-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_4235.1052', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.29994909127701064, -0.9539552099769126], 'a3': [-0.4067366430758002, -0.9135454576426009], 'a4': [-0.8200610852841911, -0.5722759967030896], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.9934817353485502, 0.11399140989054063], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.7919022459222751, 0.6106478796354381], 'a9': [-0.6691306063588582, 0.7431448254773942], 'algebraic': True, 'analytic_conductor': 19.66725731711931, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [7, [1]], [11, [1]]], 'bad_primes': [5, 7, 11], 'central_character': '4235.1052', 'coeff_info': ['x^660 - 1', '0.999954685354173 + 0.00951983393957664*I', '\\\\zeta_{660}'], 'conductor': 4235, 'conductor_radical': 385, 'conjugate': 'dirichlet_L_4235.4078', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^527', 'a^451', 'a^394', 0, 'a^318', 0, 'a^261', 'a^242', 0, 0, 'a^185', 'a^537', 0, 0, 'a^128', 'a^523', 'a^109', 'a^236', 0, 0, 0, 'a^95', 'a^52', 0, 'a^404', 'a^33', 0, 'a^324', 0, 'a^112', 'a^655', 0, 'a^390', 0, 'a^636', 'a^629', 'a^103', 'a^328', 0, 'a^186', 0, 'a^525', 0, 0, 'a^622', 'a^221', 'a^579', 0, 0, 'a^314', 'a^271', 'a^367', 'a^560', 0, 0, 'a^27', 'a^191', 'a^34', 0, 'a^518', 'a^639', 0, 'a^522', 0, 0, 'a^505', 'a^257', 'a^546', 0, 'a^588', 'a^503', 'a^469', 'a^496', 0, 'a^630', 0, 'a^195', 'a^212', 0, 'a^484', 'a^53', 'a^213', 0, 0, 'a^392', 'a^115', 0, 'a^50', 0, 0, 'a^489', 'a^563', 'a^88', 0, 'a^446', 'a^657', 0, 0, 0], 'euler_factors': [[1, 'a^527'], [1, 'a^451'], [0], [0], [0], [1, 'a^537'], [1, 'a^523'], [1, 'a^236'], [1, 'a^95'], [1, 'a^324'], [1, 'a^112'], [1, 'a^629'], [1, 'a^186'], [1, 'a^525'], [1, 'a^221'], [1, 'a^367'], [1, 'a^34'], [1, 'a^518'], [1, 'a^505'], [1, 'a^588'], [1, 'a^469'], [1, 'a^212'], [1, 'a^213'], [1, 'a^50'], [1, 'a^657'], [1, 'a^562']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-4235-4235.1052-r0-0-0', 'leading_term': '0.0241512588692133356616178564638-1.27224440282499818768800081501*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/4235/1052', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.27247361616047, 0.48351988779243543, -0.4379011861211417, -0.7945063056168908, -0.13447265851663937, 0.7247075585933357, 0.5314088753357435, -0.7058636211769103, -1.478858754957006, -0.6801277986225374, 0.648132519837048, 0.34546368861798493, -1.9202115587865474, -3.707879040243565, -2.678446974400935, 0.16937250766882384, 1.5341087477126594, 0.2120307190497764, -1.164935658799309, 0.07125202095707933, 2.3985311071176483, 1.8886175919944268, -1.9468845309012446, -4.733370991593355, -3.020179956758567, 0.6470994218554927, 1.0573052135296197, -2.2580617291165654, -4.296529742240236, -1.836967705956181, 1.9044511274831644, 2.0532892191660554, -0.9713615356832335, -2.624931702291968, -1.1834091911133398, 0.38623101120180475, -0.1949141733739393, -1.1493862875031753, -0.3575730837837192, 0.8767233033006805, 0.5042871870483755, -0.3806299168788875, 0.2574362973174842, 1.1852313549207043, 0.001829247856173792, -1.6851415945238006, -0.17102401025389696, 3.146140310855488, 2.2069717020959634, -4.002052681093056, -7.841483732736142, -3.333542909876815, 4.468445421283013, 6.213418873025528, 1.3531958990255726, -2.2985426780804428, -0.825611081355566, 1.4530785194572764, 0.733373520928004, -0.5406551928624804, 0.42140535765735476, 1.448350763352662, 0.16798819215527297, -1.0474154856803117, 0.36041483113688316, 1.910312257525615, 0.5720450740658997, -1.2169767515442704, 0.2916902753843994, 3.0741368395561697, 2.609360799556191, -0.17867201522249357, -0.851290107380458, 