-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '651492796608654561680987054199', 'a10': [-2.903817275657367, 0.0], 'a2': [-0.7935447358946561, 0.0], 'a3': [-2.2512325996385485, 0.0], 'a4': [-1.3702867521338804, 0.0], 'a5': [3.659298769569119, 0.0], 'a6': [1.7864537787176122, 0.0], 'a7': [-0.28678651732278654, 0.0], 'a8': [2.6744733106113387, 0.0], 'a9': [2.068048217675338, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.20770826531158, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [-1.0, 0]]], [17, [[1.0, 0], [-1.0, 0]]], [43, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [11, 17, 43], 'central_character': '8041.1', 'coefficient_field': 'CDF', 'conductor': 8041, 'conductor_radical': 8041, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7935447358946561, 0], [2.0, 0]], [[1.0, 0], [2.2512325996385485, 0], [3.0, 0]], [[1.0, 0], [-3.659298769569119, 0], [5.0, 0]], [[1.0, 0], [0.28678651732278654, 0], [7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [4.960778890443011, 0], [13.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [3.3724619076581144, 0], [19.0, 0]], [[1.0, 0], [-8.028230810739265, 0], [23.0, 0]], [[1.0, 0], [7.238270616179177, 0], [29.0, 0]], [[1.0, 0], [9.15449995145674, 0], [31.0, 0]], [[1.0, 0], [-1.9270980021014392, 0], [37.0, 0]], [[1.0, 0], [1.294458943918054, 0], [41.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [6.410415989582446, 0], [47.0, 0]], [[1.0, 0], [-8.873834003771385, 0], [53.0, 0]], [[1.0, 0], [-0.7444767070453023, 0], [59.0, 0]], [[1.0, 0], [3.95811665795065, 0], [61.0, 0]], [[1.0, 0], [2.2974988200578568, 0], [67.0, 0]], [[1.0, 0], [-14.556646091744396, 0], [71.0, 0]], [[1.0, 0], [-8.891062134244793, 0], [73.0, 0]], [[1.0, 0], [6.5859628950421145, 0], [79.0, 0]], [[1.0, 0], [-10.540395384147061, 0], [83.0, 0]], [[1.0, 0], [-15.223168050425425, 0], [89.0, 0]], [[1.0, 0], [-9.868033566642293, 0], [97.0, 0]], [[1.0, 0], [14.913288412931657, 0], [101.0, 0]], [[1.0, 0], [4.509235714563941, 0], [103.0, 0]], [[1.0, 0], [-14.798213304242946, 0], [107.0, 0]], [[1.0, 0], [-5.418125265491851, 0], [109.0, 0]], [[1.0, 0], [-6.599807016565589, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 110, 'label': '2-8041-1.1-c1-0-110', 'leading_term': '0.73016978637677512369064477916970', '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/8041/2/a/j/1/29', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [0.7301697863767751, 0.7236772288022912, 0.7042275200162348, 0.6719088152246117, 0.6268819124219085, 0.5693999065987312, 0.4998335010803039, 0.418699999459919, 0.3266937234211798, 0.2247154804653754, 0.11389872885393526, -0.004369768147031696, -0.12843676797510195, -0.2563785179593906, -0.38600718125919653, -0.5148886548488126, -0.6403723204005862, -0.7596328649500326, -0.8697238990592306, -0.9676426892129748, -1.0504049121995376, -1.1151279374222696, -1.1591207554960716, -1.1799783071070038, -1.1756776357269003, -1.1446730035030965, -1.085986884397275, -0.9992935954664925, -0.8849922585288197, -0.7442658115133249, -0.5791229207549282, -0.39241988892161883, -0.18786001150056794, 0.03003169254506386, 0.25595986766753026, 0.48393713405296784, 0.7073893615058634, 0.9192870990709652, 1.1123014642126277, 1.2789818822411645, 1.41195215954303, 1.5041205042215775, 1.5488983076581515, 1.5404218033531671, 1.4737701575483213, 1.3451731499114754, 1.1522013990524949, 0.8939320993485049, 0.5710834792487662, 0.1861116768076357, -0.25673554221756667, -0.751412831137918, -1.2901224918495553, -1.8634129174860905, -2.4603307264900836, -3.068625391330976, -3.675003416233331, -4.265427350964667, -4.825453201952298, -5.34059818048388, -5.796729273840518, -6.180461900557367, -6.479556973127741, -6.683304091328709, -6.782878368997483, -6.7716585874755655, -6.645494987998282, -6.402916066430277, -6.0452652046956725, -5.576759835618161, -5.004468047143684, -4.338200028101019, -3.5903144666906237, -2.775442848569619, -1.9101374679468737, -1.0124517602902547, -0.10146418395975255, 0.8032407838023479, 1.6821190125963945, 2.5162234333052633, 3.28775314517275, 3.980576621989272, 4.58071103145179, 5.076740651030706, 5.460158986559752, 5.725621442595141, 5.8710981971094816, 5.897920213522853, 5.810714974276122, 5.617232416748671, 5.328065553839, 4.956274217333954, 4.516924117132322, 4.026556809869003, 3.5026090708156383, 2.9628024316430177, 2.424525172505911, 1.9042297544721896, 1.4168684924761015, 0.9753891786273956, 0.5903103860627064, 0.2693933669948131, 0.01742389416066836, -0.163886794242974, -0.2758774460621142, -0.3227890950245397, -0.3114997072290973, -0.2511516050851455, -0.15268670734861334, -0.02830870304638261, 