-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_68.7', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.3826834323650898, 0.9238795325112867], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.9238795325112867, 0.3826834323650898], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.9238795325112867, 0.3826834323650898], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.7071067811865476, 0.7071067811865476], 'algebraic': True, 'analytic_conductor': 0.31579067238822034, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [17, [1]]], 'bad_primes': [2, 17], 'central_character': '68.7', 'coeff_info': ['x^16 - 1', '0.923879532511287 + 0.382683432365090*I', '\\\\zeta_{16}'], 'conductor': 68, 'conductor_radical': 34, 'conjugate': 'dirichlet_L_68.39', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^19', 0, 'a^7', 0, 'a^17', 0, 'a^6', 0, 'a^21', 0, 'a^12', 0, 'a^10', 0, 0, 0, 'a^18', 0, 'a^4', 0, 'a^13', 0, 'a^14', 0, 'a^9', 0, 'a^15', 0, 'a^11', 0, 'a^8', 0, 'a^8', 0, 'a^11', 0, 'a^15', 0, 'a^9', 0, 'a^14', 0, 'a^13', 0, 'a^20', 0, 'a^2', 0, 0, 0, 'a^10', 0, 'a^12', 0, 'a^5', 0, 'a^22', 0, 'a^1', 0, 'a^23', 0, 'a^3', 0, 'a^0', 0, 'a^0', 0, 'a^19', 0, 'a^7', 0, 'a^17', 0, 'a^6', 0, 'a^21', 0, 'a^12', 0, 'a^10', 0, 0, 0, 'a^18', 0, 'a^4', 0, 'a^13', 0, 'a^14', 0, 'a^9', 0, 'a^15', 0, 'a^11', 0], 'euler_factors': [[0], [1, 'a^19'], [1, 'a^7'], [1, 'a^17'], [1, 'a^21'], [1, 'a^12'], [0], [1, 'a^18'], [1, 'a^13'], [1, 'a^15'], [1, 'a^11'], [1, 'a^11'], [1, 'a^9'], [1, 'a^14'], [1, 'a^20'], [1, 'a^10'], [1, 'a^22'], [1, 'a^1'], [1, 'a^0'], [1, 'a^19'], [1, 'a^7'], [1, 'a^21'], [1, 'a^10'], [1, 'a^4'], [1, 'a^15'], [1, 'a^8']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-68-68.7-r0-0-0', 'leading_term': '0.735550573652010915994854152546+0.584322225725875269766568750954*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/68/7', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.9393972055935887, 1.2565295459173007, 1.793056854812461, 2.3260211557305253, 2.658287530498133, 2.646620668933826, 2.226401790982864, 1.4400332339397783, 0.4453656374140382, -0.5124208188165534, -1.168016613918408, -1.3271108241789755, -0.9508083774743621, -0.1968367586318616, 0.6097819542772741, 1.079784018624883, 0.9078514703782672, 0.010989610025983422, -1.4048581923488945, -2.8916107528749655, -3.9169107843865465, -4.079226927991156, -3.2910540915677675, -1.842406284317337, -0.3008927311909243, 0.7230098245022168, 0.8480687051442186, 0.10462363927313448, -1.0695468740623868, -2.0328708363675974, -2.2558269149713612, -1.5953874299108075, -0.38196535262356046, 0.7408947807004602, 1.1562616990390335, 0.621640995704408, -0.5659265173016602, -1.693633957050851, -1.9995636890803001, -1.0960071936779479, 0.7838650685316665, 2.8672369651375504, 4.226372685689674, 4.26715386499431, 3.049633155253518, 1.250773724818087, -0.22119714815471117, -0.7454802581295756, -0.3363800700975572, 0.39353438946859554, 0.6419821347113066, -0.046437603267220025, -1.4508846723172188, -2.7730228893075672, -3.123432816246203, -2.104142821890415, -0.11657699196429469, 1.820837670887307, 2.657531992452107, 1.9459981625012537, 0.12502526631951627, -1.7422837027750822, -2.6237776623876137, -2.1542186558005785, -0.8401732152660071, 0.3040320245816069, 0.4517645337689318, -0.47437788146179666, -1.7594685175581524, -2.4092271128028178, -1.871809572270458, -0.4638002579961842, 0.8141576957798917, 0.9670237519401658, -0.2685636403886559, -2.1784496000066316, -3.5049125012375684, -3.2865190543189957, -1.530595372399634, 0.7589081654969548, 2.2360510309454673, 2.1068312644323823, 0.6405531788365375, -1.060608706036965, -1.8659771016080668, -1.411429775438853, -0.3055354389428911, 0.40172036302614167, 0.08591570070126102, -0.9122231264863334, -1.5047367624381485, -0.6941353323176359, 1.5903641217294864, 4.3070958833062445, 5.948502992592989, 5.576424006232935, 3.4900957561597608, 1.021279830243008, -0.4076048176863056, -0.27156071067595505, 0.7551644372300378, 1.4001430227055656, 