-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_55.4', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.30901699437494745, -0.9510565162951535], 'a3': [0.8090169943749475, 0.5877852522924731], 'a4': [-0.8090169943749475, 0.5877852522924731], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.30901699437494745, -0.9510565162951535], 'a7': [0.8090169943749475, -0.5877852522924731], 'a8': [0.8090169943749475, 0.5877852522924731], 'a9': [0.30901699437494745, 0.9510565162951535], 'algebraic': True, 'analytic_conductor': 0.2554189261963547, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]]], 'bad_primes': [5, 11], 'central_character': '55.4', 'coeff_info': ['x^10 - 1', '0.809016994374947 + 0.587785252292473*I', '\\\\zeta_{10}'], 'conductor': 55, 'conductor_radical': 55, 'conjugate': 'dirichlet_L_55.14', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^7', 'a^1', 'a^4', 0, 'a^8', 'a^9', 'a^1', 'a^2', 0, 0, 'a^5', 'a^7', 'a^6', 0, 'a^8', 'a^3', 'a^9', 'a^6', 0, 'a^0', 0, 'a^5', 'a^2', 0, 'a^4', 'a^3', 'a^3', 'a^4', 0, 'a^2', 'a^5', 0, 'a^0', 0, 'a^6', 'a^9', 'a^3', 'a^8', 0, 'a^6', 'a^7', 'a^5', 0, 0, 'a^2', 'a^1', 'a^9', 'a^8', 0, 'a^4', 'a^1', 'a^7', 'a^0', 0, 'a^0', 'a^7', 'a^1', 'a^4', 0, 'a^8', 'a^9', 'a^1', 'a^2', 0, 0, 'a^5', 'a^7', 'a^6', 0, 'a^8', 'a^3', 'a^9', 'a^6', 0, 'a^0', 0, 'a^5', 'a^2', 0, 'a^4', 'a^3', 'a^3', 'a^4', 0, 'a^2', 'a^5', 0, 'a^0', 0, 'a^6', 'a^9', 'a^3', 'a^8', 0, 'a^6', 'a^7', 'a^5', 0, 0], 'euler_factors': [[1, 'a^7'], [1, 'a^1'], [0], [1, 'a^9'], [0], [1, 'a^7'], [1, 'a^3'], [1, 'a^6'], [1, 'a^5'], [1, 'a^4'], [1, 'a^2'], [1, 'a^9'], [1, 'a^6'], [1, 'a^5'], [1, 'a^1'], [1, 'a^7'], [1, 'a^4'], [1, 'a^8'], [1, 'a^5'], [1, 'a^8'], [1, 'a^9'], [1, 'a^2'], [1, 'a^3'], [1, 'a^0'], [1, 'a^7'], [1, 'a^2']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-55-55.4-r0-0-0', 'leading_term': '0.887474371266729624167254415216-0.276739131254223502582985152437*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/55/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.9296210552814623, 1.0284265469520744, 1.2210567349322163, 1.2979315293934268, 1.157073630056221, 0.7827281738774882, 0.23484442340593506, -0.3607495033001207, -0.8392079213654744, -1.0437463345251468, -0.8837937103995961, -0.3857177331084599, 0.2858791761006305, 0.8532304836652467, 0.9998969342361861, 0.4784819489420286, -0.7823836740475089, -2.613824967221206, -4.619615640357951, -6.276460618666232, -7.0982191690110135, -6.809956901089898, -5.464387667367321, -3.4466936334843696, -1.3528923870345404, 0.22133454372407346, 0.9016704703754455, 0.6736972619478934, -0.12566959403314445, -0.9677494844692457, -1.377541265392256, -1.1548417974525527, -0.4646307161482847, 0.2532816331455493, 0.5187980421231819, 0.07780775739168036, -0.9372630095731819, -2.045657950338237, -2.6505346873196616, -2.3559103548640743, -1.2030854295074564, 0.3103341634968732, 1.45969802215743, 1.6682056468773718, 0.8346830484936845, -0.5706618157471369, -1.7160883480484141, -1.8346484288810272, -0.6501513850678726, 1.4316650437049956, 3.4890074854059865, 4.539768093489013, 4.054611071573201, 2.2494846254447007, -0.011595652511403393, -1.6622447017683806, -1.989852425479175, -0.9956140112057595, 0.6423869401240828, 1.978575370261587, 2.3412519599154877, 1.6880613241054359, 0.5700939239811081, -0.2617294831670678, -0.3527387563502176, 0.17685092576256717, 0.7521362928222476, 0.7838014914618687, 0.13212881080362454, -0.7314654742382505, -1.0035256646386117, -0.11246205868389432, 1.7987197985766747, 3.8161764027236003, 4.715664345545736, 3.6927882196543735, 0.9153086930638555, -2.471858086078411, -4.933115323330718, -5.390212288232531, -3.820997960073626, -1.2380385542002883, 0.9409031090630364, 1.7346429283267386, 1.123376548462725, -0.06253303737375626, -0.7891440567385535, -0.549136388642987, 0.3214350623989758, 0.9434532414379774, 0.5832511672763678, -0.7713594113455607, -2.366707423589987, -3.207949621335855, -2.7764133323617415, -1.4151700786333514, -0.09042507860910198, 