.78113954811839421842516908239', '198.56890893978191745920738414299', '198.94760240285579797774788398887', '199.64162198024639934287053974007'], 'prelabel': '1-837-837.355-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8870116586608887, 'root_angle': 0.37859771282035964, 'root_number': '0.372217018591369790674454310267+0.928145727281525482113632566079*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.18929885641', 'prec': 44}, 'spectral_label': 'r0-0', 'st_group': 'mu(45)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.859292291178685329183767610919+0.0237313730126762620257821823313*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.42116597999', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.57380329542', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.04398985169', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 3.8870116586608887, 'bad_primes': [3, 31], 'central_character': '837.355', 'conductor': 837, 'conductor_radical': 93, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/837/355'], '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': '1-837-837.355-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': '1-837-837.355-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8870116586608887, 'root_angle': 0.18929885641017982, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.42116597999', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_837.355', 'Lhash_array': ['dirichlet_L_837.355'], 'label': '1-837-837.355-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/837/355'}
Lfunction data - 1-837-837.355-r0-0-0