-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_6003.1021', 'a10': [-0.2621016829391022, 0.96504026226914], 'a2': [-0.9632356771877736, 0.268657831065114], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.8556459396147774, -0.517561615675607], 'a5': [0.511731315809637, -0.8591455408833462], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.9668002242694236, -0.25553341533465307], 'a8': [-0.6851417149678442, 0.7284097956582691], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 27.87781479921304, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [23, [1]], [29, [1]]], 'bad_primes': [3, 23, 29], 'central_character': '6003.1021', 'coeff_info': ['x^462 - 1', '0.999907521857918 + 0.0135995489615099*I', '\\\\zeta_{462}'], 'conductor': 6003, 'conductor_radical': 2001, 'conjugate': 'dirichlet_L_6003.5515', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^211', 0, 'a^422', 'a^386', 0, 'a^250', 'a^171', 0, 'a^135', 'a^361', 0, 'a^410', 'a^461', 0, 'a^382', 'a^315', 0, 'a^345', 'a^346', 0, 'a^110', 0, 0, 'a^310', 'a^159', 0, 'a^210', 0, 0, 'a^281', 'a^131', 0, 'a^64', 'a^174', 0, 'a^87', 'a^94', 0, 'a^95', 'a^287', 0, 'a^181', 'a^321', 0, 0, 'a^319', 0, 'a^38', 'a^59', 0, 'a^370', 'a^162', 0, 'a^285', 'a^421', 0, 0, 'a^14', 0, 'a^61', 'a^30', 0, 'a^342', 'a^334', 0, 'a^332', 'a^275', 0, 'a^385', 'a^354', 0, 'a^279', 'a^298', 0, 'a^305', 'a^149', 0, 'a^157', 'a^306', 0, 'a^36', 'a^142', 0, 'a^239', 'a^392', 0, 'a^70', 'a^225', 0, 'a^198', 0, 0, 'a^68', 'a^269', 0, 'a^331', 'a^249', 0, 'a^270'], 'euler_factors': [[1, 'a^211'], [0], [1, 'a^386'], [1, 'a^250'], [1, 'a^361'], [1, 'a^410'], [1, 'a^315'], [1, 'a^345'], [0], [0], [1, 'a^281'], [1, 'a^87'], [1, 'a^287'], [1, 'a^181'], [1, 'a^319'], [1, 'a^162'], [1, 'a^14'], [1, 'a^61'], [1, 'a^332'], [1, 'a^354'], [1, 'a^279'], [1, 'a^157'], [1, 'a^142'], [1, 'a^225'], [1, 'a^331'], [1, 'a^307']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-6003-6003.1021-r0-0-0', 'leading_term': '-0.125444774890255395706105916926-0.581890625231594263801887475990*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/6003/1021', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [-0.5952588439323535, 0.12327479978767497, 0.3350381739336998, -0.3757558402276635, -1.2874127784481655, -0.8078258722167935, 1.3609196293783459, 3.1321561661120403, 2.224663742842714, -0.5078839905552842, -1.2959078874681624, 1.9442398074974432, 6.148040918819202, 6.092617134069872, 0.9387476011071029, -4.225905642908886, -4.509036774158348, -1.1420440356790216, 0.8086296923061461, -0.4517762256215956, -1.7259546355855726, -0.5058909760368522, 1.046486363845412, -0.10400734149503257, -2.6942358005853215, -3.083603134557068, -1.025717193534664, 0.23114173460378923, -0.5802014717601982, -1.1182045892611117, -0.14750605658786997, 0.14363090809796134, -1.4253418387431713, -2.1170460530153474, -0.01485061787689641, 1.7349584424705997, -0.1614472452438561, -2.6863949700077816, -0.6430280586676497, 4.240976317718075, 5.040086001958534, 0.6189224350730387, -2.387910247275833, -0.6241041399393094, 0.41714282517443735, -3.848281079205193, -8.51680719625269, -6.742508844819685, -0.7955769067595557, 1.8388340753284007, 0.018772138618261932, -1.1865812990835387, -0.07879491328682885, 0.24932931858902402, -0.7446157002842364, -0.14347257457093132, 1.8441833942944146, 1.772356936988579, -0.07711564031370068, 0.18367568594270228, 2.4174463052255417, 2.377719261619794, -0.0883035990930639, -0.6126257311984314, 1.1145453979118243, 0.8725332973563014, -0.9256037354978183, 0.8589971855113365, 5.261414763548982, 4.8849757454084, -0.6147802879488843, -2.026515575791544, 3.9245222553233132, 8.097397814954032, 