0.8251416880426878, -0.7134185761581243, -2.089683632962078, -2.2375958977726302, -1.0409283248257486, 0.5388267873656329, 1.2199490826857255, 0.4522414966348034, -1.0864195761251996, -1.9781624683518775, -1.1853869731620643, 1.0740098643944518, 3.409256988674535, 4.266667022687052, 3.0957696229539984, 0.7593102715408799, -1.1385242671120437, -1.4748492204629238, -0.4123163524303754, 0.8437458611029426, 1.1114662319645006, 0.22655562968830747, -0.8657619380951534, -0.9939105341428582, 0.1367482518872985, 1.5797285643634398, 1.8751750290568436, 0.2964761278191568, -2.4277648872699937, -4.561555851457424, -4.665839120930108, -2.718858372096832, -0.1352316640437249, 1.3423127080451016, 0.9774468055700295, -0.48495777779335125, -1.5676075141153452, -1.3694698523943516, -0.3074337281352136, 0.3359614006325752, -0.35499312746440603, -2.016517183215538, -3.242770690833216, -2.79774806920197, -0.7518380604283964, 1.4768960423411022, 2.2647480388064247, 1.1563611383708643, -0.7169728594898714, -1.565882691256374, -0.4510894308675636, 1.911935880641355, 3.74490932951085, 3.6896948085143535, 1.9090337367479202, -0.1292260862359572, -0.9638133748456331, -0.37088501294404524, 0.5722315378509486, 0.6162217683845949, -0.39671576976176304, -1.3225725533652324, -0.7886351977010598, 1.4109091336719048, 3.8990609815998205, 4.737542320009733, 3.0486812901516416, -0.1798374451628545, -2.8443869795253627, -3.4079407489552347, -2.067891237217235, -0.4161622424458912, 0.06194165325388319, -0.718518825760429, -1.505651881026388, -1.021569466371642, 0.737450339383586, 2.4483015974568527, 2.716772340043314, 1.45822575327705, 0.07220033490958905, 0.1883816850441768, 2.1117869975009804, 4.423558845630289, 5.164484812848071, 3.5686104240094427, 0.7759040312195501, -1.1424798293397225, -0.9781945683681185, 0.620441062082942, 1.8382106794967756, 1.400342728040149, -0.2940196838930603, -1.6422156804665746, -1.4222300732201445, 0.0447672390563951, 1.268366260781105, 1.1243168706458173, 0.038892740269077755, -0.3738747229578133, 1.0720753994711287, 3.8071505228457116, 5.796862023446139, 5.275172896162086, 2.3553100697153333, -0.9856659516868322, -2.5665148072121116, -1.8004470115471878, -0.008698253724461702, 0.9712373388916662, 0.5095216692639565, -0.39882843568674964, -0.35557028922468514, 0.8559650923282581, 1.9423642949037432, 1.3885808886661757, -0.9077430934901075, -3.3204623955709742, -3.90148176095203, -2.2093759165975198, 0.21307494105077704, 1.2274546693149206, 0.07219828883159095, -1.9529804561641433, -2.7476838804257575, -1.410740178708138, 0.932464528076728, 2.2448079792793543, 1.522597797622797, -0.3245259280495165, -1.4778497206139982, -1.0480936166119659, 0.11024538185786417, 0.4127007526332944, -0.6729191943563753, -1.935636276763575, -1.5947114652274788, 0.7947835880022265, 3.643880307507875, 4.640108675434305, 2.877530613160187, -0.24649995639501704, -2.2680088123511237, -1.865118041445247, 0.06266713723168177, 1.4292427254210995, 1.0260693313746927, -0.4366258538682011, -1.2784085190583594, -0.7241889219506916, 0.27305686988769895, 0.12086204671780794, -1.5637484764903478, -3.325706491820118, -3.2181269666769174, -0.8242586263433864, 2.1171056713060556, 3.2128810855810737, 1.6361434027331074, -1.109871880805438, -2.6481675400208218, -1.9719879582071553, -0.2721362044931843, 0.4190662073325419, -0.6596070865617906, -2.2819107295156362, -2.5981695857808673, -1.1174048402848809, 0.770120549631774, 1.2633192684671695, 0.05040888427009233, -1.385366916607445, -1.4069050706444781, -0.09035243442767231, 0.6994690777935013, -0.7905887979353919, -4.231393509948987, -7.237854576560755, -7.474100964667494, -4.797644370623945, -1.3304632044509639, 0.5819236271314805, 0.45947810207492934, -0.22022095497210986, 0.1274928962710838, 1.4413861691312757, 2.2111979661696894, 1.340538426162784, -0.417175068535303, -1.094780601873714, 0.37904190462391946, 2.8483699210440814, 3.8964298412085463, 2.230748556998062, -0.9427198129448764, -3.0176343882973145, -2.4918972883726958, -0.3521136766044094, 1.0433308218444628, 