-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2705930618687952620232973058651,5291140023052781711270705831952', 'a10': 0, 'a2': -1, 'a3': -1, 'a4': 0, 'a5': 0, 'a6': 1, 'a7': 0, 'a8': 1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.0012911575573494203, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [1, 1, 1]], [3, [1, 1, 1]]], 'bad_primes': [2, 3], 'central_character': '72.1', 'coefficient_field': '1.1.1.1', 'conductor': 5184, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1, 1, 1], [1, 1, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, -1, 0, -1, 1], [1, 0, 1, 0, 1], [1, 2, 3, 2, 1], [1, 2, 3, 2, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, -2, 0, 1], [1, -1, 0, -1, 1], [1, -1, 0, -1, 1], [1, 0, 1, 0, 1], [1, 0, -2, 0, 1], [1, -1, 0, -1, 1], [1, 0, 1, 0, 1], [1, -1, 0, -1, 1], [1, 0, -2, 0, 1], [1, 2, 3, 2, 1], [1, 0, 1, 0, 1], [1, 2, 3, 2, 1], [1, -4, 6, -4, 1], [1, -1, 0, -1, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 2, 3, 2, 1], [1, 0, -2, 0, 1], [1, 2, 3, 2, 1]], 'euler_factors_factorization': [[[[1, 1, 1], 1]], [[[1, 1, 1], 1]], [[[1, -1, 1], 1], [[1, 1, 1], 1]], [[[1, -1, 1], 1], [[1, 1, 1], 1]], [[[1, -1], 2], [[1, 1, 1], 1]], [[[1, -1, 1], 1], [[1, 1, 1], 1]], [[[1, 1, 1], 2]], [[[1, 1, 1], 2]], [[[1, -1, 1], 1], [[1, 1, 1], 1]], [[[1, -1, 1], 1], [[1, 1, 1], 1]], [[[1, -1, 1], 1], [[1, 1, 1], 1]], [[[1, -1], 2], [[1, 1], 2]], [[[1, -1], 2], [[1, 1, 1], 1]], [[[1, -1], 2], [[1, 1, 1], 1]], [[[1, -1, 1], 1], [[1, 1, 1], 1]], [[[1, -1], 2], [[1, 1], 2]], [[[1, -1], 2], [[1, 1, 1], 1]], [[[1, -1, 1], 1], [[1, 1, 1], 1]], [[[1, -1], 2], [[1, 1, 1], 1]], [[[1, -1], 2], [[1, 1], 2]], [[[1, 1, 1], 2]], [[[1, -1, 1], 1], [[1, 1, 1], 1]], [[[1, 1, 1], 2]], [[[1, -1], 4]], [[[1, -1], 2], [[1, 1, 1], 1]], [[[1, -1, 1], 1], [[1, 1, 1], 1]], [[[1, -1, 1], 1], [[1, 1, 1], 1]], [[[1, 1, 1], 2]], [[[1, -1], 2], [[1, 1], 2]], [[[1, 1, 1], 2]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 0, 'label': '4-72e2-1.1-c0e2-0-0', 'leading_term': '0.125660786681104900027400087330833114519663857311256313796292052900000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0, 0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/72/1/p/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [0.1256607866811049, 0.12723342092812123, 0.13033190092122965, 0.1361510377080228, 0.14455793622599933, 0.15530631844467924, 0.1685005600405017, 0.18426992012105609, 0.20265590130730804, 0.22370260596020217, 0.24747502025457174, 0.27403054329818094, 0.3034094467344351, 0.3356374354300233, 0.3707197375129754, 0.40863476174706104, 0.449326550300962, 0.4926997182183599, 0.5386111433712245, 0.586864628500227, 0.6372011745287831, 0.6892952221319739, 0.7427433864430631, 0.7970630553313914, 0.8516802976711159, 0.9059312014832976, 0.9590504111495791, 1.0101754427555896, 1.0583372745984643, 1.10246852954895, 1.1413968190123869, 1.1738586150858747, 1.1984952330972352, 1.2138746418893265, 1.2184899044746282, 1.2107901383044866, 1.1891827569595883, 1.1520717587464226, 1.097867809861072, 1.025028551117609, 0.9320823701080811, 0.817663278525602, 0.6805537508903475, 0.5197071437213746, 0.3343111833862691, 0.12379498429703452, -0.11209307313364492, -0.3732889071987735, -0.6593367120714175, -0.9693914515680839, -1.3021656736733032, -1.6559194790713219, -2.028448489743766, -2.4170557704290094, -2.818591068078489, -3.2294087745792486, -3.6454565745630805, -4.062234436292746, -4.474918607164924, -4.8783430749040955, -5.267140472012606, -5.6357607756136225, -5.97861814827536, -6.290146415041628, -6.564951046049381, -6.7978861947047236, -6.984217352204447, -7.11969598594843, -7.200737089162766, -7.224468423627944, -7.188916612095104, -7.093018436344164, -6.936794179557538, -6.721320580077996, -6.448861524228371, -6.122807280617115, -5.747735963406954, -5.329320277261149, -4.874307395887454, -4.390385941230063, -3.886091284280785, -3.3706199448505503, -2.8536803730661977, -2.345250669362061, -1.8553943442014151, -1.3939767408691441, -0.9704593327839881, -0.5936090893007294, -0.27128196986493314, -0.010168767420857596, 