-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_85.48', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.7071067811865476, -0.7071067811865476], 'a3': [0.3826834323650898, -0.9238795325112867], 'a4': [-7.040766286173228e-31, 1.0], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.9238795325112867, 0.3826834323650898], 'a7': [0.9238795325112867, -0.3826834323650898], 'a8': [0.7071067811865476, -0.7071067811865476], 'a9': [-0.7071067811865476, -0.7071067811865476], 'algebraic': True, 'analytic_conductor': 0.39473834048527545, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [17, [1]]], 'bad_primes': [5, 17], 'central_character': '85.48', 'coeff_info': ['x^16 - 1', '0.923879532511287 + 0.382683432365090*I', '\\\\zeta_{16}'], 'conductor': 85, 'conductor_radical': 85, 'conjugate': 'dirichlet_L_85.62', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^10', 'a^13', 'a^4', 0, 'a^7', 'a^15', 'a^14', 'a^10', 0, 'a^15', 'a^1', 'a^8', 'a^9', 0, 'a^8', 0, 'a^4', 'a^6', 0, 'a^12', 'a^9', 'a^11', 'a^11', 0, 'a^2', 'a^7', 'a^3', 'a^13', 0, 'a^1', 'a^2', 'a^12', 0, 0, 'a^14', 'a^5', 'a^0', 'a^5', 0, 'a^3', 'a^6', 'a^6', 'a^3', 0, 'a^5', 'a^0', 'a^5', 'a^14', 0, 0, 'a^12', 'a^2', 'a^1', 0, 'a^13', 'a^3', 'a^7', 'a^2', 0, 'a^11', 'a^11', 'a^9', 'a^12', 0, 'a^6', 'a^4', 0, 'a^8', 0, 'a^9', 'a^8', 'a^1', 'a^15', 0, 'a^10', 'a^14', 'a^15', 'a^7', 0, 'a^4', 'a^13', 'a^10', 'a^0', 0, 'a^0', 'a^10', 'a^13', 'a^4', 0, 'a^7', 'a^15', 'a^14', 'a^10', 0, 'a^15', 'a^1', 'a^8', 'a^9', 0], 'euler_factors': [[1, 'a^10'], [1, 'a^13'], [0], [1, 'a^15'], [1, 'a^15'], [1, 'a^8'], [0], [1, 'a^6'], [1, 'a^11'], [1, 'a^13'], [1, 'a^1'], [1, 'a^5'], [1, 'a^3'], [1, 'a^6'], [1, 'a^0'], [1, 'a^2'], [1, 'a^2'], [1, 'a^11'], [1, 'a^4'], [1, 'a^9'], [1, 'a^1'], [1, 'a^7'], [1, 'a^10'], [1, 'a^4'], [1, 'a^1'], [1, 'a^8']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-85-85.48-r0-0-0', 'leading_term': '0.483505959606458003428691613489-0.656076337879127051214765971974*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/85/48', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.8149933583164026, 0.7391293592406356, 0.6511076493237276, 0.39457521069618795, -0.009950031881331558, -0.43027403707444517, -0.6821378942675725, -0.5991337697620369, -0.11140240314328631, 0.6921723323380946, 1.5509118409323992, 2.0905697736116027, 1.9486278510531991, 0.9293741033245583, -0.8733223703418967, -3.048982240567621, -4.973254349308981, -6.0210130418271, -5.814183909057768, -4.397738491135934, -2.2531009862332585, -0.12219953713351434, 1.2964018712714656, 1.647236425687534, 1.068631868029172, 0.1102382998427113, -0.5543610796704889, -0.48185134349492287, 0.30433216474527836, 1.3291082828895036, 1.9359215077742236, 1.6712029897200225, 0.5665313522632218, -0.8536165037053237, -1.8599202903029723, -1.9465979959583903, -1.1469131325268636, -0.03237660310636588, 0.6265564885016686, 0.34841310533058567, -0.7241624453707227, -1.8727793764750174, -2.239523927001583, -1.403523386765489, 0.2661538404000659, 1.7366609540958988, 1.8864442021523176, 0.20564991862590215, -2.812145457887908, -5.859978067952379, -7.512676828719368, -7.025990118237511, -4.752904172786347, -1.9142886873881888, 0.13654320622725621, 0.6924617272274565, 0.0248822768871952, -0.9228281540750567, -1.2465990284728024, -0.6958735401091659, 0.23034065993412572, 0.7491808621300312, 0.4551227111710596, -0.33459756043079614, -0.8270626988542078, -0.417544520618887, 0.7433456914513314, 1.7516471645878542, 