-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_828.463', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.7860530947427875, 0.6181589862206052], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.5800569095711982, -0.8145759520503357], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 88.98095772994952, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [23, [1]]], 'bad_primes': [2, 3, 23], 'central_character': '828.463', 'coeff_info': ['x^66 - 1', '0.995471922573085 + 0.0950560433041827*I', '\\\\zeta_{66}'], 'conductor': 828, 'conductor_radical': 138, 'conjugate': 'dirichlet_L_828.583', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^26', 0, 'a^43', 0, 0, 0, 'a^91', 0, 'a^56', 0, 0, 0, 'a^6', 0, 'a^93', 0, 0, 0, 0, 0, 'a^52', 0, 0, 0, 'a^28', 0, 'a^35', 0, 0, 0, 'a^69', 0, 'a^18', 0, 0, 0, 'a^26', 0, 'a^97', 0, 0, 0, 'a^55', 0, 'a^20', 0, 0, 0, 'a^54', 0, 'a^51', 0, 0, 0, 'a^89', 0, 'a^46', 0, 0, 0, 'a^16', 0, 'a^41', 0, 0, 0, 'a^63', 0, 'a^60', 0, 0, 0, 'a^2', 0, 'a^67', 0, 0, 0, 'a^73', 0, 'a^32', 0, 0, 0, 'a^42', 0, 'a^33', 0, 0, 0, 'a^53', 0, 'a^4', 0, 0, 0], 'euler_factors': [[0], [0], [1, 'a^26'], [1, 'a^43'], [1, 'a^91'], [1, 'a^56'], [1, 'a^6'], [1, 'a^93'], [0], [1, 'a^28'], [1, 'a^35'], [1, 'a^18'], [1, 'a^26'], [1, 'a^97'], [1, 'a^55'], [1, 'a^54'], [1, 'a^89'], [1, 'a^46'], [1, 'a^41'], [1, 'a^63'], [1, 'a^60'], [1, 'a^67'], [1, 'a^73'], [1, 'a^42'], [1, 'a^4'], [1, 'a^40']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-828-828.463-r1-0-0', 'leading_term': '0.948247600266961573009932778156-0.185240834235550290865468046143*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/828/463', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.9661716607727299, 0.2616309363783394, -1.032691045806428, -2.2546611382507153, -2.610641333255202, -1.643068961910254, 0.32836773994795715, 2.242208639497023, 2.9585062164523386, 2.1380225584326187, 0.6003508125407746, -0.27168918427632993, 0.2890278099969432, 1.672778013879048, 2.336432598777082, 1.2040983996937973, -1.2029999421624282, -3.0543610045746643, -2.8103620025558165, -0.6979014294316738, 1.4177829719767303, 1.7667781638394409, 0.367470356031597, -1.0594234823179005, -0.9511414193844945, 0.3635178595052894, 0.9562723935839083, -0.5720128199339891, -3.3725699235376667, -5.006356872898807, -3.9289044695764774, -1.157108849148062, 0.7799328209335092, 0.5448322809776458, -0.6377362468748484, -0.5254581944200211, 1.4161234717266764, 3.2865916037846086, 2.9565241559702793, 0.6679208365363443, -1.1073420010192523, -0.5196609276316781, 1.4275732783045125, 2.008895217844833, 0.032397576029726094, -2.667276635046867, -3.369587348468939, -1.7062197525857576, -0.03897847988987097, -0.4839794866621412, -2.276725114474032, -2.8177190495108175, -1.1205468482331642, 0.748748084332536, 0.20629263249093333, -2.4691791755039088, -4.27840816732329, -3.1411090136354156, -0.4741818049105451, 0.6120112881936418, -0.7745934152793282, -2.320365566772529, -1.6941474882053273, 0.3284593700044548, 0.9901302508403187, -0.5558686193149571, -1.8759723348708799, -0.4310769935030091, 2.8343614188929944, 4.382628467411037, 2.4763288705096307, -0.6507282349782582, -1.7096932586073228, -0.4492052928031336, 0.5281111953106651, -0.1998895211838724, -0.725634240558273, 1.3463987221502607, 5.017816954242253, 6.595743989357632, 4.342090992754982, 0.8149906845393634, -0.39713905958756424, 0.8097982202706983, 1.3907892173628276, -0.2919987363268021, -2.1765178604065842, -1.670812606255632, 0.36010341418188935, 0.6682480215020594, -1.6368233140562767, -3.5138461037264364, -2.067068794520662, 1.3556768776254535, 2.895530937166537, 1.3865800183620152, -0.2968085126989769, 0.4273756788265919, 2.1625875567107853, 1.8188483886914937, -0.57319383584175, -1.715135056355658, 0.10355177035254905, 2.3013136376039287, 