Lfunction data - 1-2475-2475.1913-r1-0-0

Formats: - HTML - YAML - JSON - 2024-05-17T01:36:01.059999

• lfunc_lfunctions •

  Column	Type
  A10	numeric
  A2	numeric
  A3	numeric
  A4	numeric
  A5	numeric
  A6	numeric
  A7	numeric
  A8	numeric
  A9	numeric
  Lhash	text
  a10	jsonb
  a2	jsonb
  a3	jsonb
  a4	jsonb
  a5	jsonb
  a6	jsonb
  a7	jsonb
  a8	jsonb
  a9	jsonb
  accuracy	smallint
  algebraic	boolean
  analytic_conductor	double precision
  analytic_normalization	numeric
  bad_lfactors	jsonb
  bad_primes	bigint[]
  central_character	text
  coeff_info	jsonb
  coefficient_field	text
  conductor	numeric
  conductor_radical	integer
  conjugate	text
  credit	text
  degree	smallint
  dirichlet_coefficients	jsonb
  euler_factors	jsonb
  euler_factors_factorization	jsonb
  gamma_factors	jsonb
  group	text
  index	smallint
  instance_types	text[]
  instance_urls	text[]
  label	text
  leading_term	text
  load_key	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  origin	text
  plot_delta	numeric
  plot_values	jsonb
  positive_zeros	jsonb
  precision	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  root_number	text
  self_dual	boolean
  sign_arg	numeric
  spectral_label	text
  st_group	text
  symmetry_type	text
  trace_hash	bigint
  types	jsonb
  values	jsonb
  z1	numeric
  z2	numeric
  z3	numeric

  
  {'Lhash': 'dirichlet_L_2475.1913', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.20791169081775934, 0.9781476007338057], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.9135454576426009, -0.4067366430758002], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.8660254037844386, -0.5], 'a8': [0.5877852522924731, -0.8090169943749475], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 265.97568886669694, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [5, [1]], [11, [1]]], 'bad_primes': [3, 5, 11], 'central_character': '2475.1913', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 2475, 'conductor_radical': 165, 'conjugate': 'dirichlet_L_2475.1352', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^17', 0, 'a^34', 0, 0, 'a^35', 'a^51', 0, 0, 0, 0, 'a^13', 'a^52', 0, 'a^8', 'a^21', 0, 'a^36', 0, 0, 0, 'a^37', 0, 0, 'a^30', 0, 'a^9', 'a^14', 0, 'a^16', 'a^25', 0, 'a^38', 0, 0, 'a^33', 'a^53', 0, 0, 'a^28', 0, 'a^5', 0, 0, 'a^54', 'a^59', 0, 'a^10', 0, 0, 'a^47', 'a^9', 0, 0, 'a^26', 0, 'a^31', 'a^28', 0, 'a^2', 'a^33', 0, 'a^42', 0, 0, 'a^1', 'a^55', 0, 0, 'a^54', 0, 'a^57', 'a^50', 0, 'a^10', 0, 0, 'a^44', 0, 0, 'a^45', 'a^11', 0, 0, 'a^22', 0, 0, 'a^12', 0, 'a^48', 'a^11', 0, 'a^16', 0, 0, 'a^29', 'a^27', 0, 0], 'euler_factors': [[1, 'a^17'], [0], [0], [1, 'a^35'], [0], [1, 'a^13'], [1, 'a^21'], [1, 'a^36'], [1, 'a^37'], [1, 'a^14'], [1, 'a^16'], [1, 'a^33'], [1, 'a^28'], [1, 'a^5'], [1, 'a^59'], [1, 'a^9'], [1, 'a^28'], [1, 'a^2'], [1, 'a^1'], [1, 'a^54'], [1, 'a^57'], [1, 'a^44'], [1, 'a^11'], [1, 'a^12'], [1, 'a^29'], [1, 'a^20']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-2475-2475.1913-r1-0-0', 'leading_term': '0.0308784282858554605948076642123+0.0213016008397399729465594800475*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/2475/1913', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.03751313812173447, -1.2217938641624333, -2.037835576946983, -1.326715155174825, 0.9739493672794259, 3.357284497539634, 3.5876893979940383, 0.6943056796814618, -3.682805296081189, -6.30933030762351, -5.225893685834725, -1.7137319607898733, 0.9057686953270481, 0.6421538454070106, -1.2083625833342895, -1.7616157402886778, 0.02086746690648498, 2.2136790448165584, 2.4301914870806294, 0.7625944114559384, -0.5724845402069474, -0.304978986147374, 0.30257173475782384, -0.4804306670679303, -2.0990294355447734, -2.330999087372728, -0.560932547854353, 1.0655762881102082, 0.5972300962154939, -0.7652927394443557, -0.2839695203776575, 2.1008929389582582, 3.2567158005686516, 