1.5812545622552008, -0.08757056761255178, -2.472647963457433, -4.086341047324084, -3.7125211313387023, -1.2943722200198073, 1.9258736147333653, 4.1691935322660525, 4.286378056524871, 2.513202285322605, 0.2688039161311069, -0.8655577512238978, -0.251181416288311, 1.4199926553654312, 2.722049089723467, 2.6085121505838407, 1.1913079669907687, -0.39910793736394334, -0.9410238355830274, -0.09407902666992576, 1.3508731861534056, 2.1307077167453174, 1.5347478450779088, -0.03842320601030236, -1.4387166152542088, -1.7287054620425346, -0.9419863574068413, 0.0053561734072349355, 0.17376507758777665, -0.5174288802373603, -1.1798078566469736, -0.7696953743665621, 0.8381952549933502, 2.473605173819588, 2.4259710310586033, -0.17554152560003072, -4.455245446428379, -8.166125918377933, -9.170052032528949, -6.941910192728922, -2.943910987655263, 0.4314771613054195, 1.5410271252872358, 0.5112015951506015, -1.1301461768458119, -1.8185632260770341, -1.1552644199385425, -0.00010763890477240264, 0.504361964628421, 0.03280095344823416, -0.6922548739606962, -0.7027074811826257, 0.17265642353275584, 1.0405419308268953, 0.7467275625311959, -0.9670560197638457, -3.050191602179739, -3.9384728209035558, -2.9166491885749926, -0.8292092135277233, 0.5666089317393739, 0.1161984622648142, -1.6609561988008639, -2.9359358232166675, -2.1290507065928734, 0.6599975089626082, 3.6210456824161374, 4.686624768230837, 3.251321243352864, 0.6743555004656128, -0.8819434520642512, -0.2801350669307455, 1.6763648612488882, 3.013314611830331, 2.3351103295853264, 0.006527481770478705, -2.238854091870505, -2.8482162561120843, -1.732926588323417, -0.16719289419136488, 0.5073782216827594, 0.09693592297467074, -0.440592207018772, -0.12473252258248402, 0.9662421209328313, 1.7740592935842066, 1.4323129723880212, 0.32507511517868937, -0.13192416391091732, 1.0875722081480481, 3.336017514132899, 4.507372773754424, 2.7767013211293357, -1.6061979416188825, -6.152981956486051, -7.922289270200967, -5.8202620926467175, -1.452284944954705, 2.2098803711737465, 3.17853645468532, 1.79741406281341, 0.02917739640991917, -0.5012967120617522, 0.1524801950679759, 0.6790359656859147, 0.0980825879868677, -1.1492497629593126, -1.6847550770234707, -0.6992323888105083, 1.1059005541119402, 2.143180123271964, 1.52431594070513, -0.0067420627288883525, -0.7802957426432091, 0.11942765450229179, 1.8889429050686253, 2.7695551193928227, 1.8204060656605523, -0.08446228922949112, -1.10028287196753, -0.31780144463919435, 1.1855402512704811, 1.3046872087209103, -0.9517249800354581, -4.226888920508018, -5.810879043586391, -4.061702201046932, -0.010024211527130329, 3.406788233821924, 3.8309078598535136, 1.4238064508693598, -1.4765038109014017, -2.5573131624781436, -1.4725974494435659, 0.216459343788162, 0.8290848223780571, 0.18482746006247708, -0.5027567930062319, -0.15529215389335618, 0.9549085298149658, 1.5930422428265925, 1.0483179249236483, 0.004115523578242379, -0.24413645365665637, 0.593333968946638, 1.190268379994043, -0.1314395683028475, -3.4288095788883006, -6.565343506323147, -6.890586044417501, -3.7303140815207665, 0.743436169294903, 3.2595655224897175, 2.2790598273076035, -0.7383885243687642, -2.8153347975807903, -2.230148237956552, 0.07556520541581076, 1.700271175585528, 1.2511472318165018, -0.4284377926816042, -1.3918287870077755, -0.7513490915721824, 0.44196441474360637, 0.4648610246393338, -1.1012538779042202, -2.8383809084709433, -2.9726919761150707, -1.2642183882827156, 0.7284618400057921, 1.2827202298227265, 0.2735652860660883, -0.8300695611944733, -0.6875989147219748, 