-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1633207465409543609296710649526', 'a10': [-1.8622082769235904, -1.075146449968984], 'a2': [-0.7071067811865476, -1.224744871391589], 'a3': [0, 0], 'a4': [-1.0, 1.7320508075688772], 'a5': [1.3167801005943869, -0.7602433455417118], 'a6': [0, 0], 'a7': [0, 0], 'a8': [2.8284271247461903, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 24.03275931657819, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.7071067811865476, 1.224744871391589]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '882.325', 'coefficient_field': 'CDF', 'conductor': 882, 'conductor_radical': 42, 'conjugate': '761301556943523770451756889136', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7071067811865476, 1.224744871391589]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.3167801005943869, 0.7602433455417118], [12.5, -21.650635094610966]], [[1.0, 0], [0, 0]], [[1.0, 0], [-6.861369883779724, 11.884241248229445], [-60.5, -104.78907385791707]], [[1.0, 0], [0, 17.954362095953186], [-169.0, 0]], [[1.0, 0], [-22.36371547101239, -12.911697147269201], [144.5, 250.28134169370276]], [[1.0, 0], [16.464307166490983, -9.505672174594253], [180.5, -312.63517076618234]], [[1.0, 0], [-9.67049958706606, -16.749796619372262], [-264.5, 458.12743860196804]], [[1.0, 0], [-10.519900919559836, 0], [841.0, 0]], [[1.0, 0], [13.065415727979298, 7.543321287623218], [480.5, 832.2504130368455]], [[1.0, 0], [29.285564348639543, 50.724085380171445], [-684.5, 1185.5887777808964]], [[1.0, 0], [0, 54.074620674643626], [-1681.0, 0]], [[1.0, 0], [-73.88180147884094, 0], [1849.0, 0]], [[1.0, 0], [0.9425775257082033, -0.5441973881997226], [1104.5, -1913.050116959825]], [[1.0, 0], [-38.531869470845784, 66.73915563411701], [-1404.5, -2432.6653592304883]], [[1.0, 0], [59.32002496638453, 34.24843238267743], [1740.5, 3014.634430573631]], [[1.0, 0], [61.61928561883847, -35.57591113930882], [1860.5, -3222.4805274818964]], [[1.0, 0], [-59.1592864688153, 102.46688990351011], [-2244.5, -3887.5880375883453]], [[1.0, 0], [-11.002146576375502, 0], [5041.0, 0]], [[1.0, 0], [29.619336366742004, 17.10073182455657], [2664.5, 4615.049376767273]], [[1.0, 0], [-30.833066805858227, -53.40443826091189], [-3120.5, 5404.864545018681]], [[1.0, 0], [0, 97.00294084667686], [-6889.0, 0]], [[1.0, 0], [0.020742984685285765, -0.011975967791846022], [3960.5, -6859.787223376538]], [[1.0, 0], [0, 20.138103739205732], [-9409.0, 0]], [[1.0, 0], [38.4545203303175, 22.201727664266745], [5100.5, 8834.325144005059]], [[1.0, 0], [106.03499623779028, -61.21933362140918], [5304.5, -9187.66350874911]], [[1.0, 0], [72.33414009404598, 125.28640576469265], [-5724.5, 9915.124847928038]], [[1.0, 0], [-75.96591607472403, 131.57682628493532], [-5940.5, -10289.247822362915]], [[1.0, 0], [-80.08193235365805, 0], [12769.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 26, 'label': '2-882-7.3-c2-0-26', 'leading_term': '1.462572157489980146118261561833261020296636027687311604', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/882/3/n/f/325/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.4625721574899802, 1.5694225307786627, 1.6652366194434822, 1.7489372932145821, 1.8194405708804104, 1.8756571383761818, 1.916499850169604, 1.9408974268490655, 1.9478142807674859, 1.9362761296910191, 1.9054008058807228, 1.8544334420078266, 1.7827850198927022, 1.690073104972044, 1.5761634587425657, 1.441211122555615, 1.285699498379528, 1.1104759153350001, 0.9167821655293799, 0.7062785203320143, 0.4810598007131833, 0.2436621748812584, -0.002940504616645789, -0.2553518322124281, -0.5097802351246615, -0.7620791364330308, -1.0078001152771676, -1.242258945043292, -1.460614020696981, -1.657956293224609, -1.8294094214939098, -1.9702384404587465, -2.075964841718459, -2.1424855813957593, -2.166193185348163, -2.1440938275064507, -2.07392002818102, -1.9542344694089675, -1.7845213665520752, -1.56526188033994, -1.2979902099656482, -0.9853272813544841, -0.6309893375961275, -0.23976924917264547, 0.1825110157281558, 0.6290775959886807, 1.0923116407719284, 1.5638850543298952, 2.0349233000769416, 2.4961925374753724, 2.9383074322657703, 3.3519550906366735, 3.7281297543310243, 4.058372189896799, 4.3350071437761235, 4.551371845892343, 4.702028354468322, 4.782952565766727, 4.791692979988942, 4.727492827246629, 4.591369915797391, 4.386149560324208, 4.116447163484954, 3.7885984325607245, 3.4105367790996897, 2.9916191289413314, 2.5424031115215984, 2.0743803435398562, 1.5996722112996762, 1.1306961244760163, 0.679811597911808, 0.25895665599432094, -0.12071411008573409, -0.4491780170733854, -0.7178673861607712, -0.9199556722468657, -1.0505957869836648, -1.10710095261684, -1.0890600061200724, -0.9983810259770264, -0.8392594245737315, -0.6180691694760667, -0.34317848509951654, -0.024694149306037073, 0.3258587641658016, 0.6959122430317697, 1.0722739755041992, 1.4415754326668828, 1.790733974303305, 2.107412498812861, 2.3804596870975496, 2.6003140548230483, 2.7593558505200577, 2.8521923162886074, 2.875863934165431, 2.8299619580600277, 2.716650695744167, 2.5405915505554635, 