0.1091053608083037, 0.2466191165612913, 0.3718501080618355, 0.47355542210033297, 0.5421637089731361, 0.5702295158897628, 0.5527888868635861, 0.48759920621943265, 0.37525113019114825, 0.21914597027749388, 0.02533783588268165, -0.19775404116600392, -0.4397513605932463, -0.688824100918615, -0.9322770659429537, -1.1571894093945208, -1.3510778839928947, -1.502552792461865, -1.6019352303597478, -1.6418052615361056, -1.6174531498093652, -1.527209612139891, -1.3726361211202143, -1.1585623691053921, -0.8929648601536266, -0.586687922804152, -0.2530159089023288, 0.09288738354017127, 0.434649298252973, 0.7554403039046761, 1.0387740842086521, 1.2693192053565356, 1.4336842163740282, 1.5211381733786944, 1.524230509147276, 1.439277856026664, 1.26669074970569, 1.0111198890713737, 0.6814095246051217, 0.2903542528034115, -0.14573538338268388, -0.6076439697438429, -1.0740157727273068, -1.522241751411844, -1.9294314536726243, -2.2734272663104647, -2.5338154181448065, -2.6928871434982686, -2.7365046017524732, -2.6548295147408574, -2.4428779202743707, -2.100871736594443, -1.6343666829211638, -1.0541461162158154, -0.3758810681963754, 0.3804323017226892, 1.1912360059295077, 2.0303426688420783, 2.869997043215295, 3.682019849260087, 4.438982619074281, 5.115360052194596, 5.688606749730205, 6.140108122787977, 6.4559606672075684, 6.627544437709088, 6.6518601008304925, 6.531613956167556, 6.27504626646185, 5.8955105491778514, 5.410823546938725, 4.842416804936479, 4.214330566428052, 3.5520985418103717, 2.881577592067111, 2.2277791869577244, 1.61375947740171, 1.0596219287602942, 0.5816808135611417, 0.19182571952520755, -0.10288301411234822, -0.300369852459875, -0.40344535743526, -0.41946111511884127, -0.3597389927847031, -0.2388071817148089, -0.0734855757509349, 0.11812909018900157, 0.31772270372812705, 0.5078099541097029, 0.672710205050732, 0.7994000010804894, 0.8781960194288572, 0.9032317164428766, 0.8727024277426246, 0.78886665314248, 0.6578049899730317, 0.48895191898424145, 0.2944286311695351, 0.08821657790767522, -0.1147792310919919, -0.29972151934561714, -0.45282743679978404, -0.5622912956574116, -0.6190872286468169, -0.6176021629503806, -0.5560589679076563, -0.43670155500795527, -0.2657274402781432, -0.05296806288885028, 0.1886678433954742, 0.44395816857457926, 0.6962960994138944, 0.9287303891269886, 1.1250563558546767, 1.2708924485668092, 1.354676659073505, 1.368520340920665, 1.3088640091347947, 1.1768901103198968, 0.978661038025709, 0.7249661135700137, 0.43087800698985423, 0.1150361912505756, -0.20130848218573483, -0.495439100321152, -0.744446513819917, -0.9265611661416183, -1.0224671863146504, -1.0165220473102785, -0.8978085673249289, -0.6609538406334494, -0.30666147488948264, 0.15808130976659487, 0.7201424007977323, 1.360730636588552, 2.0562101745335384, 2.7792055006012313, 3.499941663058484, 4.187749586676849, 4.812655322163499, 5.346965529424496, 5.766759860210051, 6.053204396876459, 6.193608826114592, 6.18216319057905, 6.020307198946114], 'positive_zeros': ['0.51393719727767176755125658660706', '1.54054210096713524521605724007806', '2.31729453138115903985051842357420', '3.56772230478822332904864542360982', '4.78507052544141974114103687629291', '5.11925232670320225126820029355501', '5.63060847708683575250384373133129', '6.40932625091120475915271274665045', '7.01599529047727906605467299977337', '7.71131378684132759066849113697949'], 'prelabel': '2-8041-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.012971250747851, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.51393719727767176755125658661', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.54054210096713524521605724008', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.31729453138115903985051842357', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 64.20770826531158, 'bad_primes': [11, 17, 43], 'central_character': '1.1', 'conductor': 8041, 'conductor_radical': 8041, 'degree': 2, 'index': 110, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8041/2/a/j/1/29'], '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': '2-8041-1.1-c1-0-110', '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': '2-8041-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.012971250747851, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.51393719727767176755125658661', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '651492796608654561680987054199', 'Lhash_array': ['651492796608654561680987054199'], 'label': '2-8041-1.1-c1-0-110', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8041/2/a/j/1/29'}