-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1608677682740946022952088542816', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.5996764100727928, -1.038670010346586], 'a4': [0.0, 0.0], 'a5': [1.5615528128088303, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.536102794997064, 2.6606080865834745], 'a8': [0.0, 0.0], 'a9': [0.7807764064044151, -1.3523444052434932], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.3217767240852654, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-3.342329219213245, -1.3523444052434932]]]], 'bad_primes': [2, 13], 'central_character': '416.289', 'coefficient_field': 'CDF', 'conductor': 416, 'conductor_radical': 26, 'conjugate': '1809029177362418917903627116661', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.5996764100727928, 1.038670010346586], [-1.5, 2.598076211353316]], [[1.0, 0], [-1.5615528128088303, 0], [5.0, 0]], [[1.0, 0], [1.536102794997064, -2.6606080865834745], [-3.5, -6.06217782649107]], [[1.0, 0], [-2.7354556151426497, -4.7379481072766465], [-5.5, 9.526279441628825]], [[1.0, 0], [-3.342329219213245, -1.3523444052434932]], [[1.0, 0], [-1.0615528128088303, 1.8386634067025478], [-8.5, -14.722431864335457]], [[1.0, 0], [-3.6718820000669212, 6.359886183513535], [-9.5, -16.454482671904334]], [[1.0, 0], [1.7990292302183786, 3.1160100310397585], [-11.5, 19.91858428704209]], [[1.0, 0], [-2.5, -4.330127018922194], [-14.5, 25.11473670974872]], [[1.0, 0], [-6.670264050430886, 0], [31.0, 0]], [[1.0, 0], [-3.0615528128088303, -5.302765021840302], [-18.5, 32.04293994002423]], [[1.0, 0], [2.0615528128088303, 3.570714214271425], [-20.5, 35.50704155516198]], [[1.0, 0], [0.3367499748514784, -0.5832680658903022], [-21.5, -37.239092362730865]], [[1.0, 0], [0.525852870442629, 0], [47.0, 0]], [[1.0, 0], [-1.5615528128088303, 0], [53.0, 0]], [[1.0, 0], [-5.134161255433821, 8.892628148662991], [-29.5, -51.09549882328188]], [[1.0, 0], [2.6231056256176606, -4.543352217189534], [-30.5, -52.827549630850754]], [[1.0, 0], [-2.4725291799213354, -4.2825461628203625], [-33.5, 58.023702053557386]], [[1.0, 0], [3.6718820000669212, -6.359886183513535], [-35.5, -61.48780366869514]], [[1.0, 0], [16.684658438426492, 0], [73.0, 0]], [[1.0, 0], [15.739233741152942, 0], [79.0, 0]], [[1.0, 0], [8.543116820279428, 0], [83.0, 0]], [[1.0, 0], [-0.8423292192132454, -1.4589570043771636], [-44.5, 77.07626093681505]], [[1.0, 0], [5.403882032022076, -9.359798237570782], [-48.5, -84.00446416709055]], [[1.0, 0], [4.06155281280883, 7.03481582940918], [-50.5, 87.4685657822283]], [[1.0, 0], [-10.41596959012797, 0], [103.0, 0]], [[1.0, 0], [2.4725291799213354, 4.2825461628203625], [-53.5, 92.66471820493493]], [[1.0, 0], [7.123105625617661, 0], [109.0, 0]], [[1.0, 0], [-4.18465843842649, 7.24804102767652], [-56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-416-13.3-c1-0-4', '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/416/2/i/g/289/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.4399197630582203, 1.4314221630168997, 1.4139804544964805, 1.381993118289543, 1.327440283199367, 1.2409851332851933, 1.1131719334087786, 0.9355952311381173, 0.7019926697635139, 0.4092429683080588, 0.0582392133404707, -0.34541997288157833, -0.7910033497136325, -1.2625773694223335, -1.7393813735603543, -2.1967114022783947, -2.6073357382678424, -2.9434106266850666, -3.1788004502650242, -3.2916394891859317, -3.266910432725961, -3.0987672879533985, -2.792306609326166, -2.364499250878616, -1.844040735374506, -1.2699634910854496, -0.6889751919999206, -0.15163512411004895, 0.29235981889242535, 0.5993555418944977, 0.7368405618182177, 0.687846587867326, 0.454029767077167, 0.05689336637359462, -0.46322170633501025, -1.050511212272404, -1.6392852496839236, -2.161274039128505, -2.553895191506902, -2.7684922054151944, -2.7774404873832723, -2.5790462218554553, -2.1993505360010093, -1.6902904015969835, -1.1241281803221865, -0.5845901661931466, -0.15567942581972677, 0.09043099428021134, 0.10474004471440128, -0.12974185931458698, -0.5931867449362076, -1.2292426618983376, -1.9508151041352637, -2.650916879730798, -3.2173452418817816, -3.549239933080335, -3.5731137144966554, -3.2558280584230594, -2.612264614698916, -1.7061104693920393, -0.6431581289637656, 0.4423155636442541, 1.4063631851355998, 2.116676687549837, 2.473106875709184, 2.4240261458089987, 1.9756544759177492, 1.1924809545607793, 0.18831476940008143, -0.8909273469205871, -1.8901124883380476, -2.6697657339667975, -3.1287118326900694, -3.22047632204212, -2.960381654717548, -2.421827655819077, -1.7221593082706217, -1.0004622867750699, -0.39122334982616486, 0.0012759247078761233, 0.12291599541313115, -0.01997148619017514, -0.36227667342550995, -0.7937811924913581, -1.1824783539633426, -1.4031631505298883, -1.365650327937021, -1.036790682528389, -0.4514410189605413, 0.29043058486321643, 1.0406098766029626, 1.6306968087411955, 1.9061230427891398, 1.7593783820680993, 1.1555102134631146, 