-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_3381.359', 'a10': [0.9427549306723099, 0.3334863425884907], 'a2': [0.24895333196586994, -0.9685154818086757], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.8760444770061827, -0.48223031251359944], 'a5': [-0.08828470455058088, 0.9960952820601133], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.6851417149678442, 0.7284097956582691], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 15.701297990361368, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]], [23, [1]]], 'bad_primes': [3, 7, 23], 'central_character': '3381.359', 'coeff_info': ['x^462 - 1', '0.999907521857918 + 0.0135995489615099*I', '\\\\zeta_{462}'], 'conductor': 3381, 'conductor_radical': 483, 'conjugate': 'dirichlet_L_3381.2006', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^365', 0, 'a^268', 'a^122', 0, 0, 'a^171', 0, 'a^25', 'a^64', 0, 'a^36', 0, 0, 'a^74', 'a^40', 0, 'a^455', 'a^390', 0, 'a^429', 0, 0, 'a^244', 'a^401', 0, 0, 'a^117', 0, 'a^28', 'a^439', 0, 'a^405', 0, 0, 'a^131', 'a^358', 0, 'a^293', 'a^45', 0, 'a^291', 'a^332', 0, 0, 'a^407', 0, 0, 'a^147', 0, 'a^304', 'a^184', 0, 'a^186', 0, 0, 'a^20', 'a^25', 0, 'a^215', 'a^393', 0, 'a^342', 'a^158', 0, 'a^343', 'a^308', 0, 0, 'a^387', 0, 'a^202', 'a^34', 0, 'a^261', 0, 0, 'a^245', 'a^196', 0, 'a^410', 'a^384', 0, 'a^162', 'a^194', 0, 'a^235', 'a^104', 0, 0, 0, 0, 'a^310', 'a^115', 0, 'a^441', 0, 0, 'a^50'], 'euler_factors': [[1, 'a^365'], [0], [1, 'a^122'], [0], [1, 'a^64'], [1, 'a^36'], [1, 'a^40'], [1, 'a^455'], [0], [1, 'a^117'], [1, 'a^28'], [1, 'a^131'], [1, 'a^45'], [1, 'a^291'], [1, 'a^407'], [1, 'a^184'], [1, 'a^25'], [1, 'a^215'], [1, 'a^343'], [1, 'a^387'], [1, 'a^202'], [1, 'a^245'], [1, 'a^384'], [1, 'a^104'], [1, 'a^441'], [1, 'a^241']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-3381-3381.359-r0-0-0', 'leading_term': '1.89040755217952947259749674868+0.428647824386853094247378509300*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/3381/359', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.938396159377382, 2.4574865954608067, 2.3430119763929658, 1.1438727363486976, -0.2611373026023416, -0.5275054239057579, 0.5542633149990344, 1.6749971818587728, 1.4643952994722684, 0.1758408034331646, -0.5789221323401633, 0.05397742555618657, 0.8895388778283546, 0.229013435572645, -1.5482090160676285, -1.996848547798494, 0.20410785219153657, 2.940331229916768, 2.875391678764979, -0.09249895099611849, -2.1686232993721104, -0.4176349962075025, 3.0114321490977742, 3.271830820265317, -0.7448874108853765, -4.52284308282556, -3.565023155825226, 0.7795144131091152, 3.2161510549455863, 1.481201480550694, -1.228263081545716, -1.3154597938314552, 0.37459097503428584, 0.7027059885835599, -0.6313283355620996, -1.054606389962752, 0.2903844570580273, 1.1590972202277106, 0.2512340871663381, -0.3219286116374132, 1.377194004419212, 3.3865232782224464, 2.635480761653581, 0.05247522197132917, -0.6805347095240262, 0.8917167367758513, 1.308335499224394, -0.5841176330886529, -1.0266465649994263, 2.271239235796986, 4.867645076192577, 1.3343310923114167, -5.742057036578757, -8.087938413058609, -3.132812186356649, 2.479057043436843, 2.554658566127549, -0.6400980766772925, -1.496376000498932, 0.14397089771170707, 0.38593326403148226, -1.1885677825771692, -1.2788488685696975, 0.598515093350916, 1.1070449196441365, -0.6959071011756176, -1.4777997051638851, 0.37320692703854036, 1.8037091400680534, 0.6134839291240769, -0.6713860359384309, 0.33630264104983737, 1.4469668340170272, 0.3478842045901751, -0.5609015400421045, 1.1275474311588316, 1.915889423216402, -2.296502906678225, -7.511833621369821, -5.986207051412996, 1.4199409759481685, 5.496314241391585, 2.401095947287488, -1.1963030350778103, 0.39849264669864465, 3.3698754116313934, 2.2803049625142964, -0.5501512968262257, -0.11225772995474331, 2.2087184684311416, 1.8987536948162878, -0.1385035587270726, 0.28076040287012227, 2.528824673455396, 2.491927155533128, 0.25842948020556217, -0.5213991056740583, 0.3318242842615408, 0.012184916244671221, -0.9089741160678486, 0.27612128436603384, 