0.39027422239203546, -1.337940932841942, -2.076611206974263, -0.9309963397546563, 0.9133831298111463, 1.5617005760782796, 0.5241599305173973, -0.7549329403272074, -0.545144228055886, 1.14751107057748, 2.4405562520584994, 1.5627163725142925, -1.12374074679054, -3.287020773335357, -2.9183266931095146, -0.4073713091721378, 1.7847309197252141, 1.5579438631460225, -0.7831025063553254, -2.951050263204735, -3.050052148012224, -1.379717526389496, 0.1603564237071626, 0.2790383426739818, -0.3719826920852181, -0.18409439297419292, 1.2763849552178919, 2.4755173726302733, 1.4794955762231636, -1.754385203168655, -4.924691232066589, -5.441846304322645, -2.9525014253295563, 0.2997441389760216, 1.6853539980130448, 0.6881552014275075, -0.8671572882180479, -0.9826164072214946, 0.3531606841970403, 1.318931741313814, 0.45572212516016153, -1.5967224360861416, -2.7659418246181215, -1.857190543773754, 0.09848326334074398, 1.0016395603206074, 0.08070852580419469, -1.1719206120084684, -0.6483972666607076, 1.9001106958903404, 4.322115749336436, 4.172510722475704, 1.284707312750795, -1.948077195322077, -2.920019891925315, -1.3221078998417866, 0.7949018141229601, 1.3498512263913116, 0.35276484731581215, -0.43816545411307956, 0.22156665714863463, 1.5474628079714496, 1.7042042178999943, 0.1252139490975919, -1.5695951229719205, -1.2526299621349604, 1.221940462067034, 3.5497766451406902, 3.21996408676436, 0.15198047226817868, -3.1204957598821186, -3.9653396103347385, -2.2090394126482096, -0.05902894858924699, 0.3997182835722387, -0.6737805151714328, -1.4036587758844823, -0.614583663384891, 0.7130556453604884, 0.6277639692675612, -1.3694574060480356, -3.5253163106177197, -3.68091783743227, -1.7231841338000033, 0.1823037329877533, -0.05147804809129379, -2.068511133418967, -3.3765973645575142, -2.0652896506695884, 1.036820019951259, 3.163380247579604, 2.513757113193358, 0.08897657412240587, -1.5017097590790558, -0.8632865213561862, 0.8753758716406996, 1.6047618020449224, 0.7179728376477529, -0.3699021251613329, -0.19961417425769484, 0.6917984820991699, 0.2122229205085261, -2.7302296187012343, -6.506541501378923, -8.04242991906699, -5.896933919778989, -1.8191550011454334, 0.97010125971048, 0.9506223245856943, -0.4686114008836, -0.8681194084463884, 0.39620651732596907, 1.6703111025442097, 1.1827977939460368, -0.7349119019042155, -2.0143934416529405, -1.337284983140461, 0.24160660540235995, 0.5204535224630228, -1.158201023727147, -2.935344556765826, -2.443879109211748, 0.41700454979777474, 3.1506208525669477, 3.27189259889492, 0.9922502422131252, -1.030935721978353, -0.6091308053924356, 1.6579236136908397, 3.206545944117756, 2.443992535025915, 0.41948190362762683, -0.5883893311731976, 0.20972903641344967, 1.3155977894811035, 0.9401093670874259, -0.6809098111866009, -1.511361310089439, -0.2851388436255482, 1.6616216082147603, 1.6395430902383308, -1.313243335479128, -5.035426087194168, -6.269965676638639, -3.9901596895203095, -0.3854054335086665, 1.5270039387986543, 0.9436374219019131, -0.3621175479525158, -0.5145856442790739, 0.22292171691755786, 0.06080890105250481, -1.7435167531659883, -3.6158386072494477, -3.370267061431541, -0.9113601228076922, 1.3696950083802073, 1.1571926125787244, -1.1561253561360494, -2.864272321852034, -2.0090846046307598, 0.38127593698769807, 1.467928337260988, -0.14538212046030835, -2.817096084588021, -3.737717162604076, -2.0669339188609728, 0.2685434661416926, 0.9272419503801435, -0.20454910976184235, -1.166189876577747, -0.5360861862098245, 0.7756679461814047, 0.777903771169837, -0.8575021129940668, -2.0236112355904807, -0.5303240755102593, 3.0963662254557285, 5.7743695363635705, 5.032177392558025, 1.6762319342381358, -1.0784522804456687, -1.039427058862929, 0.8390400538034721, 1.9174382244920734, 1.0265846194645698, -0.4141920160791721, -0.46078461515769026, 0.8069648282010435, 1.4314991355394204, 0.19935440895429696, -1.5915448956022544, -1.5528764679717593, 0.7841776186944202, 3.0566597212313287, 2.560402454055846, -0.634105825946853, -3.5993973512835575, -3.692080656833524, -1.3430796790052868, 