-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_3751.1264', 'a10': [-0.009519833939576644, -0.9999546853541729], 'a2': [0.362807705350641, -0.9318640292114523], 'a3': [-0.9135454576426009, 0.4067366430758002], 'a4': [-0.7367411378764049, -0.6761749002740194], 'a5': [0.9283679330160726, -0.3716624556603275], 'a6': [0.0475819158237423, 0.998867339183008], 'a7': [0.9998187455235258, -0.019038805103346677], 'a8': [-0.8973984286913584, 0.4412211012432213], 'a9': [0.6691306063588582, -0.7431448254773942], 'algebraic': True, 'analytic_conductor': 17.41957076659139, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [31, [1]]], 'bad_primes': [11, 31], 'central_character': '3751.1264', 'coeff_info': ['x^330 - 1', '0.999818745523526 + 0.0190388051033467*I', '\\\\zeta_{330}'], 'conductor': 3751, 'conductor_radical': 341, 'conjugate': 'dirichlet_L_3751.549', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^267', 'a^143', 'a^204', 'a^310', 'a^80', 'a^329', 'a^141', 'a^286', 'a^247', 0, 'a^17', 'a^28', 'a^266', 'a^123', 'a^78', 'a^26', 'a^223', 'a^227', 'a^184', 'a^142', 0, 'a^111', 'a^284', 'a^290', 'a^295', 'a^99', 'a^203', 'a^282', 'a^60', 0, 'a^15', 0, 'a^293', 'a^309', 'a^160', 'a^5', 'a^164', 'a^171', 'a^121', 'a^157', 'a^79', 'a^152', 0, 'a^266', 'a^48', 'a^228', 'a^221', 'a^328', 'a^227', 'a^169', 'a^232', 'a^241', 'a^36', 0, 'a^140', 'a^40', 'a^219', 'a^8', 'a^327', 'a^30', 0, 'a^285', 'a^282', 'a^8', 0, 'a^190', 'a^230', 'a^254', 'a^246', 'a^106', 'a^97', 'a^34', 'a^272', 'a^103', 'a^101', 0, 'a^108', 'a^266', 'a^58', 'a^242', 'a^94', 'a^142', 'a^16', 'a^6', 'a^89', 'a^95', 0, 'a^279', 'a^203', 'a^27', 'a^315', 0, 'a^165', 'a^207', 'a^158', 'a^174', 'a^265', 0, 'a^164'], 'euler_factors': [[1, 'a^267'], [1, 'a^143'], [1, 'a^310'], [1, 'a^329'], [0], [1, 'a^28'], [1, 'a^26'], [1, 'a^227'], [1, 'a^111'], [1, 'a^282'], [0], [1, 'a^5'], [1, 'a^157'], [1, 'a^152'], [1, 'a^228'], [1, 'a^241'], [1, 'a^8'], [1, 'a^30'], [1, 'a^190'], [1, 'a^106'], [1, 'a^34'], [1, 'a^266'], [1, 'a^142'], [1, 'a^279'], [1, 'a^174'], [1, 'a^261']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-3751-3751.1264-r0-0-0', 'leading_term': '1.58136878000521428591847559069-1.43645538470018581979066942054*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/3751/1264', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [2.136382758451616, 1.6671896135515145, 0.6773370174013188, -0.4420622061891809, -0.6341921017754073, 0.20227595147829522, 0.7394050515031635, -0.3188820620892576, -2.4357431870255004, -3.4668522267615587, -2.0606875649531204, 0.5389804585748105, 1.768395479836232, 0.7912480257048111, -0.5739705066123685, -0.41498795716923437, 0.6569870169336773, 0.6311551123144429, -0.5213759342332942, -0.431957339367908, 1.7872588936750593, 2.864109828328238, -1.1351939872828443, -8.780383386102667, -13.300538948569836, -10.079504189289565, -2.469587209993047, 2.031502842441122, 0.5977273155336735, -2.5518649115729226, -2.7216440402127455, -0.6049143785343307, 0.2085423896561564, -0.8739467519230085, -1.2673710308018078, -0.016011163834082513, 0.8155096128437289, 0.13749488431052578, -0.09789314831735389, 1.4701292665760488, 2.736633852412594, 1.5305477574150488, -0.28761074496619127, 0.3937025802350793, 2.391311539722696, 1.7368059841519858, -1.3794078665066325, -2.028594031176249, 1.480896602279919, 3.824302735550137, 0.36535917658476247, -5.17240431600011, -5.730627913611903, -1.3017336354126199, 1.576438494909269, 0.03538108126274718, -1.7823704213539329, -0.7789132354307158, 0.07729834697954326, -1.9444540473428593, -3.502201412022219, -0.6421482451403657, 3.7864946870840033, 3.9875990838172584, 