0.5308187376702194, 0.3783396544643396, -0.7935954200476467, 0.5770049169869343, 3.0486189281114946, 1.6154618951591453, -2.5196135925429344, -2.7735103320615937, 0.7272942148389695, -0.20115014414060847, -7.713142339629351, -12.51949113019786, -8.00495222846784, -0.5947159918900375, 0.9247959807000564, -1.6231207431875543, -1.537751295625175, 0.8758879913642003, 0.9805263453508278, -0.7666995441744126, -0.6930878421381937, 0.6123648083496857, 0.3808340347405653, -0.3134756305480983, 0.5479344469498821, 0.9304555565244863, -0.9541735524069774, -2.0084851159862604, -0.2543462101312729, 0.19038909022124959, -2.98468661849156, -4.063964781214026, 0.9577216461167208, 5.581022437841241, 3.201847671004689, -0.8399367804510338, 1.5530950489821205, 6.676794913481231, 5.696000183619073, 0.18157781315778923, -1.6619156231520025, 0.34978461157522356, 0.16520317982328636, -1.9432890694551193, -1.003221645490417, 1.7713517140933506, 1.470884674729381, -0.3255381326138429, 1.099226495798832, 3.6136808239503218, 2.20230013126527, -0.9993336351762141, -0.780386870743156, 1.354838049297616, 1.0051363145758565, -0.45239025126751853, 0.1395732116874624, 0.7737119664065761, -0.6042284766950884, -0.8406150898067408, 1.3780932222475095, 1.5712410960163499, -1.0220565804257562, -0.4926903215537408, 2.8287200337783776, -0.5177272384894868, -11.542879624135615, -16.72755440399775, -8.672196366786228, 1.568522789116162, 2.621223505399483, -0.9611351847204999, -0.7464073495950421, 1.0645936303075128, -0.37691328156200277, -2.264186558964015, -1.1561446506846957, 0.2263604168494574, -0.05737433762454638, 0.5580391799426896, 2.0379697186660697, 1.1520090434878556, -0.6844451277603822, 0.4333555582133709, 2.1052424703248427, 0.11341055578612286, -1.9113191854208753, 0.9059365144692215, 4.10649990846197, 2.163619995555288, -0.26789038183725067, 2.205195174857051, 4.468302357330384, 1.5851072313889711, -0.37890235488309826, 3.39676492867967, 5.860749814246747, 1.6473763586348642, -2.225356173031459, -0.24865744858280006, 1.4113571546583121, -1.4921992254033771, -2.704547803045213, 0.9196401579546676, 2.6287105997121847, -0.44555192103179736, -1.9017039728730352, 0.6971642012428823, 1.9096257553353753, 0.20450596116752634, -0.21474440195665567, 0.7361047267197991, -0.032627967493420645, -0.901732018175366, 0.4238219477622468, 0.9064845810918142, -0.8884350228772202, -0.9600911695380536, 0.5474622911120373, -1.3317008791376785, -3.3537549767903125, 2.940404501403494, 12.561281373019206, 11.393539501780772, 0.9868866204836486, -2.858897995776851, 2.8883124046544615, 5.664331459360671, 1.3390170436243172, -1.4497000929795187, 0.004703649652705261, 0.045083418392656616, -1.52451235912057, -0.6122542290132097, 0.9440744181938212, 0.07454797400239142, -0.3233404571962712, 1.0731607052231862, -0.015297296711764921, -3.331999982648881, -2.9726143656789157, 0.3748308810491572, 0.5603249277620641, -1.101209543117203, 0.7748080696873605, 3.359773314599043, 1.6877185651197333, -0.45039013858226984, 0.8338824265362327, 1.0906628875938724, -1.0992401213112246, 0.7073617113528063, 5.714093380447214, 4.3728300865025425, -2.218513948354162, -2.4708304636885035, 3.3403567459031978, 3.7601055191313666, -0.9362519862560612, -0.18133748842238392, 5.158875190362638, 5.30667834998829, 0.9072153574937566, -0.3722811170505957, 0.8203961910424518, 0.09142904596147604, -0.5531202138674675, 0.7966426493401964, 0.7997181866398179, -0.8841388948260506, -0.6789655377181729, 0.3068434409671955, -0.548333727856322, -0.12037104980225616, 2.6410836981801844, 1.8593256750334026, -2.1083480377406145, -0.3117028828402185, 