-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3266682249787816182296529483344', 'a10': [1.3982074301369292, 0.0], 'a2': [1.0, 0.0], 'a3': [0.4625984229747742, 0.0], 'a4': [1.0, 0.0], 'a5': [1.3982074301369292, 0.0], 'a6': [0.4625984229747742, 0.0], 'a7': [-3.184210129198181, 0.0], 'a8': [1.0, 0.0], 'a9': [-2.786002699061252, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9741749046596212, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [61, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 61], 'central_character': '122.1', 'coefficient_field': 'CDF', 'conductor': 122, 'conductor_radical': 122, 'conjugate': '3266682249787816182296529483344', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [-0.4625984229747742, 0], [3.0, 0]], [[1.0, 0], [-1.3982074301369292, 0], [5.0, 0]], [[1.0, 0], [3.184210129198181, 0], [7.0, 0]], [[1.0, 0], [-0.32340427608647765, 0], [11.0, 0]], [[1.0, 0], [-2.3234042760864777, 0], [13.0, 0]], [[1.0, 0], [-1.7216117062234069, 0], [17.0, 0]], [[1.0, 0], [2.8608058531117035, 0], [19.0, 0]], [[1.0, 0], [6.5076144052846585, 0], [23.0, 0]], [[1.0, 0], [-0.06439099283784509, 0], [29.0, 0]], [[1.0, 0], [-5.10940697514773, 0], [31.0, 0]], [[1.0, 0], [-8.98062498947204, 0], [37.0, 0]], [[1.0, 0], [2.657220713385562, 0], [41.0, 0]], [[1.0, 0], [-11.443223412446814, 0], [43.0, 0]], [[1.0, 0], [4.796414860273858, 0], [47.0, 0]], [[1.0, 0], [-12.959800667046826, 0], [53.0, 0]], [[1.0, 0], [6.601792569863071, 0], [59.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [4.69182453448284, 0], [67.0, 0]], [[1.0, 0], [-3.41758244066489, 0], [71.0, 0]], [[1.0, 0], [-13.98062498947204, 0], [73.0, 0]], [[1.0, 0], [-4.194622290410788, 0], [79.0, 0]], [[1.0, 0], [16.154422957457612, 0], [83.0, 0]], [[1.0, 0], [-2.518026566497265, 0], [89.0, 0]], [[1.0, 0], [6.184210129198181, 0], [97.0, 0]], [[1.0, 0], [4.312992114873871, 0], [101.0, 0]], [[1.0, 0], [-11.572005398122505, 0], [103.0, 0]], [[1.0, 0], [2.342779286614438, 0], [107.0, 0]], [[1.0, 0], [2.3234042760864777, 0], [109.0, 0]], [[1.0, 0], [4.9058218354215875, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-122-1.1-c1-0-3', '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/122/2/a/c/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.5810701883474823, 1.590872408928751, 1.6193511373646232, 1.6638467783814193, 1.7202861566246588, 1.7835734645671943, 1.8479488145807044, 1.9072720546688604, 1.9552451305085528, 1.985610412709119, 1.9923607090998092, 1.9699832983374865, 1.9137451028971442, 1.8200130646940538, 1.686593586538907, 1.5130671877360466, 1.3010889369054854, 1.0546217272475524, 0.7800682843850822, 0.48626932326126665, 0.18433987686240136, -0.11267624279675445, -0.39034260322438763, -0.6335513396139392, -0.8274070524194691, -0.9582330304490558, -1.0146414428212014, -0.9885929879938478, -0.8763590637675601, -0.6792927659214029, -0.40431569510380455, -0.06403700939704447, 0.3235598704882039, 0.735899128342837, 1.1470625593637263, 1.529464519752515, 1.8558629780372724, 2.1015734249685525, 2.2467139695806657, 2.2782824261011014, 2.1918542064028643, 1.9926971255002757, 1.6961281018763423, 1.32698752623189, 0.918177779618673, 0.508298496098529, 0.13850576616498375, -0.15118336968652518, -0.3258363307946716, -0.3594333287626374, -0.23818049959886595, 0.03708274988806733, 0.4497222191464267, 0.9676396830723888, 1.5452107744995054, 2.1267850975662315, 2.6515305542372607, 3.0592354108614557, 3.296537747537212, 3.3229521189888565, 3.116024189367763, 2.6749772313231066, 2.0223238380924515, 1.2030973806365917, 0.28159679424510775, -0.6641872973579873, -1.550016662744149, -2.2940181044292896, -2.825570556726899, -3.093470184058788, -3.072385867167177, -2.7667466629795596, -2.2114471512034144, -1.4690955943749577, -0.6239289897034105, 0.22706714735080058, 0.9849196210251261, 1.560105835239451, 1.8833102523901266, 1.9141465432938782, 1.6466738369332108, 1.110879349743429, 0.3697725163093561, -0.4877165954899822, -1.3572878218052002, -2.132037816039917, -2.715863618512069, -3.0357709375840085, -3.0514307659887794, -2.760634323128857, -2.199803917899849, -1.439365899840718, -0.5744969765555071, 0.28758112717338113, 1.0420593715626065, 1.6007506480861353, 1.904026455763695, 1.928729014879623, 1.6908481955129715, 1.2424948784444423, 0.6635426610060575, 0.04912460635470365, -0.505165394563855, -0.9181157639642494, -1.135468802326173, -1.1382010388336792, -0.9451202014656523, -0.6092599409373478, -0.2085432249640538, 0.1678635327273621, 0.4353281075230888, 