4.0237634433316085, -1.7036491325737964, -1.4950368567217263, 1.2453587117590155, 0.45192968905223524, -1.738059414363977, -1.0480154264908117, 0.3459467495320222, -0.5839925738935866, -1.157599793409139, 0.8034645270964061, 1.7899066698440707, -0.17947061575012935, -1.094936610768941, 0.9953045912745335, 1.977779527040067, 0.14375529577217452, -0.5297589607794587, 0.9451891085992952, 0.6520880467125106, -1.1303876224440925, -0.24259922543621695, 0.7136092136938941, -4.674055198077943, -12.121913582968562, -10.233487545957146, 0.003987375943352601, 5.333381174373054, 1.4896368585557418, -2.1396003901685905, -0.6988038024051247, 0.22781782798091899, -1.2511032398383894, 0.11611939226264181, 4.10498867296797, 4.210587319330297, 0.4578871199681025, -0.79172427941958, 0.9267326572280591, 0.889481102774617, -0.5059071266316907, 0.10905135186602431, 0.9749965447089887, -0.36768218221213733, -0.837518893093321, 1.310647709967497, 1.9008069350657735, 0.06346841560673745, 1.0578473428704647, 4.603042968866472, 3.8050357135529906, -0.5694432830002323, -0.3554338384841548, 3.4275729946064097, 1.8753482689430494, -3.3814637917201074, -2.363617214372147, 3.2811695821457123, 2.690170125900443, -3.4923661979404943, -4.878603590876406, -0.8937988618797383, 0.5278954898293727, -0.6900063901712606, 0.7610117975898726, 2.807496991178178, 0.9634528345832835, -1.5349080673810656, -0.7029769895696343, 0.4409390228015321, -0.3500616904124523, -0.2295205112918159, 0.4338250496212007, -1.8374571709474274, -4.113807457772799, -1.3467163117910332, 2.5196264254067797, 1.5755354699183692, -0.5701827357147773, 0.4256915349895511, 0.2009268762478282, -2.8121986268785304, -1.3487104571766986, 4.504174574344896, 3.6254059597958905, -4.587648056735294, -6.348509293542655, 1.644801867111327, 6.372396490922371, 2.4669804345209583, -1.0368251523363816, -0.14355511825659392, -0.2134970950492266, -1.6682972371574445, -0.6053691400122473, 0.6559762459129204, -0.8775625679941927, -1.1378920702397168, 1.7215074565816888, 2.2482658191185685, -0.6920172264651909, -1.455458963001043, 0.2843670815227443, 0.05126077943567722, -0.8448245213637554, 0.2629770147413131, -0.30300923889515213, -3.20166312182796, -1.7601791486028304, 3.173752473131774, 1.963356043604, -3.8991392323658465, -2.836429315352655, 3.310384138219754, 2.0758866369354134, -4.557622980014662, -4.23747592526798, 1.5207106379076039, 2.3865407269412144, -0.15542679778789412, 0.5991697411784239, 1.5463345996662412, -0.9878781914235013, -1.9338416395635025, 0.6728632379860371, 1.2492273069111404, -0.4761638337826643, 0.4895824887506888, 2.3587603281923037, 0.8728510806758082, -0.8240889189001879, 0.2076903444178948, 0.5292463008532313, -0.12725491556233673, 1.674451531432611, 2.3018653775251217, -2.466908996971007, -5.389249886242189, -0.8189807982907181, 2.393025198217058, -1.3366740141041207, -2.435674250485369, 2.9137850696112464, 3.8943600142408488, -1.8954623886558801, -3.386569836274059, 0.5066660831418572, 0.1642576847355805, -2.9103488361493897, -0.2870653731680959, 4.1949963475633085, 2.7503455285658607, -0.6094129074892076, -0.2563590033960121, 0.5856614602670386, -0.023193096847189284, 0.6603272407906008, 0.8369263404160041, -1.823079327606839, -2.440011712044263, 0.9095010757250751, 1.7490395214419578, -0.941526629555653, -0.850683350490707, 1.0811342909608634, -0.029140390002665606, -0.35270952175104386, 2.678195272916109, 1.4333003376638656, -4.437374792696281, -3.1897724268324685, 4.690341559499403, 5.038140606525902, -1.6819076663928696, -1.71468414047574, 3.7881952762705478, 3.159500643009431, -1.241080431171801, -0.6713736568163888, 1.53803006312639, 0.3157743937934786, -0.2983433163329643, 