1.7917383898990706, -0.38110740713582386, -4.271860994741523, -4.129597734766098, -0.6733131544811872, -0.1336368994805335, -2.539152559615477, -1.0149745816989746, 5.240153544748762, 7.921824581281436, 3.426806506311474, -0.6993297028367211, 1.42740030729941, 4.564962231218417, 2.5181284710819347, -1.1124498420839941, -0.3378778524006753, 2.567964432872194, 2.2438799072801965, -0.09223898565752366, -0.31462126268499635, 0.5826680748347275, -0.23661885327605112, -1.1154473400487075, 0.05385426508355573, 0.4984212800750392, -1.9983086833728156, -3.715296367543469, -1.5871581299886217, 0.7059876472165183, -0.28526242324063644, -1.3535769137166527, 0.0964556388343967, -0.08609297803155556, -4.177893104080725, -6.082841732466818, -2.0324068849101287, 0.8312344285745329, -3.569242352247097, -8.239470561248632, -4.313560717730641, 3.527742245710914, 4.957068179857692, 0.6433215151520171, -1.3039047678334736, 0.1904401835645873, 0.3491009770177255, -0.6537012549605637, 0.5036918636046105, 1.9292288893380618, 0.18223571564986263, -2.0424877324405846, -0.8861367607899218, 1.079777613936741, 0.3377085165457757, -0.5053147386764512, 1.324917034212332, 2.6148101695096635, 0.9145406834425202, -0.3577708940941631, 0.27783721693258306, -1.2954918727269842, -4.955206035716947, -3.9003806514849995, 2.010022803396175, 3.060733337604882, -3.529477816127035, -7.179626263223987, -1.7710411869131515, 4.074649979214219, 2.671600734760353, -0.6848792665772656, 0.15660089235061886, 1.4799662238417004, -0.44241526951261373, -1.380702413400587, 1.2245306129423006, 2.3864103402139225, -0.34679336298110697, -2.105937575836643, -0.573317624883426, 0.3390606943220902, -0.5402436256780622, 0.07575896676640129, 1.6998314854862433, 0.9275672521689077, -0.4843538713512144, 0.9200784144276672, 2.0818792987332535, -0.4544888547948179, -1.8898769887879232, 1.9563616936318653, 4.884061582653273, 1.4680841893441474, -1.5653342849422631, 2.1730214323069617, 5.806780107666274, 2.0691473924179102, -2.663761449392269, -0.7611503672725463, 2.4170887345916334, -0.04223503673411052, -3.1807840895684794, -0.7306233140378389, 2.8599733352023007, 2.001672978088092, -0.04603313184626784, 0.42727859209807295, 0.7322222072107789, -0.38160090330161617, 0.37576334349112606, 2.472857666700582, 1.67830343986232, -0.716731926076645, -0.3980961019927457, 0.5155377440552036, -1.7680099390494541, -3.580323674916399, -1.089152648081029, 0.9205654487808275, -1.2788137381470415, -2.2326746510054094, 0.7526636802623542, 0.817585182326634, -3.3464962931869233, -1.5604518846594062, 8.635895219273081, 14.29192754084441, 8.346831285288765, 0.7911511304760603, 0.011977584697907884, 1.0223940127063407, -0.6327536740504875, -0.8944918230394694, 1.4726675654750525, 1.6880913697314355, -0.2504811123353145, 0.07272237864160278, 1.3236019175861733, -0.30280620995584767, -1.9911566157100609, -0.27592264400440086, 1.0997945712901933, -0.735722353974253, -1.5545363270308221, 0.48749024336512964, 1.0015532990506453, -0.34457892083199104, 0.45947383784639084, 0.664486131614457, -4.526729148832287, -8.431518316248548, -2.3716726050707755, 6.2536896038013206, 4.993805596642178, -1.8102123131475907, -2.2256306318246297, 1.575826446688812, 0.5951671852016853, -2.696665735500596, -1.6378374229485744, 0.5377069277997575, -0.7733731572386345, -1.4437620638589554, 1.319824994031213, 2.416327544565984, 0.11256466988014176, -0.41251651175601467, 1.4558296777909348, 1.0951822524273152, -0.7596349117362722, -0.31811359763180963, 0.5391804909036222, -0.2956313773598502, 0.7573825265211405, 3.857224910194809, 2.9065490330595596, -1.3299525678282083, -0.9506415744036316, 2.579381459077779, 0.3744209316877517, -5.041190293314946, -3.9018343781064058, 0.5224053890533026, -1.9028946896147598, -7.366064813620585, -5.720902462855177, -0.5636280634756634, -0.7538719843316666, -2.7101907262250076, 0.19929194233762565, 3.409679926569777, 1.6198036279563888, -0.6020571864020037, 0.3828064180701213, 0.7436422245178114, -0.5601742565660077, 0.007927968048062194, 1.131338066938044, -0.3811580694175382, -1.293699900795473, 0.8975042332987031, 