-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3460542932014932184807584656998', 'a10': [0.0, -884.1195729124115], 'a2': [0.0, -14.02331163936204], 'a3': [84.51962676392634, 0.0], 'a4': [59.346730665333105, 0.0], 'a5': [63.04641839597829, 0.0], 'a6': [0.0, -1185.2450657531037], 'a7': [0.0, -1667.887266964483], 'a8': [0.0, -4422.205478573933], 'a9': [582.5673083134133, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.481164710672401, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.0', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [-4865.286360202659, -13808.977863449052]]]], 'bad_primes': [11], 'central_character': '11.10', 'coefficient_field': 'CDF', 'conductor': 11, 'conductor_radical': 11, 'conjugate': '2361767908253743658919771432368', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 14.02331163936204], [-256.0, 0]], [[1.0, 0], [-84.51962676392634, 0], [6561.0, 0]], [[1.0, 0], [-63.04641839597829, 0], [390625.0, 0]], [[1.0, 0], [0, 1667.887266964483], [-5764801.0, 0]], [[1.0, 0], [-4865.286360202659, -13808.977863449052]], [[1.0, 0], [0, -16178.345298348662], [-815730721.0, 0]], [[1.0, 0], [0, -58233.06005387282], [-6975757441.0, 0]], [[1.0, 0], [0, -17200.063610205376], [-16983563041.0, 0]], [[1.0, 0], [-290115.14385628764, 0], [78310985281.0, 0]], [[1.0, 0], [0, -1157359.8241613691], [-500246412961.0, 0]], [[1.0, 0], [504456.0080820788, 0], [852891037441.0, 0]], [[1.0, 0], [562440.4284493346, 0], [3512479453921.0, 0]], [[1.0, 0], [0, 957088.2329721724], [-7984925229121.0, 0]], [[1.0, 0], [0, 6285629.748339599], [-11688200277601.0, 0]], [[1.0, 0], [-7141502.265503367, 0], [23811286661761.0, 0]], [[1.0, 0], [5444720.517742683, 0], [62259690411361.0, 0]], [[1.0, 0], [16322654.71122682, 0], [146830437604321.0, 0]], [[1.0, 0], [0, 16690267.797088703], [-191707312997281.0, 0]], [[1.0, 0], [-23097002.685315404, 0], [406067677556641.0, 0]], [[1.0, 0], [16677777.471059427, 0], [645753531245761.0, 0]], [[1.0, 0], [0, 50107698.71211797], [-806460091894081.0, 0]], [[1.0, 0], [0, -40510512.75180517], [-1517108809906561.0, 0]], [[1.0, 0], [0, -46592657.55419114], [-2252292232139041.0, 0]], [[1.0, 0], [-94949327.07275048, 0], [3936588805702081.0, 0]], [[1.0, 0], [34205580.143071994, 0], [7837433594376961.0, 0]], [[1.0, 0], [0, 71364705.80373703], [-10828567056280800, 0]], [[1.0, 0], [118764726.43479827, 0], [12667700813876160, 0]], [[1.0, 0], [0, -30268679.69567565], [-17181861798319200, 0]], [[1.0, 0], [0, 116680173.54975511], [-19925626416901920, 0]], [[1.0, 0], [-154630350.1036622, 0], [26584441929064320, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-11-11.10-c8-0-4', 'load_key': 'CMFs-workshop', 'motivic_weight': 8, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [8], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/11/9/b/b/10/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [2.192059836002884, 2.302126772044636, 2.382665700896537, 2.4314374942019046, 2.4463921743004886, 2.4257029371361125, 2.3678255131590755, 2.2715822844917586, 2.1362690160519007, 1.9617803722867215, 1.7487486034117576, 1.4986879432279838, 1.2141354413993466, 0.8987772654523152, 0.5575480932907286, 0.1966902466032367, -0.17624111834253842, -0.5524399419141794, -0.9219899587115217, -1.274093077659196, -1.5973903330165358, -1.8803749450049274, -2.1118904449836573, -2.2816992244516183, -2.3810986326498202, -2.40355340410923, -2.345305423526812, -2.2059154316624894, -1.988687119795874, -1.7009230389626167, -1.3539646756707078, -0.9629765545534119, -0.5464466735240812, -0.1253929223512537, 0.2777131354120908, 0.6402686843501835, 0.9410450962694242, 1.1617868941758298, 1.288791464721334, 1.3143393030977144, 1.237835810172454, 1.0665281121274672, 0.8156759503205939, 0.5080853385180301, 0.17295707683347486, -0.1559424858892098, -0.4427172793794375, -0.6522455254784039, -0.7533491234901025, -0.721971168664831, -0.5440672935480063, -0.21790358020502915, 0.2445297190798109, 0.8172305522005432, 1.4611843796067585, 2.1267018983417025, 2.757016642750152, 3.292924614819045, 3.678113661340956, 3.8647165785330104, 3.818544700096636, 3.5234318804917386, 2.9841522288199522, 2.227472776994378, 1.3010613575277685, 0.27017928045347617, -0.7876708053022066, -1.7897243783252728, -2.65592023674337, -3.31703888408956, -3.722111106880584, -3.8442040863553424, -3.683813343793587, -3.269316912765008, -2.65426534830401, -1.9116555507133648, -1.1257245906309168, -0.3821517013350248, 0.2421783250472246, 0.6885631735772042, 0.9237632780354254, 0.9441162778643651, 0.7757898714217777, 0.4709643146497954, 0.10028959821005834, -0.2574907156608094, -0.5273968012027487, -0.6499002688294991, -0.590712688473836, -0.34711690861737654, 0.05029941952745219, 0.5410278641514201, 1.0429141363632888, 1.464329913062553, 1.7185767742897544, 1.738396336740234, 1.4882992453743886, 0.9726142492692322, 0.23769557766943414, -0.6324458873980532, -1.5268151421730145, -2.323099754634414, -2.9061216751747603, -3.1862622478528246, -3.1148653388060916, -2.6939229943490703, -1.9781169382579304, -1.068433539464237, -0.0979240201628425, 