0.9638076089098582, -0.20937271212792724, -1.764148365125424, 0.3110350860243674, 1.7741614220305335, -0.20204867184529368, -0.5970076744578152, 1.0182543055938855, -0.32084183336520916, -2.1112428752877026, 0.07582424529935794, 1.6033340905477111, -0.24237980900577055, 0.04990697964948575, 1.5685905149252948, -1.1245625860712463, -0.4947018854121727, 11.352068792909744, 20.83116583457026, 13.697554060945372, 1.2570370457098716, -1.3710661707173313, 0.37407603419389757, -1.165941867833875, -1.162752169259834, 1.3669623938772875, 0.5527544132367177, -0.7961043751808, 2.579020686732612, 5.011339154834483, 2.0234902110233564, -0.3465512885044144, 0.3444742096487563, -0.4543763687022545, -1.6487226674196804, -0.02601755760807357, 0.8231311687890359, -0.3710726096488671, 0.4730763461483071, 0.7841954438527844, -3.6103782250167558, -5.894032366599592, -1.7286207268625096, -0.13953333260813602, -3.5529931201531944, -1.7669636017066896, 3.94788063574428, 2.2229437431694694, -2.346044867051408, 1.6446367118173748, 7.097139180764387, 3.7643703760231655, -0.45479989371110596, 1.624447107500624, 2.38277290706236, -0.9032226295967929, -0.9092864107108082, 1.56620468748518, 0.6845129622570401, -0.46789727047723906, 1.0926740111054278, 0.8875894660578602, -0.9970850243281135, -0.0986999473889785, 0.9447414890990576, -0.5436799751769591, -0.1516705415918006, 1.4054288020758547, -1.5106152019437769, -4.4133947491194725, -1.151558232200967, 1.3909540739829185, -1.337505196147761, -1.4821483993028122, 1.3085326527686743, -1.1719292680616527, -3.1537430873344925, 4.725588406424902, 11.301772432702188, 4.999922204495305, -2.2246073929718535, 0.660322635961944, 4.122985686912527, 1.464766359634904, -0.29425183115101455, 0.4455268035308144, -0.7014335451824087, -1.1661802076818346, 0.544355598565691, -0.4950459147150763, -2.6935693184684784, -0.5911145750481412, 1.7090536520909716, -0.01903199779037605, -0.4616426544868816, 1.6793940183155704, 1.0102838841616706, -0.5256585671224061, 0.8613483058530387, 0.6699887140334058, -1.1326617031880273, 1.4015341013307516, 1.7983520591213604, -8.298671548933779, -15.993042423402489, -8.433130859621512, 1.5627683487055388, 1.3645037229293662, -0.03759973209457404, 2.5778152558869825, 0.5619844534429755, -4.604513563395878, -3.421136058516785, 0.4485750060994732, 0.20860786486524807, 0.07222115414250914, 1.6169932170842212, 0.04516855944154219, -1.6924423935143222, 0.8786449498501392, 2.371657480450512, 0.13203649530668235, -0.3306002540866124, 0.6645688208689985, -0.5379854080913249, -0.48065589532050096, 1.316721539713928, -0.49656932627155714, -2.1937441922125176, 1.584687485934968, 2.2893489428074307, -4.0514622353833705, -4.71594132327905, 2.15568057257523, 1.8845537386830071, -4.775988579461942, -4.058192479869645, 0.6043879997116562, -0.6913742299012947, -1.667592397124909, 2.2810267303850207, 2.351696915914303, -1.685029963281527, -0.7091873974393516, 2.4362814585085384, 0.7417602943560767, -1.3056909877132485, -0.13011618389698032, 0.20347068823924555, 0.01675085849604412, 0.9421968949686002, -0.9056497813205178, -3.5614996586908747, -0.5177415119286474, 3.4336939705939957, 1.6204504098084975, -0.16278718212772664, 1.1098491378149957, -0.583274579482285, -2.3978433766603464, 1.2520364200907763, 1.872867936495565, -3.83924611734861, -2.3025979366142146, 6.909276659741711, 7.019262323176217, -0.5629580571240388, -0.24637706140214904, 4.572433331644629, 2.702900653906184, -0.6226740640769339, 0.18983114717264019, -0.46304187663128316, -2.310282671893631, -0.3967418951037374, 1.1537137216577602, -0.4685201893074549, -0.21330744895482456, 0.9483540260727232, -0.9812760851248074, -1.2852889998602048, 1.7612153278146714, 