0.1979818487099314, -2.1408442066070847, -1.0342311839705014, 0.26442809505070886, -0.09126264131770274, -0.19059038547677037, 0.5069939079031909, -0.3376425698960247, -2.650646647961691, -2.865849776680691, -0.3429683861414696, 0.923849525082323, -0.24750456571540036, 0.5495465533300438, 4.60540620601794, 5.40877396030818, -1.104754560417243, -7.640725911818486, -5.121445243365844, 3.098943471849347, 5.944180635455804, 1.1215196498270965, -3.0049402168372867, -1.5166397255984028, 1.1270726794780008, 0.728671219425822, -0.4235078317924402, 0.04381695643536779, 0.05089345620372045, -1.5167013235592404, -1.843428033933931, -0.018878579467525563, 0.7422421685313059, -0.23923240692066716, 0.871540593938482, 4.556583955080198, 5.491657967511646, 1.756398340677529, -1.0819047236253274, 0.545311872418802, 2.392243169359929, 0.9644113433628286, -0.193849386658711, 1.5454524122334565, 2.0370253024503624, -0.8486831680872664, -1.1033198648970077, 4.790987059141093, 9.351150599717856, 5.422226590606246, -1.4728955774318007, -2.162143941034059, 1.5094530847659693, 1.7715483612390708, -1.1190884075275478, -1.2686271522495365, 1.0439164367909084, 1.0042927139394173, -0.7423196913661337, 0.031366221873390644, 2.2745863495356162, 1.9511571197474586, 0.09276701370280885, 0.20229466809668742, 1.2174191031418686, 0.6008767578138441, -0.08039861183951413, 0.501531150210859, -0.40214185389106083, -2.433681238716913, 0.7847837971521308, 9.663383251365698, 13.286199224463305, 5.4533835862168445, -3.811334469839661, -3.5060219591704165, 1.540389926168022, 1.0158809761864038, -3.3089793273054515, -3.417316109301605, -0.1540836966008076, 0.5512980002021289, -0.42401764445461015, 0.806724835879449, 1.9961788919779424, -0.07634659376647779, -2.014210206423133, -0.45404771773826275, 1.069299418663208, -0.27339150649455984, -0.5206885925698611, 2.585846282206079, 4.217262141675791, 1.740229525898411, -0.3448634483390561, 0.26448632419158313, -0.14938903635982112, -2.158745413965737, -1.576236489168921, 0.6284164804850781, -0.8887762995453836, -4.197148648682903, -2.668082630800865, 1.269099877274003, -0.17699018278800258, -4.280580808910845, -2.087406294543298, 3.461343349328058, 1.511672794617573, -6.3662565014568875, -8.054211512585969, -1.7958621254735818, 2.330721518473362, 0.5821476361171746, -1.087806494928032, -0.24310124954003395, -0.10247088695232463, -0.7367595756607154, -0.031004746420554945, 0.3570399085072234, -0.8151848619429792, -0.4410091030108555, 1.7450483776480978, 0.9295542965717862, -2.619274130049298, -2.4617008296282403, 1.2842235946551976, 1.4961027413831087, -1.6781868742010182, -1.4286657858189582, 0.4882132228667634, -3.5623566307955024, -9.930483654486938, -7.90444432566609, 0.3302907996774296, 2.915168902131013, -0.9430062227273798, -2.0549512729050963, 0.6659749044671129, 1.0606979644997707, -0.23128368840472047, 1.1013083051765618, 2.1778626463826787, -0.664677374483545, -2.7647948556839563, -0.3138104659953311, 1.47350097255904, -0.9649569046218054, -2.4360757492198917, -0.029773276534299526, 1.459237592755974, 0.11471968188411638, -0.1077744805301765, 1.0634954238588967, 0.45262278052304594, -0.3027625820148175, 1.1509035159055145, 1.0848670494303743, -1.8003526902744418, -1.2885096575567305, 2.221532267980783, -2.460423595385388, -16.040084569588533, -21.664989230238298, -11.174266081458212, 1.2367122744907302, 2.896192115733706, -0.16958755029008643, 0.17449454698189193, 0.8403992566251408, -0.7924889545598328, -0.5182015597535033, 1.8347425900583496, 1.318296823545098, -1.1930700860437493, -1.0550302622014611, 0.35420806242234704, -0.046361149822254775, 0.06135269271163143, 1.661407316959617, 