-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3397348715145021403278377246101', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.258617235339597, -3.0385707993933844], 'a4': [0.0, 0.0], 'a5': [-0.8240794760640088, -1.9895038475870443], 'a6': [0.0, 0.0], 'a7': [0.08374944013370386, -2.644425463361993], 'a8': [0.0, 0.0], 'a9': [-5.527474814272619, -5.527474814272619], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.154596021106726, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-0.08374944013370386, 2.644425463361993]]]], 'bad_primes': [2, 7], 'central_character': '896.111', 'coefficient_field': 'CDF', 'conductor': 896, 'conductor_radical': 14, 'conjugate': '1012367719388624996385592483275', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.258617235339597, 3.0385707993933844], [-2.1213203435596424, -2.1213203435596424]], [[1.0, 0], [0.8240794760640088, 1.9895038475870443], [-3.5355339059327378, 3.5355339059327378]], [[1.0, 0], [-0.08374944013370386, 2.644425463361993]], [[1.0, 0], [-0.6233991921273162, 0.25822040015156517], [7.7781745930520225, -7.7781745930520225]], [[1.0, 0], [1.2430977111645807, -3.0011033536484835], [-9.192388155425117, -9.192388155425117]], [[1.0, 0], [-2.68128258094683, 0], [17.0, 0]], [[1.0, 0], [-4.544954505767262, -1.882581796657507], [13.435028842544403, 13.435028842544403]], [[1.0, 0], [-0.871276465749054, 0.871276465749054], [0, -23.0]], [[1.0, 0], [2.6057058543866227, -6.290730413215158], [-20.506096654409877, -20.506096654409877]], [[1.0, 0], [-4.752139789207365, 0], [31.0, 0]], [[1.0, 0], [5.975215680634111, -2.475015373023033], [26.16295090390226, -26.16295090390226]], [[1.0, 0], [-3.3791978013881105, 3.3791978013881105], [0, -41.0]], [[1.0, 0], [-11.887126385720535, 4.923808966608517], [30.405591591021544, -30.405591591021544]], [[1.0, 0], [0, 3.01477144142486], [-47.0, 0]], [[1.0, 0], [-1.6266478717179957, -3.9270753531069156], [-37.476659402887016, 37.476659402887016]], [[1.0, 0], [2.083900790870247, -0.8631799702184751], [41.71930009000631, -41.71930009000631]], [[1.0, 0], [-5.362600165000823, -2.2212617179275385], [43.1335136523794, 43.1335136523794]], [[1.0, 0], [6.527907252385123, 2.7039477178516047], [47.37615433949868, 47.37615433949868]], [[1.0, 0], [9.164141874652735, 9.164141874652735], [0, 71.0]], [[1.0, 0], [-3.684196445073235, 3.684196445073235], [0, -73.0]], [[1.0, 0], [5.817998932830609, 0], [79.0, 0]], [[1.0, 0], [4.189003159965187, 1.7351419216813324], [58.68986283848344, 58.68986283848344]], [[1.0, 0], [-0.8720914868046736, -0.8720914868046736], [0, 89.0]], [[1.0, 0], [0, -16.020142494042332], [-97.0, 0]], [[1.0, 0], [-0.5559560766661067, -1.342196700371051], [-71.4177848998413, 71.4177848998413]], [[1.0, 0], [-4.23865520243926, 4.23865520243926], [0, -103.0]], [[1.0, 0], [7.887508886999875, -3.2671131543336642], [75.66042558696059, -75.66042558696059]], [[1.0, 0], [4.759699978381038, 1.971532283872353], [77.07463914933368, 77.07463914933368]], [[1.0, 0], [0, 10.226123226170833], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 29, 'label': '2-896-224.83-c1-0-29', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/896/2/x/b/111/28', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.725483954490863, 2.058029046919128, 2.4182549724004967, 2.8062292091411933, 3.216406475429183, 3.6370392052487412, 4.050479954443711, 4.4342172811740115, 4.762505487546854, 5.008487001621503, 5.146705382981293, 5.155860691974048, 5.021587776412982, 4.738967809372165, 4.314436826756774, 3.7667494571279136, 3.126702966325426, 2.435430603450627, 1.7412300894827948, 1.095089593839637, 0.5452870103529718, 0.13163833823789517, -0.11987734068600807, -0.20131971317216962, -0.12506057589878095, 0.07646022044774252, 0.35379674212789125, 0.6462918238654183, 0.8900832682219239, 1.0273762930996653, 1.0157001048216354, 0.8356880262929564, 0.49595788828751447, 0.03395152330654449, -0.4878901613247274, -0.9905399394168345, -1.3905203183820483, -1.6141485557031912, -1.6117038263629044, -1.3690631619989106, -0.9144842897270813, -0.3187756136745756, 0.3119562692358279, 0.850574030903163, 1.1684887404242772, 1.1577018722305268, 0.7516978763081991, -0.0586169845690065, -1.2172493026467472, -2.605897030107098, -4.057668887952199, -5.38030395302871, -6.385589191644017, -6.920251814156304, -6.892940711033277, -6.292208607430478, -5.1916958894165335, -3.740835487664838, -2.1420007999727595, -0.6176304741903562, 0.6270347013313163, 1.4388371460708063, 1.7425845325379767, 1.5527740693939054, 0.9685938288241562, 0.15287904722227497, -0.7010389363944003, -1.4080634137929189, -1.8277842182313881, -1.8910761728856031, -1.6111925654142145, -1.0769279550394057, -0.42930445880929147, 0.17306670242890193, 0.5921271665723086, 0.7432158191956391, 0.6148345513022568, 0.2704362685476226, -0.168504855865959, -0.5543681596188195, -0.7526320681865206, -0.6787854243014463, -0.32335358001088166, 0.24197784854508875, 0.8797289386809007, 1.4207274537528944, 1.7092174416267976, 1.6479064674708348, 1.2311312862837922, 0.5565210782709754, -0.18966418678923996, -0.7719777394731985, -0.9620387622462149, -0.5987444195095657, 