1.5103772900396961, -0.9356928340196304, -0.005933669917045174, 0.12740216457470252, -2.5017084895663273, -1.3135527867157653, 1.1167013711541927, -1.215016836794693, 0.38437464213732203, 9.18756363598335, 9.046611535617025, -2.390240243909078, -5.494605019608292, 2.037031054302731, 3.596931760667399, -0.8930524981634862, -0.9358694048295981, 0.5805886669857725, -0.16213208609074178, 1.2665697722858427, 2.467526699083076, -0.7802266961353059, -1.7244610166903338, 2.2458643598718937, 2.9871351258615197, 0.14147480617299973, -0.12329040575283347, 0.2619669867395102, -0.6002232481630274, 0.5489668112966475, 0.8313142421305028, -2.191703482583584, -1.6320398384168953, 1.96503418644564, -0.2890569506621518, -3.320827737478329, 1.20711753593884, 3.3486454820270923, -2.4906458335163175, -2.7381792851528606, 4.222328885431848, 3.8347375398808263, -1.6318497337984212, -0.49088169322455655, 1.234791023472099, -2.674326695859008, -2.8840696019150647, 2.064788593607762, 2.4893557569273823, 0.02257178459074501, 0.7275726756848915, 0.6868288555003461, -1.1167687338690304, -0.03823860522452057, 0.9594854357850345, -0.849968824914261, -0.260508644947301, 1.9224923764838993, 0.5722725993722141, -0.3252449022084044, 1.1732978958426719, -0.8648854773866637, -2.7504331666139237, 2.222030042898577, 5.0379797087103535, 0.04272511220345845, -1.4378481504625735, 2.1939418441957512, 0.9392680822311179, 0.7683902683370014, 9.342506719820477, 12.562921741768369, 3.2223585162232657, -2.3649315120094907, 1.4362131343668647, 2.412974988745442, -0.2568081422047694, 0.13502144061748428, 0.13490428722278086, -1.726999773439708, -0.6539410244365111, 0.6835408340551414, -0.6431287785811456, 0.10549990560650463, 1.3839868939817244, -1.9600719016252033, -3.95775124889456, -0.4680631096513337, 1.1760288945621875, -0.18180133064176868, 0.4584707839146753, -0.0008680952974638027, -1.627909870917896, 1.8658517541496602, 3.668426979745045, -3.6134891296572227, -5.601381057677359, 5.255820835772894, 10.010596628064068, 1.801716343389875, -2.1571935566125897, 1.2943298392920735, 0.9979297837364367, -0.22624154441014477, 2.410447151792591, 1.786604481512517, -1.7533966965283836, -0.8307980249062002, 0.6331434107072149, -1.3486715746049505, -1.0187848752143267, 1.098037521058819, 0.05822818967074994, 0.040089034372528864, 2.671589502649814, 1.9310315546154837, -0.25488344286165715, 0.631106783446974, 0.36193328482518977, -0.5623846602642671, 2.7887893254691063, 3.7677877468360452, -0.7793883259127041, 0.6035749003601234, 6.0864660470532765, 0.9494510655242422, -7.3619052952831865, -3.148530882557321, 3.7217439102632475, 1.5460174981851211, -0.1740892791314581, 2.21173718267459, 0.7111733158708344, -0.4091374514704744, 4.18597185911082, 5.353626810906697, 0.8650090391254474, -0.17953407966960425, 1.1327571225548996, -0.19817161509777345, -0.10259344275259913, 1.6850143164883664, 0.7069096056542803, -0.13360116001579186, 0.269367251021957, -2.0187251438413085, -2.2480089896680684, 2.8592781100276508, 3.4788627608447356, -1.6890215986714754, -1.8551636232113378, 0.8681332152837435, -0.275321196006106, 0.7557955855757669, 2.15767885952237, -6.787721798522898, -15.2814990007785, -7.876668135637181, 1.8781812714764186, -0.2764641019576601, -2.9798880619065597, 0.04776834866835053, -0.25229640760003047, -2.189909452061998, 0.296302576336963, 1.447387817636223, -0.41477524447725717, 0.2980656135714917, 0.8511363921528341, -1.1167457470349702, -0.4072579596385629, 0.9743172224240891, -1.3722497815681542, -1.6310746270415521, 1.4335571738434076, 0.9245239467986592, -0.3992102796353871, 1.6279895024192983, 0.9653924762778434, -1.2102051660153408, 1.4612975069435994, 1.252687918064181, -4.969344683187725, -3.5193402886122964, 