0.9068646071514304, -1.2820257183480124, 0.5797397171508234, 3.918083543455179, 1.5311527109914458, -3.0531738456011546, -1.2709339807360704, 3.4953043078040475, 2.8420636154918806, -0.24422292102777887, 0.38787212469845855, 0.4365918510791872, -3.8148536838408673, -5.078330780406739, -0.05398018055104818, 2.091400225509969, -2.2412327538028762, -3.763577000825767, 0.63261962647125, 2.1214978174063086, -1.5733038420198495, -2.639786192952536, 0.12464895770869558, 0.4819922131835351, -1.2954301193995972, -0.6500247523783237, 0.6102335523331558, -0.49751185921764335, -1.084854100671397, 0.10667129935822563, -0.3462333109263619, -1.6728631343597613, -0.3576382559552475, 0.5442664937239916, -2.1788830909651167, -2.9753148529527333, 0.7562537809180354, 0.8894808102640861, -3.877442240870794, -1.304629648635923, 10.55866245202729, 15.572757008321533, 7.260321200142144, -0.4640344515027459, 0.6190165979983555, 1.83541042540537, -1.5759635579143232, -3.085787288517639, -0.8487396600675199, 0.1173017959142435, -0.2808495699373885, 0.30652360858613, -0.2648113205724905, -1.5110193853597316, 1.6032524511103976, 6.751241146332271, 5.947040847588189, 0.9570086090164328, -0.09298076393423227, 1.7366462728639114, 0.9404819421270569, -0.16449946573306173, 1.2847594346989621, 1.2813747542680984, -0.6535351301214745, 0.390590806219764, 1.4230553508057415, -4.002234173553976, -9.281214114019269, -4.836779384597105, 2.1807687724689884, 1.0418703060462355, -2.087004359730604, 1.3286198761961985, 4.274857223484914, 0.408486379505094, -1.9493435260501912, 2.3143553192180106, 4.8164725001317805, 1.518818256189768, -0.7057035032150435, 0.399463595446832, 0.3201510543591457, -0.5012032653951305, 0.6424061624581275, 1.1805140998881476, -0.10100603291047949, 0.001995193920505853, 0.4643375681105778, -1.7009777299324502, -2.6248331691319744, -0.07353088735578286, -1.0357544970847061, -6.346209873522513, -4.865594933934881, 4.243736496198126, 6.541225578878546, -0.757462375078887, -3.8411055605660716, 0.5398397569460686, 1.6376307127942937, -1.5810564044427193, -1.1218144837657413, 1.0351282308822132, -1.007471971273865, -2.8071710220836446, -0.34004837978569813, 0.5771100360347637, -1.9497489238464691, -1.5674987804069476, 1.4631325412749732, 0.9700729884894121, -1.1625293783105288, -0.13547038056955302, 0.8530414135527413, -0.44792408241762083, 0.8027458647503154, 4.334702794838294, 3.6708728700647524, 0.15410009743738287, -0.13217801308122185, 0.8557232044279766, -0.10734166026924598, 0.4316823684937823, 1.7143853746826159, -1.6238437015623401, -3.6216204233925575, 4.589535029823213, 12.182519767521944, 3.9043699789955095, -10.065889068377867, -10.385121201569822, -1.2635116408728713, 1.8893810673120635, -0.2124927024095643, 0.08391682830828451, 0.6839766000081351, -0.8896353748440484, -0.9725857912052903, 0.033034510589837064, -1.2305811351496512, -1.9887688451840368, -0.07607504871843783, 0.21391577122256383, -1.5065026341715226, -0.7456666714628799, 0.22632977593020695, -2.325276760801626, -2.577081734940667, 2.7727028888417755, 5.125200121899428, 1.2642107290442177, -0.41899467030971427, 0.4654925844180786, -3.8055520355471515, -8.368607907217722, -3.4011044686211336, 3.855853456643924, 2.1899224173534253, -2.2166049421743317, -0.8964556552886728, 0.5738293337353226, -1.6162304756124173, -1.3713972351906838, 0.9793053133911873, -0.7713177621263434, -2.6662517155398158, 1.287951998803366, 4.496784057368204, 1.0631479641634873, -2.2457293537999687, -0.8292894986579118, 0.2982669223145925, -0.4218846283690983, 0.16225299564903306, 0.6098489942530948, -0.29644958229116003, 0.400555234700723, 0.800437096475298, -2.432920389228941, -2.794159371922666, 