0.3623896844836635, 1.823980957804092, 3.5538072201911954, 5.224877297730518, 6.481230440215501, 7.015394420254133, 6.639775767545437, 5.334787226558942, 3.2613215051708555, 0.7332583663341007, -1.844838096764574, -4.061139020255957, -5.581979705017993, -6.219373041172314, -5.964808291453484, -4.981683665544195, -3.558893484830954, -2.0377027817214364, -0.7305869109590647, 0.14756468851639723, 0.5190912321221721, 0.4452862277344202, 0.09175290456004608, -0.33126459473664827, -0.6356461202928363, -0.7098204882172182, -0.5454439994508334, -0.22939091743663995, 0.09538332305690621, 0.287048726673929, 0.2614551460077248, 0.029257389273624097, -0.2994425845631445, -0.5460374534182831, -0.5217359244564754, -0.09580159897657063, 0.7480324509309506, 1.8864574025045524, 3.0738258094906223, 4.000368484663709, 4.377235356165056, 4.024886115595842, 2.9385399021084466, 1.3093112870248798, -0.5087151862911741, -2.07998392404029, -2.997546545197285, -2.9922927433274626, -2.0105927511158397, -0.2371861877325115, 1.9452187756963308, 4.050498946134469, 5.613041226690955, 6.307302154213889, 6.029830207696035, 4.920759553886856, 3.3188130661198314, 1.6628494735116266, 0.3683699234039236, -0.28545449661092204, -0.22598669570803698, 0.4048116898221097, 1.3051972243020806, 2.1133187868048204, 2.520534581196437, 2.363595973386476, 1.6680884067317427, 0.6311768378056368, -0.44906500422121937, -1.2737308283032576, -1.6396377669340625, -1.5011834544977603, -0.978161354717711, -0.3082638940875742, 0.23861032358063924, 0.45450965142003746, 0.263693449087321, -0.25499503496869513, -0.9010494366931566, -1.4286089008738636, -1.638808492985457, -1.4546639302567574, -0.9504747643416828, -0.32331082962186786, 0.18527986063842916, 0.3906447489295174, 0.2528263737101491, -0.08333863190718545, -0.3151890436701752, -0.07314725940368502, 0.9504282506785423, 2.8758125979176667, 5.5574646470167774, 8.583648552100925, 11.361507683913796, 13.267391391382466, 13.819788229760528, 12.822578957486586, 10.433202076866769, 7.132090492812097, 3.5997758413714767, 0.536826560623934, -1.5200803492110662, -2.3312227548915754, -1.997244958112939, -0.9024030057719455, 0.4214375857552888, 1.4648104375627848, 1.8901445371767671, 1.6149043615448844, 0.8060298147122159, -0.2064584733339496, -1.0622340312571472, -1.5013884952203258, -1.4478506480455702, -1.0190960925262293, -0.46329524032295155, -0.05132050581755434, 0.03340503871395586, -0.23511588981274065, -0.7215582665928009, -1.1913798782917944, -1.4130841044915352, -1.2589953372601486, -0.7631697861444839, -0.11152862928604887, 0.43405045422518435, 0.6491447088967139, 0.4525828224757779, -0.0400308860665874, -0.5416585654901508, -0.69509098940512, -0.21692768705072304, 0.9683688379336224, 2.6576182891459497, 4.39504023598879, 5.595632833733696, 5.730281604110038, 4.511985460705556, 2.017975131643302, -1.2989653700066053, -4.720611495806078, -7.464102660134359, -8.910525355490842, -8.787085351362641, -7.242821622291757, -4.792924708085138, -2.1507844576723016, -0.004519501771676957, 1.1873253606245235, 1.3143042424735385, 0.6113227227804701, -0.4579653878322399, -1.3849425847964616, -1.7987429642183828, -1.5832194421594192, -0.8903786031681259, -0.0523159970360887, 0.5686345026784165, 0.7303310932220387, 0.4030815146802408, -0.23006479609194225, -0.861353046972251], 'positive_zeros': ['2.68003558278074296358196817064481', '3.08439669521409364518419850116800', '4.13338616940626576998728391655720', '5.18752456460507389872549306934818', '5.86758945002151462033760227304079', '7.43245271099247924832852666037830', '8.146967028002469093320820136051658', '9.086189135009058738504426397708276', '9.702548601342647365245976123006895', '10.32536135965032690983782444883292'], 'prelabel': '2-896-224.83-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6748076605817332, 'root_angle': 0.9870200502710988, 'root_number': '-0.999168704192414 + 0.040766414638183576*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.493510025136', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.68003558278074296358196817064', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.08439669521409364518419850117', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.13338616940626576998728391656', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 7.154596021106726, 'bad_primes': [2, 7], 'central_character': '224.83', 'conductor': 896, 'conductor_radical': 14, 'degree': 2, 'index': 29, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/896/2/x/b/111/28'], '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': '2-896-224.83-c1-0-29', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-896-224.83-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6748076605817332, 'root_angle': 0.4935100251355494, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.68003558278074296358196817064', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3397348715145021403278377246101', 'Lhash_array': ['3397348715145021403278377246101'], 'label': '2-896-224.83-c1-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/896/2/x/b/111/28'}