-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '327069421002279359522054833438', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [1.4259717762973458, -1.722383375791636], 'a6': [0, 0], 'a7': [-3.119717712314301, 3.119717712314301], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.498457891064382, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.4259717762973458, 1.722383375791636]]]], 'bad_primes': [2, 3, 5], 'central_character': '1440.593', 'coefficient_field': 'CDF', 'conductor': 1440, 'conductor_radical': 30, 'conjugate': '2130233234520576645667829247541', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.4259717762973458, 1.722383375791636]], [[1.0, 0], [3.119717712314301, -3.119717712314301], [0, -7.0]], [[1.0, 0], [-1.177941901604814, 0], [11.0, 0]], [[1.0, 0], [2.1509963289335023, -2.1509963289335023], [0, -13.0]], [[1.0, 0], [1.3350748883841916, 1.3350748883841916], [0, 17.0]], [[1.0, 0], [-0.32244416754653693, 0], [19.0, 0]], [[1.0, 0], [4.713466033905697, -4.713466033905697], [0, -23.0]], [[1.0, 0], [0, -6.630433965571774], [-29.0, 0]], [[1.0, 0], [-0.06758257309433098, 0], [31.0, 0]], [[1.0, 0], [7.60937766491232, 7.60937766491232], [0, 37.0]], [[1.0, 0], [0, -3.1968357644045673], [-41.0, 0]], [[1.0, 0], [6.705053444866373, -6.705053444866373], [0, -43.0]], [[1.0, 0], [7.342790931404675, 7.342790931404675], [0, 47.0]], [[1.0, 0], [-5.734318418229065, -5.734318418229065], [0, 53.0]], [[1.0, 0], [0, -8.684484873357265], [-59.0, 0]], [[1.0, 0], [0, -12.561997433276824], [-61.0, 0]], [[1.0, 0], [-1.8773954980899838, -1.8773954980899838], [0, 67.0]], [[1.0, 0], [0, -4.182208705724702], [-71.0, 0]], [[1.0, 0], [-3.978931177278452, -3.978931177278452], [0, 73.0]], [[1.0, 0], [0, 9.666441809335913], [-79.0, 0]], [[1.0, 0], [-0.5851187026162336, -0.5851187026162336], [0, 83.0]], [[1.0, 0], [-0.5573221541947196, 0], [89.0, 0]], [[1.0, 0], [10.57719619511848, -10.57719619511848], [0, -97.0]], [[1.0, 0], [-9.52870311356827, 0], [101.0, 0]], [[1.0, 0], [-0.16244957615894975, -0.16244957615894975], [0, 103.0]], [[1.0, 0], [-11.795527963546727, 11.795527963546727], [0, -107.0]], [[1.0, 0], [-10.860116581722954, 0], [109.0, 0]], [[1.0, 0], [8.744755525071996, -8.744755525071996], [0, -113.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-1440-120.53-c1-0-2', 'leading_term': '0.696040457064928141084377074820588762893137073451299804', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1440/2/bj/a/593/17', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.6960404570649281, 0.5452352707129579, 0.39031274862576315, 0.2310665179955334, 0.0673356049836174, -0.10092391828532198, -0.2735729808307632, -0.45023272039685824, -0.6302393814528285, -0.812612489337887, -0.9960370662689575, -1.1788600263674196, -1.3591004560412523, -1.5344732170408009, -1.702425146724346, -1.8601830170665181, -2.0048123049870035, -2.133285691466661, -2.242560030983014, -2.329660314347927, -2.391768894968027, -2.426317975138416, -2.4310830732172266, -2.40427493415681, -2.3446271249457684, -2.251476392370416, -2.12483277091994, -1.9654364292099213, -1.7747983467442745, -1.5552221285641614, -1.309804598840185, -1.0424132668891697, -0.7576393268328777, -0.4607255265359057, -0.15746900878103803, 0.1458999310396649, 0.442861334910396, 0.7267685705386006, 0.9910271652664111, 1.2292849741770222, 1.4356283940225918, 1.6047786763043572, 1.7322818894161927, 1.8146857648540442, 1.8496965655757207, 1.8363092593816785, 1.7749046830888349, 1.6673080520119417, 1.5168041017365157, 1.3281053325567276, 1.1072712372782885, 0.861577995137413, 0.5993398623385421, 0.32968532725184674, 0.06229296126434963, -0.19290628625667217, -0.42605190349765076, -0.6276917968444795, -0.7891242628619405, -0.9027318906706833, -0.9622948490886712, -0.9632709801887553, -0.9030305749291068, -0.7810346645018658, -0.598947120649708, -0.36067279594796386, -0.07231630569984925, 0.2579412101237219, 0.6200469906274917, 1.0023596794157932, 1.3920036841295016, 1.7752849159495547, 2.138155001987445, 2.4667084611228876, 2.747695213245764, 2.969029272247353, 3.1202736556363746, 3.1930815056322817, 3.1815742063642825, 3.082638914630765, 2.8961303767669864, 2.624965123227119, 2.2751000198305116, 1.8553915790739899, 1.3773372334540608, 0.8547047559051734, 0.30306097131037557, -0.2607843824464323, -0.8193995369133099, -1.3553926426907197, -1.8520884140637246, -2.2941914392156533, -2.6684076346042507, -2.963996075252964, -3.173225457700119, -3.291712718240273, -3.318625745557447, -3.2567375450710556, -3.112325428790401, -2.8949155677062897, -2.6168802636707276, -2.2929022575475355, -1.9393269605225085, -1.5734293486370883, -1.2126270881190095, -0.8736749866916876, -0.5718778692327144, -0.3203592937071903, -0.1294220684909399, -0.006033300827285094, 0.046538219078754335, 