3.7163540161182693, 6.308045926908289, 0.2782779473475474, -0.9931393555184808, 6.715307920774281, 8.480436543964236, 0.8983094966559193, -1.3541416161773547, 3.873413410883895, 4.038214218199267, -0.9995465226769759, -1.6063004847701372, 0.7367349640119396, 0.288275865268067, -0.05811101281965714, 1.4668128994742125, 1.0223606829555663, -0.30446782650225696, 0.5521772429168299, 0.4059828303567209, -1.1030418726324158, 1.542688375752853, 5.673854334195863, 3.4809082826802227, -1.0273931621193289, -0.09368178395434629, 1.8947390120617253, 0.2266393433984091, 0.25802826089622255, 2.4719113922187104, 0.3213623630002326, -2.7024924577701728, 0.37520577442083, 3.076882097661609, -0.15490177466947713, -0.3807963234350054, 4.60773029292335, 2.417429156973934, -6.926973527449939, -8.368346524466315, -1.2661659304487416, 1.5140281989827107, -0.41626888325949113, 0.5672454420876311, 2.0655134470013383, 0.3315097198843292, -0.5163451194626218, 0.2617778357006798, -1.0374835103927345, -1.9696115965759362, 0.026858116242170396, 0.4227053786685761, -1.5556711240038337, -1.0205678338908795, 0.47405061067856286, -0.5235904325664288, -0.40843224380103493, -0.250962644718272, -7.162139125896373, -13.840745586351819, -6.262615514962899, 6.202250476224279, 4.0003780880812885, -6.514925245052083, -6.849406046621275, -0.1617889396481949, 1.2586057324998179, -0.20147258293295245, 0.18671397081257557, -1.0757805085006076, -2.7060110428223054, -0.10532912208963514, 2.1622414021048515, 0.2744523890447501, 0.09168215269149732, 2.5799631011015305, 1.2286101151378626, -1.8159324102627692, -0.24815370120928734, 1.7954325386278462, -0.13599934052906637, -0.9806003191382996, 0.7119524605215604, 0.27237348414243273, -0.12440799354585418, 2.611604052020787, 2.7615124412765946, -0.7107931886269867, -0.46358230132652833, 1.0334954645423258, -3.2213635896703066, -4.826039967854293, 3.8352857946696988, 9.261864600442273, 2.0381973115981107, -3.9679866014624103, -0.3595552641510071, 1.5052538282819898, -2.05356275087921, -1.3621511702581635, 2.7854451919871623, 2.122319345694121, -0.5813973004961948, -0.04810015755951352, 0.49791768011357246, -0.39470833135092476, -0.02060528342210792, 0.043764640440181614, -0.8424217895223143, 0.6789417888210056, 1.6512421220867295, -2.0119801079786064, -3.0136883977757263, 2.939020925528643, 5.208547020576372, -0.07734693825777893, -1.735375109485086, 1.5933005191846843, 0.25200466837382884, -2.709651981321173, -0.09156032910896199, -0.03898968904725909, -7.42592134313272, -9.828174538905984, -3.0270033084633345, 0.6916695480803471, -1.3824678453172747, -0.9154156211170018, 0.8498293814547739, -0.41886622969082893, -0.10460213350705243, 2.13132006497218, -0.23445333468526813, -3.908715807619642, -1.749550020377773, 1.1875258413847696, -0.5623036482347059, -1.64155895707769, 0.09565443266274924, 0.07577682025818874, -0.3951428874827725, 1.1852896156111865, 0.8826786943506392, -0.8869985272597585, 0.39257171601061264, 0.8239624251834228, -1.190009909860286, 4.2697088798981, 14.84497503793058, 11.927425538683185, -2.656370565258639, -5.787466892108132, 3.919704118859056, 6.702149833790052, 0.8989584363065406, -0.6300475333184528, 1.2320936270139984, 0.1200100487046071, -0.6888855649236132, 0.1425673570114252, -0.9727154809450651, -1.4467761414557392, 0.8345028245038597, 0.8514303779055865, -0.9968691131533852, 0.74987422282431, 2.7324051363663355, 0.594253068396152, -0.5063632254942018, 0.738171421456661, -0.9986995991825773, -1.9437806517504665, 3.0026907885273406, 5.237948435230489, 0.2704428754660859, -1.0981085848544847, 3.177687590502103, 2.505913337247915, -1.0386541227132495, 1.5387462880844172, 