0.4119432223005339, 0.9716077735629136, 0.18370160057512758, -0.8687034612364759, -0.2241212972021731, 2.641947778977295, 5.712817625042465, 5.988170069284344, 2.39344517671321, -2.854408351456821, -5.9605232251389095, -4.8473570875855225, -0.9069591603052095, 2.4321524614565937, 2.85366572783681, 0.9593034294037732, -0.8297541094838732, -0.8822708515511457, 0.26312867423463354, 0.9468997911066876, 0.4232323836469537, -0.4517340184402059, -0.5042881932021026, 0.16522709045679396, 0.2431793574594282, -1.1162231298814365, -2.995765412139706, -3.4705245001902103, -1.737204281329206, 0.7652214131630564, 1.6769475636181175, 0.22993494661258343, -1.767835011932704, -1.7062652087990573, 1.0293188391937935, 4.2051244396980705, 4.855934853517605, 2.2603241014589814, -1.314022911015753, -2.8890559234478923, -1.708374096831002, 0.21280360365395454, 0.40719982549118483, -1.3945016885710944, -3.0928897743595645, -2.6095084699423747, -0.17840505626470568, 1.9220119276418963, 1.8146979469879574, -0.06750583506946661, -1.6252852829844282, -1.4365810652286215, -0.1432377212467662, 0.5612406627874688, 0.01296606103840518, -0.7481213199868083, -0.4380687217467437, 0.7201497985938751, 1.1636032992639718, -0.024102279207526632, -1.7046101191317042, -1.766988285646535, 0.2664939849785158, 2.0923744124772687, 0.5976671572086367, -4.801729907859783, -10.974876619211479, -13.557215930739572, -10.821812837068276, -5.127988716421822, -0.5677996183654771, 0.7207793172347767, -0.08700117990407344, -0.49637305125374226, 0.44458435690547926, 1.5066653645866792, 1.208635478046298, -0.21536765539109187, -1.1374703601005702, -0.614332321503825, 0.4013844265321058, 0.23867544922618747, -1.3336651997853395, -2.6274859600024767, -1.9386310904569126, 0.3453860549039885, 1.9856779056853593, 1.3523644923546358, -0.6828028382175247, -1.6836430217432306, -0.44930523778564707, 1.5305901935039643, 1.743844063885831, -0.35752118782527725, -2.4974724364169507, -1.9932581946661698, 1.1391960308747082, 3.910932198714261, 3.3894188371877614, -0.17926032142753404, -3.5492706405880985, -3.7763855743629624, -1.092789435345489, 1.6382630145937396, 2.089508935482039, 0.7056598652650901, -0.26798410865830025, 0.4492883121852348, 1.8757610418673993, 2.2329175193035207, 1.1737398733106328, 0.04530238720287709, 0.022366996258886582, 0.5925378712618273, 0.36428830618996483, -0.8413203626751451, -1.415622236117666, 0.07381502976146226, 2.630720073738732, 3.2653996280890185, 0.11966260008667891, -5.064598723146604, -8.152791040562173, -6.584307388078613, -1.9814588967562021, 1.44689557886006, 1.0691592906824048, -1.8209577745047736, -3.7990686245808534, -3.0494884581981863, -0.9268736349742773, 0.07833324669400768, -0.6957740975287499, -1.6426547959134037, -1.2110505962665103, 0.04391069619364528, 0.20992136715869203, -1.4371553488651603, -3.3122152817213784, -3.2822051899930256, -1.211102257099498, 0.8123590599063242, 0.8776781843831509, -0.5951059580687348, -1.534498381802451, -0.8484136635787276, 0.27733433950560804, 0.05822045722984649, -1.3297895909781556, -1.6501356440400126, 0.6285987762938186, 3.961598767213858, 4.880202396831273, 1.7554015131287128, -3.0243099261469792, -5.168370972452313, -2.8283782899614516, 1.5115886795913047, 3.657141516720961, 1.952709508973217, -1.3954072077664836, -3.0641344585039523, -2.0954354366369152, -0.3216145925697916, 0.2555699992796929, -0.2904625801088485, -0.4772603364468376, 0.26585534249882253, 0.7970156889071469, -0.036717093550539884, -1.5767104019505385, -1.9874501556874247, -0.6884738444421321, 