0.3102237434185397, -0.36731376009098815, -1.4283349826203475, -1.8609748752814559, -1.1387626345982367, 0.3070999434269671, 1.3324287770943413, 0.9104887242048255, -1.0348123236961628, -3.421068783479714, -4.6345117900874495, -3.6032070417128406, -0.5795702345910304, 2.9349912598941255, 5.105344854936065, 4.909036887070012, 2.7357455350034714, 0.04404771075395169, -1.656701467003176, -1.7667601414325673, -0.8372149798835593, 0.02032744231494277, 0.05450392945489883, -0.5932364285812125, -1.1268859258834976, -0.8651134639218755, 0.1183747672881985, 1.0288423445735833, 1.0439012279694602, 0.09127996926556046, -0.9658902815492788, -0.955172007947814, 0.6175911190084781, 3.011763566685881, 4.635730258895297, 4.161519102984959, 1.5586725042362617, -1.760843271033238, -3.8549905885091995, -3.5857405129044544, -1.3944455868603856, 1.0624283501242653, 2.1438883478308726, 1.3928292801208533, -0.23072274051983235, -1.1961827610137437, -0.6392062437226304, 0.986756289061131, 2.3348213784870984, 2.290588004477789, 0.8739530749844123, -0.8063415564706022, -1.4834340992455184, -0.7635780894640138, 0.5944881857955371, 1.3648810014714694, 0.9060167364342744, -0.3225786544351056, -1.214153420975764, -1.0334029173999433, -0.09286820033241419, 0.5384457837458894, 0.07573612303607592, -1.101673479853107, -1.5673481156565903, 0.020222802940450195, 3.6494576118667936, 7.636793149181052, 9.638006282821493, 8.296729771936842, 4.27280905423395, -0.1714152885605614, -2.7367138605101875, -2.6161676720350338, -0.8460175044902496, 0.7113768507300383, 0.8657570457704916, -0.13046734441645422, -1.0743588273852511, -1.0247054714514154, -0.12824642791692678, 0.6354868726935023, 0.48732215506477816, -0.34003013273524835, -0.7912272307264616, -0.022947368251148067, 1.6763264096817316, 2.9786091832169284, 2.6188249546495426, 0.5622286100547496, -1.8345869789590936, -2.8951660954222636, -2.0533273945368364, -0.39245001339798263, 0.23436803327195577, -1.1953202503941736, -3.9173639853870466, -5.929043264188294, -5.625015969056431, -3.151752476751068, -0.32052471558041323, 0.8656199884421611, -0.1672936915798108, -2.158955034439558, -3.1432932489619683, -2.119126965559494, 0.16645105955462305, 1.9480432993166439, 1.9879863218758853, 0.5664241080228627, -0.9055318538779001, -1.215774142710999, -0.37383687303139684, 0.5778674883045671, 0.7048282605418701, 0.1260684097684036, -0.16601626373541592, 0.571446396185039, 1.901621467439614, 2.4709303834160807, 1.3302504459136595, -0.9052767885955116, -2.2567801897740862, -0.9568396605129441, 2.893469613884446, 7.08928384912744, 8.858717946276695, 6.9794036862732085, 2.7237449602088017, -1.160855845525243, -2.5720981151958373, -1.502084401850655, 0.3188606409446845, 1.1245390581289798, 0.5813299763296401, -0.22677463504900455, -0.11868389387620645, 0.9185770685348916, 1.740770707131152, 1.268470801731698, -0.3290402048257263, -1.6895089222628752, -1.5320089332785134, 0.08201889784340158, 1.7513412731816889, 2.0415081871357827, 0.855125212636766, -0.475073408514767, -0.49995658692066336, 0.8756032908499644, 2.2204435257503214, 1.9427200409222283, -0.07309988430835627, -2.1666401767691053, -2.3405471514831957, -0.17686962089907848, 2.5699869227658785, 3.357499619790168, 1.0561148622546568, -2.9919370964910796, -6.027860132541417, -6.128298825954653, -3.6790123550231404, -0.8344162377103851, 0.43978636610039623, -0.07712739472081095, -1.0318177500804675, -1.043456164299155, -0.03348458042230365, 0.9070823225611381, 0.8337693872457141, 0.004247842439699736, -0.43368517199214396, 0.2357623868508944, 1.4080793872863853, 1.7290040634537938, 0.6211674119463098, -0.8226218691399754, -0.6547405034138398, 2.0159509485056573, 5.840070915802643, 8.06123479689668, 6.791519324575202, 2.7135698700687994, -1.3903624086637933, -2.9287423155109065, -1.5799610272284215, 0.6760383016102409, 1.513459562817546, 0.3339316383813762, -1.4326458221712783, -1.9402052027208387, -0.782733939882468, 0.7112047203571865, 0.9389751126916945, -0.3037632092750143, -1.6340828877742046, -1.5307014705789697, 