4.166223169863947, 0.5888373611113914, -1.0510798587364727, 0.8152543903536658, -2.450751132699521, -5.9880796608842495, 0.2705211982737025, 7.694173137943121, 5.334375218322828, 0.3507807719482713, 0.04566333924819095, 0.03881056832793958, -0.7662413946949259, 0.4617857931978888, 0.6074739248077203, -1.2539404724509795, -0.6508836652797055, 0.8230497934399258, -0.026767750231205256, 0.7728268814566464, 2.841920945938869, 0.32737152259560315, -2.2742271736109836, 0.2670562959948946, -1.637588595996573, -10.419528434999473, -9.843340271007138, 1.6317231172119118, 4.416898929943413, -3.275419253748559, -4.521907045401019, 0.3352943175699763, -0.36171165804794947, -2.8508224438895216, -0.5519347320548247, 0.8999105656951691], 'positive_zeros': ['0.798448173889582526244791726872', '1.49903172547112745600104722790', '2.130408077372829009608124048639', '3.36851043419190178282897815923', '4.218021712686801175379011361159', '4.80647483993936638154134076886', '5.486236512177971350978729945925', '6.01832858008541670005363417724', '6.8183217986503821783637984834', '8.247397043227851242943302832452', '8.80413489053359442360270898393', '9.8074189263604690789138692314', '10.090283594449830798089562955588', '10.940909733211264437498814640991', '11.61252856290737717034864789108', '11.91062456190930575465654581183', '13.0491665732104811227558691693', '13.367927877484319617863933332814', '14.23869671577903333926394891055', '14.88975390351625272366936060403', '15.64449735640836722439959249890', '16.65515969234206561800902845756', '17.19169797833748198214488004409', '17.98196497648263864213201895599', '18.155516746164965433493414227962', '19.10423888256584317992638398997', '20.015852553367547364282381751556', '20.82644437545436303107826206358', '21.2064286653447498921549682119', '21.6483434571754158685352969246', '22.129991483521705194250438898143', '23.1677729233188609848514113843', '23.6873935610433031720769966917', '23.99366948205083595576632858113', '24.95913031450071877650213125148', '25.81720477598895137390967686012', '26.62161555127680430155170950755', '27.33578289441468849639643417593', '27.96667024169973856863214255434', '28.41999104418851243167459898760', '28.76500052400130688791382873744', '29.69063875574448418630144412263', '30.2276132036077239156397313975', '30.50573054225740126256959190654', '31.70004166785644690933426884838', '32.12558617048170770106051117301', '32.974710115759760610171134399158', '33.19364464912441109254294286062', '33.97921741104512984917328710265', '34.45829234977763487428737448608', '35.542153961782915444727383759466', '36.11866794433427286317706348563', '36.75025630114673466067337814450', '37.35447379914150838823928672516', '37.97485867031339007774664645453', '38.43312473975186549999077211431', '39.40191825464930327782242188333', '39.62529595626712913364989875341', '40.50664409727577716775288056329', '40.69886419319053928125930951062', '41.187479444371777485231383964830', '41.83855608201647406799628652227', '42.96984373387156003246295443338', '43.6387896447175353510496870032', '44.13642860505450697576010164996', '45.01918002191239682232055407900', '45.45543580178524982064989945100', '45.80385940308885702879729024754', '46.5545261572686632482898335331', '47.24540977658845263278812890109', '47.765438310212856745457118696627', '48.19816699534357709958472589969', '49.27085482781105535886571362138', '49.599404918440851709720387200389', '49.97206746973266660890148991079', '50.82031092725103615217037954570', '51.162397362052047756248927668236', '52.062571998454490553340118221378', '52.48718245787360692438939994984', '53.23056807325236096237075801515', '53.81432805022033165732654201