0.5290579644974982, 0.4163184810601396, 0.10337441874615698, -0.3642223144272976, -0.9082939986394131, -1.4307619638315943, -1.8304649438881224, -2.0213032049462187, -1.948581617329037, -1.6005892015423524, -1.0131398521601285, -0.2659176745998311, 0.5291507802562226, 1.245862677744484, 1.7652080919669477, 1.9967401572360748, 1.8960699190845893, 1.4751911284249297, 0.8034283637310043, -0.001662538102201419, -0.7923771658841167, -1.4152249089635363, -1.7376213699777636, -1.6723495365610386, -1.1953930613718329, -0.35369616337044407, 0.7389877813837938, 1.917987600393828, 2.993102967957336, 3.779481964125093, 4.128849282382521, 3.955683457765677, 3.253628964829333, 2.0989827537341195, 0.6402688448606026, -0.9246604045928313, -2.380312106452165, -3.5286934675671544, -4.221831445007084, -4.385938391164665, -4.032879716789359, -3.2568113045020186, -2.216502395494159, -1.1064638893096115, -0.12207618742432293, 0.5749454294031777, 0.8844315304492075, 0.7838757722299791, 0.32986450836286973, -0.3553407358447373, -1.1094045307349747, -1.7627022327285857, -2.171898538924113, -2.2477748362986785, -1.9718875354531775, -1.3988455372530322, -0.6438564743039131, 0.141854735199365, 0.8026984380903404, 1.210939127505476, 1.2928424310054207, 1.0433406530479448, 0.52616644048709, -0.14057647927052405, -0.8103743878084186, -1.340300567572516, -1.6222141651965212, -1.6064199642633419, -1.3125814007898644, -0.8253560956427964, -0.2754958685948392, 0.1896679513390335, 0.4400358707213789, 0.39345264922423634, 0.03643515053035348, -0.5699414653370715, -1.300710380813183, -1.9923374385677137, -2.477518950765357, -2.6220293464116082, -2.355529847968951, -1.6893533234505864, -0.7169641397262871, 0.40348982244521775, 1.4811554192900893, 2.3322757680945454, 2.819172052882236, 2.8796981210373334, 2.540344180785239, 1.9096417254262372, 1.152864079161377, 0.4532797778442303, -0.03156281449885983, -0.20862459305882158, -0.07411588650760297, 0.28206785018432756, 0.6940789534724453, 0.9569025075218063, 0.8746094255848373, 0.30956713560664706, -0.7785712219610887, -2.3134548435732993, -4.107560874090966, -5.892671066418715, -7.36976821389115, -8.268314962093317, -8.402452820430847, -7.7119223404858515, -6.278476134859961, -4.31364529894372, -2.1198445620946322, -0.03261886839889468, 1.6439619435995076, 2.6951339929357787, 3.034240660165723, 2.7143487758968203, 1.9104656336955634, 0.8766073003174932, -0.11250059753517659, -0.8219733060525075, -1.1060850093654242, -0.9355681327500844, -0.3972583204373574, 0.3331311115934221, 1.0381226168650857, 1.513961602046409, 1.6211618893649042, 1.3181463335328865, 0.6702024709541531, -0.16801272564427958, -0.9917822372681174, -1.5975674036468888, -1.8334669651732065, -1.6364781154007955, -1.0474753951006708, -0.20038734618368076, 0.711524441684042, 1.4836847547046144, 1.9503801138796864, 2.02445077507633, 1.716550138715841, 1.129239284465373, 0.4276233684327677, -0.20573169495999505, -0.6197855292081884, -0.7350390741081848], 'positive_zeros': ['2.57695791663702807327213774398738', '3.89655477077336814827851751078068', '5.80455678809977194165861904381576', '6.36138462219540663594656656337199', '8.037056548278346649509330033226903', '9.340890118945758451597297700292097', '10.30512615411416245655845002568722', '11.58227983111631737057892631778710', '12.63528687892073181496647482020781', '13.56636525188667121607541374277618'], 'prelabel': '2-122-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9870029912110809, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.57695791663702807327213774399', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.89655477077336814827851751078', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.80455678809977194165861904382', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.9741749046596212, 'bad_primes': [2, 61], 'central_character': '1.1', 'conductor': 122, 'conductor_radical': 122, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/122/2/a/c/1/2'], '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': '2-122-1.1-c1-0-3', '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': '2-122-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9870029912110809, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.57695791663702807327213774399', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3266682249787816182296529483344', 'Lhash_array': ['3266682249787816182296529483344'], 'label': '2-122-1.1-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/122/2/a/c/1/2'}