1.4479708172757357, -0.38906635897414826, 1.8681995917960976, 7.38150559170224, 10.354983891897353, 7.111015910754345, 1.0005479087651783, -1.743153338260678, 0.2505099569172999, 2.5911255832276607, 1.7922375472349317, -0.28920891698784523, -0.151459155106415, 1.7707867536823367, 2.1161576452701745, 0.09135617594300911, -1.3933667892618382, -0.4737658438320753, 0.8899047205688336, 0.43929649519802905, -0.648718922559054, -0.0833171084482966, 1.2508144874296314, 0.6283595229650663, -1.5400223478578539, -1.781548082130527, 0.7517978139125694, 2.4051015786110215, 0.8033150995035669, -0.9043408164796404, 0.9422775145913762, 3.7012782245470177, 1.5029010113128296, -5.391789696248751, -9.608198638655724, -6.626799158264946, -1.0426801013854607, 0.3282548931528252, -2.1399225676062015, -2.915697578658465, -0.42692379568071814, 1.4057674753361566, 0.42599458069765345, -0.5579877948014448, 0.6295841703903408, 1.6032498663301462, -0.060281263898535796, -2.2357300281034043, -1.8230616478826378, 0.01027221979410638, 0.25386603653994466, -0.4932259573713392, 0.36594074688289663, 1.8149800833687828, 0.5136194757363342, -2.6536811875874284, -3.0309235883407424, -0.09967571238019172, 1.0111928294272936, -1.7201319708823466, -2.931797374069832, 1.398131396880972, 6.218890307047331, 4.510663923504909, -1.5169629407636096, -3.58252033359378, 0.0287207540630915, 2.7134650455395795, 0.657378820353281, -2.000472600252652, -1.2663813359773448, 0.44332460670347923, -0.13984759377122546, -1.1603352964050193, 0.10078095238816154, 1.6430213698264375, 0.5532853349545848, -1.2933535327296142, -0.6522902797180886, 1.019505212560607, 0.4237152771714039, -1.2756946452488716, -0.8944002380405806, 0.30373775490515653, -0.8961924206898031, -2.477858125570282, 0.06246963344032324, 4.62043626608638, 4.39783336266806, -0.5226843438991423, -2.2955706271336727, 1.7756502034314552, 4.38411167572122, 0.4245909658718481, -4.419936417795381, -3.3421909262508294, 0.6229533257637985, 0.730419769627826, -2.112926276047719, -2.3368749377237097, 0.05851128259045087, 0.6639568462543254, -0.6494442928171837, -0.32452543580546744, 1.3566369065153658, 1.0543207445061504, -0.5674185706941429, 0.023010781262016604, 2.0425219675299595, 1.679333725548961, -0.3676042554841858, -0.11760139358262742, 1.822776097166618, 1.518363993843261, -0.03123301707589116, 1.3807866440562617, 3.668901395731691, 0.5643617482396586, -6.135854528243884, -7.106040999364295, -0.49917734929233853, 4.391461116751192, 2.1209936476936266, -0.9976900519346438, 0.8910808243803594, 3.415686002185354, 1.2077302500583846, -2.2175774431326696, -1.5642919085257887, 0.8312742640625944, 0.47258871221985205, -0.8993868015799691, 0.1522666425149255, 1.6525747567714144, 0.6897449960914857, -0.4964829275708323, 0.5800935028497186, 1.2456951189111254, -0.6865858691852031, -1.8297149112213609, 0.19307647610953393, 1.5320974283335378, -0.47555215414118635, -1.7949718539576176, 0.12482100443914326, 0.7040070999022835, -2.13176313938351, -1.5311638775704417, 6.399607624993733, 13.057507472196448, 9.7915326325343, 1.9377120045306442, -0.4122040161591998, 1.6640229783494958, 0.7644801079969712, -2.55794077419405, -2.5178706497286583, -0.08194556386334273, -0.5005490433887878, -2.782371877863504, -2.273020781693469, -0.07151288449924999, -0.23798693281036848, -1.4917729850468147, -0.4959933421209572, 0.9533368084786661, 0.10935839220370043, -0.49744918561015977, 1.421304359797956, 2.2429897621877943, -0.44090099588031134, -2.1259925276912788, 0.048306527064502953, 1.325988144614397, -0.8236546413448564, -0.5484072681881723, 4.684860031554574, 6.928584847891205, 1.535067198042552, -2.8955044493911086, 1.3042897848432773, 7.444848642469386, 6.2738667321101005, 1.0738052714945872, -0.30529515410675084, 0.9262853590394508, -0.05092523973213808, -1.2477407982678081, 0.6420416893874333, 2.247672256084488, 