0.18441639832994305, 0.30871566256790284, 0.3607044707608617, 0.3401765962820312, 0.24884375712309661, 0.09032559220171846, -0.1298718026280623, -0.40445022767921557, -0.724489701476991, -1.0796130673720188, -1.4583063113745742, -1.8481379466938739, -2.2362036420839595, -2.6093774824099834, -2.954839369790339, -3.2603181465430073, -3.5146568546337917, -3.7079917527223434, -3.832309327852829, -3.8815035186197804, -3.8518732704405108, -3.7420179432304805, -3.553216178607994, -3.2891521406761237, -2.9561145792480854, -2.562579145394334, -2.119185613780964, -1.6382197781588153, -1.133366235585173, -0.6191404429107737, -0.11045952195158487, 0.377920272543651, 0.831938204029475, 1.2387219544418566, 1.5871398535843633, 1.8681471636291282, 2.0752779860991395, 2.204765851847865, 2.2559137574923582, 2.2309337874799735, 2.1351468492835677, 1.976534573140455, 1.7657337985858215, 1.515352085614294, 1.239744697819252, 0.9541922377559752, 0.674486974029586, 0.4160915197969207, 0.19361172571958252, 0.020051280261506755, -0.09371434637267885, -0.1394852639196251, -0.11214266859553634, -0.009913278849906863, 0.1654384776985883, 0.40868400107202946, 0.7112033360367749, 1.0613960691913311, 1.4450359761883818, 1.84593909944083, 2.2465902985044646, 2.6289134361640656, 2.975125812384305, 3.2684202557302235, 3.493951214427338, 3.639264612651534, 3.695253640021935, 3.656253083303888, 3.520755711120418, 3.2911750353793088, 2.974142866554272, 2.5799882484432963, 2.1225430755810515, 1.6183991409567728, 1.0862827466233034, 0.5461639832505523, 0.018369852633190905, -0.4773498211766519, -0.9227584448628169, -1.301955340031405, -1.602176436215982, -1.8143169154186904, -1.9334682878146083, -1.9589871416385292, -1.8946844646202465, -1.7483949606104536, -1.5317692691055795, -1.259437739731767, -0.9484038780436944, -0.617007028069088, -0.2839966863633271, 0.0324674960130554, 0.31587501829930215, 0.5521271502360254, 0.7304745402123404, 0.8439054534236343, 0.8897204009891959, 0.8694727154091842, 0.7890351494789054, 0.6580853918231977, 0.4896573133801441, 0.29924616923706876, 0.1039590164949895, -0.07858407391661665, -0.23131169399529267, -0.3387487637353171, -0.3880628809569014, -0.3697995267302202, -0.2786739311553448, -0.11381129224190357, 0.12092822911674926, 0.41725542860066656, 0.7627179410964822, 1.1414755054954524, 1.5351285290896965, 1.9237953878518708, 2.287309281309378, 2.606371724606113, 2.8638149389409127, 3.0455684382232824, 3.1416811439812897, 3.1468287294934116, 3.0608865783402703, 2.8887592391193633, 2.6404264626131195, 2.3300370255142475, 1.975452725534671, 1.5967726037712482, 1.2154866992516444, 0.8527826248033754, 0.5285103800491029, 0.2596920515331418, 0.05958131761133554, -0.06327263432676489, -0.10555626255928716, -0.06938253356122279, 0.037821565141385766, 0.2038862575775104, 0.4126951311108167, 0.6453797509528761, 0.8816110788262962, 1.1011366555052073, 1.2852210779608824, 1.4181210568059304, 1.4883034461008686, 1.4893952303427977, 1.420887337301571, 1.2881923006442428, 1.102653414828329, 0.8806009276972538, 0.6426172218308753, 0.411802686888118, 0.21241768691516338, 0.06781806469061433, -0.001203521509198371, 0.02173687239814142, 0.14714168156805196, 0.37849527884181766, 0.7114684831884706, 1.1338492336930353, 1.625701854051338, 2.1605505441346877, 2.706425769584064, 3.2282338806279136, 3.689332177415658, 4.054651993811125, 4.292362448813764, 4.3769165287023375, 4.2904470931072645, 4.024761649573739, 3.582168599560971, 2.97572209087452, 2.229174494668177, 1.375366700698763, 0.455046508426233, -0.4860598750431007, -1.3995967369575697, -2.2379238882631616, -2.95718770209263, -3.5202477058415456, -3.8994930331618036, -4.078830510744723, -4.055098280281285, -3.8388548332716583, -3.4536208925794734, -2.9353426697602982, -2.3294687891515804, -1.6890712688838723, -1.07055921897245, -0.5307061498214877, -0.1221992460137926, 