3.583813799856112, 0.022346525493661173, -6.353220437424124, -0.185082675967823, 6.7564744699211, 2.871127823750724, -0.8000011730979038, 0.6796306537614212, 0.17346617437735187, -0.5281159758206697, 0.8542999219992311, -0.2450974004934611, -0.2879404443297724, 4.5756125281048465, 5.892553443182244, 1.406713320984016, -0.40985063602666133, 0.12619586818143744, -0.8161899735197561], 'positive_zeros': ['0.24801356651749748896262835040', '0.81567239854321433508375609477', '1.69782226622228548932934874770', '2.7517708128601031338274825221', '3.29113063347152334365435387208', '4.42196038964163468845734604810', '5.43167362191470595309350878983', '5.86519552993198977642001981497', '6.63925258280101818392744680496', '7.1741939769061017744015711819', '8.31012131573366049624055194909', '8.58800283046683144103068718245', '9.41863949819403779375547301979', '9.73364542938687921852354195476', '10.6266775824042779799596096894', '11.23429232315935639159454509701', '11.91758654512165682771564697034', '12.85234341469340790824461329105', '13.51416721102519312393636321512', '13.80913396664860010530049759461', '15.05026192001398826400754824855', '15.62748270137954203494785835289', '16.27015806141818264305475595623', '16.64792411720623820578596364853', '17.21153221948917086245260093378', '18.10788698515797697294297985284', '18.40381101236458975046704845720', '19.36249677976137950383349127119', '19.80700977778506193318870979091', '20.44498786315455836129903400671', '20.86458548663551220207496541358', '21.83910459723924837890507430966', '22.32301213295171954635499265289', '23.31783867384577902835273624370', '23.8991080359736432276153294370', '24.429710170220081959441140349371', '25.18499535374889833631477677454', '25.50020296418509890456012523309', '26.144531883906500168272391745258', '26.85116875251247392017426298250', '27.37573291941608525675593356355', '28.14811001199066248315470050589', '28.56309716805037604965304011311', '29.1658569368960197507762717749', '29.72238288578198533349479347953', '30.08274593849500018196717975629', '31.24987476937752984774004280826', '31.96238333403260223288854955414', '32.60848963233707369042950910530', '32.87380263466848482348845310356', '33.42729521009187992089031566513', '34.420439248378955494157289657335', '34.84217103528057278819846242532', '35.4867062416086376506660883825', '35.91385134731111293012328601388', '36.49732890439602251964850351595', '37.0182454793549782019079624973', '37.82948061970998182649537602176', '37.97976703463242078429878214971', '39.0128050946335218963654137197', '39.40577349373318309648904706739', '40.10488163985592858782271389518', '40.75109120383666721044454383544', '41.38896668496610312922757468865', '42.27528120691266298296448979078', '42.625998417657989643770391051776', '43.03242440216394077264999118100', '43.842499188411551237917188286578', '44.50279669605163968415068913800', '44.89058888518963249491554793905', '45.37757499440761337242494105187', '45.73600354975124953937543086527', '46.65056180607580907819502132574', '47.36986678015268260083762497898', '47.729253540060506495083625126362', '48.14991723649123691623088889454', '48.8244508188746480325904661286', '49.519585932791912604663475417963', '50.25575507331003106429281538948', '51.10100907582834280354848939343', '51.599976382439338837750779436511', '51.82393637813369732673933963931', '52.593178338135178944147964834', '52.98735018893620211713141434561', '53.576931218322565972478198349336', '54.302823434253602122790075053613', '54.93936665965627921375967639692', '55.32424204118351752700615329985', '55.87436440515326168283576319721', '56.20859439937267491105996526930', '56.98133339334947439667863279120', '57.60