0.16658735145139555, -2.0470491189442526, -1.0326378428450085, 0.2834049340762365, -0.25777505336139633, 0.31814540828009485, 2.637044149520156, 2.590016618174296, -0.024532728483531056, -0.6291351720380496, 0.3197011535727635, -2.024067686769217, -5.673804873709297, -4.039999002449145, 0.6308290673325117, 0.18321035277038558, -3.676249967480891, -2.013590814802403, 3.6836692832932485, 3.141195081326426, -3.686846328169548, -6.172607852647996, -1.7845406270787252, 1.1143532734046464, -0.5794886758015076, -1.3432198785825298, 0.31064923424198315, 0.21979958453129822, -1.1619121884099992, 0.19902459935194214, 2.6110983140171475, 1.8244749041472774, -0.13193629791456496, 0.5538517811991102, 1.554792095735146, 0.05283457080215781, -0.7992991666024593, 1.0038908943941047, 1.5281481070422107, -0.1636024864472483, 0.9996762115931017, 4.760147971907268, 3.996836910235237, -0.9098036232374617, -0.9438814652461095, 4.3047825965566435, 4.693733527600551, -1.4107209951941437, -3.690398473119009, 0.8031292782076074, 2.853504715479719, -0.8709227488617759, -2.6546668119192853, 0.321235838237059, 1.6211722054179063, -0.7496604806713936, -1.6207233299217694, -0.14774002174610396, -0.23067860126505468, -0.9794387502733641, 0.8529190269052704, 2.6161288937443365, 0.9252274935654352, -0.7737266434745788, 0.753358632841767, 1.893955278976795, 0.36666858558157717, -0.03126156533722079, 1.2032733760281427, -0.6794596517351307, -4.217910459954533, -2.5767949125559957, 1.9310694698963422, 0.4830771982689302, -4.447044129335078, -2.148410990499963, 5.808477287436281, 7.487322083007561, 1.959034263219726, -0.760801627096666, 0.8794464248588723, -0.24450138534684804, -3.65685302216369, -2.809769926895992, 0.8598116025057291, 1.2160093741922677, -0.4502866260788018, 0.18204791861673555, 1.1027493252705463, -0.22564489043582414, -0.6315952486352387, 1.0785130423304436, 0.6971155956125764, -1.8754908015753076, -1.5977315679830193, 0.9385087568357631, 0.6131839811267286, -1.1958902393068984, -0.28398453910975885, -0.027157588381855575, -3.887945786676597, -5.191042988494695, 0.7239942140221548, 4.726954137589714, -0.44763804870055834, -5.702591315238039, -1.9814214123480125, 3.4329847507655127, 1.6963546029576368, -2.021675782787206, -1.0609106204564303, 0.3971968810710276, -1.361341655792998, -1.553379849758672, 1.6093663880499396, 2.520762504392501, 0.010295219752257709, -0.8685804222401621, 0.1462046591277805, -0.6404257052747498, -1.6748587226833158, -0.2180551883342379, 0.3877958521127031, -1.8576542918749759, -2.1436810590054547, 0.8417634880430968, 1.303414788388764, -1.302678764727656, -1.0759690007562863, 0.6475720480130502, -2.3584036341673773, -5.851751398529867, -1.5230795265619315, 4.652691766436455, 1.313844013160306, -6.702000236649501, -6.813116589284462, -1.0550985273897195, 0.3839055796972757, -1.4898761133317442, -0.2901811937825363, 1.3807474090361782, -0.709862337021234, -2.4481722577409766, -0.7320883633875669, 0.020862607832067562, -1.6571117625083804, -1.1478379634060838, 1.4444980649265593, 1.4083572768223498, -0.27692467717494273, -0.0545581197605489, -0.28506572883251935, -2.72262352204863, -2.556123273641116, 1.1003390876498005, 1.4984216954777867, -1.7816198532825278, -1.221575656841589, 2.4095096042165096, 1.307804259142606, -1.4022622592143952, 3.4493799164672074, 10.666511330021597, 8.065887750509921, -0.6487636099227824, -2.944953917926889, 0.1469908597521196, -0.19830448322071448, -2.396908157329153, -0.8018250396976477, 1.2730156957712393, -0.12470070885375498, -1.0193628577969378, 0.6291122876771941, 0.5723954578622459, -1.090855091724317, 0.2596172088859742, 2.876070669243882, 1.9825395080611965, -0.090517648999258, 0.13988159712872816, -0.2298791628753181, -1.9226015656855426, -0.054148239793926675, 3.8743908727243737, 2.655412771629813, -1.172817941416712, 0.5808264078832726, 3.9594413262942556, 