6.183434557675777, 5.742058852766843, -0.7550095288407896, -0.290327155527441, 6.727142235128734, 7.207796351976589, 0.7523339788649166, -1.4972523118875065, 0.898709432362528, 0.32996092176353053, -1.7329283019016142, -0.41434427904987414, 0.7950161629927717, -0.9046547376241835, -0.8287337561151447, 1.5366462177261226, 0.509709459933449, -2.539385763660405, -1.4108556626886153, 1.3680726118238067, 0.12064178849298925, -1.834908094715799, -0.2841462393652375, 0.8950426925461766, -0.3502388260298401, 0.22524095460112162, 2.1569217272704515, 1.0220482704138103, -0.6693557808599029, 0.04442346503068293, -2.5439702556646706, -9.30279935914119, -9.146414526968002, -0.3210993326919246, 2.7684365519796152, -3.5055522437104694, -4.435564893851521, 4.237671433413447, 8.611895056060838, 3.594707297904846, -0.4929468650378629, 0.2884987241378863, 0.3108929994777711, -0.5083820428329879, 1.0180920894904797, 1.9113736247235857, 0.13925189304266095, -0.48925280185721054, 0.4022946230164609, -0.37117607124619745, -0.7231197310313651, 1.261639819416053, 0.5476258878963303, -3.529105353036083, -3.176303957539352, 1.6098248348821558, 1.988097668133343, -0.8276439852828582, 1.4131034605139519, 4.560523419854879, 0.36347448477521654, -4.483515359487676, -1.4906106655648867, 2.012678292026505, -0.9296129550674808, -2.788448613113129, 0.7333361126021107, 1.995710662441474, -0.4167076490334014, 0.7096673213500083, 3.71114666301189, 1.884271075097335, -0.7156652136366851, 1.7488839527119182, 3.930109708544494, 1.492160396705933, -0.006682758038287573, 1.6361660332715697, 1.5202370175945426, -0.05302911999506607, 0.6856841006735355, 1.3643752077878033, 0.013289194607608275, 0.23093525788890856, 1.2413097832482363, -1.1209246342465924, -2.772203799047295, 0.08344146229062648, -0.6333968865177908, -7.470226264258037, -6.425502425520135, 6.484155845581849, 13.049737347318452, 4.8996593827932475, -2.3308116660375893, 0.493037782345807, 3.2806299847103033, 0.9663869729457668, 0.020576888555535383, 0.8833779654344083, -0.7386084290317634, -2.0313754894698395, -0.4342362270678958, 0.029301941711898462, -0.9818702889251337, 0.12272326016024206, 0.7042646387451109, -1.7392051595947304, -1.5567459598673783, 2.595416609090953, 2.982939991176095, -0.7977685934401655, -1.1224012889837622, 0.6844159576308612, -1.0470279742673747, -1.903441526613777, 1.664354757839892, 2.2538484237363563, -1.73266384000731, -1.4946297921696465, 1.6293623036771265, -1.740023888849545, -6.779754796788759, -3.4639092328727097, 1.444056878760841, -1.1582321214447737, -3.5834449431515103, 0.6678291413450207, 3.050156208077241, -0.4096556146358962, -1.583048250285381, 0.9487691219375716, 0.7538355895814994, -0.9963430660655328, -0.04081981911758648, 0.7492849538035773, -0.322087101433325, 0.021220704462664858, 0.6142454111670274, -1.0365363825903358, -1.0741024818675098, 1.280451931860866, 0.5149998161910824, -1.193935607678528, 1.9006930537420046, 2.407100954834021, -6.357274330626351, -11.207153267240686, -1.9427406897294726, 7.080021938493502, 3.809643549463435, -0.7783903828477858, 1.685580879865867, 2.5666342435006677, -1.2131234667562567, -1.8578176348057702, 0.395511735144095, 0.04841404218593196, -0.23643540672689126, 1.6040962959351004, 0.9209558712401132, -1.1988583378809448, 0.45884598161975665, 2.006238000073423, -1.0034134546921902, -2.514952302897251, 0.41273525304716707, 1.0375752310660507, -1.3225959039710824, -0.775188504274651, 0.7083374094670729, -0.6146658657589066, -0.3264486271054149, 2.1929640971260413, 0.8087672672549502, -1.740749991488175, 0.3491286987711319, -0.27875925472860047, -8.146922550975194, -10.09905345316567, -1.064721928064658, 