0.0842018169147715, 1.7462259019331345, 1.921038591406942, 0.5337663735707489, -1.0034484929346053, -1.271616472478916, -0.2821131864535333, 0.6318818480613878, 0.35159435398798566, -0.7110295202041268, -0.992056954275484, 0.43395855966107755, 2.500872437029694, 2.7971952035832715, -0.18525608464164425, -5.309733944166465, -9.366247685758157, -9.629587882607266, -6.143916661005769, -1.647190264351816, 0.7888667355835581, 0.235582980942117, -1.6904161984898851, -2.6665345004701293, -1.8389770463777777, -0.2922369212163551, 0.39920241027201975, -0.13763463546983978, -0.8853471594693368, -0.7869574508824622, -0.03306737029116283, 0.17595794338510654, -0.8738430352956881, -2.358832401965576, -2.5915475318599843, -0.8285680451165225, 1.7076670566375491, 2.8216887294039164, 1.4994806316948401, -0.9485168460781592, -2.03579180716204, -0.5250102595620382, 2.259683177184499, 3.6117941469098795, 2.033992515455321, -1.2834460149715703, -3.565247458306862, -3.062491608577849, -0.6156841946109921, 1.3236853611753825, 1.1693897304173135, -0.3214079750933271, -0.9897410883302358, 0.4126859912817257, 2.929164466350837, 4.3920228609956835, 3.60492056701208, 1.4508237601536411, -0.13660842998566125, -0.15509905290368003, 0.6348993968138218, 0.8084876074880744, -0.017350520996661373, -0.7967936346870301, -0.3920505817137853, 0.9319129525651919, 1.652808652986976, 0.7575854574449236, -0.8024670985390892, -0.7612972332694476, 2.1016535734925554, 6.259304724991436, 8.346587358997537, 6.08909788655928, 0.5236553367603717, -4.694373427081255, -6.341734372247697, -4.209128013667304, -0.8800216330922708, 0.8807565854968429, 0.486854869944473, -0.5256887547561475, -0.5643353591637299, 0.3029416474151832, 0.7208121927748444, -0.13306759312538996, -1.4558895602733872, -1.706805745704273, -0.4385537177282597, 1.0544478133515298, 1.087612657192853, -0.5121104413479375, -2.096941633720208, -1.924577092375786, -0.09506031064491662, 1.4536124593550825, 0.9888207253944894, -1.092454574507665, -2.591220110077229, -1.8441170607945554, 0.38986930766428773, 1.5881862717189092, 0.10308514508078699, -2.953530789990807, -4.636208768659127, -3.0691585047652534, 0.6072155557955811, 3.258398182338455, 2.739631205872031, -0.14830570990861613, -2.6215836696070385, -2.687694038200048, -0.8716381219633048, 0.7128504563766713, 0.7284384603076002, -0.17134824893924255, -0.41763906620206515, 0.527150893065425, 1.6102367253283192, 1.5580036569205347, 0.45972033049956706, -0.365256767550846, -0.08915353388059516, 0.3985703614650749, -0.6066170467803953, -3.419113890013989, -5.983433298436083, -5.5448536161745725, -1.5138514713198972, 3.470485526514958, 5.639782585890881, 3.48210955100218, -0.9040349445167464, -3.843701651476002, -3.4733590461331336, -1.147707722639354, 0.349666909735704, -0.2657721082383324, -1.764073136641502, -2.1260898239020025, -0.8947716511067931, 0.45921173225432005, 0.40952401775903635, -0.7747719674775064, -1.3429200965630848, -0.1542650865865745, 1.8851200030883493, 2.7271963803737047, 1.438181484076638, -0.7430637455894262, -1.7547569441553412, -0.9490919547332326, 0.3219124596693556, 0.4264149631177929, -0.5351497376660368, -0.8303342470174779, 0.7004027001263655, 2.8673974841427636, 3.024937951796252, -0.06331794561883945, -4.456710839861662, -6.507002262101018, -4.311013452060186, 0.33816831374021966, 3.5686824951724083, 3.036773178817734, -0.0801764065157988, -2.575458661452402, -2.4575851338124948, -0.5763378146471565, 0.7894119729073155, 0.5269370281131863, -0.4132566241376098, -0.5344099449389608, 0.31183018571484605, 0.9179370265883434, 0.45929633489947763, -0.2894092123856951, 0.13358054120915022, 1.8798282127859527, 3.213386963172601, 2.302380728701178, -0.5258771227891024, -2.7641820231480767, -2.265037538416974, 0.30806272474980645, 1.917690148608855, 0.2404331309164378, -3.7963407003286527, -6.789876969690009, -6.221955097914086, -2.899419382757195, 0.045469314937554746, 0.42965413665633, -0.9639128747857422, -1.6606783353567145, -0.4521534376368252, 