0.25126386125008054, -4.754500028518435, -1.1803251389126443, 4.75855698512171, 2.8774132948075906, -1.2664607063368694, 1.0528368029485353, 4.485622161855982, 2.2000296485191533, -0.7515316669642029, 0.28707261459851807, 1.014198332143828, -0.229890095176696, 0.6560460653873039, 2.6013542299446217, 1.3773846113949597, -0.3210153883088792, 1.1365746464156739, 2.024319304668248, 0.085740886911109, -0.1670899898395076, 1.7537244458788264, 0.8963306068401616, -1.3479021299339593, -0.3961931334548322, -0.048680628854895595, -3.7105091391288725, -3.441091747701742, 4.764311697083488, 9.393744020025247, 3.6674120155818626, -1.4737953726505155, 1.1535671250691388, 2.719728837251088, -1.185751982818567, -1.9375418135390936, 2.6044911281164302, 3.745634823839358, 0.3086198485666264, -0.6147378149074924, 0.7272115629205724, -0.43197920667589906, -1.7070675579273438, -0.043030401597235944, 0.77027999735455, -0.6125151509939704, 0.13785017266966734, 2.2898857070134246, 1.3242029345974835, -0.19266944907523026, 1.7501336345194993, 2.969970374725625, 0.6169873953135341, 0.08521165856496644, 2.2990888166690517, 1.2694769902372345, -0.24280216054737036, 5.758283099505747, 12.828967991826659, 8.609947748640545, -1.0974398079321426, -2.2675140735208026, 2.172685256021198, 1.5715353980231812, -1.1461147074508105, 0.6538514571206282, 2.1433927640434827, -0.8506781663624717, -2.2712210181850354, 0.3660545080186251, 1.167856987934231, -0.5422607245349598, -0.026540898896083485, 1.2294982981357125, -0.1674679045878555, -0.9889971031055139, 0.4599668939549656, -0.1859890067603342, -2.4535772858345695, -1.129068180581712, 1.4227327969444907, 0.08314185925062681, -1.089477234727319, 1.5909271402469107, 1.8756498685897518, -1.8852127632714837, -0.9074670532292666, 4.222342685612585, 1.5639074338698173, -7.355457460592846, -7.879694893297065, 0.1593869471775905, 3.242606953123187, -0.026845114841646835, -0.6606060915896095, 0.7427582472376136, -0.8934046065008449, -1.765838893244684, 1.205166853206914, 2.374341362495314, -0.05686803858154912, -0.5425949620525791, 0.9409503199395393, -0.052477014150065344, -1.4741055950303539, -0.32843395154823046, -0.2011025297934843, -1.9163703814783672, -0.6764523224996458, 1.8354767831694818, -0.09938559776397554, -2.813986776934439, -0.9971311939638093, -0.29720014778167225, -4.092504349979457, -3.5393034944573656, 3.3522867895582755, 4.758165018531521, -0.957209777179876, -0.8528600333034457, 6.119934805985664, 7.148237278963167, 1.4533333221700953, -0.22862204400909275, 2.166486387229135, 1.5357656091963805, -0.2680153192569372, 0.4102780139148732, -0.2763909432804556, -3.008262868142542, -2.2180775082311097, 1.084251259429501, 1.0899430836290807, -0.47995236988960505, 0.11804710529558658, -0.12118911908281083, -2.0392762716014983, -0.9640068557883009, 1.5105238350016246, 0.014754899012547545, -1.6924149636103492, 0.8012934267417374, 0.8144200676568412, -4.529117147888305, -5.01598678662112, 1.6689731915736181, 3.3111127633382846, -1.9012998018664002, -1.8745373051303549, 3.359708128860297, 2.173976613473454, -3.67717841526496, -3.5254894937911776, 0.38376506034329216, 0.31271219022153524, -0.7799191543267953, 0.9913740470293184, 1.3740443481662932, -0.5112330146398031, -0.10380673806015894, 0.8812363873255558, -1.4172007655705146, -2.9454811855836716, -0.7671320190998075, 0.0938414697013009, -1.5589435621357768, -1.028215547843439, 0.19738405403880827, -1.3732129863621372, -0.9158611442538759, 3.458637330565481, 3.5234805737577015, -1.0288056473734881, 0.6719102496557109, 7.221393918819903, 5.801150215582315, -1.2878683122033499, -1.2365030640837322, 2.940383477717752, 0.5455885686202835, -3.8280443286724744, -1.8113303622116363, 1.1687458253457248, -0.1901776557312943, -0.20538708451057228, 2.829928797619219, 2.7986497595722226, 0.15881666325791163, -0.1257731557459458, 0.10359973024174421, -0.974498064210287, 