1.4209594654491071, -1.1586698370596618, -0.8351582416248416, 2.6110933879838165, 2.452735924224798, -0.3790852525739012, 0.1749018048086104, 0.7107470482366121, -3.8273285566410693, -5.480135742089271, 2.680307351968218, 9.856430917242823, 5.417339628993489, -1.9541314350748107, -1.606586871254105, 0.8601215167647289, -1.4541663988416693, -3.2877964094249537, -0.7972873358865415, 0.7436572181585275, -0.35452332724895985, 0.14874530643314596, 1.3464957347564812, 0.0598696343478454, -0.23679277132335982, 2.8764598824302583, 3.9605059107060168, 0.8245903290825582, -0.909411249280358, 0.07509719813182185, -0.37606137103212867, -0.807366097375448, 1.8487405762906841, 2.944036102350291, 0.10942576959246576, 0.508485719425009, 4.803130315470001, 2.2260454888571144, -7.334182204160425, -9.53873183805598, -1.9945857715702324, 1.533999993544041, -2.4312659976738864, -3.3791848643718945, 0.36534711884376525, 0.9281798066819495, -1.1261599660903014, -0.45802018461726374, 0.037823093808884115, -2.58153356794608, -2.93273629412912, 0.8005363287684484, 2.2242017317175966, 0.08288288058270542, -0.4183594093298633, 0.477086595788062, -0.3119062912202027, -0.25598767195159505, 1.6030950946585807, 0.4698166296093313, -2.7640120293494834, -1.7703344270781227, 1.0176018361895964, -0.4903478313400977, -1.0265914909148048, 4.972184198355831, 8.156135235905523, 1.2989253769664457, -4.874006134891982, -1.9076398275841568, 1.4406081176687056, -0.512344807364058, 0.16301110754718184, 5.044667957148283, 4.870553793708473, -0.3327722604250309, -1.4493099672782945, 1.082311604285623, 0.7110300355075564, -0.7914504333233625, 0.19347730197945545, 0.3794312547013231, -1.2912062226372272, -0.7231445642514797, 0.9393115466112794, -0.054147206268277105, -0.37883791847148235, 2.463102854734507, 2.8453466414504023, -0.559773392131994, -1.0073665784875507, 1.0805950526516033, -0.8741976070963404, -3.515788294197137, -0.6703580465752734, 1.1388363634445562, -3.4195443010663324, -4.352153275097218, 3.282816698844951, 6.526923938139564, -0.6731387911425907, -5.610655165346192, -1.9098829005442801, 1.02014200469434, -0.553902880181849, -0.38143747557274316, 1.3839156329353477, 0.3890342313042493, -0.5015481035133444, 1.0921772975361441, 0.7522819362676505, -1.6055687036459045, -0.8207967370685095, 1.1524542355526866, -0.4889378139997863, -2.10713204034191, -0.2324060408358517, 0.47866965801756134, -1.1420486802628282, -0.18357574613889627, 1.3621627496115885, -0.9967305826986985, -1.5724268574581255, 2.904238505592404, 1.9101294151336163, -7.678865668055539, -10.905140877523056, -2.274507012046937, 3.389422153197385, -0.5165100880641265, -3.1315786626231876, -0.6647793648434461, -0.3405648182381311, -1.63115688694088, 0.3241148442642911, 1.368414907842367, -1.755483099329847, -2.984041603295932, -0.5389890610730278, -0.3626173189507839, -2.1381651501496486, -1.1222697817372418, 0.24971880781679973, -0.8737861042014661, -0.5421612988081178, 1.6174681458893527, 0.9522223678154628, -0.41577075609376857, 1.1467289746807234, 0.22231393718227216, -4.793859047947301, -4.156910907218596, 2.691437735395297, 2.796586196082453, -4.318514136453652, -5.40222668048151, -0.6560811802809473, -0.8270960447917135, -2.7647824503864284, 1.799910687639014, 6.082199330391735, 2.5940313484157835, -1.2310108425247464, 0.10558959303770785, 0.4531479362078729, -1.715099040664627, -0.9804127923777374, 0.9334650467642913, -0.37255160653499814, -1.4833639545481532, -0.08896512568142237, -0.06392291556278824, -0.8127981042429803, 0.9104036220547459, 1.0262439144802817, -2.6999430386561594, -3.082438343140388, 1.2886478500002718, 2.2155404155811924, -0.15367534825069884, 0.7345748799534879, 0.7361942780001313, -4.628028461196654, -5.581080093793608, 2.139582142351167, 4.9500115111496665, -1.9155798881400432, -4.400449424269366, 1.5956311370645855, 3.9214760216893247, 0.4576759582682169, 0.02783457269915739, 1.7551205289613716, 0.21228549757117754, -0.9889138504385491, 0.7764315055459672, 0.8829852355410636, -0.5724874306514063, 0.15018079710236595, -0.20801656054893267, -3.755494055557832, -4.219863690461109, -0.42186876364659465, 