486', '54.77561070724592500083899196102', '55.37948509171891957182740559328', '56.03667990152883054240488400658', '56.19509466868954698717950126192', '56.88394596926771772993475750803', '57.30236363091054152080195805582', '57.87805486419832004543533406386', '58.5214623859648428368360298023', '59.2638631438569603426902375658', '59.832816766331090696771916450873', '60.484479705735437177255328933067', '60.72453690352865725314174576996', '61.86059651868323145754228004890', '62.4291693597994780253297750064', '63.047077171337329835551981068094', '63.653176078724199399601391183265', '63.88482516917992504318228077487', '64.63218896857453968655379063214', '65.34177517348003619533626375599', '65.84341653273827970629938683674', '66.56567939342465199108678700599', '67.21371810153564159174548135145', '67.53032174816486368739726350589', '68.2293678354962439725558148155', '68.53870545529983505239904569327', '69.18739270770541369065653706372', '69.79033952782056576852680476528', '70.23074010480851427961890415703', '71.51668814623693930246586527436', '72.15992335245181696401110076659', '72.46475768183484888886474794681', '72.986876935828520405755159519827', '73.507559858588417186728730234353', '74.21421938246666816413184847912', '74.888539569934735525582357691475', '75.29482125163504791094453831569', '75.6093880921414376083693004129', '76.358562660549088569399574957360', '76.82708316523509903824792514775', '77.5883626305740339812273854369', '78.20002849547762299325227586817', '79.019978981479299427692737466856', '79.30430583518907462208926953456', '79.73409415256506262617943008658', '80.62811222694429285959601819342', '81.11223192981368615592442991104', '81.83338006077324180398386420934', '82.379778990144588869824590107256', '83.10932496224274710054582217520', '83.51919165733542820455717701096', '84.17560853606244634488865678680', '84.590833378903550736125866359817', '85.278755526757842636331625113638', '85.54893277928950357193701300293', '86.30341479531979140387471912434', '86.656541909258956142686044592298', '87.43893860884051276930824299637', '87.87749631179353767028608970198', '88.47966187938551525563746345390', '89.647238891537401244646920684571', '89.93667622496007478670314372414', '90.50109586453283563059874022370', '91.41120872145926116997871076236', '91.64217555047594020132821007203', '92.05359162523904914706624110042', '92.44572693114581238887975111671', '93.02272964485581732561972525495', '94.16052336577977739635398812123', '94.39304478506963060372195825852', '95.17636258412726864535563628456', '95.3813618853446586226373344394', '96.12499463541309455615078820663', '96.51156713550612609054883804258', '97.00079722799047086197718283175', '97.998433012178018514976224616847', '98.50980942127844537864090688760', '98.98232051379610459498833135150', '99.71288629108602702520669016243', '100.17547706497569350545587007471', '101.07584542720930377284230109169', '101.469103596232252792841008894195', '101.95855916201641687148535035659', '102.37089894954368081754237969812', '103.096883345484120079272761419126', '103.43689004784383548194115656387', '103.85279816670251367479790944557', '104.69840875438333079275089846467', '104.90578516769878296067791406035', '105.795674811410406671219191134313', '106.53202911541435630896608859182', '107.15120383702789116198953316097', '107.65711538910365348917894569001', '108.24790474536544276928284004698', '108.65220741923933482668194011344', '109.412799911657413215361590224037', '109.77380835424107795754131514235', '110.46308024163307769844627775796', '111.05309155949963868776124074361', '111.58363049774805557737425176024', '112.08018319517934735178194777899', '112.41274026378546872158