0.5989112083711821, -0.17687654296660385, -2.6334544887085745, -3.941985969927295, -1.9790430495236322, 1.9125502613688927, 3.9967792297123106, 2.1390261498541174, -1.7422616967273532, -3.6551202740923574, -1.8023377538245389, 1.6416911269919494, 3.148778015918585, 1.7195207692931795, -0.40179016608025414, -0.7479510258259598, 0.4068683106388653, 0.6433715033456587, -1.3689976167474573, -4.061992377367821, -4.771811484892939, -2.8838916165394335, -0.4824953430164078, 0.18380860359539297, -0.7706427635132538, -1.3804384282082627, -0.5341549188557881, 0.6513244231288016, 0.4723801554667998, -0.9579866006666561, -1.7759871141872947, -0.8717862701024235, 0.5111334873454012, 0.41892131787763337, -0.8314862429447829, -0.32920819665140466, 4.10514792176458, 10.6311418763358, 14.334249533169366, 11.925978179475972, 5.204607696775867, -0.6149790003996959, -1.954270054574774, 0.12939079577810586, 1.937903607682858, 1.4144021813458758, -0.1963681443654166, -0.6771924039920322, 0.20774153755186736, 0.7664509134933759, -0.053576694832622264, -1.1978326787322888, -1.0422329731016144, 0.2540984554278962, 0.8561582399688247, -0.21565656738189187, -1.5096431077270358, -0.8169510177397259, 1.854829541715527, 3.883331480910801, 3.0092315833701004, 0.14637981021087162, -1.5655952259469206, -0.4992518707088305, 1.4754147762283853, 1.3087019371292379, -1.3447999218852795, -3.4782514520869645, -2.2706703686569867, 1.3947181426608612, 3.743312279445545, 2.3860985294648103, -0.9962350731873408, -2.7086829086584365, -1.3078973464238812, 0.9875126510035965, 1.2181715063961067, -0.7915084825007885, -2.511886993129603, -1.9894001086138793, -0.10325699016437229, 0.8382873889766942, 0.07219601795422168, -0.9439960708939179, -0.7791718443415719, 0.030251423480507682, -0.018680004281552098, -0.9562796333721375, -1.043873875381667, 0.6858686084824138, 2.4558808009161455, 1.4412469423883254, -2.4715495721101024, -5.623959927974489, -4.171175501803018, 1.4526601671471713, 6.4935580797906605, 6.663625365662536, 2.496075333101812, -1.5666553908144492, -2.1079066592259252, 0.0275067103971813, 1.5578560010724543, 0.9168687832586272, -0.370656114787095, -0.27755328583826816, 0.9507635898778237, 1.4233314278442384, 0.4858455638454283, -0.2302539515259515, 0.9242353686710252, 3.1088970722125437, 3.7463595112645853, 1.731668887004156, -1.0500419097724942, -1.9545630923950523, -0.7431386929971863, 0.39889493932660547, -0.023953153701947286, -0.7355583653596591, 0.49698903222974355, 3.4797465546419937, 5.2650542178113025, 3.692006590169399, 0.4222225866867294, -0.6539311950332326, 1.9338119005415932, 5.173779196714742, 4.857880933730226, 0.48606254009877503, -4.026163912472927, -4.675690464174157, -1.6115548000953097, 1.5280033811381104, 1.9846777597047793, 0.56279673653187, -0.19643920676431734, 0.5361291159425858, 1.267102444062426, 0.7158547813551589, -0.3103750116421129, -0.24397848351161816, 0.7946151200709147, 1.070433539377091, -0.14597040871148576, -1.1598969429522916, 0.03729467715105231, 2.7227668241607237, 3.784988783474303, 1.5840513186098852, -1.4315119493826414, -1.0864322277123324, 3.569360799695662, 8.683093179328678, 9.58133238345856, 5.788173051866146, 1.2378542570909623, -0.37090627765969514, 0.6073065587385864, 1.109442121399778, -0.32505328888955715, -1.888171292622472, -1.308091583629477, 0.8826656536201885, 1.978840102305387, 0.676303226387031, -1.230692803645595, -1.251092510360749, 0.5445655759739998, 1.7134713405928916, 