-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '173334475627499819721962924900', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 8.141529148565482], 'a4': [0, 0], 'a5': [11.180339887498949, 0], 'a6': [0, 0], 'a7': [0, -63.603203473104436], 'a8': [0, 0], 'a9': [14.715503123058623, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 33.078388186830196, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-11.180339887498949, 0]]]], 'bad_primes': [2, 5], 'central_character': '320.191', 'coefficient_field': 'CDF', 'conductor': 320, 'conductor_radical': 10, 'conjugate': '2147182972280075134410573091517', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -8.141529148565482], [-81.0, 0]], [[1.0, 0], [-11.180339887498949, 0]], [[1.0, 0], [0, 63.603203473104436], [-2401.0, 0]], [[1.0, 0], [0, -33.3807834158538], [-14641.0, 0]], [[1.0, 0], [274.4867945848777, 0], [28561.0, 0]], [[1.0, 0], [284.94990824416533, 0], [83521.0, 0]], [[1.0, 0], [0, -5.179877510690386], [-130321.0, 0]], [[1.0, 0], [0, -584.7401023074285], [-279841.0, 0]], [[1.0, 0], [344.1350023852697, 0], [707281.0, 0]], [[1.0, 0], [0, -1466.6870374588154], [-923521.0, 0]], [[1.0, 0], [1931.7616506923293, 0], [1874161.0, 0]], [[1.0, 0], [976.7946987253433, 0], [2825761.0, 0]], [[1.0, 0], [0, -2045.4667973725473], [-3418801.0, 0]], [[1.0, 0], [0, 2561.7449421256656], [-4879681.0, 0]], [[1.0, 0], [121.92201213282905, 0], [7890481.0, 0]], [[1.0, 0], [0, 3456.33189175222], [-12117361.0, 0]], [[1.0, 0], [4135.1379842828865, 0], [13845841.0, 0]], [[1.0, 0], [0, 1694.0744680647244], [-20151121.0, 0]], [[1.0, 0], [0, -7646.835455707455], [-25411681.0, 0]], [[1.0, 0], [6008.297639117239, 0], [28398241.0, 0]], [[1.0, 0], [0, 4017.607588408789], [-38950081.0, 0]], [[1.0, 0], [0, 3016.1307479438083], [-47458321.0, 0]], [[1.0, 0], [-1190.40124448236, 0], [62742241.0, 0]], [[1.0, 0], [3021.433191223278, 0], [88529281.0, 0]], [[1.0, 0], [-754.4787772465214, 0], [104060401.0, 0]], [[1.0, 0], [0, -2192.609934132042], [-112550881.0, 0]], [[1.0, 0], [0, 13277.729127722072], [-131079601.0, 0]], [[1.0, 0], [-11298.92216000724, 0], [141158161.0, 0]], [[1.0, 0], [801.2905866539039, 0], [163047361.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-320-4.3-c4-0-1', 'leading_term': '0.498784608985642844574642020551163864646285131710534400', 'load_key': 'CMFs-workshop', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/320/5/b/d/191/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [0.49878460898564286, 0.2704537578351842, 0.0425503794725171, -0.18247815070232187, -0.402224958584986, -0.6143411613115579, -0.8165540766186894, -1.006686353449772, -1.1826761597480202, -1.3425984848085908, -1.4846875247898987, -1.6073600238131482, -1.7092393425668744, -1.7891799247168982, -1.8462917320438907, -1.8799641254680435, -1.8898885843183593, -1.8760795836118147, -1.8388928918155971, -1.77904051244378, -1.6976014744748704, -1.5960276812070173, -1.476144056616174, -1.3401422838869805, -1.1905675133291376, -1.0302975265316385, -0.8625139798116334, -0.6906655115043003, -0.5184226823403735, -0.3496249231675728, -0.18821988585023192, -0.03819582675748927, 0.0964921075389241, 0.2120005819821331, 0.304680417212504, 0.37116101009432173, 0.40843506427006304, 0.4139416929274496, 0.3856458208252546, 0.3221117212020295, 0.22256848228620624, 0.08696521370725963, -0.08398611995196766, -0.28878220941294397, -0.5251160171457042, -0.7898819869719603, -1.0791999935204952, -1.388458777187033, -1.7123791547974327, -2.045096794911142, -2.380263810430164, -2.71116786275442, -3.0308669058435282, -3.332337141440845, -3.6086312257751354, -3.853043281360685, -4.059276843319581, -4.221611525790086, -4.335063947269109, -4.395538319294269, -4.399962093509115, -4.346402187733138, -4.234157578508965, -4.063824458017534, -3.8373307050801584, -3.5579371062948124, -3.230203572363312, -2.8599195096251164, -2.4539985062492207, -2.0203385505838125, -1.5676500861024711, -1.1052552903514663, -0.6428630091724981, -0.19032474590434964, 0.24262203814763675, 0.6466163461462435, 1.0129342954271636, 1.333740177609159, 1.6023200232940353, 1.813289926229129, 1.9627718020767062, 2.04852993843844, 2.0700626282276606, 2.028644351271343, 1.9273153532073557, 1.7708170313069762, 1.5654732303694723, 1.3190193274677944, 1.040382785181021, 0.7394206177612901, 0.4266208797614939, 0.11277678807074125, -0.19135663574789874, -0.4754125227304238, -0.7297571732031678, -0.9458183067485493, -1.1163848371937288, -1.2358670025995588, -1.300506640661843, -1.3085287688651042, -1.2602273764427196, -1.1579804161730063, -1.0061913377485077, -0.8111570568054526, -0.5808649191117781, -0.3247239034648504, -0.05323790944594641, 