1.311781405891792, 1.4339778731425403, -0.487840127647531, -2.5269311097225717, -2.5591608088357303, -0.5861167078381585, 1.365243029450133, 1.553795336710425, 0.3419009760437528, -0.4995556321646625, -0.031611878875001026, 0.7968265667525339, 0.50250376057882, -0.8983520748960324, -1.7660096592343186, -0.9001558258008393, 0.7038864587293033, 0.753066894769138, -1.5244473683105828, -3.8681548216797212, -2.8666714208570125, 2.4230575983308147, 8.958924491161559, 12.160285032667131, 10.024630626255808, 4.794068989051034, 0.5847002242412433, -0.4454414900108807, 0.4952356796598155, 0.9056947609632808, -0.1034971559847762, -1.2635764550999389, -1.166996250370298, -0.1495501903528196, 0.22384820593154198, -0.7328922025346148, -1.8617266882862755, -1.6020888220295255, -0.06996668071576076, 0.8746597035166868, -0.1780212684882018, -2.3106023965929325, -3.0969979031297274, -1.3604053660262387, 1.3019653717553987, 2.1445050462052255, 0.34608218085097764, -1.9759283218444745, -2.0890804250989623, 0.23434165594671583, 2.3626293748087055, 1.7188893115255994, -1.259144126301859, -3.4702182651904376, -2.48723086227484, 0.8001857859320436, 3.150831171256609, 2.4354345565012756, -0.2366299915820403, -1.9610056000032752, -1.2649796364817036, 0.5232663741833263, 1.098783302261394, -0.12837551593973695, -1.5887373789152253, -1.6425811939558579, -0.5184167745610944, 0.20341604877160332, -0.25780259004481976, -0.9087879024210181, -0.4340871545418373, 0.8332485664518504, 1.1185972342713018, -0.39704362125322357, -1.9219416223529597, -0.5456418145673617, 4.3793324543496635, 9.780214553938048, 11.371258007004611, 7.801224826756375, 2.07920607109085, -1.3253632490225118, -0.7017304630575112, 1.723117233591673, 2.6174042121910857, 1.0685687324039737, -0.9652623315438534, -1.3453099850138952, -0.19137557573682185, 0.6671868981551407, 0.2271616637001551, -0.4465521980513071, 0.23777492874053113, 2.1142670500044427, 3.1956988092549237, 2.0181749848694284, -0.4597779229271291, -1.8062819018256961, -0.8741827766224738, 0.9210194233221571, 1.3600894496539657, 0.09544138108528577, -1.0324920268061626, -0.462216347432266, 0.8810543335331137, 0.5048586926094191, -2.495905876647642, -5.831996374926751, -6.166902768135611, -2.840096136062286, 1.079059462432833, 1.8220299678332925, -1.1579465739878756, -4.662070499873941, -5.16697472722874, -2.40441721134623, 0.7143633197907607, 1.4521065185027044, -0.032082689892959385, -1.436282669006787, -1.2335051188688122, -0.1628558644496514, 0.2092772044813171, -0.29994598807358414, -0.39781566625063675, 0.6836583361965848, 1.8849383050058046, 1.590194041485699, -0.08017575159553741, -1.0505414897685377, 0.22960298821766437, 2.5216823317566983, 2.780109734504925, -0.3565374278859454, -4.545463989085297, -5.820453220302389, -2.7566064434897486, 1.8722722471573339, 3.88742982482772, 1.93641880849659, -1.4329764658835134, -2.837391152077967, -1.6309916453112048, -0.03756770665822448, -0.06837079522959133, -1.1100153042932512, -0.979847551960576, 1.0764240365724187, 3.248881428188418], 'positive_zeros': ['1.99667011438049429979367967689', '3.61939879193141055867415378074', '4.82770641940531080252354209309', '7.756868236998142656203630729035', '8.706775998583808217769480336450', '10.189293925504757294865244026834', '10.96742498374779404832200407491', '12.74727808666989897976320159439', '13.93976664877493562105266950396', '15.10686625051322361705336870071', '16.87329332309144695559088663513', '18.00536664344550772669720782242', '19.560915611623006716801028801319', '20.22773333891576712674693451361', '21.29612351392970691878104624523', '22.21038148346257492280334461505', '23.83410430655072663162705406317', '25.47123473733393843780748900906', '26.54503379534831116338914749913', '27.39209869300254187503985681420', '28.28061126150332577244767077548', '30.0308861233454996119172354424', '30.50156761839451478970885696910', '31.81034538560283580572690419', '32.66927930203567886792795546578', '34.11252305543507664542679573411', '35.63077075597366750