1.6024203281121265, -1.1916676343814503, -2.2814628085893904, -0.33266524205615505, 1.6328717301553561, 0.6908864875132028, -1.751146651107661, -2.1667012012977285, -0.20346141954911942, 0.8912528410179735, -0.68165726179873, -2.450091911596186, -1.4625003761247397, 0.9932074917474832, 1.0352912890261665, -2.034700080993159, -4.44689478623015, -3.237096589921588, -0.3403878848195172, 0.4805085177805333, -0.8947747174094801, -1.3175121388797049, 0.2551439958876261, 0.9418069595227296, -1.343050222377879, -3.997044644053298, -3.0592425026711636, 0.9321728028329773, 3.4318790304266424, 2.1852427940516472, 0.016116457827391115, 0.16179119606006354, 1.5299143115823701, 1.0856893989910081, -0.7339780969936238, -0.43120412656509166, 2.780494269912125, 5.066926882324319, 3.3722655853030856, 0.046344592408935036, -0.5173260398140125, 1.769508978771773, 2.969823908450598, 1.360691849746137, -0.18686206863148658, 0.7988204535786766, 2.249482084698863, 1.0275240457208596, -1.589639970742774, -1.4745323737458502, 1.8656780578519088, 4.125323489313886, 2.461796711984468, -0.4300004203520658, -0.6895172011973819, 0.8859858363770428, 0.6856304479275594, -1.453913353667633, -1.8521784434158006, 0.8731066217247533, 3.1877316104312983, 2.0154548329468613, -0.439304500167712, -0.2708170957145515, 1.8167589827156552, 1.6706281582258629, -1.4602967812530387, -3.4297937234705604, -1.5556514552290568, 1.3074695624334898, 1.404018970459055, -0.22297070277120282, -0.14044073850410513, 1.239807274861299, 0.2000264198325638, -3.6744437146280577, -5.882552946230385, -3.5730568901277673, 0.021954691065238733, 0.4854131017403414, -1.2941670907103606, -1.246650264389663, 0.9821094508377424, 1.7458677229373083, -0.1239587979009477, -1.2101710395974496, 0.5474208833100865, 1.9290161606701897, -0.4770682721870649, -4.284815834141759, -4.493131130877654, -1.0591339499221153, 1.2199489302362236, 0.1542582387923443, -1.1694431822169131, -0.34342997922785207, 0.26069199198142534, -1.8128172326600724, -3.940273788245026, -2.1606300541117234, 1.9964544136155407, 3.2053750027275623, 0.3391180324203427, -2.0457152973316455, -1.0108349369554044, 0.6871904178957834, 0.04523249950100328, -0.8970061973234459, 1.0377601749030327, 4.006505049688585, 3.680694832220472, 0.5006713419164037, -0.7396062430764677, 1.3716317626840842, 2.6614136417079353, 0.43579424767817737, -2.0226044415345514, -1.018579050065163, 1.411049858543585, 1.1048125370346384, -1.187042119669788, -1.3877781522092643, 0.5863661342729364, 0.5756060860359042, -2.436967472575729, -4.119579574554319, -1.8905436698008389, 0.6413913549353253, -0.39449368577674804, -2.742584453347173, -1.948343741449143, 1.1305914370496792, 1.9333225414298139, -0.09633705056322744, -1.0295837317774685, 0.26139066530270316, 0.08325398009116032, -3.1162466993704245, -5.1123193301704095, -2.500110491041074, 1.4136841810901488, 1.6558989611011754, -0.6824067106709658, -0.8476714485563571, 1.4876317820375147, 2.2642767517375537, 0.5447153399796693, -0.05284344580302889, 1.5827915562231964, 1.4423626265475518, -2.5162163748494346, -5.812064584965632, -3.9632036437476743, 0.4225341928244757, 1.8519884114329952, 0.2857143827299737, -0.18609121816750354, 0.8756444635570171, 0.027723480332665994, -2.7618784086634056, -3.0139949050206174, 0.5379247139526521, 3.004296345886235, 0.9969908694284876, -1.9028906524704623, -1.2661252798098437, 0.9698797583512296, 0.40539279937767103, -2.0200662381015846, -2.0286784878462436, 0.12316860657057443, 0.1685625104574613, -2.2164878251739535, -2.5078762993127945, 0.5634020440527095, 2.3033316690591015, -0.06957666451531275, -2.5806468594129837, -1.24754283652759, 1.2968170659348819, 0.7232939611279656, -1.4642889011218883, -1.05141469693687, 1.045940531506774, 0.48724445924383786, -2.341236972339644, -2.6187970222901673, 0.4203532506742572, 2.0054480303449265, 0.2310222933631499, -0.5739354473579512, 