-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_475.202', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.7431448254773942, -0.6691306063588582], 'a3': [0.4067366430758002, 0.9135454576426009], 'a4': [0.10452846326765347, -0.9945218953682733], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.9135454576426009, 0.4067366430758002], 'a7': [-7.040766286173228e-31, 1.0], 'a8': [-0.5877852522924731, -0.8090169943749475], 'a9': [-0.6691306063588582, 0.7431448254773942], 'algebraic': True, 'analytic_conductor': 2.205890726241245, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [19, [1]]], 'bad_primes': [5, 19], 'central_character': '475.202', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 475, 'conductor_radical': 95, 'conjugate': 'dirichlet_L_475.388', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^53', 'a^11', 'a^46', 0, 'a^4', 'a^15', 'a^39', 'a^22', 0, 'a^48', 'a^57', 'a^7', 'a^8', 0, 'a^32', 'a^59', 'a^15', 0, 0, 'a^26', 'a^41', 'a^13', 'a^50', 0, 'a^0', 'a^33', 'a^1', 'a^16', 0, 'a^54', 'a^25', 'a^59', 'a^52', 0, 'a^8', 'a^57', 0, 'a^18', 0, 'a^2', 'a^19', 'a^5', 'a^34', 0, 'a^6', 'a^31', 'a^43', 'a^30', 0, 'a^10', 'a^53', 'a^31', 'a^26', 0, 'a^54', 0, 'a^9', 'a^32', 0, 'a^28', 'a^47', 'a^37', 'a^18', 0, 'a^52', 'a^49', 'a^45', 'a^24', 0, 'a^26', 'a^1', 'a^53', 'a^50', 0, 0, 'a^3', 'a^11', 'a^56', 0, 'a^44', 'a^55', 'a^9', 'a^12', 0, 'a^58', 'a^27', 'a^27', 'a^28', 0, 'a^22', 'a^59', 'a^5', 'a^24', 0, 'a^36', 'a^41', 'a^23', 'a^10', 0], 'euler_factors': [[1, 'a^53'], [1, 'a^11'], [0], [1, 'a^15'], [1, 'a^48'], [1, 'a^7'], [1, 'a^59'], [0], [1, 'a^13'], [1, 'a^16'], [1, 'a^54'], [1, 'a^57'], [1, 'a^2'], [1, 'a^5'], [1, 'a^31'], [1, 'a^31'], [1, 'a^32'], [1, 'a^28'], [1, 'a^49'], [1, 'a^26'], [1, 'a^53'], [1, 'a^56'], [1, 'a^9'], [1, 'a^28'], [1, 'a^41'], [1, 'a^40']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-475-475.202-r0-0-0', 'leading_term': '2.33920607463966727805190743863+0.155189132191457686471088535553*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/475/202', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [2.3443482519415615, 2.7084943166456785, 2.9891259558392305, 2.5274007871148516, 1.251030756286134, -0.34075064014353623, -1.5030892133461342, -1.7133706418590613, -1.0288466870970725, -0.0721857221157758, 0.39959488340532234, 0.06685710326559664, -0.6834167138318916, -1.0580473134523205, -0.5473060092550698, 0.5563677342369436, 1.3200313203274259, 0.9900719604234957, -0.17645080870925095, -0.8669036516519961, 0.315754954091684, 3.542077016504355, 7.241475932302674, 9.01270249090052, 7.408957096749216, 3.1782975321978, -1.1642571591591082, -3.2081642366711876, -2.4540447747667877, -0.521114199621859, 0.414944601952438, -0.4576623723015019, -2.0440881146507976, -2.61457903017116, -1.5955398757181276, -0.09891527726254754, 0.3127700145693832, -0.6741310428128899, -1.7552586676100694, -1.3930098392256878, 0.4847004531870796, 2.302363966989523, 2.4319170009635065, 0.9013801639952885, -0.6384319169836542, -0.7004663605128469, 0.4331469574289243, 1.0955593309075635, 0.23384211928432092, -1.2467925778431277, -1.4634719175044202, 0.07682819338059588, 1.431803905939726, -0.0046598108485842735, -4.526944167608431, -9.169678574227436, -10.1425360940584, -6.419062487643962, -0.8215959435324935, 2.6044235009717025, 2.291228785704852, 0.1915183111937335, -0.697259072904747, 0.5201271430492358, 2.151887903376393, 2.270281158036126, 0.9428097468300052, -0.1749132548561209, -0.0875223812762473, 0.39714295916747655, 0.012549179581758049, -1.0108100024860687, -1.0837126994906994, 0.5215505330403689, 2.253519626773878, 1.8054639435140138, -0.9739292363741474, -3.418214955749767, -2.8474327927456913, 0.21830865472442906, 2.3643352878500754, 1.0778444797523168, -2.255062624116202, -3.7659517280140684, -1.4536292092923406, 