0.6701476057130235, 0.5213860257070677, -0.6994659106999883, -0.5750088363501148, 1.5387837157955881, 3.673709533842022, 3.6253041605383247, 1.5852812611430733, -0.1858079994356356, -0.1888596322139783, 0.5294877944918575, -0.10630848116809904, -2.248794328782431, -3.49532437536035, -1.5886197485380036, 2.6580875980842307, 5.795145119383473, 5.246629029011618, 1.9628594638260755, -0.7763543386494278, -0.9505918704018784, 0.3590355511316522, 0.790874627652807, -0.27470045694022055, -1.208906440152425, -0.5806231430957732, 0.7146794855233247, 0.46790175364249414, -1.8848826165466193, -4.135030437489538, -3.646781651958556, -0.5090154623524563, 2.3440448986029923, 2.355564580931424, 0.1943457292984837, -1.1222608847107196, 0.2126258892543859, 2.7605010789010054, 3.664643026910108, 2.0509002153727516, -0.08405197252218777, -0.43552912367080915, 0.8502420304546578, 1.5976128413730017, 0.5551374633934727, -0.9165880860205586, -0.5913413741039842, 1.6408918238998098, 3.3948357888363616, 2.654891791676322, 0.40936155688663234, -0.30807577904913624, 1.997755018048428, 5.332137385207468, 6.313493258832856, 3.9323994737689003, 0.584594073358498, -0.7446919393332015, 0.27686758291548474, 1.426101214364264, 0.9563606704622843, -0.34379428080815433, -0.5432805879430604, 0.574198535255163, 1.0295187764547367, -0.7033813853104902, -3.295979201526335, -3.684886446509152, -0.6467551330397251, 3.4559305584371622, 5.036299071915551, 3.121514641333149, 0.20978659598849866, -0.7758727009655794, 0.2659884088855414, 0.9718263002390842, -0.20522919408133156, -1.9814356771260382, -1.9555200310132201, 0.22176051096004692, 2.28532397343275, 2.1178788701581857, 0.32069531295953585, -0.6871692004209905, 0.10070779529774586, 0.8801485402903801, -0.6237576506649617, -3.9436876645003127, -5.922916980443343, -4.230455042646218, -0.19222455558143664, 2.5289781894337655, 1.9147592105391735, -0.43664097964545656, -1.5318942912262339, -0.5241014939435069, 0.7098848748797466, 0.3769361726779678, -0.8274379683077061, -0.8001555269435275, 0.9310616189606797, 2.3207762160633445, 1.4020036097447812, -0.9054564931286055, -1.538082469010486, 1.0487498697779714, 4.7394472834567765, 5.917508753587177, 3.4918628097805553, 0.02466607341957741, -1.3227199049587437, -0.28355202866132767, 0.7091185360708604, -0.1137786854873169, -1.681181298999043, -1.7402601609350232, -0.025753138820196447, 1.2652022718673002, 0.340473203845274, -1.7221673908805148, -2.212880581115104, -0.26778755347315153, 1.8646981080047627, 1.527131145953299, -0.9699194883046602, -2.5828322637566283, -1.2250555266361467, 1.602654839556767, 2.5271568446883617, 0.3044556967301993, -2.7564326433681896, -3.5949776922263412, -1.89099264630042, -0.030269449934727508, 0.11853835009879264, -0.6588963261900675, -0.511742431432625, 0.49887796812097107, 0.20237954056024493, -2.643291394881119], 'positive_zeros': ['2.63852168854888205208940764878', '4.135073604262902445775594756', '5.31532210919947948252396777270', '7.571936324624049233450331493534', '8.467796374136064714519430362318', '10.094658899700320153740435448953', '11.11186057373821780131180580609', '12.382005586334026035158121385398', '14.31484484114913413990603565786', '15.13971080528547196703241369671', '15.924617274045452965092161242769', '17.516893117785268874948941832346', '18.769112160384508074344542876490', '20.20708289276609101304511490603', '20.810404247939170302704655399782', '22.28427618520297255186074601274', '23.07562638261696675718215502289', '24.58025096399572127350054250903', '25.73527793401785434806002669658', '26.97137937013894714436703981030', '27.53219188844512795168478951977', '28.551113698918095228051001936308', '30.49461669828625147117906654616', '31.03181185753534237315346196962', '32.05407155458239634877225146027', '33.32253513429455857102804413180', '34.15876915573390485641223179224', '35.17893275592732983051077014302', '36.66683561019904028502421572978', '37.59160834266772020939169653037', '38.49557918630655926587842179241', '39.34667838874252721397271061059', '40.35011