0.797198552262547, -0.49284602719432763, 0.2667647837050314, 0.1478378003108817, -2.21898898542732, -0.7166707999744271, 2.4452647140859987, -1.4300430259766976, -6.139258106167346, -0.6281557421384545, 5.929507314096196, 0.8601891463401461, -6.101413996459632, -2.997811137408177, 1.7893821940994743, -0.027966225543577763, -1.6706583066941025, 0.07580035885886918, -0.1500448876653828, -0.6720867990674081, 2.5123583999711587, 4.02375847883611, 0.8745386651944043, -0.604767791879209, 0.664730887968631, -0.45367423595903567, -1.967818523933425, -0.2138576266390142, 0.7684742811222416, -0.5547236433423135, -0.08619876296732776, 0.11590667224185827, -2.869190433047384, -2.381975774874499, 3.1970043834012416, 3.2704735678744807, -2.5415533987417045, -2.047798597080128, 2.7068882323842134, -0.5104340350850995, -6.524399673936589, -3.5395750965400667, 1.7413383122369435, -0.07599445085030931, -2.0973908867909854, 0.32958461260143246, -0.23863621827845752, -3.8132281050623575, -2.5010105052123417, 1.1182577712032615, 0.5557208562733842, -0.579095040574248, 0.8736267466667017, 0.8235971531550459, -0.4683353891340356, 0.2787601060115944, -0.09621449792833502, -2.5067990796341078, -1.1893899660591354, 2.3134608623940727, 1.3266094976568747, -0.2942104077925685, 2.569993705474305, 3.28418383910148, -0.5868486120945292, -0.6664591353173659, 1.183943224405736, -4.540148351270238, -10.65845378498081, -5.449786489331384, 1.9764601643283863, 0.44794201127065514, -1.1331878494925252, 4.0489186125690635, 5.975891689601122, 1.0640904766459671, -1.3943266553441425, -0.02918292228764294, -0.36405363541060415, -0.6753391233275842, 0.5280071100691048, -0.8779630306101984, -2.965489629795616, -0.9060420432805714, 0.8548448953626586, -1.4707188984697896, -2.252081238777786, -0.19738967634831123, -0.503753652453018, -0.9252428437538712, 1.9875798224471333, 2.26749453961503, -1.3262012912066052, -1.1142310284064108, 0.294478608633208, -4.3844944713124985, -5.625796012993633, 5.409440673174985, 13.813544746965993, 7.178837117758165, -1.3950043216239987, -0.7964183119611089, 0.7555767382637826, -0.9992140648226066, -0.20170107936263115, 1.2789716620005311, -0.7973702947498933, -1.1304570977115518, 2.027738675827344, 1.982889521495361, -0.5088482764586155, 0.33959516055317884, 1.5465299668142065, -0.008402165571539588, 0.23633519913178652, 2.1468762514266273, 0.9672024770800316, -0.37666591958689066, 0.9253164151387343, 0.03719565079899409, -1.535741013327427, 2.5014094847100257, 5.028077662997857, -1.8660206632585472, -6.76931918764015, -1.0587170148793186, 2.591956715471386, -2.2794104934024872, -3.454071231539568, 1.392655586070307, 1.4607319856131613, -1.355380886971495, 0.9634681551504423, 2.7402631026085706, -0.9303779587377877], 'positive_zeros': ['1.17859027283730886105081569629', '1.7449506222805337113605231949', '2.85613879992423773454711871463', '3.421621523820065360795857450591', '4.10691147091503224537855436636', '4.97908527145962589321514672210', '5.92875926209024000099524621997', '6.59998949191916045139405112118', '7.45260279238176195905321748846', '8.38226848880666721464003585755', '9.213244538857339916268082818470', '9.92652721105446164242285484706', '10.49001172883289989852172507901', '11.19370409583292420041064213132', '11.93984124282316926489169070999', '12.29070731626345493722474206729', '13.44510744694973072240514470529', '13.90622867793136626121131758616', '14.60170270070045474523146074990', '15.12989716557185398736211411747', '15.99800103218040013368795100972', '17.02394782315492286339089310470', '17.74501276973855966395552133790', '18.40903201126274701685603696919', '18.83846429526580995279954344002', '19.592151482264166342397423592816', '20.20747019687219634908433446462', '20.88811261594470855632471392401', '21.66661922793977846221478836788', '22.12424958072956044527364091565', '22.87817820118067864698517037129', '23.274723328059925558204024799031', '23.93386971569371255707195611584', '24.9417691346964058583193564523', '25.79008188426470613071813077213', '26.21356707397883199959274187158', '27.10661278983322093916444286650', '27.51548996585