610209904', '113.4586089213460452447541654910', '113.77959830802911582518467333145', '114.34223753880192974178324279284', '114.606081431609867245014118143698', '115.20450262483253086371496073820', '115.8035074471891466991465917971', '116.64083667619112633020470931856', '117.55643590193664724397790002702', '118.085617168780455668201849072369', '118.41895021778290086739512474876', '118.90359447853731721164798239990', '119.64313310096785531781693691435', '119.73478165846902702008466044019', '120.63766552755548662650525384775', '120.97924735184636927957679516428', '121.69020811695578612542341875673', '121.92820270641334214458367108341', '122.6683276474118240494917010838', '123.55356932974417353769403268997', '123.84996979091245123238376428935', '124.14117356144177230373492369328', '125.12045941786740022265906726095', '125.75037266824000999782033467064', '126.350365893261758354493485199333', '126.67128691081002036962445995885', '127.341136084676480356849642063893', '127.73891501469451494504093351169', '128.36336166621756991046305408335', '129.13028970944258381865183066188', '129.822440531818696447128754353093', '130.13579701394122535901290615327', '130.58013854011749896233663530527', '131.13690669782495623763390861174', '131.47422822778483892305028591830', '131.980561067942071791164838996100', '132.65461246496553990846160350516', '133.451581856789648220453161359467', '133.80477965200006056948784576599', '134.72863394242998638342005952121', '135.095977719139261954041853316195', '135.8675533549891463638214481993', '136.440930377659690616308356356675', '136.94806713570950852821034910621', '137.203863041405245478298160415918', '138.00369519478795245613869818726', '138.299201074006117137428701401427', '138.820382981551653887138550918910', '139.26327030781752347000659412536', '140.212918596735745385430844214196', '140.634698563903492631915512127372', '141.28977475943008722530621845452', '141.520700905391739936651399726624', '142.21078054277956584268717018449', '142.788418276620297903459132093285', '143.42457938708578729786333763318', '143.778865950105225788026361710784', '144.4599358901471965920112126133', '145.37907900619250553079768933176', '145.85701660560575446996446636641', '146.17189725369470839030197496736', '146.92618228187938349661734046392', '147.35838401228025899281523203029', '147.63247442609878042958378843822', '148.43357139463774399779838002731', '148.82230636086265953006782136634', '149.53614739937926901860457637915', '149.883417525539732627301251250437', '150.40407550239929034825233742618', '150.59142834471905625991024702822', '151.69871834696413996139578437575', '152.30019057582294913853555648620', '153.13520621033892117570225751686', '153.670898921898442068976139916081', '153.95110089501937132127165930097', '154.20118382855364040798583767436', '155.00861851920419639223401270124', '155.66679371300335229419303906121', '155.92328211233718422956702653820', '156.66440658118399861704302885733', '157.211386518842405766324630902912', '157.79580596926811976073919188514', '158.30172141760910940682639565544', '158.80907137656370053682971864525', '159.086193841690621177007310630281', '159.92751118620928024024065948306', '160.367482959147531505066064549418', '160.74494536206187366664698230140', '161.448743237197182154290359327504', '162.25483851803973349120440302813', '162.83527171734267375341601048894', '163.268033708529078642894248367695', '163.84554637834049159043656725904', '164.58879917181313786241243824731', '165.01075558324417411932534874179', '165.478060677755745268506295284526', '165.94553317510891571107299642290', '166.26471605362694706055533401739', '166.78614442997482414576622075483', '167