2.8236475525455837, -4.288464386704578, -7.468876307365193, -2.1593208416088374, 0.2655915369949793, -1.4328056334042827, 0.28700967916497766, 2.903248441568548, 1.498970324009706, -0.09531448927787511, 0.09377445038857932, -0.876391128018765, -1.226120303295012, 0.7340291231252226, 0.7053419403989882, -1.1632206827850626, -0.20711348583043312, 0.6287333326906771, -1.571815104491324, 0.18444760489396894, 6.361159744038176, 5.568109426368993, -1.4493826735725581, -1.9010528760534422, 1.7013528917038843, -1.8849534399745431, -6.632196823982677, -2.98604428369521, 0.6647124167957166, -2.7336143068421896, -4.319271299156378, -0.6051794669990807, 0.6315998817792987, -0.2935197976995754, 1.5180139954844931, 1.361901086679322, -2.9043463653960204, -3.2202855249098032, 0.9393636653159635, 1.4071726090389376, -0.4804234176284868, 1.0055443025311424, 2.002486350657774, -0.4617628445925711, -1.1992840828368565, 0.17362607451956247, -0.47146665403317417, -0.6284798752665799, 1.247374296882694, 0.40067951007649466, -1.2142191627647412, 1.6044031755935226, 2.4632895596401436, -1.945935237402141, 1.3661011980731435, 14.353254734049525, 16.933619791684357, 4.195043189158398, -3.7333026723367007, -0.3211340426257746, 0.674301524467726, -2.888662948533273, -2.064599751081856, 0.8702122398898626, 0.311931453888844, -0.18329699712955036, 0.7445834179919637, -0.2520073715356314, -0.7445043064796864, 1.2392730347227163, 1.097092003805975, -0.7003298843892098, 0.5231536249136577, 1.0461888468905745, -2.0561690215969195, -1.491430901435772, 3.3636204400969847, 2.9037577087302093, -1.4355906148617548, -0.7967361534815033, 0.9382887756382878, -1.2778354883005998, 0.045375026813113006, 5.31586010879035, 3.2827862719654695, -3.4635683445999477, -2.6683572250327283, 1.5945839766520509, 0.5279173997170699, 0.5661324251641279, 5.127228592939318, 4.426454198813154, -1.4767188192637457, -1.9814662259138305, 0.8590524204046704, -0.7728101012621206, -2.5662956421927228, -0.3318168379290876, 0.5781969032603079, -0.6201411062849133, 0.25931732026467635, 0.7860770070481437, -0.963157979054834, -0.8672790875204228, 0.35698626318705695, -0.27365328768327835, 1.2028541135608606, 4.246965741261633, 1.384439766504588, -2.5251791543823185, 1.8693214967461331, 4.226859889059362, -5.806707983976142, -12.497882516951572, -3.4185523812622955, 5.455093153918652, 2.279632806901873, -1.4420838711314148, 0.32207088858699984, -0.039306439934536995, -2.02010019602992, -0.6057184191297207, 0.28618870820091186, -0.987053401573395, 0.17162577656694267, 1.6105969759273275, -0.03362237376446277, 0.17033169858188885, 2.5587934981684404, 0.6738571624254789, -2.29262154886727, 0.04137525072949029, 1.911912025836953, -0.9947317137562754, -1.9382599478621247, -0.06863626281231708, -0.9043040794366111, -1.011685894756578, 2.1075338066650833, 1.0064537806637732, -3.055095169620148, -0.8060989596484547, 1.8662731130338086, -3.8578369595558324, -7.109753617344833, -0.45861884264572184, 2.2747750798852358, -3.720915910511268, -4.300082556641034, 1.9589854366799802, 2.852181269489742, -0.3605845749239967, 0.01753507684268036, 0.48625780681138964, -1.4808491528250902, -1.1402111589305215, 0.39074189712416924, -0.42945816482624677, -0.5012941110747093, 0.5864425129346956, -0.535565663188666, -0.8550304362476513, 0.9741261174995679, -0.7676534097381701, -3.1896736836886657, 1.2768808917275227, 5.188604368312354, 1.288812611534214, 0.9300418644380473, 8.13908430008109, 7.326945653831235, -2.884582223367813, -5.3964042090766045, 0.06754876991721735, 0.6556052960365627, -1.137325760305879, 1.083594248561686, 1.3161199912698809, -1.6671248567743813, -0.8808326307707989, 