-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '663332174922187459879782590192,2710077021220307413944018918162', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.684980786677827, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [1]], [17, [1]]], 'bad_primes': [3, 17], 'central_character': '2601.1', 'coefficient_field': '1.1.1.1', 'conductor': 6765201, 'conductor_radical': 51, 'degree': 4, 'euler_factors': [[1, 0, 0, 0, 1], [1], [1, 0, 0, 0, 1], [1, 2, 3, 2, 1], [1, 0, -2, 0, 1], [1, -2, 3, -2, 1], [1], [1, 2, 3, 2, 1], [1, 0, 0, 0, 1], [1, 0, -2, 0, 1], [1, 2, 3, 2, 1], [1, 2, 3, 2, 1], [1, 0, -2, 0, 1], [1, -2, 3, -2, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, -2, 3, -2, 1], [1, -2, 3, -2, 1], [1, 0, 0, 0, 1], [1, 0, 2, 0, 1], [1, 0, 2, 0, 1], [1, 0, 0, 0, 1], [1, 0, 0, 0, 1], [1, -2, 3, -2, 1], [1, 0, 0, 0, 1], [1, 2, 3, 2, 1], [1, 0, 0, 0, 1], [1, 0, 2, 0, 1], [1, 0, 0, 0, 1]], 'euler_factors_factorization': [[[[1, 0, 0, 0, 1], 1]], [1], [[[1, 0, 0, 0, 1], 1]], [[[1, 1, 1], 2]], [[[1, -1], 2], [[1, 1], 2]], [[[1, -1, 1], 2]], [1], [[[1, 1, 1], 2]], [[[1, 0, 0, 0, 1], 1]], [[[1, -1], 2], [[1, 1], 2]], [[[1, 1, 1], 2]], [[[1, 1, 1], 2]], [[[1, -1], 2], [[1, 1], 2]], [[[1, -1, 1], 2]], [[[1, -1], 2], [[1, 1], 2]], [[[1, -1], 2], [[1, 1], 2]], [[[1, -1], 2], [[1, 1], 2]], [[[1, -1, 1], 2]], [[[1, -1, 1], 2]], [[[1, 0, 0, 0, 1], 1]], [[[1, 0, 1], 2]], [[[1, 0, 1], 2]], [[[1, 0, 0, 0, 1], 1]], [[[1, 0, 0, 0, 1], 1]], [[[1, -1, 1], 2]], [[[1, 0, 0, 0, 1], 1]], [[[1, 1, 1], 2]], [[[1, 0, 0, 0, 1], 1]], [[[1, 0, 1], 2]], [[[1, 0, 0, 0, 1], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 0, 'label': '4-51e4-1.1-c0e2-0-0', 'leading_term': '0.675572288173207149201965036216958483016583877080747579081157300100000000000000000000000000', '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/2601/1/b/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.029296875', 'prec': 37}, 'plot_values': [0.6755722881732071, 0.6761840597562565, 0.674526079798784, 0.6728983221430737, 0.6703595491865132, 0.6657862121473502, 0.6586003374704361, 0.6480230623450945, 0.6329919193399244, 0.6124051029172686, 0.5850914621633206, 0.5498330734271554, 0.5053856111167321, 0.4505170161939026, 0.38404937452237975, 0.304873414979425, 0.21200816195251476, 0.10461836288035158, -0.017939374688433776, -0.1560792362553932, -0.3099645667542392, -0.4794570522039565, -0.6641101935025945, -0.8631280717792215, -1.075357738469161, -1.2992758828258988, -1.5329778571186414, -1.7741930224838767, -2.0202826876792184, -2.2682758561795877, -2.5148869681990202, -2.7565705767966184, -2.9895558448224326, -3.209927691153693, -3.413670141490763, -3.5967714438388443, -3.7552838524196686, -3.885425178771657, -3.9836782723706095, -4.046854907453627, -4.072243140222621, -4.057627614377911, -4.001448525633684, -3.902814429349993, -3.7616065353459622, -3.578523668992319, -3.355092043439029, -3.0937334503319933, -2.7977035780234636, -2.4711170485157172, -2.1188784187643335, -1.7466004209264008, -1.3605611393725052, -0.9675151077138603, -0.5746488554460712, -0.18934679704904805, 0.18091157775636874, 0.5287624365932455, 0.8471366952082857, 1.129426373745888, 1.3697032314209103, 1.562851823206651, 1.704774660201175, 1.7924933023339706, 1.824309464230117, 1.7998506975080217, 1.7201769392278325, 1.587749323048069, 1.4064647777616905, 1.1815507012350717, 0.9195043716932633, 0.6279274286785952, 0.31536696114134927, -0.008904363028332411, -0.3351219616289817, -0.6532945629913023, -0.9534862435999312, -1.2260901150379042, -1.4621463397690078, -1.6535693876242097, -1.7934792220993634, -1.876351925012049, -1.8982997196264995, -1.8571567374144358, -1.7526285788159677, -1.5863253082708206, -1.3617449950394012, -1.0842255732846477, -0.7607946036785319, -0.3999890220718958, -0.011625281718056945, 