0.10969755862211496, 0.13066051067219941, -0.08006770669511201, -0.5278920697418069, -1.2019008187190134, -2.07528415797849, -3.106398635164087, -4.241510863328047, -5.4175090246403395, -6.5666080128615105, -7.619806283484178, -8.512564721361569, -9.188001420034231, -9.602062895870906, -9.725624384646263, -9.54765275548129, -9.07564067165708, -8.3358395724085, -7.371719231376874, -6.241322388632585, -5.01378669252185, -3.764761571847021, -2.5715994139543774, -1.5082031817641337, -0.6400614565586673, -0.019927700350225556, 0.31593930417155436, 0.35007989493322117, 0.08538621961075753, -0.4554063847637812, -1.2305967460443046, -2.1830786355240583, -3.2430306814754988, -4.3340335479737435, -5.376416870914732, -6.2946807551590345, -7.020231084333696, -7.498398879559558, -7.689515934438702, -7.573917683212565, -7.150747552651437, -6.439946263611479, -5.478767411778631, -4.32060777324475, -3.0299340206220706, -1.6785587836498697, -0.34030486789224706, 0.9141541227956546, 2.0213321267820348, 2.930163512201218, 3.6034990025158398, 4.022103505256422, 4.183127982380904, 4.101947702231893, 3.808016377845434, 3.3443235397579443, 2.7617070334967475, 2.116519751493857, 1.4647861379103058, 0.859249225450603, 0.34470972768633, -0.04426337421200167, -0.2858321029294545, -0.37158700028597774, -0.30652777760582417, -0.10784127081086303, 0.19721016665794056, 0.5741685328312643, 0.9844738521007982, 1.3892880967973154, 1.7521759420294871, 2.0429096636388144, 2.2385868065182213, 2.326467520803552, 2.3030311111295974, 2.1752223967093705, 1.9576965667939463, 1.6724456650488, 1.3450351769570583, 1.0031988641854388, 0.6731292563020856, 0.37796673692011723, 0.13515376154799513, -0.04433629498793288, -0.15692333325715116, -0.20601461325050213, -0.20114354153938996, -0.1564583258388896, -0.08867375062600168, -0.014947824376867445, 0.04931605048678681, 0.09246217344771573, 0.10790108861470539, 0.09521392121907345, 0.06001217262454738, 0.013659493525946134, -0.02825224508596945, -0.04753111876745654, -0.025668086944979834, 0.05382574977740232, 0.20327679929106712, 0.42879812925812544, 0.729182508373243, 1.0950205499751229, 1.5092349643607006, 1.9477506267336797, 2.381701029570417, 2.779445807130147, 3.1097265081164447, 3.3444091785768877, 3.4612863364731146, 3.446709336847525, 3.2967100855693783, 3.018665031994479, 2.6300291885519096, 2.158388364834803, 1.6380751430605962, 1.108473185101012, 0.6096248468170604, 0.17939642883705514, -0.15050302123977669, -0.3572180504387716, -0.42911628139129465, -0.36697182404054846, -0.18401810927933368, 0.09512871364145128, 0.43678368474040613, 0.8012652760420963, 1.1468577445676909, 1.4337770804861145, 1.6283283636889572, 1.7063626338905518, 1.655868762769477, 1.4787059755146847, 1.1903500967681837, 0.8191841945431116, 0.40327922511324216, -0.012743998927781712, -0.3827391143672309, -0.6636980738525337, -0.8206658113140305, -0.8312176790626957, -0.6884150161041867, -0.4031437337980286, -0.00392330807035371, 0.4641310249589828, 0.9429243766899534, 1.3655912142844315, 1.6628075910986038, 1.7685474294650885, 1.627352432641982, 1.1993670695406198, 0.46611759164985356, -0.5671527928009629, -1.8694246173940685, -3.3854575326629766, -5.038287975309232, -6.734892102919209, -8.372098871677675, -9.845477303692743, -11.055996652687085, -11.920086958520807, -12.37414331607005, -12.382799359683625, -11.93943678135203, -11.0698003758155, -9.828219274085, -8.295185849205117, -6.570315746625241, -4.7648298962549065, -2.9931751398038493, -1.3633226656804849, 0.03055875372766674, 1.1164213218621122, 1.8482520528292468, 2.2102831803673166, 2.2159706430243338, 1.9070070646557935, 1.3475414537734511, 0.6187340810053359, -0.1897131401001377, -0.988065626754704, -1.6938217593594218, -2.2384882598638653, -2.5751035486419, -2.685000468893823, -2.5648690130393055, -2.2294993438840613, -1.7445709074890086], 