1.155299649954365, -0.3501986011333074, -0.48064616388267395, 0.9879385581170721, -2.3433113877087317, -6.04992014920451, -3.12292236954309, 0.3235428617452955, -0.5109352738912021, -0.4009206989028636, 0.5780893378377383, -1.3123709045731342, -1.7948068092982954, 0.5815234896216375, 0.18963553756399446, -0.991413010662526, 0.401757852128735, -2.3420332135663404, -7.803710263087474, -3.9786780408808298, 2.727454384612103, -3.382231809753576, -11.762066400842704, -5.099204166815488, 5.049088012049416, 3.416993740327695, -0.8366803402401681, 0.594683539054814, 0.6184311293685296], 'positive_zeros': ['0.472256584181712127185155284391', '1.2919279981666972516298402419', '2.02393922885127942725458150535', '2.95574152627659288698836703912', '3.50046655210012425193302610069', '4.66777033907216904623653648348', '5.34594835919144062692453204810', '5.928205534017678504572664722341', '6.732805233931518764616051877712', '7.74669978770864275495618369140', '8.24651095864361761583485343123', '9.19991576966948409946125262749', '9.906761853173905280957212221004', '10.81701174612986589679920095590', '11.20132541504258974256412685670', '11.94900386303197076998211074707', '12.64237038776506846249560001675', '13.05874599923031653419245530924', '13.75027073555301146418309717508', '14.39102696932052671326745595315', '15.12807364601290638894423241404', '16.06308533108743007680566705899', '16.95408976257968022810078017884', '17.58756188451247682689192132564', '18.258167481356593058386556052467', '18.66741724236722472174626450845', '19.40213216151701866301071188962', '19.94871764394363801979817112935', '20.69912391134137408220584032822', '21.21872392343742063367409000779', '22.16411959373853394442171337186', '22.69140628952632298890661608478', '23.209393647313177295589156546544', '23.6791592418095758608783438685', '24.49427465028340567553761015923', '25.24097604773373828804217094406', '25.612079526286697276537255868395', '26.914091211027189543191718259952', '27.30839833661619069616114463314', '28.00394015881955438230496032335', '28.60566693135025457257983388545', '29.21368731834060200551091232747', '29.806494209171505294583012099417', '30.16927169316381484114689976620', '30.80638393491887730919498881293', '31.60342918982698364150635140354', '31.905812949466745989653750389240', '32.76661454627577290923509583913', '33.648295989591366656992171827508', '33.95896159365309932142081605701', '35.01225420719142217143237745174', '35.56858685190704926956511011443', '35.962440163961696678132623964283', '36.66641613059165997401048765364', '37.40927913269443064925126842721', '37.672630072680227824745610329609', '38.63265646382435936009985696302', '39.16788281418693162913576531107', '39.86995789402414349449514150374', '40.27857235682367169093825386128', '40.824690319388874825116403652684', '41.38348428255866601351030171015', '42.06292045135747419217567829641', '42.54583651836164532348546625059', '43.105465123650491205084841173676', '44.30874444662579910960488946186', '44.90096995543836375887603751684', '45.41282925331964413260871547800', '45.89170327359268106995765875165', '46.777496372351460691924528775944', '47.141954776542493056271443316414', '47.34569086836722621362095911452', '48.28696730574665766672735703287', '48.690223243563172348838290179373', '49.38593443529108671441574900133', '49.934235853336914027726033078705', '50.84575892894433635963070178677', '51.03197971006920588638123640748', '52.02036934617709830420431956990', '52.25077548597892298419353395338', '53.21757428790144931164748062824', '53.77331007111814774194995361845', '54.245976464221200928963159864825', '54.932128854989130231526635953