2.546043566557917, 4.414831560800122, 2.918162662136161, 0.48145814923789365, -0.011498081623321381, 1.3521884746305202, 2.0007779720345478, 0.44561869616124383, -1.69806919880764, -1.7714790843875428, 0.49304239558545726, 2.5721098349806115, 2.2500188736657547, 0.21936193859720507, -1.0525339059738221, -0.5273184604434034, 0.3776345110118946, 0.10817904997863596, -0.7427627505776071, -0.42701560049103865, 1.1171705773186187, 1.7823573112140494, 0.2341431186436703, -1.6652667686448595, -0.761421844894889, 3.0205442849869764, 5.56459196537485, 2.9004581332822763, -3.8050619082411457, -8.834802491358335, -7.855671871380172, -2.4153724235228147, 2.145556684649946, 2.6184219305881746, 0.6342040526537096, -0.43827886558345636, 0.21065545596798957, 0.7215526140914019, -0.05602174518207019, -0.8516187101274714, -0.163738122589076, 1.1840923601998659, 1.0715050998228892, -0.7269559559562466, -1.9493854395078591, -0.9913185222828738, 0.6022640837333672, 0.0841184687738441, -2.5516361815785547, -4.206399072035027, -2.7432772432414576, -0.025062839326021675, 0.46640353781595334, -1.577909699483489, -2.70064072700379, -0.37413321758493934, 3.286290787169145, 4.030522487311468, 1.0600877062032747, -1.8264871226715709, -1.2173318049209634, 1.4091388932285165, 1.7070483004668435, -1.7024193326125672, -5.372379620335451, -5.478835324477519, -2.4879082795663843, -0.009943147944278603, 0.09346929012443048, -0.4729804435903264, 0.3312419210897672, 1.7560650801444044, 1.6916406956107917, 0.10532868823723761, -0.8770126062722343, -0.26150280835461004, 0.38220852210385414, -0.32120778470492706, -0.9859173011472562, 0.4326551288830991, 2.6106952042607414, 1.438148451144392, -4.390537114015345, -10.246787027562986, -10.14379938386972, -3.9456667660338254, 2.1385555624152586, 2.769826793057245, -0.6815630512231015, -2.8302275174210125, -1.3517098814983937, 0.9610841026000662, 1.0098849360440088, -0.3746543819937759, -0.4422384128653084, 0.9969679231771207, 1.520306977885251, 0.16796452848897037, -0.9303783394461064, 0.051739490714684575, 1.5641210430682713, 0.8828000081033733, -1.598065563608035, -2.6094684006837774, -0.6883912187500446, 1.6257484639154625, 1.4425130565022186, -0.3983042977787309, -0.9247305224029301, 0.23846751055641027, 0.4563508228760524, -1.1845098525485271, -1.4777765520701918, 2.496213313546657, 8.173840524043573, 9.713465935727337, 5.4949327165172726, 0.6323026924579774, 0.5753015582256511, 4.26073865967054, 6.010721568393026, 3.259799057044634, -0.558379984688197, -1.2985702757470379, 0.49101241171856996, 1.321718892639001, 0.1184344330328787, -0.9163001062173506, -0.36191967399319136, 0.3503857563825386, -0.19167962683457163, -0.8286328269115084, -0.029605584538249824, 0.9571553119218016, -0.2341814556411576, -2.7885358856725313, -3.0299080353232197, 0.13357502389631304, 2.789023138145206, 1.1885685045444112, -2.4531630672697666, -2.4366373161274577, 2.468096505931312, 6.861060059679448, 5.775505389207337, 1.1762911426479699, -1.1138486345029839, 0.6577730569206159, 2.654862127583628, 1.7182666328715255, -0.38154214845285017, -0.5623940403284021, 0.4747316299714893, -0.25729031110710027, -2.7006005480667303, -3.3723307567724143, -0.7020460780785227, 2.3005747782446413, 2.2909876346800147, 0.21804315631294138, -0.6177582992672268, 0.3438370742780469, 0.725941241668233, -0.2768392716329699, -0.4587191452710199, 1.3385569252975311, 2.672148369331031, 1.2339992190695661, -1.0158431052506005, -0.6948646058122847, 0.9721697293024556, -1.0316763995881426, -7.692148486625588, -12.633748296567417, -9.489771843102288, -0.49848223175759004, 5.830089910558663, 5.031762486419825, 1.0256643309630937, -0.49026997918898974, 0.7229160322065905, 1.1899395316172527, -0.023792352962675154, -0.5602303356230933, 0.5348666023414043, 