'positive_zeros': ['2.13460287732343082794920450962737', '4.17397350823654265270160808926321', '4.47388984368426759808121563855459', '5.63538510576822836356840705679966', '6.52229259023448238669588328169903', '6.70640051462313961974619854325426', '7.78292414143922961147563368342139', '8.479371373944274566855562461374137', '9.026004063438331298527805431677961', '9.352510038710622356505889286642288', '10.42530837244236248432447086564183', '10.58013683892231668704707658550907', '11.43543784024726873689769103532866', '11.46457120346775008809481426108630', '12.39764694798549826442099294177376', '13.14488498825266391224630030240726', '13.25301324941013762299050072314777', '14.34571041592205361528943903242286', '14.49356786122127795921995434995695', '15.34043328614189626901675784065010'], 'prelabel': '4-72e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.1895591752186535, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c0e2-0', 'trace_hash': 691516436078150477, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.13460287732343082794920450963', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.17397350823654265270160808926', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.47388984368426759808121563855', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.0012911575573494203, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 5184, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, -1, -1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, -1, -2, 0, -2, 0, 0, -1, 0, -1, -1, 0, 1, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 2, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, -1, 1, 2, 0, 0, -1, 0, 0, 2, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, -1, -1, -2, 0, 0, -1, 0, 1, 4, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0], 'euler11': [1, -1, 0, -1, 1], 'euler13': [1, 0, 1, 0, 1], 'euler17': [1, 2, 3, 2, 1], 'euler19': [1, 2, 3, 2, 1], 'euler2': [1, 1, 1, 0, 0], 'euler23': [1, 0, 1, 0, 1], 'euler29': [1, 0, 1, 0, 1], 'euler3': [1, 1, 1, 0, 0], 'euler31': [1, 0, 1, 0, 1], 'euler37': [1, 0, -2, 0, 1], 'euler41': [1, -1, 0, -1, 1], 'euler43': [1, -1, 0, -1, 1], 'euler47': [1, 0, 1, 0, 1], 'euler5': [1, 0, 1, 0, 1], 'euler53': [1, 0, -2, 0, 1], 'euler59': [1, -1, 0, -1, 1], 'euler61': [1, 0, 1, 0, 1], 'euler67': [1, -1, 0, -1, 1], 'euler7': [1, 0, 1, 0, 1], 'euler71': [1, 0, -2, 0, 1], 'euler73': [1, 2, 3, 2, 1], 'euler79': [1, 0, 1, 0, 1], 'euler83': [1, 2, 3, 2, 1], 'euler89': [1, -4, 6, -4, 1], 'euler97': [1, -1, 0, -1, 1], 'euler_factors': [[1, 1, 1, 0, 0], [1, 1, 1, 0, 0], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, -1, 0, -1, 1], [1, 0, 1, 0, 1], [1, 2, 3, 2, 1], [1, 2, 3, 2, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, -2, 0, 1], [1, -1, 0, -1, 1], [1, -1, 0, -1, 1], [1, 0, 1, 0, 1], [1, 0, -2, 0, 1], [1, -1, 0, -1, 1], [1, 0, 1, 0, 1], [1, -1, 0, -1, 1], [1, 0, -2, 0, 1], [1, 2, 3, 2, 1], [1, 0, 1, 0, 1], [1, 2, 3, 2, 1], [1, -4, 6, -4, 1], [1, -1, 0, -1, 1]], 'index': 0, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/72/1/p/a', 'ArtinRepresentation/2.72.6t5.b'], 'is_instance_Artin': True, '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': '4-72e2-1.1-c0e2-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0, 0], 'order_of_vanishing': 0, 'prelabel': '4-72e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.1895591752186535, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e2-0', 'trace_hash': 691516436078150477, 'z1': {'__RealLiteral__': 0, 'data': '2.13460287732343082794920450963', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 24602841
{'Lhash': '2705930618687952620232973058651,5291140023052781711270705831952', 'Lhash_array': ['2705930618687952620232973058651', '5291140023052781711270705831952'], 'label': '4-72e2-1.1-c0e2-0-0', 'type': 'Artin', 'url': 'ArtinRepresentation/2.72.6t5.b'}
-
id: 19809268
{'Lhash': '2705930618687952620232973058651,5291140023052781711270705831952', 'Lhash_array': ['2705930618687952620232973058651', '5291140023052781711270705831952'], 'label': '4-72e2-1.1-c0e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/72/1/p/a'}