-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1633087468552149644823176264482', 'a10': [0.45861591526543105, -0.28002547062105954], 'a2': [-0.015198495239497754, 0.015198495239497754], 'a3': [8.404082575173481, 8.404082575173481], 'a4': [0.0, 15.99953801148491], 'a5': [-24.29981962842328, -5.875267315288285], 'a6': [-0.25545881802224035, -5.229873426171118e-60], 'a7': [-13.095800853708795, 13.095800853708795], 'a8': [-0.48634482613368085, -0.48634482613368085], 'a9': [0.0, 60.25720786066905], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.6179487079345525, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [24.29981962842328, 5.875267315288285]]], [7, [[1.0, 0], [13.095800853708795, -13.095800853708795]]]], 'bad_primes': [5, 7], 'central_character': '35.8', 'coefficient_field': 'CDF', 'conductor': 35, 'conductor_radical': 35, 'conjugate': '4256187606577547500254995757107', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.015198495239497754, -0.015198495239497754], [0, -16.0]], [[1.0, 0], [-8.404082575173481, -8.404082575173481], [0, 81.0]], [[1.0, 0], [24.29981962842328, 5.875267315288285]], [[1.0, 0], [13.095800853708795, -13.095800853708795]], [[1.0, 0], [-178.54136702933508, 0], [14641.0, 0]], [[1.0, 0], [-130.15105244790323, -130.15105244790323], [0, 28561.0]], [[1.0, 0], [-219.29973210128884, 219.29973210128884], [0, -83521.0]], [[1.0, 0], [0, 255.1733227906007], [-130321.0, 0]], [[1.0, 0], [54.15848297296858, 54.15848297296858], [0, 279841.0]], [[1.0, 0], [0, -438.9593550046096], [-707281.0, 0]], [[1.0, 0], [1449.3851178477867, 0], [923521.0, 0]], [[1.0, 0], [-914.3264209497105, 914.3264209497105], [0, -1874161.0]], [[1.0, 0], [1734.8180365311268, 0], [2825761.0, 0]], [[1.0, 0], [103.89252791527636, 103.89252791527636], [0, 3418801.0]], [[1.0, 0], [-1422.265982083535, 1422.265982083535], [0, -4879681.0]], [[1.0, 0], [-3305.5382834592556, -3305.5382834592556], [0, 7890481.0]], [[1.0, 0], [0, 4661.122150815098], [-12117361.0, 0]], [[1.0, 0], [3974.313711941713, 0], [13845841.0, 0]], [[1.0, 0], [3729.397401598686, -3729.397401598686], [0, -20151121.0]], [[1.0, 0], [1249.546800905703, 0], [25411681.0, 0]], [[1.0, 0], [3437.164967994104, 3437.164967994104], [0, 28398241.0]], [[1.0, 0], [0, -11135.868840324083], [-38950081.0, 0]], [[1.0, 0], [-3632.7707330986063, -3632.7707330986063], [0, 47458321.0]], [[1.0, 0], [0, 8157.708687916434], [-62742241.0, 0]], [[1.0, 0], [-4381.162105169113, 4381.162105169113], [0, -88529281.0]], [[1.0, 0], [-410.0970084617111, 0], [104060401.0, 0]], [[1.0, 0], [3073.5655242831153, 3073.5655242831153], [0, 112550881.0]], [[1.0, 0], [-11506.00519883738, 11506.00519883738], [0, -131079601.0]], [[1.0, 0], [0, 13007.313665277947], [-141158161.0, 0]], [[1.0, 0], [6514.254849024435, 6514.254849024435], [0, 163047361.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-35-5.3-c4-0-3', '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/35/5/g/a/8/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.6411923872994012, 1.5135336443546357, 1.3789752492004435, 1.237459699822834, 1.0888941686728977, 0.9332187991218974, 0.7704790503229724, 0.6008996495728812, 0.42495757925620886, 0.24345139270815003, 0.057564008855020915, -0.13108401950519552, -0.3203939182259615, -0.5077640525609014, -0.6900845384149217, -0.863754315022336, -1.0247236234950379, -1.1685643496399363, -1.2905699487587288, -1.38588565338955, -1.4496683681024647, -1.477274095056582, -1.4644689496498902, -1.4076578814671732, -1.3041232011355794, -1.1522630418811572, -0.9518180898639759, -0.7040734501838382, -0.41202153516625917, -0.0804715271287173, 0.2839085734646606, 0.6726299290681883, 1.0755111153662889, 1.4809034739406075, 1.8760159936583904, 2.247336848195657, 2.5811427154029127, 2.8640805728886742, 3.083800155812488, 3.229609098309273, 3.2931174297817827, 3.2688340558068445, 3.1546756059642456, 2.9523480158890556, 2.667563778359675, 2.310063168288367, 1.893415970116049, 1.4345911630693757, 0.9532952766369429, 0.47109511132843446, 0.01035640310721049, -0.4069542231520276, -0.7605421742881318, -1.0330588621924732, -1.2112946486580602, -1.2872052495525932, -1.2586883693525173, -1.1300358973807718, -0.9120019824158823, -0.6214483741795196, -0.2805547126125915, 0.0843884367595015, 0.4445539431033802, 0.7704382838400655, 1.0338970975536277, 1.2102223183697614, 1.2801116999314712, 1.2313762338532792, 1.0602372867183523, 0.7720839580226221, 0.381591978607296, -0.08785284995327847, -0.6054334747074578, -1.1348340855537842, -1.636721279093974, -2.071616108625849, -2.4029549591229533, -2.600106024945525, -2.641094052841908, -2.514791752860427, -2.22236318585995, -1.777792039999286, -1.2073936187166023, -0.54828928879584, 0.1540899026461363, 0.8493150187403438, 1.4858495547569106, 2.0152152848893086, 2.396087155744569, 2.5979557686387715, 2.604013128625088, 2.4129674432068193, 2.0395735732376683, 1.5137718501626674, 0.8784510421680921, 