1.1866788698384547, 0.14445050861082076, -0.753933458960873, 0.05132988063293849, 0.7701521590039196, -0.8307513154926688, -3.177648439309185, -2.8467606891972137, -0.16614738076393687, 0.8069737027487257, -1.3533430243502862, -2.7104219746794866, 0.16289420672457763, 4.439301692575243, 4.693832607794099, 0.8353159191807207, -1.8175986305137717, -0.5493232083136835, 0.9687804083902817, -1.1218255770087686, -4.502367379129705, -4.143294935054994, -0.1364056899512981, 2.3329843572866595, 0.6982758230307861, -1.5966579118342272, -0.8830237010303572, 1.2295207314259777, 0.9859328258635658, -1.3746528509637452, -2.3162034467981583, -0.8149675278223022, 0.3977616549966827, -0.31811205796722714, -1.0677582169691338, -0.1981086601929934, 0.7025224355632793, -0.079072809019867, -0.9042283670759936, 0.3038195391262008, 1.493204736570698, -0.8783994593988041, -4.961370173863769, -4.112078671940848, 3.7800321962849814, 11.6483447441982, 11.444352691618349, 4.40680530584309, -1.0987546695811496, -0.7686816442723405, 1.4513022074370807, 0.8476075827303658, -1.3468355750949268, -1.4076566668633408, 0.4090829660248785, 0.9245735914514499, -0.2909465302611436, -0.6410638310673302, 0.5019516244400528, 0.744353507935046, -0.5832434798001637, -0.5813503038288166, 2.3068450097480224, 4.859183548177386, 3.5668196199423416, 0.1793400267837958, -0.9028099642236412, 0.6693349578793648, 1.3299711273801238, 0.10757105019424852, 0.25027693590895456, 2.9987213111540423, 4.330921531548305, 1.1389323733689363, -2.8397274415378737, -1.8340349641726155, 3.0734227838585544, 5.109326234826415, 1.8066137413809458, -1.4969961636416647, -0.00914287786148914, 3.4029938668155237, 3.076580220198011, -0.7804965661554588, -3.0030861851525175, -1.5353319934379763, 0.3728341684740034, 0.15189011178129933, -0.5794266795048482, 0.02441165262328881, 0.6019636770118487, -0.36402309315507086, -1.251981835736179, -0.22802852759783476, 0.996473637684705, 0.09178984824300818, -0.982827083125648, 1.4295563388767885, 5.796069463159848, 6.320435991956734, 1.9003797247633665, -1.0034797177801478, 2.4898209650590246, 7.923827082542421, 7.536591451931278, 1.390451126042695, -3.0887201006565332, -1.8960635161163744, 1.0412204650551322, 1.207033434273082, -0.16629252158617153, -0.06613224570427377, 0.43890145594544056, -1.2646437819701233, -3.6704419420101964, -3.0158192196636238, 0.2706124306897438, 1.8592609275637337, 0.3615151510178272, -0.7951589831136834, 0.5454883644349352, 1.7970461896489522, 0.5274562880393526, -1.142895360066391, -0.38457647194241606, 1.2460079669167183, 0.6938087675000679, -0.8879617957358618, -0.2131724263731256, 1.5724860219512415, 0.09689359987556992, -4.044853515261677, -4.359070617213695, 1.6714038430714093, 7.1191424566462915, 4.562452048512576, -3.2108412692465347, -7.043272202011542, -3.9764054855668833, 0.12274278761411891, 0.3018786264716395, -1.3473061592800826, -1.1426993715172842, 0.08566176861707041, -0.11609823577906331, -0.8062573527737128, 0.2083891180380302, 1.7651404198500766, 1.2545053273455007, -0.5019695080453633, -0.7109592257154441, 0.10774474240239999, -0.8618289787395086, -2.6590752137156506, -0.9180894474389355, 4.432668622582322, 7.270474776859268, 3.974555182568017, -0.7519205819476316, -0.9960257208080338, 1.3319102920565102, 0.19546404264170197, -4.279736822936871, -5.910321803973127, -2.5791108824909816, 0.5037259973087157, -0.5401897743734476, -2.427344187729425, -1.009873808383562, 1.6268499438352768, 1.1955809633606462, -1.1954730754403948, -1.0998371033882512, 1.4981986216947287, 2.2860402849777177, 0.08755186419085623, -1.4007078638848318, -0.1713801940945422, 1.020263389052837, -0.007708872595206016, -1.16952812243426, -0.4075356008404906, 0.5355473036733658, -0.01980585200397892, 0.07494038795434449, 2.4634823530126875, 