2.3383346019424507, 4.937558953998774, 3.1320680591586347, -0.37861580447382787, -0.9843640731857125, 0.2403426778090736, -0.37325454544867753, -1.6018138815650416, 0.3632996239124133, 3.8953323133359934, 3.391939082752452, -1.3673209085260194, -4.2863496490525455, -2.480483624041812, -0.0622841791422294, -0.2792276393738682, -0.4323946153438073, 1.8754729965453332, 3.472025599939722, 1.4361372661542977, -0.8336995019981002, 0.859839055212215, 3.8207317096032787, 2.7051972905595023, -1.3112993210215054, -2.5203021665138916, -0.25088346103349485, 0.7504553077654262, -0.8832928334514132, -1.3565537031672714, 0.3708509773478276, 0.26361179279692026, -2.859933728544562, -4.045148719199194, -0.48471805480549124, 3.1216089036616115, 2.0824271711565245, -0.8481806209248599, -0.9225000050806329, 0.4717792173787218, -0.5625672573965623, -2.4634255030295904, -0.9967238947123263, 2.4377642569009943, 2.763260564619504, 0.2771152242918546, 0.15730052306730896, 3.039679491318993, 3.7993869385149837, 0.8527564379138862, -0.9467742546244562, 0.9275449283733596, 2.2759252602755398, 0.03693211341355239, -2.16643457763735, -0.8565872826254056, 0.9887980243178934, -0.1392447228646053, -1.4097454347847633, 0.9944916859097509, 4.100211715137339, 2.7947791860394364, -1.0421467594559677, -1.5505044819764557, 1.1816028735175705, 1.9412969022118693, -0.09891103084866754, -0.7021300020758758, 0.767340576697827, 0.18076425972904034, -2.7947908853262, -3.0679850566938582, 0.6531722518688161, 2.720719959502897, -0.026622991165953895, -2.8975615473363163, -1.6236769949043017, 0.7107282917049226, 0.08222080717378143, -1.3006640652186396, -0.19062269688075878, 0.8088414923501035, -1.6534665994490543, -4.234987806972951, -2.018945809258387, 2.406073196756206, 2.788537562752179, -0.39206882458165926, -1.4099064691952183, 0.5226730259962821, 0.9065313640458466, -0.9410683760920524, -1.0306708405774, 0.676093374825246, -0.5785381341676672, -5.025625647426883, -6.574813620413885, -2.9011186001372935, 0.6046956365800297, 0.22939896802714466, -0.44453986153488895, 1.5843112095597227, 2.7521094465583253, 0.05672686100785605, -2.6079762028604163, -1.2542709596801356, 1.0347556018581632, 0.1875489299790945, -1.0966606476792549, 1.2081544312285373, 4.0892123019070645, 2.4229685057689427, -1.5719137298199735, -1.9942321072446556, 0.5993951736512291, 1.101778584344269, -0.3849395644752066, 0.5365392688732633, 3.2735159251743955, 2.874865279674439, -0.4404539766440716, -1.346654981028121, 0.5961535545328618, 0.007151898818268984, -4.008225607247272, -5.612177768098784, -2.5384563302421475, 0.04485689353840315, -1.0147616520890634, -1.9196357226489975, -0.08092543688625603, 0.9976548462435624, -0.579895395313257, -0.46400969614092097, 3.577702735798831, 6.093078978993582, 2.7935247795035325, -1.765824174367553, -1.8325110062288612, 0.43759888416499865, 0.3766848627602836, -0.606388427311699, 0.6462487567118884, 1.4893028968843147, -1.558349457800242, -4.800281732630436, -2.8303728463864473, 1.7089100885310182, 2.450678364165868, 0.15238124091963895, 0.3121929140776608, 2.636475014288897, 2.2296181146110894, -0.5471893322463702, -0.8830611488075157, 0.923372489338619, 0.1916333308069668, -2.384729766813769, -1.3419421657444595, 2.993977472782349, 4.19775656631486, 0.9264826482387811, -1.0861607077693631, 0.3386865367905401, 0.7217629130878077, -1.4737302471039415, -1.681042959547431, 1.443914048364026, 2.7807314983878295, 0.298581696966518, -1.0873008666525603, 0.9299189033284389, 1.5158490130217952, -1.8353014130533187, -4.022997754544571, -1.6629739033225528, 0.6534858193518097, -0.955757280804133, -2.7016603127425682, -0.8789451155460357, 1.092187045660446, -0.18515261623021273, -1.282347442068046, 0.8671894484735356, 2.115046033516328, -1.2120714790995464, -4.499402319719686, -2.526107519899021, 1.2383270132652078, 