0.14420907130444954, -1.1447020821798999, -2.522255024043853, -3.774234185047081, -4.701553053607415, -5.1590301749997804, -5.0844741366549435, -4.51169596578793, -3.564215511712701, -2.430406440152914, -1.3248102398766777, -0.44347671728498717, 0.07726494567808474, 0.18964355545518036, -0.05564794225391583, -0.5210690749915576, -1.0133014657915371, -1.327337804114489, -1.2940790695168887, -0.8208798121243298, 0.08422596206340784, 1.3104581745749135, 2.6653650438746888, 3.9147931445215307, 4.8331011011852905, 5.252423578638953, 5.099766976046719, 4.413295097616005, 3.3338194412124906, 2.0732117653377875, 0.8668880468872372, -0.0786270796972705, -0.6307263217235878, -0.7576171606020219, -0.5306058991583923, -0.10118681038860387, 0.34146867352348886, 0.6220894168931829, 0.6269730409458948, 0.3355063343291636, -0.1728710042044973, -0.7386059614389408, -1.1643828229791782, -1.2694807555084742, -0.9422836035100003, -0.17706503279548177, 0.9152891411390409, 2.1266313098694547, 3.1973820541220213, 3.878270536143464, 3.9928825031353314, 3.485081736219222, 2.438597771690406, 1.0626820755254465, -0.35384823732365356, -1.509736919603721, -2.163416973910181, -2.192201809153646, -1.6233722320286945, -0.6287348500287121, 0.5166840960638003, 1.5019987706569877, 2.0572350509305233, 2.0201902576405772, 1.3763290210386843, 0.2614022668265271, -1.0739896735798844, -2.3287953796040193, -3.228168381711863, -3.5923911359999616, -3.380060935343577, -2.6943357380354884, -1.750902230631957, -0.8166286755697686, -0.13580682589097537, 0.1357327057999813, -0.029479512927470267, -0.5275434839439787, -1.1576745613895485, -1.6842064442415305, -1.9082571307810123, -1.728288498062104, -1.1717606982372175, -0.3882087253372892, 0.3948631447747118, 0.9409714646493257, 1.0786370865702684, 0.7584622670493748, 0.07571154682581518, -0.7496323771642837, -1.431169581949555, -1.6971963107657213, -1.3718570440775728, -0.43270729526772966, 0.9729686907153021, 2.5594565009402594, 3.9744020017891217, 4.892101687661652, 5.1025447133848925, 4.57091762573302, 3.4500283392462183, 2.0410946796901346, 0.7129527418788836, -0.19821687318526982, -0.4806171971908011, -0.10402264808236819, 0.7740045966943178, 1.8548483539027507, 2.7852882669205923, 3.2588895943440614, 3.103118605988449, 2.327033145914798, 1.1158715529987693, -0.2255603762885271, -1.3637023993392297, -2.0341245307714457, -2.1172798115959797, -1.66959513948144, -0.9008621924054745, -0.10518148368837527, 0.43312044010114964, 0.5294796468784589, 0.15705722005086994, -0.5454479300622351, -1.318758423908472, -1.8669090520553704, -1.9539017981759756, -1.4826654716232712, -0.5310573503013277, 0.6671513944027352, 1.7911697386706857, 2.53098036152203, 2.6835787834428917, 2.217205869828255, 1.282773799782932, 0.16811267706031957, -0.7912172257105806, -1.3167239548487093, -1.274100550802921, -0.7144380943316068, 0.14446494846134394, 0.9916689706765297, 1.5286579436007117, 1.5731096250396368, 1.1267710741722285, 0.3840087182367543, -0.3238928445766852, -0.6330008706937194, -0.26773028338421695, 0.8597007976802651, 2.604005170818857, 4.612238278460547, 6.414570435590374, 7.5544654805110305, 7.719422184735829, 6.832524500899694, 5.076597732717802, 2.843290419359782, 0.6224911398081137, -1.134157934244176, -2.134133580081868, -2.3131220476659387], 'positive_zeros': ['1.26902293301586231921026772178354', '3.41423376194738707303960877100267', '4.13999949445329229275002042387845', '5.81557893796569280607005239699402', '6.07182774737405550416393444596822', '7.57331267482323241668368161001313', '8.521928362724309967004931463206283', '9.874390970967482523255709634025337', '10.11499899378857857207809387805865', '11.07770905856058798251044243227515'], 'prelabel': '2-416-13.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.822574202628048, 'root_angle': 0.018504012351454654, 'root_number': '0.9932489348975145 + 0.11600238499683055*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0185040123515', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.26902293301586231921026772178', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.41423376194738707303960877100', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.13999949445329229275002042388', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.3217767240852654, 'bad_primes': [2, 13], 'central_character': '13.3', 'conductor': 416, 'conductor_radical': 26, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/416/2/i/g/289/2'], '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': '2-416-13.3-c1-0-4', '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': '2-416-13.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.822574202628048, 'root_angle': 0.018504012351454654, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.26902293301586231921026772178', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1608677682740946022952088542816', 'Lhash_array': ['1608677682740946022952088542816'], 'factors': ['2-416-13.3-c1-0-4'], 'label': '2-416-13.3-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/416/2/i/g/289/2'}