0.7316792211550784, -1.0520732452149515, -1.3461713714045351, -0.019960474388920936, 0.8480696210802122, -0.03284852644268352, -1.349475038201076, -1.1612842748099306, 0.05924772198496553, -0.2064921180507747, -2.8054688592695474, -4.809103302837605, -2.4467827579212083, 3.991017803211072, 9.454120718333966, 9.104686731015903, 3.4598616995983638, -2.2657418160750966, -3.7845931242317636, -1.7569645295606706, 0.06862167125015277, -0.32983488766424224, -1.4764139781879149, -1.1990791875510425, 0.2781757049585938, 0.9814998181319552, 0.1900198788984802, -0.6243995281605448, -0.12257756635996377, 0.8331348259456341, 0.48345901670923896, -0.9543577762576284, -1.122357910306622, 1.2894646878872327, 4.242215281052527, 4.420502870044991, 1.388666600481696, -1.5882534215989899, -1.44601906582335, 0.8656154013263825, 1.6219317530377089, -0.8219335960257179, -3.757275367558842, -3.439213885083768, 0.15948784713046874, 3.205693497406513, 2.647385329717964, -0.25598393853808205, -1.8671168552964874, -0.8695972638633339, 0.3489067050141742, -0.81605420796184, -3.60404727228556, -4.875294281951192, -3.1745933778706994, -0.46317583043246446], 'positive_zeros': ['1.24294292325636769259470645234', '2.54966463234721573519823738463', '4.23696427884595079105771809307', '6.58318633413908131986664177376', '7.85100219543112826691617175627', '8.651038553636665302868709556093', '10.124050870248236340051526870883', '11.57262720307467449073060142976', '12.307758943115994055210283106955', '13.70336601173702337621071676005', '14.71249292873629549827927551464', '16.84486504699872211126419204871', '17.507846827989395203775661419393', '18.66915527010179125297751149865', '19.560195757485165615218198956725', '20.43890626938582189633499939135', '21.55021157288570519892875858065', '22.93773321246940343105155564654', '24.42140524154161508566958267263', '25.05434420036120617704310278252', '26.47151892910547702551463427197', '27.20892570631402607720163995901', '28.43042801628379852547250954308', '29.68499102492270388028005100563', '30.10930920992300185714454190656', '31.10662923970379651712503434054', '32.17264779578698079766590977993', '34.010239127861147131482934131964', '34.78102857633148098147960872133', '35.93753434454416276840503126481', '36.57558214180887800374933252188', '37.44984899621637635638219746308', '38.28627871365615706527280105002', '39.831170187862948560183943641188', '40.33831497020413797879743282275', '41.498567365910913548941909317877', '42.90850921083322211489757521178', '43.489717006794892409328324315334', '44.68827875843191751043382413374', '45.98102621962634999205321725254', '46.60656122255361661646932401148', '47.23161603943924314259985263937', '48.55293335281348849371573209209', '48.82515689830496761828020448701', '50.21022425351260892037414585952', '51.66771886107024783764589849925', '52.819612622975221292970344817048', '53.381059659970017825804526138696', '54.08938909090408005779719550655', '55.12341583505405936501697220257', '56.248522821566074944631534997241', '56.85112929131916160842256342583', '58.11013720794447190905834080089', '58.81438371240155649382439963252', '59.58659203011006562826031942542', '60.93823420506296839530280668688', '62.01682486946232902554377130834', '63.07753175758657924589173199365', '63.81356432836111056907177927226', '64.42551688963364068063916999924', '65.62655677111834129528401509695', '66.06093353163147644903955628922', '66.85819493720255715479098243052', '68.381582049572201990358337585933', '69.30111692342402232131247222102', '70.30254345782742320720900286921', '71.17149180061119921