1.0404853837413228, -1.277470248145549, -1.0294937507135147, 0.2617029547692185, -0.8557074272364181, -1.6790414916909768, 1.4671893311387956, 4.71761629561444, 2.5820221743481278, -1.8501789297839737, -1.9430789041312688, 1.136048104176508, 1.5536205198677642, -0.33755517911808736, -0.03058711284309702, 1.4676729371247514, -0.028192314443401992, -2.610293434635699, -1.3800545235604393, 1.538450293008336, 0.21509589168463517, -3.882157153858352, -4.151971477324388, -0.678533512391249, 0.5382014102424255, -1.1462500624959344, -0.9292524332189942, 1.250345747412407, 0.9510032858152679, -0.957858712620543, 0.7030303747108123, 4.8343350513945715, 5.017540725457477, 1.1468639112950423, -0.3829161304826275, 1.635958021303075, 1.9501811911218527, -0.2478947688473611, 0.06176207393019212, 3.2097758388169138, 3.642978052907938, 0.6090355095000007, -0.42607688618242645, 1.5581111964647825, 1.55778150324084, -0.8933154252795914, -0.3356174303898341, 3.564496922238008, 4.351561821069003, 0.47258209381280336, -1.911259504129073, -0.23002397380924483, 0.8147415856626918, -0.6877916476535119, -0.6793995753036242, 1.3495520788785191, 0.32047490303104575, -4.004668791755204, -5.105216991826863, -1.3308082880706222, 0.9940883595035916, -0.7726964942271872, -1.3814257170130273, 1.5305490029669846, 3.0260528761329533, 0.8313805854864822, -0.6488666855546248, 0.18992861868419617, -0.9325730893837336, -4.279688160340986, -3.7667116110587653, 1.6167526245199588, 4.589644430205999, 1.7914942910334974, -1.099135962492769, -0.28183992382948597, 0.5781110245322779, -0.4982256067325187, 0.2814018053705475, 3.3413480249107894, 3.0949186504930055, -1.3770878237828794, -3.413282764829368, -0.5637487847372213, 1.178376152361355, -1.146821493773286, -2.4503421456627428, -0.09449778536002579, 1.3268060176068317, -0.1546555815708986, 0.09124597065956758, 3.314032441991211, 4.0657257806791, 0.8495357135504658, -0.5678662641394003, 1.697429079991819, 2.016840229378005, -1.4737764104226079, -2.9701479781073323, -0.22641035926473074, 1.2735666671307133, -0.8399442469317898, -1.7245232422539538, 0.3321340514698013, 0.4759801068273616, -2.3474903758169328, -2.671078879422271, 0.5403438644885667, 1.374129495667431, -1.472782949400224, -1.9514450803939294, 1.4906029748092442, 2.7635528989901603, -0.14930206020534184, -1.7022151142577933, 0.1805106998484945, 0.9013887787253501, -0.5540370019871761, 0.34707429424652136, 3.225177231153781, 2.089853470706349, -2.8044056966566098, -4.152863575406588, -0.5726209625093192, 1.3279972319774824, -0.5603513783201256, -1.100382648525652, 1.0073673306605504, 1.2520687932126238, -0.4970553444739442, 0.3281603473595024, 2.458404998246419, -0.049804017661137324, -5.685796954293052, -6.61267637806435, -2.1754112698094685, 0.6368370385413853, -0.031187308401799858, 0.32603323625747105, 1.7321977084409825, -0.07347324353239115, -3.3820106845688898, -2.5540557873695073, 0.7912223226767527, 0.45183934705437556, -2.285138460275258, -1.2012681190822658, 2.488614882158939, 2.46505317016437, -0.4738998652852441, -0.5409217642324902, 1.492682574919668, 0.6975813874881571, -1.3541032270131006, -0.025744184217518628, 2.070572621064268, -0.19661199774099783], 'positive_zeros': ['0.383611296021801691320563210286', '1.82738797177626585919969037536', '3.28300468689906456467243500251', '3.66367181814218341597381827471', '4.85142090789095513783736191377', '6.026253577233707471538411708088', '6.94064294741030108709075322298', '7.730725653138908533698060243869', '8.36003466107916073331426253552', '9.834960946431753298302560339506', '10.44979019786092469245601645095', '11.046276839235513567951241663807', '12.2749270994611694303392979569', '12.9000559108045827873300931204', '13.753560213259410480621702626959', '15.017584093496808655034469719975', '15.173698260598114595477323732173', '16.40775823243060356121491944171', '16.9