0.7884691838714173, 1.4569857528337968, 1.8073170025250707, 1.7902893500131627, 1.417745794929467, 0.7625659680991131, -0.05165121321399497, -0.8699584420870546, -1.531564338997914, -1.8973366983094107, -1.8746203597221058, -1.4349384795346547, -0.6212030846161755, 0.4572240645838707, 1.6411823151099347, 2.7475216270577545, 3.599773330077605, 4.058353056564131, 4.044875151148115, 3.5560681954436952, 2.664567971028979, 1.5062268997004546, 0.25609069865184203, -0.9026239981375083, -1.8108001155118132, -2.360844077023594, -2.514007883894982, -2.304254673284235, -1.827934178771787, -1.2213731859371064, -0.6309718340297152, -0.1820052773571108, 0.04730478461576828, 0.04088675855192858, -0.15426578816119904, -0.44171028506727394, -0.7008739137783079, -0.8185680214879435, -0.7196166700675989, -0.38944184206571664, 0.11704119364606674, 0.6830218846737586, 1.153076224259685, 1.3677023972757654, 1.201858861742581, 0.5989050809746046, -0.4081468149775508, -1.6938061188007387, -3.0576614144930003, -4.259844431627275, -5.067786238964969, -5.304759448958668, -4.889766151846331, -3.8596693158966495, -2.3678929740725514, -0.6588699766185834, 0.9773243077008713, 2.2612101172362595, 2.9793687558340856, 3.0272745268208916, 2.430049960417827, 1.3363053994302936, -0.01395208839954066, -1.3405972016514158, -2.382734632397256, -2.9530537779836648, -2.9751254798485185, -2.495363687754624, -1.6671350909078402, -0.7109264530105311, 0.139929847854513, 0.6950619472133694, 0.8511159448219414, 0.6136006040732908, 0.09143468532299083, -0.5342110343540285, -1.0588286303740284, -1.30884000221175, -1.187402225798507, -0.699990168490166, 0.04693752505767652, 0.8740238305735758, 1.5767468022033997, 1.9804625084593432, 1.9882818297007325, 1.6089026481134132, 0.9565356730991165, 0.22228149952715812, -0.3760953033058959, -0.6530846188244854, -0.5074227001736005, 0.04708602068359007, 0.8809284295019271, 1.7796082419761823, 2.4985048950854716, 2.82786296663346, 2.650668947273465, 1.9774691762753667, 0.9478418688873014, -0.20310234477641317, -1.2053796086368123, -1.8264539321836677, -1.9359429308492857, -1.5447410457838482, -0.8068407549308025, 0.01818349725632782, 0.633440271503093, 0.7864363862303115, 0.3425910170433149, -0.6697473723779889, -2.056168555057906, -3.4975539276969028, -4.626649222205173, -5.1208279897439795, -4.787080398623646, -3.6166367096309853, -1.7941256146940916, 0.3421025213266997, 2.3789787056484566, 3.9269907269184916, 4.712385239495084, 4.639443186274363, 3.80693377717438, 2.475158229399334, 0.9932855948663636, -0.29272334843115716, -1.1263787148981437, -1.3980154321019473, -1.1587335774816183, -0.5890177888759695, 0.06689208296835765, 0.5802071985535224, 0.8062822794356732, 0.7224695326751119, 0.4246399399248926, 0.08483187378460466, -0.11535231909510026, -0.05334307347870208, 0.286770917468712, 0.8039995248055122, 1.3120930781604792, 1.6039198669905508, 1.5282859090101404, 1.0538679081961617, 0.2978142487572682, -0.4932271136950074, -1.0072816336187573, -0.9594306758134942], 'positive_zeros': ['2.72988702990547371793035530899847', '5.85417590102816912254671156200994', '7.82519504149597608241120338744488', '9.053650980498135914826333118105738', '11.47056105360012306615555929408210', '13.63746380045899782518112603201186', '14.81267030084517479038022361942364', '15.80070137687546990254844183103831', '17.27645964664228780005052606453980', '19.00253606306714551156566277055605'], 'prelabel': '2-11-11.10-c8-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.11687616800615, 'root_angle': 0.39217346554239807, 'root_number': '0.3323056048222565 + 0.9431717685574109*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.196086732771', 'prec': 47}, 'spectral_label': 'c8-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.72988702990547371793035530900', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.85417590102816912254671156201', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.82519504149597608241120338744', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.481164710672401, 'bad_primes': [11], 'central_character': '11.10', 'conductor': 11, 'conductor_radical': 11, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/11/9/b/b/10/3'], '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': '2-11-11.10-c8-0-4', 'motivic_weight': 8, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [8], 'order_of_vanishing': 0, 'prelabel': '2-11-11.10-c8-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.11687616800615, 'root_angle': 0.19608673277119903, 'self_dual': False, 'spectral_label': 'c8-0', 'z1': {'__RealLiteral__': 0, 'data': '2.72988702990547371793035530900', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3460542932014932184807584656998', 'Lhash_array': ['3460542932014932184807584656998'], 'label': '2-11-11.10-c8-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/11/9/b/b/10/3'}