0.3935170164043994, 0.803986491494587, 1.208048326316938, 1.5940418100776097, 1.950754879494891, 2.2678218811056556, 2.536031924693472, 2.747696593362727, 2.8968655367179195, 2.979599285977813, 2.9940486812508382, 2.940613183056299, 2.821832827691022, 2.642431610090162, 2.409017568568149, 2.1299886521634597, 1.8151082099840334, 1.4752400961668015, 1.121894183895687, 0.7668095279658984, 0.4215303963286433, 0.09692311465294089, -0.19718232113213058, -0.4524407657148675, -0.6622338191162852, -0.8220181501205613, -0.9293833970291707, -0.9842634994673964, -0.9887752076585286, -0.9472531101164506, -0.8658946045836992, -0.7525897272100261, -0.6164323460216016, -0.4673670241323767, -0.315627894465948, -0.17127789733581839, -0.043647218977222145, 0.059144124984926646, 0.13065239457000458, 0.16652105458566416, 0.1647593011516152, 0.12600058149279186, 0.053543932909831775, -0.04661939572886296, -0.166013967328867, -0.29390905507862497, -0.41777705377500785, -0.5237309505409466, -0.5971945475575745, -0.6234870158957253, -0.5885705261608881, -0.4797477439235192, -0.2862933400080184, -0.0001968180649163375, 0.38344769052924227, 0.8658413488843749, 1.4443123861948917, 2.112113729114586, 2.8584073898481694, 3.6685956804686617, 4.524475495532398, 5.405031922885719, 6.2868396538315805, 7.145145098956257, 7.954483298423427, 8.689933506751066, 9.327763234084909, 9.846765455842464, 10.228747073333082, 10.459732425437878, 10.530260764388704, 10.43615009970278, 10.178621984634248, 9.764456532020006, 9.205829936254117, 8.519984195217388, 7.728548941982799, 6.856988277122014, 5.9333548642277965, 4.987628069648376, 4.0501750395593055, 3.150920385258635, 2.3179544185506913, 1.576532232120483, 0.9481166069509616, 0.4494333316667451, 0.09198569554144766, -0.11850263728765671, -0.18216580118193404, -0.10495241168683367, 0.10166780807766947, 0.42135677846100306, 0.8335265144643826, 1.3144922996142532, 1.838283710984613, 2.3781299810473158, 2.9072754027168606, 3.400559814869993, 3.835067248780249, 4.191532295039142, 4.454670129807315, 4.614211934862183, 4.664766443950201, 4.606404875747638, 4.443987296361656, 4.1872656197245375, 3.849790313307918, 3.4484992423415326, 3.0024807863901257, 2.5320890917472854, 2.0578400976987417, 1.5992603861406616, 1.1740804503617261, 0.797139507124399, 0.4799551794491018, 0.22997125888985273, 0.05056138149508475, -0.05923498307394244, -0.1042610220585075, -0.09299847912599886, -0.03675947128475753, 0.05099703840803149, 0.1556386158983618, 0.2623249404047009, 0.356920575779958, 0.42701069066527986, 0.46254657622388606, 0.45666693917995815, 0.4059192066818465, 0.31069238883064676, 0.17495204663958944, 0.006168823866385082, -0.18536653390913638, -0.3871307700067931, -0.5853045084410453, -0.7657470491527716, -0.9149760389717778, -1.0212770896194383, -1.0755062144144267, -1.0720544456468106, -1.0092429900767201, -0.8899268362860951, -0.7213104583109969, -0.5150450658398543, -0.28645558443577807, -0.0540460172155173, 0.1616805593873685, 0.339287511584806, 0.45770432123078497, 0.49766477503455503, 0.4428429202393054, 0.2813186969996728, 0.0063056292167016316, -0.3827354998255388, -0.8799552996931808, -1.4726758567102904, -2.1418811857443685, -2.86266848697842, -3.6052448703776583, -4.336319519629566, -5.02035772618374, -5.621739443449437, -6.105957521630882, -6.442202042629434, -6.604123822129499, -6.572485715595889, -6.3350647920417495, -5.88907669536366, -5.239910197849453, -4.40304401241585, -3.401613805111717, -2.2675557372856376, -1.0383150630992968, 0.2428986793391274, 1.5308042379510838, 