0.6835911148719481, 4.081145832708973, 3.189382660333889, 0.14565361860683312, 0.44024728064934004, 1.0385518632528412, -0.5858744323554352, 0.37580728593522, 2.718176613006656, -0.35041535224192394, -3.781800079652241, 1.1233608657895746, 6.185135586041024, 1.2189351507703556, -4.159809705430343, 0.2309836253614319, 4.831246674688948, 1.2524932957696113, -2.050146892439236, -0.12984823961507463, 0.02384428455460956, -2.0442220643020126, -0.05360463770063573, 2.992593320457669, 1.359656295568857, -0.8846708314299387, -0.14415608541015423, -0.3627629065492621, -1.6936763346117125, -0.38353639522432503, 0.7217168783209992, -1.2312061244665766, -1.3105922696886307, 1.4755965184612019, 0.975366310893057, -1.5393821263272258, -0.07741376225878893], 'positive_zeros': ['0.01084486772511762319100721968', '1.13426470585481034930970024577', '2.23866071550910016399233893374', '3.60518826525276361905633788516', '4.176017777966464761232755928341', '4.99736019708866452264561101978', '6.07537791237072013618025313542', '6.67869813124254146759848965006', '7.07147119242043087523869111604', '8.20741641971119014504553228588', '8.873639053708962574816787654173', '9.4208097278993448505581886802', '10.50528150716258636985021630594', '10.76416863942663605331222754412', '12.25229028727502282124257102218', '12.78704666832608129310618047103', '13.69230792283495799466257247247', '14.09190110068646467748941683065', '15.012238145589678946290751232752', '15.71188388519959380439961466334', '16.35535030079981711795840799621', '16.89304536442434495208475133974', '17.59367784939103207393246760480', '18.35737307927272166762037808174', '19.16489763058214203745559021850', '19.589907453174255473454975694426', '20.39058043710935123456400133295', '21.659704997756879298041655634023', '21.93467242068351688401529572199', '22.85917920060143591427039095430', '23.520980807891362119501810534117', '23.944712764881564693345249367491', '24.68022520067602662276406907534', '25.62263036716205681970163689169', '26.03033135384427976490089980111', '26.49094472960444502649395716823', '27.23959291324472196087882460900', '28.13561532606517266096133612617', '28.58441746708421067507924463974', '29.30066017193946913843477104905', '30.230267299647068609511413750680', '30.9354790016053025199154535854', '31.62235590820309449994338279108', '32.38533225729012350216851887837', '32.78208713656702425533504044959', '33.42231917398976342676241433084', '34.140021361376884169221646118445', '34.792686022301040923702889021515', '35.38280558734346232539724344409', '36.12711430729982419275076409172', '36.415045952504559353206232640206', '37.18327688688586964816310491650', '38.0915687755589806043502154415', '38.63917398623883108354260403955', '39.397031013021859981394281306701', '40.25097034466521368653025297860', '40.71025352671740656453956838719', '41.55392098694300746693613546283', '42.03426873046343577974021307777', '42.560181078386470325805154797195', '43.30945730102931786444152965763', '43.746282932193706859750191621424', '44.61847392228500295354345898334', '45.02022392003877066040858560171', '45.92085106240311940011520507921', '46.03247999014584063002069559589', '46.902506723536915828606098760468', '47.83326875779954461090328109492', '48.60169713658143010014314795091', '48.979575710022937028540255885257', '49.77924012630974667660337574271', '50.49399546289134159542990532052', '51.02203768264650617202283986325', '51.53852099305881711173353231709', '52.31369234581892440688516685064', '52.69765059885569867617720022503', '53.34903805095253680814668008493', '54.03961677727880694103283661949', '54.63191198536066312810230095972', '55.29574056660484252459641254020', '55.72217802796588186255900995294', '56.33239672731745140512839584183', '57.6334803172380754719503087593', '57.889836895469469373632071412719', '58.50837965580341140908017215815', '59.39223118979034432853145900840', '59.60097078403