862330992771', '36.86278016229888340942921933841', '37.22542384078252614559792850934', '38.40427733518076980595284953823', '39.39856149102128576438325200460', '40.218429497617092297642054425638', '41.706254846272912539493222878594', '42.97862707143373364560986413305', '44.016843567802637387954187213112', '44.82220013481673762313870694001', '46.08966581168456835377632492789', '47.05021222754602884085228250921', '48.046409991000786109335666127134', '49.09266517029002523966492589791', '49.71060967664583981142567411388', '50.62270559402430677788526120427', '52.48606861069240075371018173138', '53.58140616402672362920744049969', '54.34080279849389510495489827636', '55.352479139837274046438408149463', '56.12966094326913711337026184999', '56.880118778696892440745527312874', '58.193741557146908357085234531957', '59.47482055260525631165328785054', '59.787948687974149304128531211340', '61.6096463616774112891659904910', '62.15825523768449277474543188951', '63.41540228283675740254768503037', '64.47985083086384574539678279492', '65.41897156970078201355496417921', '66.31780003599192289492583410658', '66.68769525091692942674426019514', '68.001354390605230763632944693732', '68.843947901716209163598326289429', '70.51463361867805443076304014472', '71.5010644985220521515422158934', '72.38912558716056229251721404613', '72.86063477778052579872024623268', '74.00425988130577872610268863372', '74.98673719018952470822692432202', '76.11643390217164738590406320002', '76.701823880426717495086322724314', '77.80308816908461549569995492589', '78.76902348290949294766997845398', '79.77410425771170838135037980687', '81.39187122188829508265754166451', '81.85104148626282237466928806778', '82.82125745044954732683544761783', '83.751587324704068761221560265099', '84.30505515782740466538546583114', '85.43258857261128372719094221783', '86.04480102090463115001871625739', '87.69161918571819386426264787473', '88.64760456410391037095179438120', '89.430988135633069272329013548016', '90.46090713351194278899815303951', '91.189602409762268826553536514043', '92.17401198730645742501075284596', '93.22006072301141532643845514093', '94.13651790129598006511069065287', '94.79640464216293170630536912109', '95.55702266495257187337536876554', '96.54943082395514622240169518065', '98.28702685191315809957605481615', '98.792263296139015159406853313428', '100.07680481000610448786563765836', '100.57438929182304786669373811622', '101.57763610511908067158378182860', '101.96386511335207335724285812526', '103.22457077965372721858744847550', '104.2506393997648750895246270774', '105.0611395967980612020143424552', '106.13227538598018333043315403975', '107.26399909579124892982068167071', '108.05889898565881167769152228178', '108.69025485399836324681356990951', '110.26717109606083609755341426591', '110.69304876018204350271664810475', '111.557326516653643258573977824122', '112.28948779762061393347908566117', '113.26743173868585519406104767143', '113.86724124735469183622157536422', '115.33950269949346795318990572460', '116.67148467480429732495042489947', '117.324287754842352222471692386158', '118.02447948347122323411613444369', '118.71834888798681627616453685042', '119.76757441467784898451837227697', '120.54200346158002859112944824035', '121.57682620172770978159762821925', '122.34842662461146454404011334633', '123.38321043139882947258698366562', '124.07433159557479074065191725696', '125.26234923313533108950893069202', '126.23544777824161464384865329889', '127.32942316395087801001056691376', '128.06334560359002544276278810911', '128.611056320030050058629591816677', '129.81855487842075491506783655523', '130.35348268006666555338755122825', '130.8248032951640675222229218621', '132.27756354790637462704314451135', '133.37281385792185168118941044509', '134.56433482341932092875667502011', '134.93635694209322617289322376405', '136.11847737785085375828521617504', '136.684501668599966968747586276072', '137.52452616183815988295836532351', '138.63819168058250672995606130181', '139.59126326720496040937486256347', '140.1528877026596946