161', '55.586597940729961759724287283225', '56.178637342936395429988632078055', '56.9158529839702225860840353541', '57.25502009088730715866648116404', '57.80570201603825288252413415595', '58.3609375116945262925621920160', '58.920062397328273638754326282396', '59.54151551356051830143062310351', '59.86302487729078618003486876096', '60.52731184940783399880899087023', '61.5965505379054397479284045040', '62.05514026256205538461861618197', '62.902846689474208578725228929216', '63.43658737019312856106263304308', '63.759142895312470711573089701332', '64.46609125692646643657954729682', '65.01690086953041749594105361201', '65.394915581518696024296751920720', '65.93593212265044684240344264165', '66.832270741005576560372189190209', '67.273763803464591263317960004729', '67.7378550395501447724002739892', '68.62805486932159738710487106235', '68.92382063561533362305728054274', '69.52490105832792602955836226924', '69.94971812487513668505759620291', '70.82485534045402270828221232270', '71.38635071529318786780694836355', '72.11506609383495176681239766638', '72.51196661285347558925240531376', '73.53192677113185556375151378633', '73.8449301601976373243242435340', '74.39495157907790151403480005684', '74.83876449855076482844959227680', '75.456384627820587651091515554383', '76.09800009438444741243070608544', '76.41501759763982412252228286114', '76.89141225954546456921020817497', '77.63735108680929732786951495265', '78.14125111063610517382855672302', '79.01860631080711072092166157128', '79.39049590855230349476802015118', '80.35557281247637213044875597970', '80.81858978609412296382656634025', '81.29020869664490597389483465904', '81.93147966185272151272979725447', '82.359414429348877505893826519826', '82.91912070498714054930491914618', '83.48497562647164636223555691933', '84.1927919830093491010486894744', '84.70085929216020225989596622690', '85.35099396859556497592618401067', '85.85264188091459082150360770933', '86.214102324116469892215523635112', '87.01072540598663888956425753963', '87.47185720501801408257131769673', '87.57340284124821744349544677855', '88.76197362693468808773022039049', '89.220678321180800699468152751202', '89.86312917980261038114279547041', '90.85454177071499254680087379329', '91.18417202281468829224179223249', '91.64163323881105152647801668165', '92.029245187444833273096009093828', '92.83628301954524834018769597288', '93.27750333108850592001257198476', '93.66361620227382978810329433980', '94.19183525299009044131880664118', '94.7344722908235467841883217997', '95.51465177969997037297090608360', '96.128432061695026395939170653372', '96.455318155676814285378048258116', '97.20423009293610675116006294534', '97.90067739905144146479249562525', '98.3701966190968181700252256971', '99.00596614346789686337930760227', '99.62246127200313257022069587748', '99.92772305411200167290755750940', '100.7917889474994226238023461675', '101.094579541095976104604673641', '102.09263092081364244437403894955', '102.190673557682448125512493117603', '103.10269222982136310316369857616', '103.27203200377020721744975099769', '104.06605940910473681466343170555', '104.32082056974190689294466869836', '104.89379071356708951944571448074', '105.61622379098507441840159973543', '105.89338946607314855389096711617', '106.73184255690085619461245846103', '107.6577701682890665958286910899', '108.09421428531719477462084834305', '108.91087368209566597075064849275', '109.05435838232546312567583089171', '109.59053778653047142964109644227', '110.40376037178050519663759832282', '110.63452842237556625877102792869', '111.22894865821604398340984492283', '111.67511667357240266361080472886', '112.31270526940078352663845684268', '113.05302257441893262