771956691307173714324097', '41.893895741159413108503900403661', '42.71505738740861706069146651690', '43.847335610576084213385573930479', '44.280701600936760482793000309359', '45.72117036189034887654211310895', '46.751032659747128551522146754629', '47.56648432638900304210564287898', '49.038083768310972533688932274302', '49.798489603166385434820827275300', '50.522705167360529451211364197199', '51.384024132829478255491384699647', '52.79559246672913380109777833194', '54.20948544973508484578337331591', '54.42524968482084956849268668691', '55.50882410728280734154203393111', '56.9047725160231191218035893565', '57.12373389305251472351722107842', '58.84672998218768498085311820076', '59.577271912259466208079113109576', '60.57498794387788280688848719924', '61.55388812397985036817953061051', '62.511792376115264071138546316973', '62.94519543512285155431219602044', '64.58532306746821351425786545799', '65.62666393171684872497074358278', '66.410057990715979696772128626255', '66.99061618096744174695172258442', '68.01798030744442374258355394473', '69.34315642801440526812343948995', '70.01151688897755508148246239768', '71.12397727448560783203261479567', '72.13244388229157158012209543041', '73.09087337919337738415496575626', '73.59458014499986009013822395203', '74.60226608085734993053454384449', '75.911858604513781250619455313525', '76.865194400436281804711461568731', '77.721168503014964755462601932864', '78.64637500517935082735890257911', '79.0964159535058693225530669562', '80.394543062722879937124598420002', '81.43398314851994794818833177884', '82.562361381390887002053308482453', '82.98558671558189957126898543501', '84.2340174049821834225149803621', '85.00946938473788549962594300990', '85.95739880111030754181156441956', '86.45717998219848772408948661107', '88.29668596357243229308743320949', '88.93421985654898681605351758569', '89.33205189720888630128891400200', '90.546893693949118320928908722929', '91.19699382410522302501822737401', '92.407572057508284882068202291848', '93.490728298144812149905101770333', '94.13691182453085559139169520381', '95.15090493693592266647853799194', '96.04630455756621225572844207444', '96.68158566700667587771167503517', '97.69204014956514042238361030684', '98.79561085548264635958535827864', '99.59633939798837690948199079828', '100.888144307682164117051910778536', '101.38319039571503403347795079419', '101.92949608759595255174349888626', '102.9723804501286769580794754599', '104.340913305318648537641158554384', '105.12403831649115489242505730985', '105.86569572185550274029304283972', '106.63781587496283873338214201751', '107.79515401852694108983530077525', '108.45446879094513466911382310591', '109.16087543858770369430872504246', '110.42476144720719152828907032342', '111.42994674168516244311194844860', '112.28282678840914881207970784122', '112.754964877915851125989885090149', '113.76914189959852794766846868705', '114.55291951795277797899603932380', '115.637788276369772124746205778883', '116.887639501298111938187135914778', '117.330725038885994689020526987181', '118.257215069382078018314493097544', '118.87518006285944496333600866458', '120.26508227791364301522381089961', '120.61343593659576952162691636575', '121.77425858602183033464097291911', '122.82402112611558830146427482696', '123.59205501359173562315017558387', '124.55256027867057595145488913203', '125.069491002457942439359987273913', '125.6599843676681793624463813447', '127.35460459238344873003744995173', '128.02007037432660972596468341750', '128.6738947187167573362449291789', '129.57537845586416796354084531446', '130.56976623990489945997848711079', '131.067610864195045536975974603344', '132.14834155023003139225921049532', '133.24765635503913528241775072180', '133.84667938284448466679507267790', '135.07783761511383456733686787174', '135.574029272033061017497453782194', '136.43786604172885373107115887850', '137.23060333344452198253351294269', '138.013335811169573290058940869503', '139.414856569633456565763024292770', '140.209718513150128634552059736876', '140.839541223034503236597752949917', '141.26708597858