116354442338001755462934333', '58.26062317384520723875105568400', '58.845686042655902052510872822737', '59.596663473895182595449201973529', '60.281207144008950685763040085661', '60.52589302276785021372496265067', '61.149249865899653767551014391987', '61.799190042693505109135071442259', '62.395037459338319671377814756268', '62.74404221521915112168546441206', '63.54752518158858236880988457529', '64.01751432884949582568303029898', '64.54904054580940247728107624659', '64.74585432269726373647878675675', '65.49161499216213948075560434249', '66.293563542021052260663936128832', '66.78724532055632953815553812319', '67.34537834807311770425114960627', '68.02735445610061510919530889810', '68.70333360001815065969436681946', '69.07757618581504846308279595194', '69.70418982574758627361930512248', '70.540774085809161463532804494467', '70.99086255825533895088727654230', '71.5407126863889862073470023095', '71.66323571385776102610675455474', '72.3090053839883591940992838992', '73.04545529023186917547100750492', '73.63929254440844904191738485350', '74.17662103851922589358203003866', '74.68284358321205843389015811323', '75.04737377429045459379895713465', '75.70336750298374424624877581768', '76.37703315427652446269384868374', '77.1019095881941074984975242834', '77.59633313930294610477884891337', '78.32870484073733305926972735325', '78.821057390819005438260538062726', '79.43063984898635329624173596133', '79.763907000155849794321628746712', '80.28490223426393285292615870852', '80.90471545834477371686078537239', '81.53398447201665056639919324351', '81.980686600996038467432759190399', '82.46257105633664486173145517425', '83.11740407867071811804206447906', '83.70933197414705631368236112371', '84.05497138512919770841589759580', '84.59063920168781039939886326392', '85.021978747056309495757461607979', '86.30366170713586525869426894735', '86.7586562346431491472041266215', '87.011581835567810877227396142756', '87.63503246517220517250742547412', '88.19476749921307801589127025864', '88.55524516650433789584428880765', '89.580472780520277484335225121949', '89.8760342873703959741812768041', '90.22889828278396289206551461627', '90.94132253997652851127216336501', '91.452352565529099507623006481593', '91.788019797050931679093736514392', '92.26971179103263045444990630723', '93.283827797053173411449684129021', '93.41437292092266243543691202882', '94.15085722914996868010949955194', '94.80539366183333299657287602987', '95.23906205429749266204587091591', '96.17105029785639629416144345203', '96.39702825194837461652344954516', '97.09928761663548155402287774139', '97.60197618670876829568778898549', '98.2299673241523169324672545125', '98.56158128073253967589122595417', '99.19064537230125157842083825254', '99.70308713296712906670995749035', '100.21002307314801512296860139687', '100.6475917940629795666301101944', '101.14089252653161854343140406550', '101.955139162615177494806963917538', '102.37392735578815286254715417730', '102.95425449591203598130531878893', '103.355040123974436665058616669174', '103.9148831812730909475797904828', '104.85683355002861252788508055400', '105.27553675142324854048048316983', '106.10433755648461557971939821643', '106.372411635809571935108511587266', '106.74609083324473607076732330520', '107.39023129854646490952541992687', '107.75256453205744041884794551572', '108.48929311203469504533766826743', '109.05985325987087520122275911430', '109.44763024568503528455771927692', '110.14469983813389617901444216421', '110.47663886806320241389621998432', '111.027980428951453601993472048705', '111.44604416759431541977416076678', '111.95849076806014287866753573498', '113.04971618988968051557593554609', '113.596605622134655621145274689020', '113.75757833009639312355688