262828476209', '113.59124103889641134337586580352', '113.93887855838227210474890314731', '114.558446587122965974262202664927', '115.17757765772139847775605042708', '115.74743817328032493818063052894', '116.15772876770688600509799421836', '117.049699515751893647684341790934', '117.421773758756544174511351334067', '118.086119100404773262780349074501', '118.71717638386247034963269138764', '119.256189301040909055598069782727', '119.7960811374927822772424717117', '120.31992845741835786457064449591', '120.8421579970727599617080917773', '121.24449984308743373421322425076', '121.70856873433210479724195386001', '122.32618540404360592712722244460', '122.87251997674679024568358871328', '123.29222439066132228214906700841', '123.863247721905663560011567699082', '124.73544627650911385245501039077', '125.516855468366536572955397968119', '125.79126067746033203173761074371', '126.46458294125399007181522611942', '127.115203569624235437960938098982', '127.5116668862578154611322017011', '127.86265438863800028924489941819', '128.54601360646894984006135318089', '129.01395018853204067117049792093', '129.60593250479836905597575862261', '130.27138533993235508799448977566', '130.75965076141403582977849035083', '131.36270260087659219138741362704', '131.76469393716418236093018333973', '132.22837775046990812576078806427', '132.883667269414453591110265271940', '133.40019426422184110776328836957', '133.73235676972829453425639395157', '134.723696334844030160446128088453', '135.15210083153924732034972710773', '136.10191905421656784636673095448', '136.31042034089230218133432742556', '136.848917311720797567862324914426', '137.75651423588211031408438958611', '137.987163882436146683669527181039', '138.20710174240375897276128598551', '138.95169888428014570523153767127', '139.48068369096046009217385035667', '140.03181510770688037331444134113', '140.420358544343205920622725659476', '140.92665035524827864107786599965', '141.80167935038908765180280939821', '142.322440502341090459997149144005', '142.71678750552453439377600586740', '143.61917330173609321365686543117', '143.86330712873395496174036798270', '144.745611692261048924520334612', '145.1512050863429243365720893986', '145.408099165845232620371537202288', '146.04791170701828831035289516301', '146.798547585603367845728594413996', '147.38031834582084670554662972282', '147.67848096505753832118427940419', '148.384168271298880374891590989009', '149.002461831906896394306790093564', '149.25710302697937282305141055026', '149.79589715479343939416159405249', '150.36147745598353496482528729843', '150.803102470423313686315797279376', '151.42548481165779281926790817797', '151.8297072909245105400985199375', '152.91832100138499870519031832745', '153.46092212246623040136223334505', '153.81448827990469695893799304671', '154.56268839181089345200082867058', '155.07121404929085807212723128625', '155.37351767583383254130225006684', '155.88971776802896784718535285258', '156.382560219644927529113520027343', '157.03358577306933995924485694633', '157.423510209728449760026761872818', '157.934143982757529118710001432002', '158.53562101869551799683425404878', '159.25322269330815745940415246941', '159.77341936503694959646812133871', '160.15966706967808644044233281283', '160.62208100706226681242147867022', '161.388507797188131435279765410249', '162.04003235190303406882543181055', '162.58105149343142619641170556331', '162.74327539467871975746460629015', '163.66284009635472735326366763683', '164.2483352314258074193954945214', '164.60956215965262668160404970727', '165.35473424109156364113922421625', '165.76254535573629170939067204430', '166.1994897933169459743288578883', '166.71442513075166838776765362