246745089819897486', '60.64207604378687538860158340206', '60.87922400363650860742084475167', '61.64186768881989836260639558260', '62.21078935969640986730336490335', '62.61504980554634012622167414712', '63.39572708049343580731377892010', '64.05717041307256938280537272496', '64.58443240692584804868736004604', '65.0452379943250352846751076413', '66.0080816859074048605136011392', '66.50395453356647815426434888164', '67.60754661179245026686299325046', '67.89040278061250703163577608140', '68.42936744368311191409079544993', '68.98836034257816122698678937648', '69.70413197081455696956950852223', '70.501343098299049105475454965354', '70.831223165274810368839382112845', '71.19124557747145791731555426004', '72.18412663009142272540577093870', '72.65899018177016200794229677949', '72.921014570497491653319103425230', '74.00729707596098268862626037022', '74.39041058494036605343653860565', '75.106944039670663822161431829373', '75.776548815932422529849773921842', '76.68711629385860326661991789742', '77.110040504418838270604234446201', '77.75101854926329518420601929318', '78.16907065514141841037035312877', '78.727033597180193325110410131925', '79.647760780437553491527798219503', '79.88183237060227348337314071104', '80.63329717232235306670278782062', '81.10290390199893852172797240806', '81.83558384157122142228048036908', '82.06989121097405531034278719995', '83.0600098141251340279804306379', '83.50291559675290763640923178494', '84.30617879449322105252867600800', '84.951574891017682531450469235137', '85.56325524769337205579931471343', '86.220626988261127721076458517761', '86.78782143227246026952839678204', '87.54610058177990803741485698831', '87.73772908968285283881784627006', '88.33490175089568735783816351888', '89.176411756518951441230741606334', '89.58146366758257649972663635110', '90.39038633162233525918619732055', '90.63394555144066046600849416083', '91.19068641340954600872916490214', '92.03487094458422232438164285680', '92.52932908854530379496324100218', '93.21206984994559255463767274233', '94.196998193586108903141603735725', '94.537128913528342189679683246511', '94.97643527112278647611913665945', '95.852118597609558541954596389870', '96.45298380640757736589569367939', '96.83801029985889288798510575242', '97.45796864837897730708949140881', '97.93928113350222832281337234372', '98.52407318476258659130346880227', '99.24654650698156840714130730431', '99.77584865606276391009681253344', '100.366625874473510078701124000309', '100.62081372673939876885727854150', '101.5314628081647610503506866861', '102.16925064850130165046433003095', '102.9027436278385633946432681318', '103.55293465031752782355655617179', '104.20835249638538089331672217158', '104.4883441979269783800160794600', '105.165322610978295622765410927906', '105.93881264888083360658950161412', '106.49728545165930211030002550854', '106.73248726566402238165058044240', '107.53692088162063683856456499385', '107.88799185284092510694596456471', '108.6637189227396964136647107605', '109.21949160095511500599817354030', '109.831494507545738470617144900885', '110.13575220894835618306045976342', '110.99912156912790137056484652338', '111.61138049168747979647604906635', '112.5854076703415599299316490695', '112.877670667609409283430159056890', '113.47223225665343214032241295542', '113.98931156744356250048229451162', '114.82125620659288742462088720168', '115.00636191415807204529640642622', '115.75808108856571977436826076231', '116.49031666044105603703984783779', '116.89733708991253134072559233604', '117.12269597004971767356719148347', '118.03013227883175529614401323819', '118.58143114601368197145719201628', '119.161303119997694112169639517771', '119.79370238865877310437240434514', '120.15891711079023216411705437461', '121.222068255485344379325949308043', '121.856046299090954824728199191223', '122.16196381950348588460810456337', '122.896376489692929577760439154249', '123.41938649717933035