316768', '114.40659277051091097798648133144', '115.25541655345858555351319574112', '115.67682434267819996962147720427', '115.92078454627550522449951223360', '116.56728639594773966733095447415', '117.1078527587642207184469691155', '117.83195265580471268935261387112', '118.20365328762934008923498787728', '118.64599006025043600274316555553', '119.13704921259624298326916941380', '119.64026749199165191649795114280', '120.206799676330015227955844758978', '120.75340915825088958521277177486', '121.4608928704755564805389668105', '121.96300471454194936591034346554', '122.74727048716248705351583070808', '123.054761996129801194128075597641', '123.58502916936212578578210087754', '124.23234007759182602593670074384', '124.74404265020851455204444980425', '125.38539076290813930504707954007', '125.968199488595659426332330960718', '126.35555249673044365824083500624', '126.55469654350896307065662895073', '127.09977672350266923267366598865', '127.84283668301846482042162632439', '128.63244520944329981615713715195', '128.81064260912084768001704909940', '129.3183954872118060534601350464', '129.914209753075728825321588238818', '130.42493302666875560607947154881', '131.01908588541170337963048790594', '131.84458490221256943183822099', '132.20240939604241990377450736283', '133.02118186789358268097578928124', '133.39066388318218060122706942511', '133.67977310277832324999080242613', '134.41739719325807732972088367408', '134.91656749644930252413038577073', '135.34973229692440092421668308904', '135.8146367222386293168338572090', '136.387080289990028265501412032276', '137.03843701667434765263312102729', '137.50103270689844255619445481540', '137.83088601584951267875230685543', '138.55546111735142186380068541955', '138.93885535826779585492151261283', '139.35647214520238742240822800355', '140.24661254059910342069371762170', '140.85458497575623909496848379023', '141.48921794446846422002856204697', '142.00816050186016591097695735271', '142.41921792039756283623620234251', '142.621328724300287881723874077506', '143.374883503011887341441281405', '143.899374192728566946568336704823', '144.71029517153705966279808774886', '145.039031642227549250195279902641', '145.40335795370486379296606155412', '145.843300250740275852589469654064', '146.350230349313878179860425332408', '146.99889703646119706049650568597', '147.48142314862099209556782866986', '148.063535679140929854277769453308', '148.62937130697581280607815443797', '149.18747141937388188858524290727', '149.88389457048245284233560432101', '150.35417136059085144259472007026', '150.75125152964328950191817735375', '151.429392527065267620484963512124', '152.19480358183448626500627937717', '152.32619568667183789676214476042', '152.918964844093610974853729307871', '153.443010615629921579208232287532', '153.92701561844211262601016416973', '154.40640807702991635811594493860', '155.08325222218593358074727327910', '155.384470495403666922578504844670', '155.86233091786343297876921926081', '156.45405747848789223519272851712', '157.189990786920786736446668811222', '157.62163818283893971449070669288', '158.231309897465333346599081224227', '158.37010332755956502678124174794', '159.482631156233269900385984488441', '159.904550083119509960649486862031', '160.58037984349233764108959121635', '160.90590314679106301989537032538', '161.27388587831468864820829774199', '161.96521748539273820351293710518', '162.36523011929989023126344996962', '162.797645190079653074665373332785', '163.295464468527932711325916449127', '164.1016333507229070703386237400', '164.62685001171098424449264294726', '164.87701190551859112133049323535', '165.312373100116466285546339067706', '165.819546965028438801133291151880', '166.43203611302225452791540019636', '167.05514