3.6420312661282566, 0.20850921286385793, -3.591863755278185, -0.4039498717807822, 8.454363429825985, 12.908315989405313, 7.7240125913365585, -0.36152347156462367, -2.7033175239979426, -0.21895081427289853, 0.4703918474526046, -1.9493521984482067, -3.0332652445020734, -1.1274446385263337, 0.47823372072466497, -0.005765655089392547, -0.34634722562973913, 0.6215787142383846, 0.7960205024941183, -0.3903874139174224, 0.024929726636787594, 3.0308948833650855, 4.717519669334731, 2.3573946417592184, -0.6273603304730468, -0.039404193674403794, 2.241202322731205, 1.9093997372604707, -0.015713522199145555, 0.7358222114931325, 3.339627034022567, 2.5764330758663485, -1.8033594634838688, -3.527904831660474, 0.19739294369203222, 3.7926845684612642, 2.2497586741201365, -0.8745169666372825, 0.16955532960352437, 3.51325234479173, 2.9812919963295355, -1.412491159251582, -3.5667734586481084, -1.2824353145500016, 0.8738267229778409, -0.2884851500395414, -1.9755348212464354, -1.2155365762764196, 0.27658197268660717, 0.15923545182777646, -0.29538859870191314, 0.3958775589638971, 0.36096782914739806, -1.7957348781442448, -3.249039104149864, -1.545767370837884, 0.4066090163983918, -0.7511687245416325, -1.9239967682034531, 1.7176884602660605, 6.828957197773452, 4.71624755877325, -5.209791391292936, -12.726643960933714, -10.45219019967492, -3.2489400073800163, 0.331274701157348, -0.1615490245892638, 0.2323540938596246, 2.137447164446827, 2.083376886843269, 0.08678262569822212, -0.2587019966027498, 1.3435101025200278, 1.5021891074228741, -0.10942629833196055, 0.13093915628701278, 2.8406476170167823, 3.839882908691848, 1.2973467069407059, -1.0200384487737915, -0.391279401713667, 0.35389761675609527, -1.4501896001604313, -3.1285237751070567, -1.7287034521676268, 0.19904926917710983, -0.7288446959615433, -2.1008908196731295, -0.079664821465398, 2.6271839777804593, 0.6938154907245465, -3.480089812003356, -1.8325502342593536, 6.284743355229525, 11.523121842222206, 7.856826945152343, 0.951085617002653, -1.1496281176417507, 0.8317754087615928, 1.31944901166748, -0.22564825773782518, -0.2288077116084766, 1.353584453999649, 1.2968926176655673, -0.4475727792129425, -0.8650948630505026, 0.26618621383519037, 0.4187377129877449, -0.2542050648494566, 0.6352083928483642, 2.0242854476967844, 0.45187897881290906, -2.7333374664392474, -2.0758681500418383, 2.445367337177713, 3.777923436273262, -1.1117679372496052, -5.552799647838479, -3.466016361324125, 0.9988131644404893, 0.6467004910530368, -3.0215517727381935, -3.1419271429266824, 0.6728507676553066, 2.4011888634333607, 0.3175834666718652, -0.858570888580878, 0.9627463023567231, 2.0168544836843094, 0.4147937837634701, -0.24612845646134177, 1.9996482627313126, 3.3156235113376886, 0.8680648771975158, -1.8963224418185873, -1.1920139528683757, 0.8258640402299184, 0.5219719987050546, -0.8301222701582389, -0.3042178831264476, 0.8470103977178203, 0.1472410040177369, -0.7444619070778968, 0.3823415105093852, 0.5780229493628122, -3.3936928613182205, -7.060462052865278, -3.4367740363126345, 4.811178603913351, 7.479180586887917, 2.0544348253729177, -2.330600537313895, 0.8725803888236741, 6.160961431317436, 5.740216566515191, 1.2772007222956507, -0.6935190436111099, 0.5197320272618614, 0.9414727688604441, 0.014009023996701054, 0.264172118143823, 1.2524260581315718, 0.5679568596890701, -0.7473367149824375, -0.014687168172568193, 1.2768183701543474, -0.21869775867145494, -2.8301878025689673, -2.059943130278425, 1.082255698705335, 1.2188109843924713, -1.8618565860604521, -2.601121963255417, 0.2750282355829098, 1.3129675512152998, -1.4790576029124387, -2.293310885706913, 2.285889238036275, 6.439696449274241, 4.370044546732386, -0.17907185900921194, -0.6359296162029193, 1.6335928843029173, 1.236303005237255], 