291697830948', '123.95315279183943591325882724539', '124.47100158213796711012997103680', '124.97199018194136295116035141446', '125.91088817401200370416699650124', '126.18994713400537383461520020204', '126.51332973062393757077197123023', '127.19159946198907033501339025604', '128.00160252483713334741430221994', '128.39474669469950707171510666996', '129.07435473844942368227626389613', '129.73835684512744375345426859063', '130.48913112485826641975125192244', '130.86356934057535336622602907980', '131.74799844835100626025366741879', '132.140291009873947543267545381477', '132.74227106086998092169822278763', '133.01862057266520356298127587080', '133.94402831553243599042573048218', '134.19771990997896781753641641371', '135.01417171922480017087279379716', '135.34335537482967751032332469194', '136.04044954264389689051890702934', '136.63208898761963268654601425320', '136.86747682622398383078795850004', '137.65120211069687232098640385735', '138.60231969964838694249380631453', '138.9755917334544858101781863052', '139.60263567839788774102455536604', '140.14619201383554129675470997687', '140.97033363582861824550739389433', '141.37641881408954354448397583559', '141.81104031001191594503242059216', '142.506394311823729509624752909974', '142.98802986460823783665904362707', '143.41832361427540902077598909953', '144.266044642701510147995609665540', '144.453787132462014874778763167395', '145.40624174747617044338732563739', '145.60817499315144482810503171326', '146.39507300895704310519354218184', '146.597029227136271334340226153678', '147.76700396046617393799303483261', '148.27586229827209287198684655340', '148.89181540108937303627683096011', '149.30900465866241902111796758387', '149.927892511849954963703497279261', '150.58497901034174739413199434182', '151.14061068868339578280495464413', '151.5671759244922720306923082547', '152.1614883943831484065742142410', '152.713970431611843157837443592474', '153.09913735452012356348100773295', '153.85905384011339010046680923472', '154.38515070408269039245038320377', '154.84280797745565828452075800452', '155.47000676505247605742433706236', '155.99218681718295223916223568803', '156.61937673912897976043063433019', '157.49340513961215348504808513664', '158.12227482875805471645723030757', '158.551810755292173938851673210934', '158.94735605330986966821649189678', '159.57881505591596978270670826771', '160.304928809896761838664738297960', '160.729877316799010353066615354518', '161.242217001274710795858854426157', '161.95957542496177558403948507215', '162.13500269197707418988589597579', '162.87952257566778922218542617873', '163.42921166186584322261448979476', '164.21027126108540603895788601532', '164.32011568785096467192394521650', '165.16668372473898525732185890952', '165.88227474664936683628721251492', '166.29551468982722756546478618686', '167.3023109331073214647584498223', '167.53729123512155314392935662497', '168.34958204932411464119038374741', '168.62919783287583540975863376116', '169.02445677378151885489736205522', '169.88293752593346888869807899816', '170.492490279816161746405649077179', '170.90149942211406951941072179038', '171.22622766356390704259697776177', '171.97378122962296985457965777152', '172.50154611300664999304444417287', '173.04473628484675680518692628870', '173.49780046881691372192745266098', '174.29897523423299199200445219461', '174.88807806059289553147791420648', '175.42281405800925036030734109578', '176.04815560128845225363778097537', '176.83226081398362886885899192518', '177.23968837183948057667722487951', '177.67046563023978693290236484424', '178.34170940697870698474833649987', '178.7690809697496430769404238293', '179.226055168592837220873645468650', '180.1175268740880007003915564222', '180.337225439067341913881918351458', '181.12522079062857310510452529097', '181.3319409719134887847897730622', '181.95027753037787549188005542173', '182.729346763157862119680949749031', '183