080667571365719175', '28.40729359713118034435056893806', '28.701326269820740702385803773652', '29.73059326427252644332478785759', '30.19055278922072674626899385571', '30.62835528173256526097019927126', '31.20831473679191885301337344368', '31.84443253221312255605485437650', '32.90520916799130129619391983747', '33.10006234240139054655949772490', '33.809781904754436712259065128010', '34.90036669004451256329059089347', '35.19215394967654312863711688850', '36.1267242225219533884154934681', '36.59732538895034614911596831830', '37.48336432260681297238778710623', '37.902513890812480417818536149650', '38.38593909467801993724249758085', '39.05176207693662048333754015375', '39.46741150349412762990109822248', '40.482023923867043496849564880922', '40.89059467458037511132225621795', '41.54454237871539721836325952417', '41.864035470339017411723718385920', '42.95156057359927139559916523453', '43.23685745759728551366668112321', '44.22333034906463459132999125620', '45.050993758272658772655692590635', '45.5869902990882898251116383177', '46.02766031651646492059262408867', '46.48294603011801834676619017829', '47.20692935485597545933124313904', '47.92379493947864574141210894784', '48.50386615829232151866523592263', '48.87983882887204420176178259121', '49.83545554448938900584961700219', '50.18194446990880750370710554516', '50.46669374028915520616222962674', '51.45620069609967563978259869776', '52.04148606779397909068536381927', '52.88464690092163003062774523574', '53.653989150135924953974590446073', '54.04056839115427625429474117814', '54.63323501721461466885862809232', '55.18931671687164285198605983246', '55.90476425499805306399716031383', '56.66599567385373316814346172996', '57.01028902820198559974570828244', '57.48614477705482854809326261898', '58.27894485442313206998093811876', '58.613984631915435711658992238579', '59.33260869620163445518805704404', '59.8759941471314170253770496102', '60.720314439550429030717415950', '61.121856030519200246057624262360', '61.9805475072434651337499133028', '62.55445925141455047175735036234', '63.12200688966570613679128489263', '63.80062858811171956788260786577', '64.67122497727981841237021840587', '64.8689487039390343366825410871', '65.50977025666174415839249058050', '65.8762962834792586374227601441', '66.76039227135300789236355213337', '67.265821130590812466717383567511', '67.61834347778390904076170231108', '68.54157240411456324374369269318', '68.92517057185162364372361642340', '69.61406350439019191703134644169', '70.06930218758009222981901961319', '70.68487563625397106628230952146', '71.94939353862236721789729327874', '72.185099277806481176245457466286', '72.71563367562143351088476857113', '73.253146627334895855830683876572', '74.01102067896591332292559959649', '74.3607982357321136424459097826', '74.963776416010605725297500038', '75.6591316442789393277373526687', '76.152992306677716263273694230528', '76.80642762641812409173835392741', '77.399079030690914621755048677502', '77.72440478475754986270154629621', '78.1909759271264658595389806910', '79.135566269019835333038360187795', '79.90404182523326453141669449709', '80.48036943987208289144358540106', '80.986856692045147685889966592397', '81.748726187128611852988214604933', '82.071839526429340143877838703503', '82.683450316720484702934408543210', '83.4533083087598371286462536436', '83.827120158116054975444850343060', '84.53800991996469477328987836143', '85.07090093836356978631760143016', '85.52345076190029294914725871915', '85.83540706704227639942839111183', '86.765303641843876744147960371846', '87.26501174267668074439158521175', '87.83303125447163079583413824186', '88.68966074470688259832042313165', '88.94147900765428835786471950942', '90.07811398642768797764952286803', '90.1985932740832306019135675288', '90.92381335940552845015520233878', '91.73583735163460266082841511403', '92.11041936273950341654323426128', '92.66991404644985994161463541140', '93.12347458707250630053174912991', '93.695649059218763027083335391486', '94.26657526547304827799202942510', '94.86444442214294849807670536492', '95.39195275926430529944054958915', '96.19168234246771235406657847313', '96.53459859653