089294564295', '140.83181001990600157123963868137', '141.87039794012722959142273245495', '143.10217671210646951870706138788', '144.05502382567977954135732064648', '145.09750505814334156813585946512', '145.79155401362105274397334828391', '146.463243651742922404734394739769', '147.35207832863535182736026630090', '147.77623903571699454152221923130', '149.00893251957999732697535562336', '149.96448517913713622791231951257', '150.647123087679129510702496876339', '152.179738238165386482656207012554', '152.61473552619537302919035161202', '153.510703489359999521375925618366', '154.31103984069248691020420895402', '155.39096283110974598356411129097', '156.33613163136638615222551400224', '156.88556387786599468460867744781', '157.62582708456234268486537042339', '158.60234757071718742394391474788', '159.19574718600669514900142017026', '160.192385907964081489024319362603', '161.957441618196597944323991374398', '162.35995735184357397732574943510', '163.10171603742915752474484889337', '164.11535546430299254128372110223', '164.48994802161863853672350871676', '165.63876598897018299593148644230', '166.22053696215704501092001897358', '167.33956165213927171220910347644', '168.16638609165862678360450957840', '169.03628369467960061738752393863', '169.87901016276183693873920988900', '170.86557472884930071688443325559', '171.84768508091863896865596194446', '172.71479742966246896352710515894', '173.41378470900333614391410544107', '174.537917844197474828686340551024', '174.89357713828772662601778757479', '175.734771435819423799894008097074', '176.49995408859068706892643306110', '177.23412527646239169687305860797', '178.8956134195845054853233490120', '179.46820651004016992445395860744', '180.460468800600148580331376383550', '181.29625773271668524892092490850', '181.95554929022108754608812448777', '182.44639085282225111625833647009', '183.690288911804188811394052406631', '184.51955460631745341523565388091', '185.33137379025546746332173227082', '186.03792916538915043355391823717', '186.63592540884365588718633142119', '188.02285586131980288405621158008', '188.65481576865466202076334333246', '189.911922214596615242132896928257', '190.619617552746315345636018492364', '191.623884176052945937028647113216', '192.031236455802471575394902249294', '192.65033816922715034090747508921', '193.73565884359748248170273878432', '194.34195631057115059395088169311', '195.28639717575153938139950057841', '196.42933671183341537985122410748', '197.36022468993805072645125135555', '198.45075348514346315045527896328', '198.723673961986902387293137649510', '199.54949367194905341520883487349'], 'prelabel': '1-55-55.4-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.2554189261963547, 'root_angle': -0.09621626289782827, 'root_number': '0.822761021268750033178975733422-0.568387457532978515621493932108*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0962162628978', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(10)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.01157706507202790787336084287-0.260543761749814509860392659363*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.99667011438', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.61939879193', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.82770641941', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.2554189261963547, 'bad_primes': [5, 11], 'central_character': '55.4', 'conductor': 55, 'conductor_radical': 55, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/55/4'], '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': '1-55-55.4-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': '1-55-55.4-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.2554189261963547, 'root_angle': -0.09621626289782827, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.99667011438', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_55.4', 'Lhash_array': ['dirichlet_L_55.4'], 'factors': ['1-55-55.4-r0-0-0'], 'label': '1-55-55.4-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/55/4'}
Lfunction data - 1-55-55.4-r0-0-0