.08850322038082915782941325297', '183.99322420333540971899832181228', '184.45629869387071240602253714134', '185.030829312207849001583313144454', '185.765073773625800269923549458473', '186.220599069815853366586992471208', '186.58870545299826493503642009685', '187.52927135532606714204911090708', '187.86202009854264490654107390172', '188.16079564789186371264129307335', '188.68436716618101746799634230954', '189.71903992435276410790641441985', '189.89685087877978771759269979892', '190.51165046745850706152428122555', '190.89431741154707553773752526756', '191.54170642780001648268555093807', '192.14109202353551008051925461744', '192.85997137194968390369375174050', '193.427402130437088870388759777918', '194.13682905103765172241415706087', '194.705964068315624887917239076', '195.00362414706398055751989027579', '195.629258307856486630542561497056', '196.39053092238419302366519954053', '196.92609113801407497417703663149', '197.08941475776981292836081289281', '197.86769947947965585629215230479', '198.271454917078287490998004635053', '198.89606098529642783944014068063', '199.47698491675865634705306248621'], 'prelabel': '1-2475-2475.1913-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 265.97568886669694, 'root_angle': -0.3844444444444444, 'root_number': '0.355106962408137051366179485483-0.934825676396014455905912026288*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.192222222222', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.583468929640232830864287649735+0.323344766101654334131748641851*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.0108448677251', 'prec': 50}, 'z2': {'__RealLiteral__': 0, 'data': '1.13426470585', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.23866071551', 'prec': 44}}
• lfunc_search •

  Column	Type
  algebraic	boolean
  analytic_conductor	double precision
  bad_primes	bigint[]
  central_character	text
  conductor	numeric
  conductor_radical	bigint
  degree	smallint
  dirichlet_coefficients	numeric[]
  euler11	numeric[]
  euler13	numeric[]
  euler17	numeric[]
  euler19	numeric[]
  euler2	numeric[]
  euler23	numeric[]
  euler29	numeric[]
  euler3	numeric[]
  euler31	numeric[]
  euler37	numeric[]
  euler41	numeric[]
  euler43	numeric[]
  euler47	numeric[]
  euler5	numeric[]
  euler53	numeric[]
  euler59	numeric[]
  euler61	numeric[]
  euler67	numeric[]
  euler7	numeric[]
  euler71	numeric[]
  euler73	numeric[]
  euler79	numeric[]
  euler83	numeric[]
  euler89	numeric[]
  euler97	numeric[]
  euler_factors	numeric[]
  index	smallint
  instance_types	text[]
  instance_urls	text[]
  is_instance_Artin	boolean
  is_instance_BMF	boolean
  is_instance_CMF	boolean
  is_instance_DIR	boolean
  is_instance_ECNF	boolean
  is_instance_ECQ	boolean
  is_instance_G2Q	boolean
  is_instance_HMF	boolean
  is_instance_MaassGL3	boolean
  is_instance_MaassGL4	boolean
  is_instance_MaassGSp4	boolean
  is_instance_NF	boolean
  label	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  self_dual	boolean
  spectral_label	text
  trace_hash	bigint
  z1	numeric

  
  {'algebraic': True, 'analytic_conductor': 265.97568886669694, 'bad_primes': [3, 5, 11], 'central_character': '2475.1913', 'conductor': 2475, 'conductor_radical': 165, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2475/1913'], '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': '1-2475-2475.1913-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-2475-2475.1913-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 265.97568886669694, 'root_angle': -0.1922222222222222, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.0108448677251', 'prec': 50}}
• lfunc_instances •

  Column	Type
  Lhash	text
  Lhash_array	text[]
  label	text
  type	text
  url	text

  
  {'Lhash': 'dirichlet_L_2475.1913', 'Lhash_array': ['dirichlet_L_2475.1913'], 'label': '1-2475-2475.1913-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2475/1913'}