059470121026529321908350154', '18.19569252878793235765267390420', '18.62057941600361586236858323556', '19.63314969954109483417972074911', '20.225105317187547748732723495991', '20.98256010439089326707875027124', '22.11320065749533974070373492577', '22.90629775174255936991163735789', '23.38283731199377036854310784108', '23.91399179514854108077656261434', '25.42613638666141421867625091242', '25.765514032929281665621314448174', '26.523172406051946502919502529280', '27.4388260781782563334838714892', '27.93108024525454275295588478561', '28.93726561846751304141957602549', '29.90812620572546857375605157916', '30.22770750937515331353713695635', '31.17827919114990331609501924902', '31.86297289165419748091580444201', '32.68123127205112752994354276272', '33.47666782247120175947472622072', '34.149685193124862720990289131596', '35.03042021296948052127379418635', '35.52947106421871511577557987968', '36.426163786178791475009820812859', '37.003311099867540180132530918721', '38.17576820422949936157826178077', '38.570851250950426732099442829575', '39.33110354880193158440374474575', '39.8583311864383810493332347720', '40.86789589377007971634585292933', '41.879100533490419596200192024173', '42.14519048570286067119620801608', '42.99068460747703575873014790717', '43.493929334937001858734008575558', '44.69344121660190270487321399969', '45.091060366841385478890293761816', '46.16866791077541311127637571743', '46.40158885743293473291538194887', '47.30286998081117927573398956099', '47.96852108573824033192441313954', '49.00190342610889888796208636112', '49.51218943903320613866974167747', '50.10952425928407272852546518263', '50.8555974634015090113106491544', '51.80200081517949030615046297375', '52.23232570377884968392336870854', '52.99454869248503868552562935037', '53.90013923689116652854925167195', '54.63549291050738310430461972581', '55.03271348425543266945739644575', '55.64564060666749572756605800336', '56.872197510315566180810006813063', '57.28084211157363329774915907419', '57.99486267168370602961522650986', '58.73255322876188585849497503665', '59.30377038576238926609963821210', '59.96156272398097315582518423326', '61.035209746403586302230135771522', '61.58757663722599044845584490100', '62.26971355069023814016152439727', '62.57479077019464057236389734451', '63.59666911344800256322999770225', '64.40525613042596390238775595006', '65.15015356892910948402287578443', '65.63439578710214148482688711834', '66.1376048898037750444958962300', '67.244358195486243336993113605158', '67.64485640631254988739684220403', '68.47961275714329980949209937374', '69.18043632400867780730897897377', '69.836186691305528208576348811907', '70.53095141282896859436509928316', '71.01480188243622191234445147479', '72.069442529809673481319788309', '72.44868213891632704251363333685', '73.31921669723430982677762008385', '74.04873176815217450629049807013', '74.62965576358964272672663321269', '75.01265057129373678836661765843', '76.117757957900732542865638765495', '76.77905777168232581108474900178', '77.313743279509493442086225363610', '78.24081741391405675066037117661', '78.45485282675118648046324638088', '79.20228501177671750899004025571', '80.27717928627571403426657452337', '80.99961820846504229098273557893', '81.31304606902112450221497845234', '81.878643034865171688850362765996', '82.77159696270938590288504195553', '83.525899443003692738620539608914', '84.220630014528369458299423311614', '84.74095053648856296888953386381', '85.60374749375153996437849322140', '85.96606594910106358250579404507', '86.82423598851412083499853181802', '87.49372150568806114886326265735', '88.25640800247898968478023713546', '88.84543942419800454166711209589', '89.520436178673973927313814577923', '90.058612482224728942239793354532', '90.89754563531700198007493826558', '91.59590763277117960404027490560', '91.971291254130646458534949016422', '93.08131451182767830743141778