2.308769629996853, 2.0302276332233897, 1.7157155849318373, 1.3772686274112393, 1.0277283547361231, 0.6802259208116826, 0.34764723902994676, 0.04210190052898658, -0.22558211648598703, -0.4463163457326385, -0.6131421447500699, -0.7215355390145163, -0.7696118769720554, -0.7582194739480772, -0.690915919958144, -0.5738256465877274, -0.4153824902532809, -0.22596613372415603, -0.017446225784445824, 0.19734755806344, 0.405207460268344, 0.5931566151805315, 0.7490581861691276, 0.8621970660206787, 0.9238070388509142, 0.9275180536166332, 0.8697012295341231, 0.7496933088239459, 0.5698873424714389, 0.33568223870777514, 0.0552901758740817, -0.26059249922026717, -0.5992387026260282, -0.9464499939767039, -1.2871980062387867, -1.6063194662743112, -1.8892330041560785, -2.122644022393504, -2.2952035289278174, -2.3980881022419807, -2.425471048924344, -2.374859249687329, -2.2472760065968345, -2.0472771655610913, -1.7827955920767282, -1.4648173699084666, -1.106901479291171, -0.7245627813565749, -0.3345454770320549, 0.04597956922788189, 0.40025549731173016, 0.712776971883833, 0.9700823897550909, 1.1614596705640143, 1.2795276962414208, 1.32066065332179, 1.2852295467595425, 1.17764370086695, 1.0061847596098876, 0.782636089167846, 0.5217210624532089, 0.24037393208214453, -0.043123662593529136, -0.3100995688470851, -0.5424943058008532, -0.7238596451539533, -0.8403003342675129, -0.8813080380116517, -0.8404405936741766, -0.7158062620055462, -0.5103215611026364, -0.23172210199249108, 0.10768189567862889, 0.4915006363245787, 0.8999922897801363, 1.3109922492697137, 1.7010017649715596, 2.0463839146087546, 2.3246075986549384, 2.5154758611656716, 2.6022736641250708, 2.572772450078353, 2.4200344070856312, 2.142968114217972, 1.7465988314264123, 1.2420305785710928, 0.6460926587726011, -0.01932035362399993, -0.7281897655892255, -1.4515541521402333, -2.158876276370102, -2.8195295520588224, -3.404329950355223, -3.887034852572859, -4.245730001998005, -4.464029541940439, -4.5320220557164275, -4.44690723300121, -4.213282748046569, -3.843058428997046, -3.354993946463887, -2.7738760618593052, -2.129370896973341, -1.4546046544284092, -0.7845417242300633, -0.15424125388855658, 0.40291870039085653, 0.8569569178527546, 1.182853646323085, 1.3618795832583972, 1.3826158286928358, 1.241606784599672, 0.9436067530304575, 0.5014022249810209, -0.06478557048349243, -0.7282905941650318, -1.4573355848285268, -2.216641291643684, -2.969227600090271, -3.678311464581307, -4.309200329605729, -4.831079024048054, -5.218593074721185, -5.45314181011719, -5.52381000453304, -5.427886345177915, -5.170939638682251, -4.766448161560225, -4.235002528001676, -3.6031264750905745, -2.9017816601291173, -2.1646406516359145, -1.426225690381946, -0.7200186732303522, -0.07664965538872953, 0.4777331924393065, 0.9228196025301194, 1.2451424587072413, 1.4386759294686435, 1.5049939527519278, 1.4529823836789084, 1.298124473523716, 1.0614046498049414, 0.7678982908200539, 0.44513394773298093, 0.1213281016966392, -0.17639981190814025, -0.4237232351526336, -0.6006117723503841, -0.6925503342080176, -0.6914000157562855, -0.595848678495116, -0.4114246031130465, -0.15007372857602322, 0.17067177546626683, 0.5288802378692802, 0.8996867586854507, 1.2569455268044856, 1.5749627466178788], 'positive_zeros': ['1.28837351957668689780884604036731', '2.55326948288497370607940686781441', '4.19931654164281220382235401276637', '4.86756583199074742201185061790799', '6.16098593781572420784398651980762', '6.80164983542540648466330575147114', '7.51068169209569518003777318788049', '8.606033250438740347396067321478730', '9.365960811876847450578011883617591', '9.943295959174090970861775803059383'], 'prelabel': '2-882-7.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.902321829151794, 'root_angle': 0.6361658509369688, 'root_number': '-0.4148497227768352588263666311468995839029993723251254915 + 0.9098899425271074689991749630565320081755493519203555138*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3180829254684844', 'prec': 60}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.28837351957668689780884604037', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.55326948288497370607940686781', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.19931654164281220382235401277', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 24.03275931657819, 'bad_primes': [2, 3, 7], 'central_character': '7.3', 'conductor': 882, 'conductor_radical': 42, 'degree': 2, 'index': 26, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/882/3/n/f/325/1'], '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': '2-882-7.3-c2-0-26', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-882-7.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.902321829151794, 'root_angle': 0.3180829254684844, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.28837351957668689780884604037', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1633207465409543609296710649526', 'Lhash_array': ['1633207465409543609296710649526'], 'label': '2-882-7.3-c2-0-26', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/882/3/n/f/325/1'}