0.22236860487773671, 0.49056023533358206, 0.7399213379087701, 0.9595923798374453, 1.1396957278882576, 1.2717344955866556, 1.3489485215772503, 1.3666126332856285, 1.3222640493779678, 1.215848051947281, 1.049773850649663, 0.828875778310491, 0.5602784916680095, 0.253168574834276, -0.08152128400762637, -0.4315056994947324, -0.7836043161785735, -1.124247573553136, -1.4400117484494703, -1.7181626999044262, -1.9471866928435817, -2.117286468191081, -2.2208214012779104, -2.252672155758596, -2.2105126679069125, -2.0949755200134734, -1.9097006792044247, -1.6612620532487792, -1.3589711823425734, -1.014562456323406, -0.6417693145493333, -0.2558057365506551, 0.12722824830865448, 0.4909945187224265, 0.8195928084030789, 1.0982371761113912, 1.313904644206297, 1.4559279402187755, 1.516505773152417, 1.4911067606245005, 1.3787469209329208, 1.1821254303529405, 0.9076089468832506, 0.5650610012302071, 0.16751950341919816, -0.26926796632968164, -0.7274350097028377, -1.1876914343208618, -1.630095363777648, -2.0348712687964636, -2.3832399264087933, -2.6582249027573286, -2.845400268622092, -2.9335459376401034, -2.9151802382815206, -2.7869439937536256, -2.5498163217974508, -2.2091493475933515, -1.774516761003817, -1.2593793133415792, -0.6805785777000636, -0.05767821514299291, 0.5878207760701055, 1.2333581520251444, 1.8562483309580327, 2.4346293562995354, 2.9483847223150046, 3.3799963566833227, 3.715289486253022, 3.944034423780687, 4.060376348127478, 4.063071664873379, 3.9555182075924806, 3.745575986482014, 3.445184977110882, 3.069796105934902, 2.6376406625202713, 2.1688713988965125, 1.6846151507782403, 1.2059815806237335, 0.753075325376634, 0.3440592545772914, -0.005685363135504421, -0.28426018188364927, -0.48377730899519217, -0.6006859476561802, -0.6358807298987905, -0.5945850306078837, -0.4860137870187963, -0.322831547105154, -0.12043206611936139, 0.10392478826868008, 0.33207528161700495, 0.5459639831385806, 0.7286533811757737, 0.8652778617817449, 0.9438911060389611, 0.9561607875057018, 0.8978717725323045, 0.7692085156841314, 0.574798551278337, 0.3235113600003965, 0.028019811556095283, -0.2958558190044022, -0.6299892716542473, -0.9549326352041346, -1.250992588754553, -1.499341611877389, -1.6831042160289338, -1.7883583939082968, -1.804995845815521, -1.7273910169713356, -1.5548382918293464, -1.2917284056249285, -0.9474486742933537, -0.5360063228465329, -0.07538924182244801, 0.41330688536716653, 0.9069427679378442, 1.3815373124198858, 1.8135446379850773, 2.1811383794972, 2.4654334181664526, 2.6515770100544827, 2.729646869438339, 2.695302889776873, 2.550151432659047, 2.3017958857402663, 1.9635637319178318, 1.5539178156865496, 1.0955768998947977, 0.6143870177220103, 0.1379996136974317, -0.30557580824267805, -0.6894685608126707, -0.9894129591619586, -1.185103683189487, -1.261364678898442, -1.209064715133035, -1.0257253263881172, -0.7157827250743363, -0.29048354068041293, 0.23258603153848037, 0.8303179856406064, 1.475208110099778, 2.1367328565717707, 2.7829062039798416, 3.381934293688213, 3.903879063622504, 4.322240414506537], 'positive_zeros': ['0.13673679134951891607173351907114', '1.95444514738432696307082485173583', '2.59587438902932485331472773582029', '4.58954717443043196854091209844629', '5.71032966578888816903760465641602', '6.63706504806386934139260206980801', '7.54762496672813931584903967234775', '8.666521451410344597803403568340804', '9.462004017865298895625319005978609', '10.50564237347018060897092989452707'], 'prelabel': '2-320-4.3-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.751381415523595, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.13673679134951891607173351907', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.95444514738432696307082485174', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.59587438902932485331472773582', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 33.078388186830196, 'bad_primes': [2, 5], 'central_character': '4.3', 'conductor': 320, 'conductor_radical': 10, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/320/5/b/d/191/6'], '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': '2-320-4.3-c4-0-1', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-320-4.3-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.751381415523595, 'root_angle': 0.5, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '0.13673679134951891607173351907', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '173334475627499819721962924900', 'Lhash_array': ['173334475627499819721962924900'], 'label': '2-320-4.3-c4-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/320/5/b/d/191/6'}