029051009549369100739760', '167.88143044224738807138110213197', '168.32358104883350780555623743208', '168.884122750714920517363588408062', '169.1073264980148931660278883411', '169.827604665371636149757591024007', '170.412354323088870410684779190711', '170.75306053359325192702100604239', '171.373053155758986934691570596443', '171.88575183505721489671761420990', '172.1814359741568664553945707786', '173.05145885874328816837335508385', '173.29597838349557457297051379760', '173.81305418859101132453289077906', '174.15087666976575037902003376748', '174.94075782201651206428573539443', '175.2790294563001837705023852763', '175.965919851786920062431936760662', '176.672087706637921745857216075591', '177.32787527936851964119332701508', '177.53050712449244507375380968390', '178.19797145318204179838656085102', '178.48283833048258724221471580265', '179.45959668009610446427851950535', '179.722740112550724351621199083322', '180.27543356407821790609201074160', '180.64206666790572060108448498228', '181.39490260239399742076554146038', '181.62849067789609097172139103831', '181.946230012364954237913562251455', '182.651100703689429628989127127335', '183.330673132806207130318547171328', '183.92264988938850308268789559978', '184.32235377849423601847875958361', '184.60559787806125297547134257111', '185.11961720406175025105958930788', '186.152946230251401681532807427223', '186.54622152487388813467162489529', '187.18194526524897844396234440117', '187.46986947975613012535882655091', '188.096839389616880917345761253169', '188.665269358481594303317448384872', '189.00931014459534294373185201855', '189.51510422995101196184754753879', '190.05411916193461710046923779209', '190.477357134309522699128927715257', '191.0972498479562029235892447502', '191.690426961819594233864177094345', '191.9657672733202229664999128764', '192.597922978979088003604355687632', '192.999015175186940681346352817614', '193.508144480612370880599278879670', '194.19820723830171373210338464043', '194.688303593730075374576965084596', '195.31815178643915974244520187045', '196.110127097513169783603664115035', '196.442689614442643606441433248087', '196.90660572831017969687702895889', '197.30705812684597130447572345653', '197.77522019524013167343343533425', '198.15273789903400418263379525686', '199.1964040023061600565502914639', '199.54057488907915080876466498061', '199.75615044797576940103154000912'], 'prelabel': '1-6003-6003.1021-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.87781479921304, 'root_angle': 0.8648253958259564, 'root_number': '-0.911177409423237939321223594704+0.412014233439522112025273763170*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, '0.587374515139252010460806234354-0.254249915438953188280648649435*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.248013566517', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '0.815672398543', 'prec': 47}, 'z3': {'__RealLiteral__': 0, 'data': '1.69782226622', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 27.87781479921304, 'bad_primes': [3, 23, 29], 'central_character': '6003.1021', 'conductor': 6003, 'conductor_radical': 2001, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/6003/1021'], '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': '1-6003-6003.1021-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': '1-6003-6003.1021-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.87781479921304, 'root_angle': 0.4324126979129782, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.248013566517', 'prec': 47}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_6003.1021', 'Lhash_array': ['dirichlet_L_6003.1021'], 'label': '1-6003-6003.1021-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/6003/1021'}