.35775455165687315277570759028', '167.98994518963921635923386234357', '168.74555203363579816515106117497', '169.22117460589947018641606971125', '169.706782222368854789416604742207', '170.32061815840477885259418783324', '170.62235592336422207192968774271', '171.72982890050768865841880552430', '172.009651106552420299495024331127', '172.61774800805788919743024209477', '173.04872346731348328799255510131', '173.451348305793309825047885124897', '174.04660230920562205440579065124', '174.82262165670513095609480806185', '175.2478723433498827006944456698', '175.91753424379342211619195688989', '176.27133341222427739076793187987', '176.66317850960027930149766560246', '177.3145578050724165682512933479', '177.75548066659121028403316114815', '178.23456674783051994008487618261', '178.586146963294260196819373867916', '179.62562724167694665225268015203', '180.19331099447508285958994281264', '181.00008350621450686825442371715', '181.34395937932721086515198759262', '181.89470452795130111757288098380', '182.41113893567782266104748692668', '182.612776176771005090438898107250', '183.328969915222560345076851182903', '183.869523255532401819448585808825', '184.29837729870219316394095155319', '185.07308673645669839958359960', '185.4298151660377727101720877345', '185.82513739532196483830548279702', '186.40242965619088561587254829352', '187.20413397905290853905224880127', '187.59021324323922680709703639139', '188.30680207242091119344784123843', '188.64070529310545770434005200667', '189.41990177657423525951564353575', '189.83863065758807568735865118111', '190.15561365147062548218984730766', '190.92875073238619837932905942269', '191.92698250273503144608042893422', '192.1706690105343893703402329416', '192.51160910665690025419369887821', '193.03644437161529898918624208964', '193.54056773315702220629955156719', '194.162101652478806784256515994789', '194.67834668169416817784552253888', '194.87130109320295536914681232127', '195.64886476935034782113221869576', '196.219666124648923897508790607971', '196.471084377018257573464854401910', '197.453242372080436816463514484929', '197.99726627332136876800489108210', '198.719622190927356530546491755272', '199.02872576138974466470391008494', '199.74416466117253709093971594972'], 'prelabel': '1-3751-3751.1264-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 17.41957076659139, 'root_angle': -0.23472675719017763, 'root_number': '0.0958173896182192736119614400508-0.995398928996184104977995651416*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(330)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.12373481002524825944516204807-0.593551853938682728620523831049*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.79844817389', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.49903172547', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.13040807737', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 17.41957076659139, 'bad_primes': [11, 31], 'central_character': '3751.1264', 'conductor': 3751, 'conductor_radical': 341, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3751/1264'], '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': '1-3751-3751.1264-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': '1-3751-3751.1264-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 17.41957076659139, 'root_angle': -0.23472675719017763, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.79844817389', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_3751.1264', 'Lhash_array': ['dirichlet_L_3751.1264'], 'factors': ['1-3751-3751.1264-r0-0-0'], 'label': '1-3751-3751.1264-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3751/1264'}
Lfunction data - 1-3751-3751.1264-r0-0-0