332602911394067403', '96.95081156849588632540962594408', '97.73244191792713751574055209943', '98.640085332923151625558679630245', '99.21170465522784629255837609418', '99.5524173000474784062194843642', '100.4018256991787042303647400060', '100.8403188338214308224983568054', '101.22047385712744843659979934914', '101.885573798415051421584920792158', '102.2239178946054908845322089310', '103.20764472218719926331243030374', '103.722190417596813218597193169834', '103.96208763718062239677896506263', '104.50165686994713777391224739809', '105.326165063712642200340356753221', '105.575243211199693026242860093846', '106.32864437054752303137372466240', '107.27790584099673847830596388594', '107.6491991318991684739755721474', '108.40391865441873537337375148616', '108.878165316293821255169706656136', '109.46896223778129669169495910840', '109.69572061362658041755756305477', '110.56143733564166986839018975773', '111.26310019731108283452874185894', '111.68099739283055695205455654556', '112.10454863758653628997561866092', '112.547593738405774940395397818464', '113.167977035974613780890540251680', '113.91232447553059445879736736433', '114.32007554258999676870282758271', '114.76664120924668094805738246734', '115.6697744975597778341451177271', '116.36969517336126459732446988303', '116.81099790050279791482460097935', '117.17420026010791358739411478100', '118.101991935883594137100905072252', '118.609007692952132572067915626458', '119.17215880144619570319652142559', '119.645942041121380915354002132776', '120.07659286130891361125398684158', '120.73278148842711611042725380272', '121.2400535276803357543007416738', '121.6206992384740107922972372257', '122.44622183149384078796845664094', '122.94295097577214037076517020027', '123.36210047657615286271897656472', '124.11362698106995491250675039745', '124.48500716194789583542594860223', '125.19430297185904319957533105257', '125.913593273972410117337062378504', '126.69454993147174275204611832018', '127.09764256603608365101746281883', '127.5584558049093533071425925741', '128.19100099166276463449650243437', '128.560570003867700459625980432283', '129.157062336363016640139340975270', '129.78617328972020799853155892944', '130.257346228303439871387816629273', '130.97050833380264399221561504847', '131.34705771571796314214310329125', '131.89858085254346796726686062025', '132.40182907046173840912495218439', '132.937720614495594122622418960227', '133.5129065446979612936748838312', '134.45064788647304698766560465959', '134.9702571251531241689728669132', '135.75409601083628521387694417111', '135.84575218292531636081018040413', '136.52658232465268597506600601102', '137.037276296998719430919304834958', '137.92141016349844051266791920157', '138.03753691247770584856671837446', '138.93497305580812044670187577585', '139.179526874671718818214006339317', '139.76343725715052469629862671632', '140.45984562735698408586214925684', '140.75217485293057193858745543633', '141.26680436583619848378391650461', '142.0622603080205573611610049325', '142.628578064677773165465479673449', '143.52146013666384307195567401754', '143.63695729641354758552452291278', '144.287750388350888406842285179179', '145.15977818309251815960260601357', '145.60959596331137636021865012635', '146.00719579833003745452160268687', '146.68543411557087507871538142503', '147.13474651410350044203477850034', '147.83451943128891673887766319675', '148.10689064706733779773595166080', '148.62053739897521604193101977674', '149.16425258686702141303528622237', '149.90863205215270732535753815019', '150.5921950055029292490081006868', '150.81851689056501643787566532190', '151.309631606468068558401883607468', '152.10893702096060398752576113788', '152.73554482906713323876253365819', '153.3623162365338856988506134665', '154.11644337720921509500554643047', '154.37034075776725521784406020847', '155.02683421370001328526619577541', '155.50458000867345581334558395425', '156.09853648642152829614676030969', '156.52536714592451864079323403325', '156.84655773582042084051417395063', '157.852975762279936443028343209371', '158.2971749932514000677895763048', '158.68817663113319288291373174898', '159.084970401859047