0.02891094314703428, -0.05440783478733855, -0.1952126738821503, -0.38197872435520425, -0.600414913734576, -0.8341689788639258, -1.0656535312955036, -1.2769553725325742, -1.4507849407182414, -1.5714194032831506, -1.6255917561512045, -1.6032794921481048, -1.498349987477548, -1.3090256326133387, -1.0381396881492908, -0.6931635467105908, -0.2859970950587404, 0.16747432317538025, 0.6480408249766463, 1.1340196499034851, 1.602259833504186, 2.029253168516306, 2.3922978710870426, 2.670657073909004, 2.846652849124263, 2.9066380925483677, 2.8417932927334397, 2.648702816291272, 2.3296755561566442, 1.8927871527579927, 1.3516349184670307, 0.7248113779101711, 0.03511721505911164, -0.6914514042999235, -1.4268934743873984, -2.1425136196337724, -2.8102866307747267, -3.4042060237599916, -3.901545972584658, -4.283969172498108, -4.538420136251805, -4.657753832956121, -4.6410629652788105, -4.493682883678729, -4.226870343982448, -3.8571701060232515, -3.4055007653785725, -2.8960072203852847, -2.354740865445728, -1.8082391371965079, -1.282082746702238, -0.7995113328625937, -0.380176127921939, -0.039101548704533765, 0.21408330742775095, 0.3755969449942774, 0.44761284282836045, 0.4380128684820979, 0.359798240537335, 0.23018983108762942, 0.06946842207163743, -0.1003782572603993, -0.2571222978191479, -0.37978864061117273, -0.45008374429864323, -0.4536715321706271, -0.3812158669991693, -0.22912141986657142, 7.82111749721179e-05, 0.2977158335615372, 0.6493773993196029, 1.035664379139273, 1.4332927051098243, 1.81646777851164, 2.1584568076957606, 2.433265903503035, 2.61732086574763, 2.691048091009127, 2.6402558153267237, 2.457225892477293, 2.1414420323692345, 1.6999010521076743, 1.1469780680334232, 0.5038432633330023, -0.2025446940125226, -0.9408170155229346, -1.676869489564791, -2.3757383324267667, -3.003567753787255, -3.5295520149844637, -3.927734079546695, -4.178549574131804, -4.2700184344369, -4.198506595742061, -3.969005277287708, -3.5949043254281023, -3.097266975746094, -2.5036443587814494, -1.8464971520012996, -1.1613170950636122, -0.4845609600855654, 0.14847735947863683, 0.7057256634992111, 1.1601951048026036, 1.491527743370046, 1.687131767866451, 1.7428314178865052, 1.6629889162525544, 1.460089134846864, 1.1538121527050786, 0.7696520978690373, 0.3371705084392502, -0.11200310116642243, -0.5462934123349485, -0.9362851170637932, -1.256673294874534, -1.4879284775252093, -1.6175644536929035, -1.640922452871998, -1.5614170058863683, -1.390224484887507, -1.1454327474698682, -0.8507069597523721, -0.5335600717393975, -0.22334425992719178, 0.05090003356298529, 0.2625895448599416, 0.38958883675863104, 0.4159056991305737, 0.3329694198578501, 0.14039724903141543, -0.15381150607689584, -0.5336755196548391, -0.976206491547664, -1.4528998621252731, -1.9316451249363455, -2.378928989724884, -2.762182260328893, -3.0521088807461503, -3.2248341982798983, -3.2637193804943054, -3.16070960893824, -2.9171139035313014, -2.5437522661244523, -2.060448763863996, -1.4948942955063225], 'positive_zeros': ['0.25801227952197030584607103718488', '2.02252574987127537397893406334457', '3.17802524719059219581691912114979', '3.88061479586521760484642899501602', '5.07059887878653598829847854998646', '6.39084381687567411472199100694407', '6.52964389136650246441053399454313', '7.47890143865354635493029805188680', '8.381789833257228770063920311529463', '9.617212499204831440619165749852009'], 'prelabel': '2-1440-120.53-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.390937612381623, 'root_angle': -0.7271351373864741, 'root_number': '-0.6545339989846375912176140594570684649961165556482858222 - 0.7560325681960919576883409613752506935850827211993773585*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.36356756869323703', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.25801227952197030584607103718', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.02252574987127537397893406334', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.17802524719059219581691912115', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 11.498457891064382, 'bad_primes': [2, 3, 5], 'central_character': '120.53', 'conductor': 1440, 'conductor_radical': 30, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1440/2/bj/a/593/17'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, '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': '2-1440-120.53-c1-0-2', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1440-120.53-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.390937612381623, 'root_angle': -0.36356756869323703, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.25801227952197030584607103718', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '327069421002279359522054833438', 'Lhash_array': ['327069421002279359522054833438'], 'label': '2-1440-120.53-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1440/2/bj/a/593/17'}