'positive_zeros': ['1.49344499670233260224339816171', '2.84082479535406066878218274550', '3.46819479339150292376030723178', '4.536380944953793000756663215672', '5.58008507037869334546045348920', '6.20439436746547490511575546975', '8.0298672130377535342797483678', '9.17075847085678772671777350225', '9.58280420031914734288949008209', '10.96561601229268997259890237436', '11.38814691498248363095383540039', '12.43034354443041850562151335468', '13.595721100260562313774370798569', '14.266845507720298855341079829378', '15.047959585289966628665986520501', '15.92505839954516506787027087958', '16.56204885064689468707697580100', '18.17783302206020466516968800425', '19.09545787549896416434233546022', '19.59327916545431304566091568418', '20.85910587792725335287780667201', '21.29843637562013638390992029176', '21.87928900711958637460834182935', '22.7323559867797662210737529267', '23.65442168451692099504211005646', '24.666712876199081833107310399359', '25.41810739274977470931288886766', '26.362344286448461699097409388', '27.61408148102663505271550966720', '27.81718094668234074192619333657', '28.808525519140457301655188067625', '29.63041774550472819031155566398', '30.659513300804709041813829279042', '31.403031836809641882317248397449', '31.9131373079705809782087298244', '32.59831610196183062353861117633', '33.46927616814965095854278536566', '34.138769711058286562885850879618', '35.144819483451231807602062152504', '36.38753734991670041599085077731', '37.304619496172472570722945675773', '37.7437876495848819647304291108', '38.42206954218727458602006617644', '39.09885423874703053750246625783', '39.88749072096444132413710320958', '40.795751814984539378593905388', '41.263338698590392735953274046969', '42.50384850401324747538986823661', '42.90737138954957369158463089980', '43.78090983377793462105377868167', '44.77798598285110871665725687335', '45.4558653764453011938503958073', '46.12194793154270832458151117126', '47.50248359676740252773679920890', '47.85216175686335531660422619905', '48.36149833774384184564481895474', '49.39507516747710300041835419951', '50.083036822069968998948528114160', '50.5313885427289354067566232060', '51.19030314804354085154275398890', '51.97304451165028764129230039303', '53.30304223199924660085841657475', '54.00598124095286379223985628268', '54.84854030901782581725871075063', '55.533426649657878251866342217153', '56.04830572971377493984500525571', '56.905878269628957002748680286060', '57.49078474061100857440413901026', '58.24337054177112289050803945910', '59.14012438334495759768844499712', '59.92890049162857159745496023011', '60.56572553429986468922874545484', '61.046755991538785164719319647996', '61.71969592682654187553373568103', '63.2207452099403921329889801648', '63.34279825477561008013982649456', '64.62887701326359170821045833583', '65.23400509561686378261340609418', '65.961155707984735312200448512646', '66.67704838820922200043880389849', '67.12277344032694068812385386160', '67.819361304187906289032602465962', '68.40555773686732331093601947317', '69.364081191070827272436723168013', '70.097639928921461230936274589032', '70.80267512468489735659210131964', '71.97190675414663820488396725502', '72.422522880193316273327692676159', '73.366280148153926203806918765471', '73.905195125449376625146532986957', '74.331658824667749520905051013616', '75.37356334404438914418430092570', '76.28769174778031654783191116788', '76.782622074092978091629336939193', '77.42364395232016485507373814883', '77.920692502093157365947805206968', '78.89991752658462456745157459465', '79.487839646760760430610049051112', '79.92254470057895189931929241600', '81.267319594085803699844162168701', '82.30557310304611385692146650997', '82.65946500717381438288964185879', '83.43189034777424897509142858189', '83.93814483964628727502361113837', '84.71941352487862253259808714781', '85.30002508768251062464399437634', '