0.18598060388206825, -0.5062191624964153, -1.1406952837026927, -1.6651197654515872, -2.037102253340124, -2.2281833726016327, -2.2265922863326417, -2.038454882554671, -1.687279280258421, -1.2117110088904162, -0.6617257298265015, -0.09359506762125419, 0.43589706481004026, 0.8754108876328505, 1.1845593719763612, 1.3383683425915938, 1.3301725113916778, 1.1725770501052017, 0.8963072371240712, 0.546991103697524, 0.18014910685018384, -0.14512429067754523, -0.37313416151434264, -0.458456728166513, -0.37192729923286305, -0.10502474370479346, 0.3279207733443364, 0.8900509727346616, 1.5249170749796288, 2.1618213698170963, 2.723067572478901, 3.1323828533543057, 3.323605618014637, 3.248660969946549, 2.8838837617734483, 2.2338983870025273, 1.3325129617546014, 0.24040876220615717, -0.9602310896096122, -2.173648110462555, -3.300167890189746, -4.246538724977945, -4.935781065235924, -5.3154006751716905, -5.362978795950886, -5.088438242213115, -4.532665141198556, -3.7625985552804067, -2.8633326394967007, -1.928154081541307, -1.0477116423778885, -0.2996460387370969, 0.26002482156642964, 0.6026698478783752, 0.7292088304499624, 0.6683804835916244, 0.4713230093009808, 0.20316734132831105, -0.06724364071240642, -0.2781197953834022, -0.38448362281434134, -0.3655362873718243, -0.22853230416518686, -0.008516809239259288, 0.2361649924554589, 0.4320886607132161, 0.5016633888728488, 0.3752815982423617, 0.003019125515092775, -0.6358052278491162, -1.52667156261683, -2.6185194931620654, -3.8274416302933263, -5.045138966569113, -6.151192819001433, -7.027639294706987, -7.5739532335773605, -7.720419873379383, -7.438021706153804, -6.743384436178932, -5.6979604669250365, -4.40139881399603, -2.979852112773001, -1.5706914650447759, -0.3056329113161235, 0.7054567702971237, 1.38785846132694, 1.7105550171408548, 1.6888341336183819, 1.3805604891948529, 0.8766374339521468, 0.28701967952587476, -0.2757038956888072, -0.7127657270625882, -0.9532965528312536, -0.963941187522144, -0.7525818690440229, -0.36561600988191506, 0.1207881493506013, 0.6141057561966826, 1.0214497961303155, 1.265628090953712, 1.2987001101642897, 1.1108251752678295, 0.7329019950068887, 0.23245990256066412, -0.296669828321941, -0.7493643629692747, -1.0265729955934655, -1.0522669344174733, -0.7872003458777195, -0.2371450797628285, 0.545913300438901, 1.4700382220153998, 2.4162915832407794, 3.2564951771530595, 3.8730959010601334, 4.178005466277942, 4.127356932670137, 3.729688039782231, 3.0460479451589544, 2.1817821006526956, 1.2710833603389393, 0.456591519665805, -0.1328199101414965, -0.4025607515358837, -0.307826084446367, 0.1385018984000111, 0.8669650089532521, 1.7616370422289604, 2.677754880271941, 3.4641519190588914, 3.986946980720162, 4.150682746927677, 3.913470623112759, 3.293636409055423, 2.3667285112656153, 1.2533275054722008, 0.09962221470125107, -0.9460644749465434, -1.7569179853809538, -2.2475079984716286, -2.3865767270546954, -2.2006034860888177, -1.7675726219437504, -1.2020497198715898, -0.6341755304114869, -0.1862544827193313, 0.048947857640449136, 0.024363030187968565, -0.25364367248219444, -0.7273560856188078, -1.2992600064826711, -1.8510067423802323, -2.2663621408146293, -2.4539447480318595, -2.365530868588418, -2.0064437856589246, -1.4359321773714027, -0.7572420941257156, -0.09898089486814618, 0.40898158803373325], 'positive_zeros': ['1.28827885874713941833061948301454', '3.65350169126799845432439031042479', '6.25292833579245983696954897473748', '7.59631694588801270959212251108215', '8.852800947726236158367508986783054', '10.47278694375587432383104282838765', '11.90814654722114426109323159512504', '13.27110069997723159192348769422636', '14.44081853205045681334477934365853', '15.03479803294494024171930997724063'], 'prelabel': '2-35-5.3-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9020906150692591, 'root_angle': -0.4982792917840484, 'root_number': '0.005405737962110662 - 0.9999853888918002*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.249139645892', 'prec': 50}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.28827885874713941833061948301', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.65350169126799845432439031042', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.25292833579245983696954897474', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.6179487079345525, 'bad_primes': [5, 7], 'central_character': '5.3', 'conductor': 35, 'conductor_radical': 35, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/35/5/g/a/8/6'], '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': '2-35-5.3-c4-0-3', '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': '2-35-5.3-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9020906150692591, 'root_angle': -0.2491396458920242, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '1.28827885874713941833061948301', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1633087468552149644823176264482', 'Lhash_array': ['1633087468552149644823176264482'], 'label': '2-35-5.3-c4-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/35/5/g/a/8/6'}