517', '93.66970680740775192588239981444', '93.98272370827114284645598332544', '94.65526791796038926631955719324', '95.54193806460725643583690849738', '96.58198185350474084822501927203', '96.77442835704763715302551720543', '97.27359105185712962918062567706', '98.27606902594947075620114910248', '98.66193493525438024374386500733', '99.58161476572664405503481540275', '100.3460642584979252403149736441', '100.79309320166831239510186287396', '101.4963975285738203557276933919', '101.91135818443989066968060883932', '102.8443334787625869964516581403', '103.64172757414423578366966667800', '104.23930246936339360648226320437', '104.601234400245748806868459124121', '105.40020861687569597692199350136', '106.29682371208335568606134853212', '106.53542360701633926479698012755', '107.58659787328835996703178058210', '108.01200581730008075692642944006', '108.75362605008209471886881135366', '109.48367005992729134706256953956', '109.97937783710618681862326354528', '110.538417221582453953706780502172', '111.46738539812460362053081543617', '112.0590958771349191435492571193', '112.79744557764819553328192390970', '113.27988219319484858793274590155', '113.77270135235018616068305450294', '114.63836188103816176810534750965', '115.3104060225450295925141589444', '116.12246385630199117409452130911', '116.57652177023089687807713678335', '117.21880230278594163445309704217', '117.65248718764859644281868841987', '118.56993092374513746391983791259', '119.33529642035139947718151155169', '119.92116081723869074089504994662', '120.473033389805177132901287897579', '121.11311372802974550039648194136', '121.505649755779170890174611455764', '122.72494704298749415978873183096', '123.1740822044312109278880333566', '123.54284194559879416117651209577', '124.3797471729140364199423302381', '125.138714904005297068236843222674', '125.6537373278830048169764489488', '126.138309512091634779870923162725', '127.05261471459660939746475566940', '127.737297660305538797452987721720', '128.340831211598134268721480108518', '128.675941784062931234470320334', '129.64307734835544941845471979258', '130.21573559559759485997765004417', '130.62575942039805997857901364867', '131.85601552053118982606670122858', '131.98384798213021909106031955732', '132.8236904227194552208462515778', '133.34082805954393552109248179696', '133.80164497559091838099037106946', '134.85529080322802255712616492268', '135.549963105530522966192455041819', '136.02453714463725940220951190862', '136.45471876199375716844948460860', '137.067735728903921758402721807247', '137.995756669294932844456520333849', '138.77962859436176641160741149314', '139.00621809665829901421278356881', '139.93131429978601698231064469461', '140.45954327919677554913798477076', '140.960836168245815563972552818204', '141.66496385769144165944426079107', '142.585768670159263682328625667598', '143.06842232761591170603176168810', '143.55740685698026299548497690063', '144.24462787454059946823320217630', '145.03262578561997722002392467156', '145.50821055124626318152127437329', '146.10500176372341397357703944853', '147.04236230122837333076894769733', '147.38266908601085485778964494968', '148.22336709988573547051708789702', '148.723052823723140199433793490501', '149.27913909712818386312885059078', '149.915767345906943039791491701476', '150.81262818069677191839258702990', '151.378995879651407022471888051481', '152.07891054235962332054976751678', '152.342098644715219311340964233891', '153.01632689049122506676303052930', '153.9163372770729696279646715778', '154.56769198347484762647548110890', '155.24556714256824407352233230910', '155.63061668771652885004608455807', '156.24704525526567892332113031391', '157.00271646919575251172286595513', '157.51736390755795877355464093109', '158.51269559005735616549096611397', '158.86755555335907639310693638925', '159.50472924022020811131589250072', '160.134523973791791027799652611762', '160.