045918656557565351', '142.60205132035409664374587907337', '143.296269219294740529496675219331', '144.32330604676787034565593358743', '144.98246192145277949163296413288', '146.20550152314784234525167681536', '146.83050914414696195854421956621', '147.61963692349111664002415936999', '148.29456320427893721021928131109', '149.11556047756987647853399303090', '150.47112975073669883573756477761', '151.11941002921942076387386882840', '152.07954244021684984120415799730', '152.63006664894381275426505370752', '153.469478949694588077874586352276', '154.28781667219323871204937592512', '155.25863828180118894526415293901', '156.42437703334515215302140182491', '157.00475956698838480909029392806', '157.60985022875101191518224632584', '159.009733852043164741477945000798', '159.449197357113338685976813936575', '159.97870089038244493374822824850', '161.06295521099881368787708899834', '162.38198285670923401032642231865', '163.03967024570052456126680975110', '163.686916962459961253605480045056', '164.50378161949208863550636616683', '165.082906206761418746563162973196', '166.29477278073964672690133043871', '167.214863606809303606431774776462', '167.78425567591842210154404523055', '169.04533732746868294307661354015', '169.50330292060104075818554391998', '170.41446249916794242707348796396', '171.03795257633280713328496277632', '172.26015110572064495936859672013', '172.57711298044664116037254574698', '174.139146887935635744622118010699', '174.63018706532188041319073329443', '175.533085791437207558848603830333', '176.10798979343565473655258837075', '176.78508713596397924303182029043', '177.85974110174131406659127777807', '179.09294598044468572206890620247', '179.62562992137078733938693165835', '180.27786572693343441442952937406', '181.22344936165776661242547411024', '182.2467136820033654710544111660', '182.78723754389561890938253110224', '183.35985634824825183167144246418', '184.70271394625161992424532435233', '185.56463747551589018197562979986', '186.35696934671211509697601674773', '186.97156670428172607813287563628', '187.66659137946184548757321451292', '188.62473348985339870959654007111', '189.28166547460098066763787201619', '190.62779822228627472441612774748', '191.310577845752499934000439121021', '191.852083769198341237902397810302', '192.816613712261617720171946318722', '193.49032054739148396010549630206', '194.40728206310340529327729258395', '195.2011279493073401919612422657', '196.070819381180953905456016583655', '196.904099374476682411661374619486', '198.13377929094372416818923426997', '198.489058250598543098659706496', '199.21917275084871149284878833461', '199.72306604501954373227130258102'], 'prelabel': '1-68-68.7-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.31579067238822034, 'root_angle': 0.42737410648195534, 'root_number': '0.226186540765664125163810475396+0.974084004989540191591479109932*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.213687053241', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(16)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.944306174428358799277274632305+0.419930838442345396526586092788*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.63852168855', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.13507360426', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.3153221092', 'prec': 40}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.31579067238822034, 'bad_primes': [2, 17], 'central_character': '68.7', 'conductor': 68, 'conductor_radical': 34, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/68/7'], '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': '1-68-68.7-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': '1-68-68.7-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.31579067238822034, 'root_angle': 0.21368705324097767, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.63852168855', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_68.7', 'Lhash_array': ['dirichlet_L_68.7'], 'label': '1-68-68.7-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/68/7'}
Lfunction data - 1-68-68.7-r0-0-0