217572167286', '72.057667252001874908296502545195', '72.62133790797363799423232632250', '73.9328653814059583703308306667', '74.75051977242509076441885836054', '75.51420143891587180012406368096', '76.295430552710400936838092145555', '76.9096517805511631768185922627', '78.26614232250907996729229821290', '79.44387970712832525806614016812', '80.452788777996710026906737231028', '81.18265559012657011092642770026', '82.01157830160113179050140471940', '82.73680396184665657668223087125', '83.21340605480275885293603781345', '84.58321558834733893044729506626', '85.34492386581471793737516042599', '86.15448127376247278700854158759', '87.376620492747509647284304210', '88.392550526251044957416348288678', '88.846092055992541842330882170888', '90.02070493738133035129076554158', '90.92745956398288990850228062336', '91.91193359597550871131974117793', '92.50438894992317218931837197472', '93.2505404157414788585523060071', '94.05827037637174562155726921966', '94.966605130419966339545812161077', '95.671730903976141621717165103733', '97.56845262155739890069094446467', '98.097580145246506606146709611010', '98.638710501015351145546417225323', '99.642540551122611770905978170653', '100.4839827338372368304158574546', '101.00098155056291842497077192863', '102.14294342478628556400699039063', '103.021368307735528547687311925077', '103.81648025078820522303345167363', '104.64516461465064851713166869941', '105.525284185215597404122369191423', '106.54891250079396225520113009150', '107.60708483529640377246356388963', '108.604766809030491556315670370232', '108.94485186366699565312452492619', '110.33614952460209294439183073197', '110.610534390660585621108810899755', '111.359000905624966030104647649833', '112.17792928023158629331971375546', '113.13280284418963043092915057715', '114.52018390120554796963515668319', '115.12812485565940378080062566144', '116.475083675001962838479912646591', '116.65057079446640795859831212421', '117.79929638409006393379131067527', '118.18869965274400917820646436618', '119.536347103401646464470360291349', '120.19789229011047447940208133650', '121.150504406880060616935595415588', '121.57906588507619785137924873508', '122.4383355394373383836386453162', '123.54988450000230036311949431267', '124.575074172380482182950302006418', '125.49142705428416506379576754982', '126.64918803841640373875638711650', '127.04911433635086670196970822429', '127.72196057461921052400957818154', '128.42960947603047581059146400422', '129.506154363378836735611664965582', '129.9702142881815557917059572983', '131.097970424661583517991870804592', '132.0465863647532731620856513756', '132.97207240616883938745336323927', '133.98845118140360634851966059625', '134.58500663626965044002327146720', '135.13832487166249531520566648357', '136.67094422696544903201871672885', '136.96605258885472607373357464890', '137.934505750147748122010524533283', '138.55474769013251389014591890286', '139.55183737295577274895028338344', '140.10883436044923023274319942602', '140.66379601813849531505871104666', '142.453860128217751680261156073420', '143.10923162051526315244196252171', '144.01870650555921980493632233424', '144.6268568123956168189567775406', '145.29951661387907887108080904297', '146.190812690348019000321428531345', '146.83194140103603759474079433774', '147.61043027441591096663112439541', '148.766457892258439406153629074232', '149.447310370820728177000996551089', '150.17344170874979531029093094296', '151.13661591975757373385030666161', '152.094013744704546738753620907900', '152.97552292508112820685497784459', '153.64532