2.7785215886325823, 3.941187470225199, 4.976799505980242, 5.849254189665828, 6.529181540394947, 6.995939918872168, 7.238106478219109, 7.25416932003845, 7.052391110801288, 6.650221520785098, 6.073427469518473, 5.354419680748231, 4.530856924588247, 3.6431694581299148, 2.7330409973941596, 1.840610884833586, 1.003128517882197, 0.25259486060345926, -0.38534400450135264, -0.8925919035563918, -1.259377939335503, -1.4840419009482777, -1.5731995843436257, -1.5404323785429355, -1.4055774348901036, -1.192860931227727, -0.9294346731831874, -0.6433701742164514, -0.36194007014830937, -0.10981051610628108, 0.09238354221286162, 0.2292853901581014, 0.29158095543052914, 0.27639834450535433, 0.18723042611728447, 0.033443038193374776, -0.17064233095436823, -0.406955158792306, -0.6551624417093512, -0.8943084884305821, -1.1044027018750275, -1.2680885725913502, -1.371932838733083, -1.4075552720830853, -1.3724417861288911, -1.2700449730774916, -1.1100162411676373, -0.9072011060287708, -0.6811535526376478, -0.4543940876247011, -0.25119628332034605, -0.09562940640478357, -0.009949900268076208, -0.012852248577678489, -0.11802477437314585, -0.33296308891198534, -0.6581823541475592, -1.0868750470152024, -1.6050744485931134, -2.192208222871759, -2.8223198199959194, -3.465291265457129, -4.088936884034059, -4.660579662855261, -5.149447285440071, -5.528311141634781, -5.775484897441172, -5.876108090456504, -5.823353801371231, -5.618726666580668, -5.2725090569886355, -4.802625535047205, -4.234423400175174, -3.5982785718033092, -2.928687614420224, -2.261338684383813, -1.6315970023920718, -1.0718302592305275, -0.6097473089203306, -0.26648363401366676, -0.05544302502392469, 0.018560098472882036, -0.04050453761788977, -0.2202088213295429, -0.5005832393499525, -0.8554446527650618, -1.254327352229977, -1.6643315389143998, -2.052668993897308, -2.388521568941808, -2.6454647892404988, -2.8029597043844188, -2.8478998141958316, -2.7753638566355323, -2.5889583212814706, -2.3004050529730162, -1.9288515793567569, -1.4991632429604391, -1.0405142898988338, -0.5838408280521404, -0.15999989478321097, 0.2027864718919142, 0.48079264742956673, 0.6566215207569834, 0.720478925317144, 0.6708891266973397, 0.5148619640885028, 0.2673694898433978, -0.049745526218625956, -0.40936635322059156, -0.7812553853255408, -1.134190192427303, -1.4387515749833253, -1.6692591338613003, -1.8065304062409782, -1.8390045813682137, -1.7646716038934969, -1.5910389815496229, -1.3356537140316735, -1.0247649173859026, -0.6923643521694098, -0.3776437738616079, -0.1229097738137998, 0.0296523093369691, 0.04063313401254581, -0.12350131856875798, -0.48788307959392313, -1.067086803517119, -1.8634745540698732, -2.8665620693599174, -4.052717035085968, -5.3863505295529075, -6.821034009139728, -8.302308951538068, -9.770131866985471, -11.162304884251595, -12.418168042300179, -13.481282592670574, -14.303881789607068, -14.847978126108817, -15.08929629403641, -15.016938631500537, -14.635334192865564, -13.962879853357341, -13.031417559857465, -11.883871183882023, -10.571976314689651, -9.152879345752604, -7.686216156441319, -6.230336428451421, -4.839410351406439, -3.560446454484618, -2.430959682067607, -1.4775001878760006, -0.7146806287203052, -0.14511175174084245, 0.23964263942204786, 0.45806617031368263, 0.5361314808481134, 0.5054253797181193, 0.40004504588383016, 0.2541919223408871, 0.09950555607425646, -0.037064666692550506, -0.1349944421294825, -0.18120342331668848, -0.17060130355471137, -0.10571018284604472, 0.00408854934457167, 0.1440167569161896, 0.2956681784851748, 0.4393198492726379, 0.5555994956255064, 0.6271248673589984, 0.6426699392016029, 0.5976021758742796, 0.4848522640688184, 0.3087310552962618], 