85.82622315109353510582406224851', '86.89620162578893348034423034293', '87.338712455206690157053972018248', '88.11373280258222779057263075408', '89.127383322641192123806116797625', '89.76172909011240094812977500770', '90.204694871479869277322845343037', '91.26031950658797342371954213930', '91.95104008623277325534966245552', '92.62015868709085711006550857080', '93.26386451696906386158734948628', '94.21424389051063334191222397040', '94.60286444404108087902349244452', '95.35881486523981918298876289146', '95.91864634805682743819024993559', '96.51170172403278899631494120897', '97.1163543331517395787179934633', '97.99753538153099506902963088302', '99.27824670779602165062396873318', '99.782145720204358272668297654667', '100.42719629144469022592252676163', '101.17814683875828989814182391063', '101.80578134897089970736407824914', '102.37605853927348951633169597406', '102.99871011536735365258724923526', '103.52557014243190477455839332513', '104.70820427082635536053894562044', '105.19868534229815073204546530158', '105.96840720312596606787291584118', '106.196433911050608788464933223908', '107.26210038194470786698701084219', '107.93690760409978811599588489636', '108.88158423350367487086324627454', '109.37581394195815356729558147021', '110.252310517677210835058460304027', '111.15794461062842272757893379615', '111.61007104088893067063953861382', '112.17997750350068302872008872444', '112.729691084336477566850948298094', '113.47984282088708459171487245495', '114.0792810255308643595460642144', '114.564600644939560291086826174217', '115.75982292707910201349172897502', '116.09346564030986857823164209718', '117.25592271803342163453404770842', '117.994611251031627014322951798922', '118.69953592498064820230877584981', '119.0865155794921191657994424480', '119.51150641792434753560560701236', '120.598763286032477167530947150884', '121.30715669234914346442333342711', '121.78636395859806240665215955257', '122.57693519177557382129981902231', '123.18850394103508983739106671458', '123.8696746450031635087301207723', '124.40829726467455610653261905415', '125.00828996858732140378503251058', '125.86679813853043605610659324827', '126.74722976529514248150083203086', '127.79703055530668189121796715739', '128.18128507324158202168132743127', '129.02928891831383557979259308940', '129.33245323456997655960160921957', '129.96261787827567278862163277758', '130.83730265665987021889588778293', '131.49208520918377446512800143880', '131.69319635482601650570843795437', '132.56230258993896822842177589751', '133.68289270250127968902124261841', '134.18804758710271213883640796449', '134.70398866435981012696791885204', '135.84725904333822765107777841024', '136.17574587955073878776304243164', '136.9798679064756645365611948214', '137.64968250305258393714563515196', '138.26607296545136585681447296896', '139.07318052672062995189547309823', '139.71629331418121855616635356255', '140.31105842501409115616146686674', '141.03276887585351065299311382941', '141.5548898185686423102868553924', '141.856976883925838212201351833', '142.82553494300888033210674285106', '143.45439928520700325091139702277', '144.66933928026849894033355654090', '145.34091644808130283587904200777', '145.70638035575907645146091764118', '146.730241430560233936858979953408', '147.18551732759339159024351443295', '147.636757589303026174879599244451', '148.33427747523525787679294828811', '148.74611513032410912902028434008', '149.90582748442963581870129840016', '150.31790854762673266927742012723', '151.24559758386499140966751956260', '151.43947469900899791053895861346', '152.37730369788881325687193173545', '153.11263837781305550782023780250', '153.94684869812652174448771186599', '154.35820911414811257346615434995', '155.21652300050436101719393642748', '156.07364724374008333545609325979', '156.520550703668523680964729054962', '157.417