56274070444772850654673073215', '161.682151484121680059956791130749', '161.96064090115754384140684558479', '162.77216244949971533463719103054', '163.11694669022324425275160845825', '164.13605816179588894780159373289', '164.46194661429035671097397478282', '165.19301522433984750037943377225', '165.657506447778082162382735640565', '166.59799559964528916736854081188', '167.219524141482656860666220108831', '167.687894470050763434496725453083', '168.23088322935640333409681124057', '168.77750160479506936942789161183', '169.79802779535947109571963973124', '170.2108340304438263913177108033', '170.79545820919790968198064074100', '171.66923848208229140048043269334', '172.117112377506101612709639247351', '172.36980900038850065213090554096', '173.350799772227649703981554894946', '174.21087484230298426184727832775', '174.74024121597612139068564347024', '175.181093119216896113480640990806', '175.588162662056893742526487028102', '176.472411153406038010357526132753', '177.24000173009929564993983276876', '177.69197953665448226895021621511', '178.44792855151811341964730936008', '179.032414441344464327710442416034', '179.362143931518930608752769537402', '180.40159798484195771075980042521', '180.732381125541996619370167619088', '181.44386460089824804518352091106', '182.209942306817254006163337532046', '182.71158084182071512149124119243', '183.38922233414528771127096666132', '183.81458943900082238820318423058', '184.63566553374754905082942833815', '185.16527988442115792720099372811', '185.81460404830925602862684823363', '186.54847085200867202874731499815', '187.161916061720362295884405781324', '187.68981411106045145438410830203', '188.082317595810772686797283999443', '188.88743823328045233539775671519', '189.73584893554525315894375441669', '190.23621541864175542160857665687', '190.797234398807788902364529793413', '191.458667671530058347013142099437', '191.83050521184100447659029069947', '192.497032057010644277633600375623', '193.618000293682096549999893939485', '194.051465662174234406621747042870', '194.29843494431759047600059986436', '194.993516142453606822108200220164', '195.84835352235717319600233531627', '196.30025602126651463624490162763', '196.9731895956358910167543293181', '197.75336286511560741368271658021', '198.204572781836823263801775329941', '198.83703226783880490686250605925', '199.37784555738696500085449913522', '199.984990567856775368044023914819'], 'prelabel': '1-828-828.463-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 88.98095772994952, 'root_angle': -0.06140869659921469, 'root_number': '0.926481800512144271560869342049-0.376339571822809123239776606761*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0614086965992', 'prec': 54}, 'spectral_label': 'r1-0', 'st_group': 'mu(66)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.769178309795380210285268591758+0.0265392407765372957808810010624*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.383611296022', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.82738797178', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.2830046869', 'prec': 40}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 88.98095772994952, 'bad_primes': [2, 3, 23], 'central_character': '828.463', 'conductor': 828, 'conductor_radical': 138, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/828/463'], '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': '1-828-828.463-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-828-828.463-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 88.98095772994952, 'root_angle': -0.06140869659921469, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.383611296022', 'prec': 47}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_828.463', 'Lhash_array': ['dirichlet_L_828.463'], 'factors': ['1-828-828.463-r1-0-0'], 'label': '1-828-828.463-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/828/463'}