484898932618895', '159.74162499404186867722588922446', '160.24407329338603217891648803815', '160.95878056757400842659840702257', '161.59159233428473362996551850436', '162.33847774422905660024345145876', '162.80989961965133482006248551952', '163.421995730576012812113689531502', '163.71748816781884929350460035467', '164.159257346413900516975014292160', '165.09021018100395168382299027386', '165.45914002935933556944350556093', '165.87441865773205765260836480808', '166.59169250502585768639718076735', '167.05602154350080938240120140845', '167.51995126852976293353110461317', '167.831724465671805924892338759198', '168.57637495933682708354643837312', '169.23424332679559019390490069079', '169.80399555730654447143412844732', '170.28993906899552834752752528184', '171.107845982202590709054232372850', '171.5563528199613341305001935364', '172.14605133895971682641774810111', '172.47692654952664123986690814004', '173.31371747686430745265771896734', '173.836539142120509377923391460203', '174.214491103177628377341860247304', '174.8495285129842309888916721948', '175.23784911759250215676440234463', '175.610222336784280550800960069039', '176.34296236619334357647295639619', '177.03497806994985351208971042168', '177.25202967677562872966670614053', '178.07411572149285190894417540252', '178.50820213723867810232373042574', '178.86825582410057632978617117323', '179.88076704901235285755297601222', '180.34718338487553587601807177013', '180.72116723367226366285362870955', '181.633195861730026277226663447984', '182.19703411966788623030964754063', '182.39070683663554215067975854267', '182.972452173119966252940989469194', '183.32927024168304545748631709732', '184.15427855074731796414379769341', '184.52773846625725505239864854825', '185.36797756977818396630051078643', '185.49526345913329843906919801213', '186.06041127973644714928306993019', '186.755143056600958139008324011021', '187.32310095848336099359088490781', '187.543521236823069834079862793807', '188.31154803299599934401755126829', '189.29372336323051691604618345737', '189.77187101558273880247961224075', '190.146430588231742802435244414685', '190.65141921784874717080578211249', '191.15647393161255915526033205390', '191.68253195491591919989680578324', '192.41188554882704860607848092771', '192.76217537185214270625844256322', '193.43576766236758028869647736212', '193.70911165941227746166559362484', '194.5164332745118393700002344640', '194.80754231301801396910039947933', '195.3170278255987452912650652963', '195.79184322883919597616270294247', '196.49763570743413440304421761035', '197.23273055353397040050946310405', '197.690325189901904764083938326958', '198.34354140544282871631310149283', '198.87877425967673700818910633217', '199.29642523106264593515791321534', '199.93300962412731728398143240748'], 'prelabel': '1-3381-3381.359-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.701297990361368, 'root_angle': 0.1419524846280512, 'root_number': '0.902198354462331660095534000102+0.431321375780821878693132370893*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(462)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.21569293470392591561035836472-0.167147431946301314414121516165*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.17859027284', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.74495062228', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.85613879992', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 15.701297990361368, 'bad_primes': [3, 7, 23], 'central_character': '3381.359', 'conductor': 3381, 'conductor_radical': 483, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3381/359'], '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': '1-3381-3381.359-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': '1-3381-3381.359-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.701297990361368, 'root_angle': 0.0709762423140256, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.17859027284', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_3381.359', 'Lhash_array': ['dirichlet_L_3381.359'], 'label': '1-3381-3381.359-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3381/359'}