466642692555308993646476331', '157.87944490950341608678313049041', '158.297716411560681838143023815', '158.824159327180173352803161398891', '159.889515508414306187060170712036', '160.19563678393866040247598089566', '160.83611090080744416609428068755', '161.72562915514891313077219696942', '163.05116378023930253471732382600', '163.37849876774742789458290998978', '163.70022418099791859874656554131', '164.70395792501485910543348491738', '165.06284472559126553113832527630', '165.91255928545395209796178053064', '166.22731180345122790590545461239', '167.320791579832101717230793696459', '167.899920503175518202444685324042', '168.2305401711185658185265614395', '169.31266123833794799590882051308', '169.55487141332283361691007319855', '170.31977237921733500677987738312', '170.98573165936524827291848207859', '171.64670064352985722284834093912', '172.876395250833094491091962865402', '173.32071447794769790231410338423', '174.012647745935971217624520516', '174.42587832945711473701370864895', '175.230195922492742135970216068118', '175.86339504048404040228630590248', '176.41324291810475019495568334504', '176.73834564477699912682664143106', '177.542403148694292177649155271313', '178.27650761969268901643784555776', '179.00682800588042762266501080632', '179.91075632745726037963156006997', '180.37122947165994531263879447379', '181.196724416661460799314262341661', '181.91568980348286810952729607623', '182.36776432440675786387207324568', '183.19977785012452157268972228827', '183.49498694199673379559060377365', '184.45191962026506690230665953786', '185.162754417078074000367239012554', '185.72885631418672160849930586099', '186.31538453184311556746023838591', '186.90778607096345782699709218027', '187.42435955569471916445861407026', '187.885947912276476188413495226310', '188.87994636951109502499045555292', '189.78784524445676501417905101755', '190.26466626483970487078190047955', '191.369967932318117941444414099277', '191.76822364199635739394131693906', '192.50681691152392349597628194981', '192.717405559585950744169338612621', '193.54815490335613130605299596549', '194.06523554722316457217191191293', '194.66302322860626490347012151440', '195.509401711961949993356618862822', '196.07180951858791092472804723183', '196.847051265250602072808666806940', '197.358006984248191998774235263540', '197.99890256178169443591969788974', '199.045272012364717941477864754066', '199.46393477302996111063476025208'], 'prelabel': '1-475-475.202-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.205890726241245, 'root_angle': 0.042173242791220235, 'root_number': '0.991235879260108382650607084637+0.132103866966261953964298587400*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0210866213956', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.77259309837904733026800188684-0.0537237545040802025866152156503*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.4934449967', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '2.84082479535', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.46819479339', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.205890726241245, 'bad_primes': [5, 19], 'central_character': '475.202', 'conductor': 475, 'conductor_radical': 95, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/475/202'], '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': '1-475-475.202-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': '1-475-475.202-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.205890726241245, 'root_angle': 0.021086621395610117, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.4934449967', 'prec': 40}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_475.202', 'Lhash_array': ['dirichlet_L_475.202'], 'label': '1-475-475.202-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/475/202'}
Lfunction data - 1-475-475.202-r0-0-0