829464888172982189499913', '154.70627767456785400830846535496', '155.330730666586744848385130041804', '156.234267784479561620827397217815', '156.553800506100549792763353050738', '157.40164749673891919001985040750', '158.25664416335192412345836276212', '159.303007552808774573999434052', '160.480224740783774651773912351659', '161.24636390028133806445509836855', '162.076971526316754501635164746232', '162.58088322874232381920794411109', '163.57792615723313125020428218796', '163.87892002838992714380726139045', '165.1828604339021465992586878971', '166.09697786822020221239664529714', '166.55483175236281025870810035467', '167.11668920680163712979356262819', '168.4891307897017845793921088017', '168.87208011168501682600070177539', '170.028699835500515000177835113274', '171.075455008251086680427541932467', '172.02371642351230949702799767', '172.32618508702464549712632702635', '173.32459126913604585621549737263', '173.83413529106684612222300431649', '174.65803691123958484508093969683', '175.307517580862589740115639286847', '176.3963790177661375862575563464', '176.972011296568960974548436903246', '178.59014187396284183285999438681', '178.91364133448158141619791583080', '179.635507936601028613375404615423', '180.50316408575984885116807083444', '181.34840161719504234888643213496', '182.10229401819111695975503294818', '182.932311396259050765087894128182', '183.75418671263509449869188986720', '184.36808619980568570681589283865', '185.29295921107930262375092855462', '185.57938168027276564672996991402', '186.69478063663681197840579507470', '187.981800362149447292916399878067', '189.03674442066633291357372366471', '189.27608142718242341261071600504', '190.25385081675008073446560338901', '190.989787692759758554671208647246', '191.59812127766786875334639180833', '192.29806873048444345194572890119', '192.99149017049977210704500271916', '194.18359117682654762668130832432', '194.88615365422734029786765546528', '195.54695229390706199665486477884', '196.550328843346703823861662141138', '197.47215765615353170235089319768', '198.29863871045566349345193145879', '198.61989738162088346990311797561'], 'prelabel': '1-85-85.48-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.39473834048527545, 'root_angle': -0.5956783047220626, 'root_number': '-0.296076410017052665742404748058-0.955164257827633600514246140152*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.297839152361', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(16)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.701329842033336698047959149465-0.515375278470323294234921808484*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.24294292326', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.54966463235', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.23696427885', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.39473834048527545, 'bad_primes': [5, 17], 'central_character': '85.48', 'conductor': 85, 'conductor_radical': 85, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/85/48'], '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': '1-85-85.48-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': '1-85-85.48-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.39473834048527545, 'root_angle': -0.2978391523610313, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.24294292326', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_85.48', 'Lhash_array': ['dirichlet_L_85.48'], 'label': '1-85-85.48-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/85/48'}
Lfunction data - 1-85-85.48-r0-0-0