732', '167.36112375354987366608732034812', '167.704595478535542061902433394986', '167.98269458803991292880400928628', '168.8261984074158682757708954374', '169.28595902878701044139130869426', '169.85224381870813318819854735173', '170.710606868320082746720684374123', '171.37838841383182151463239906297', '171.82681118254548129399170946557', '172.182260935928580849759337832118', '172.90763546705834667220974082926', '173.20261306481143939983157508247', '173.727182979465503413555786397569', '174.36914743551664102446119905509', '174.6631259920921632827428076961', '175.364072741211451602352948235866', '175.93408648712124937510641584344', '176.472916964241031535314838072446', '177.21682088326335547175725371169', '177.29759777478633759674423752675', '177.92170750174954261363876629027', '178.50558968675314715129636836677', '179.1140294321166883121652222739', '179.52039516463481609262402914880', '180.33180456017053869439120794057', '180.76261403431953715297374698196', '181.46092822405395456862809481871', '182.137086887131483500868322428187', '182.49666959696317886532341483135', '182.90163893863188698413020824554', '183.62512282745665730548283909212', '183.95751584223694113679610083854', '184.491019424004377955924252374690', '184.90209739003294044436435897710', '185.45002314327431817297270388436', '185.86935734286571018361111394972', '186.50141388564572886010766332931', '187.29916345925857172852522300439', '187.42120531837408592509145530022', '188.347062805777494925070082036379', '189.05771007548375047304159264377', '189.45322553461713321303616259900', '189.88242156379335905147688739004', '190.4453977211889383095185841987', '191.0333649819553624108453527894', '191.50919688121746076412315711067', '191.95055676809076416693678076105', '192.34279551319501489220110494312', '193.371989567072222154722876683125', '193.64037754118611053846056010536', '194.14339591646854535013672304982', '194.51435359135315736451472669834', '195.227246586961775950474951440373', '195.654517124261055195633628791574', '196.15150020786643418851662985763', '196.39803493428506172239951041811', '197.33122624309378990894313339836', '197.710366814261060922974641288875', '198.56600935957157027917573565122', '199.266292599763925072273225421936', '199.60760576532908607058676903187'], 'prelabel': '1-4235-4235.1052-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 19.66725731711931, 'root_angle': -0.9879163764324277, 'root_number': '-0.999279536524066215513062863662-0.0379527058883475972773775609838*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(660)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.616747648798381964460783405614-0.715421771116326020006191698237*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.472256584182', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.29192799817', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.02393922885', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 19.66725731711931, 'bad_primes': [5, 7, 11], 'central_character': '4235.1052', 'conductor': 4235, 'conductor_radical': 385, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4235/1052'], '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': '1-4235-4235.1052-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': '1-4235-4235.1052-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 19.66725731711931, 'root_angle': -0.49395818821621384, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.472256584182', 'prec': 47}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_4235.1052', 'Lhash_array': ['dirichlet_L_4235.1052'], 'label': '1-4235-4235.1052-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4235/1052'}