'positive_zeros': ['0.52327681997133934574765767504512', '1.62612481992632372434840412921510', '2.13787381217851492620682795108193', '2.63757267510790531800466216854852', '3.29053314577641316694381223089058', '3.73218600285115517355251786863939', '3.91299959990558752207192893874727', '4.21876732337717896777955879124256', '5.19598753866712259227529533918710', '5.29041936353379094595219217217553', '6.07578726019765806425117292528106', '6.19492924055178569594315718508471', '6.50489665714416548170838749884368', '6.92108683010153937643509465331634', '7.11969637538421973167195938367315', '7.72886470812827842660007750560295', '8.301957838272685982792047386375097', '8.657425953427082792199055691331978', '8.823622256987809291614457058668799', '9.326834246147090560417409749285230'], 'prelabel': '4-51e4-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.1393279149825302, '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': 2153206527223786109, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.52327681997133934574765767505', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.62612481992632372434840412922', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.13787381217851492620682795108', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.684980786677827, 'bad_primes': [3, 17], 'central_character': '1.1', 'conductor': 6765201, 'conductor_radical': 51, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, 0, 0], 'euler11': [1, 0, -2, 0, 1], 'euler13': [1, -2, 3, -2, 1], 'euler17': [1, 0, 0, 0, 0], 'euler19': [1, 2, 3, 2, 1], 'euler2': [1, 0, 0, 0, 1], 'euler23': [1, 0, 0, 0, 1], 'euler29': [1, 0, -2, 0, 1], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 2, 3, 2, 1], 'euler37': [1, 2, 3, 2, 1], 'euler41': [1, 0, -2, 0, 1], 'euler43': [1, -2, 3, -2, 1], 'euler47': [1, 0, -2, 0, 1], 'euler5': [1, 0, 0, 0, 1], 'euler53': [1, 0, -2, 0, 1], 'euler59': [1, 0, -2, 0, 1], 'euler61': [1, -2, 3, -2, 1], 'euler67': [1, -2, 3, -2, 1], 'euler7': [1, 2, 3, 2, 1], 'euler71': [1, 0, 0, 0, 1], 'euler73': [1, 0, 2, 0, 1], 'euler79': [1, 0, 2, 0, 1], 'euler83': [1, 0, 0, 0, 1], 'euler89': [1, 0, 0, 0, 1], 'euler97': [1, -2, 3, -2, 1], 'euler_factors': [[1, 0, 0, 0, 1], [1, 0, 0, 0, 0], [1, 0, 0, 0, 1], [1, 2, 3, 2, 1], [1, 0, -2, 0, 1], [1, -2, 3, -2, 1], [1, 0, 0, 0, 0], [1, 2, 3, 2, 1], [1, 0, 0, 0, 1], [1, 0, -2, 0, 1], [1, 2, 3, 2, 1], [1, 2, 3, 2, 1], [1, 0, -2, 0, 1], [1, -2, 3, -2, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, -2, 3, -2, 1], [1, -2, 3, -2, 1], [1, 0, 0, 0, 1], [1, 0, 2, 0, 1], [1, 0, 2, 0, 1], [1, 0, 0, 0, 1], [1, 0, 0, 0, 1], [1, -2, 3, -2, 1]], 'index': 0, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2601/1/b/a', 'ArtinRepresentation/2.2601.24t22.c'], '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': '4-51e4-1.1-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': '4-51e4-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.1393279149825302, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e2-0', 'trace_hash': 2153206527223786109, 'z1': {'__RealLiteral__': 0, 'data': '0.52327681997133934574765767505', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 24606735
{'Lhash': '663332174922187459879782590192,2710077021220307413944018918162', 'Lhash_array': ['663332174922187459879782590192', '2710077021220307413944018918162'], 'label': '4-51e4-1.1-c0e2-0-0', 'type': 'Artin', 'url': 'ArtinRepresentation/2.2601.24t22.c'}
-
id: 19884434
{'Lhash': '663332174922187459879782590192,2710077021220307413944018918162', 'Lhash_array': ['663332174922187459879782590192', '2710077021220307413944018918162'], 'label': '4-51e4-1.1-c0e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2601/1/b/a'}