-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1093161582555036961610276917206', 'a10': [64464706424466.56, -552898509093692.7], 'a2': [-23014.57089570206, -2683.3632789288176], 'a3': [0, 1929327.8449550667], 'a4': [522470035.0265928, 123512908.84366162], 'a5': [0, 24023846092.952602], 'a6': [5177087492.167297, -44402652468.77046], 'a7': [-2262465335601.9707, 0], 'a8': [-11692993657934.695, -4244573503447.8486], 'a9': [64908071431564.04, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 42.62243390642666, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '14.5', 'prec': 14}, 'bad_lfactors': [[2, [[1.0, 0], [23014.57089570206, 2683.3632789288176]]]], 'bad_primes': [2], 'central_character': '8.5', 'coefficient_field': 'CDF', 'conductor': 8, 'conductor_radical': 2, 'conjugate': '530968145629031224428777084608', 'degree': 2, 'euler_factors': [[[1.0, 0], [23014.57089570206, 2683.3632789288176]], [[1.0, 0], [0, -1929327.8449550667], [-68630377364883.0, 0]], [[1.0, 0], [0, -24023846092.952602], [-186264514923095700000, 0]], [[1.0, 0], [2262465335601.9707, 0], [3219905755813180000000000, 0]], [[1.0, 0], [0, 1449806511947235.2], [-1586309297171491600000000000000, 0]], [[1.0, 0], [0, 1681310767349920.2], [-201538126434611140000000000000000, 0]], [[1.0, 0], [860372717142515800, 0], [481968572106750900000000000000000000, 0]], [[1.0, 0], [0, 6154556838581842000], [-12129821994589221000000000000000000000, 0]], [[1.0, 0], [-29954516424723910000, 0], [3091058643093537600000000000000000000000, 0]], [[1.0, 0], [0, -1643643236243474500000], [-2567686153161211300000000000000000000000000, 0]], [[1.0, 0], [-2372537591047455000000, 0], [17761887753093899000000000000000000000000000, 0]], [[1.0, 0], [0, -29626322111502806000000], [-3005038205702535000000000000000000000000000000, 0]], [[1.0, 0], [-280362794741622100000000, 0], [58983677299744400000000000000000000000000000000, 0]], [[1.0, 0], [0, 514184551000178100000000], [-234738979284454770000000000000000000000000000000, 0]], [[1.0, 0], [-444359864548791600000000, 0], [3096263264537032000000000000000000000000000000000, 0]], [[1.0, 0], [0, 18594308952298292000000000], [-100925339366770620000000000000000000000000000000000, 0]], [[1.0, 0], [0, -66689888136096930000000000], [-2263123934140265400000000000000000000000000000000000, 0]], [[1.0, 0], [0, 43534846843747380000000000], [-5950661074415938000000000000000000000000000000000000, 0]], [[1.0, 0], [0, 89745726481463570000000000], [-90400176482989650000000000000000000000000000000000000, 0]], [[1.0, 0], [-117277870908694620000000000, 0], [485838707624806700000000000000000000000000000000000000, 0]], [[1.0, 0], [898383084416463000000000000, 0], [1087333937993221700000000000000000000000000000000000000, 0]], [[1.0, 0], [-2095538757586534500000000000, 0], [10744486076476623000000000000000000000000000000000000000, 0]], [[1.0, 0], [0, -2665558168885916000000000000], [-45005405483997304000000000000000000000000000000000000000, 0]], [[1.0, 0], [-22913113738670220000000000000, 0], [340651411429620900000000000000000000000000000000000000000, 0]], [[1.0, 0], [-63955212860579300000000000000, 0], [4134093490135647000000000000000000000000000000000000000000, 0]], [[1.0, 0], [0, -83417549435084210000000000000], [-13345038765672333000000000000000000000000000000000000000000, 0]], [[1.0, 0], [69519063020527350000000000000, 0], [23565655060093790000000000000000000000000000000000000000000, 0]], [[1.0, 0], [0, 180660667224974700000000000000], [-71142570492168500000000000000000000000000000000000000000000, 0]], [[1.0, 0], [0, 61487751384891460000000000000], [-121721820817717870000000000000000000000000000000000000000000, 0]], [[1.0, 0], [-352217448132427500000000000000, 0], [346158389003024140000000000000000000000000000000000000000000, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 13, 'label': '2-2e3-8.5-c29-0-13', 'leading_term': '0.815179457309362521277230832437188850128840435641564267', 'load_key': 'CMFs-workshop', 'motivic_weight': 29, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [29], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/8/30/b/a/5/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.09375', 'prec': 24}, 'plot_values': [0.8151794573093625, 0.882923673598174, 0.9042860031193205, 0.8803178338473541, 0.8137331702525948, 0.7088224436912111, 0.571314296932096, 0.40818954133153995, 0.22745297598398787, 0.03787008096120494, -0.15132328832681574, -0.3307292054462654, -0.4911043712612256, -0.623675285048151, -0.7204419494453109, -0.7744604535347801, -0.7800953559978813, -0.7332336470294184, -0.6314531799551417, -0.47413979999896794, -0.26254892027226584, 0.0001910401194136465, 0.30913418245375973, 0.6576306454193516, 1.0374953501004003, 1.4392274866751995, 1.8522746507362529, 2.2653340984989003, 2.666682363865115, 3.0445235057294946, 3.3873455634444043, 3.684274416345548, 3.925414185141306, 4.102163584777459, 4.2074982362905695, 4.236209855497626, 4.185094435871074, 4.053082999275502, 3.8413101607861186, 3.5531175947615314, 3.193991445001892, 2.7714347340984533, 2.294777835166246, 1.7749320113141358, 1.2240928436411198, 0.6554019992483543, 0.08257718334540837, -0.4804787730117731, -1.0200779547644259, -1.5231443702162606, -1.977595703894426, -2.37269792028519, -2.6993815268960293, -2.9505093702127057, -3.1210872379542574, -3.208410237137501, -3.2121398612370062, -3.1343087936888123, -2.9792527544010707, -2.7534710106951144, -2.465419470836447, -2.1252424826667027, -1.7444514988332442, -1.335560574521599, -0.9116901703262688, -0.4861518871657475, -0.0720275174992056, 0.3182438748745941, 0.6732572544395932, 0.9829982741663538, 1.2391532931057796, 1.4353621809337993, 1.567405148919714, 1.6333169802964034, 1.6334244243569622, 1.5703050917332215, 1.4486688591604444, 1.2751654711606892, 1.058124621579735, 0.8072372185007116, 0.5331886942219052, 0.24725703712971692, -0.03911037626635075, -0.3147261411668863, -0.5690829532078967, -0.7927492087423542, -0.9777254531451222, -1.1177482638419098, -1.2085298702838028, -1.2479239838673024, -1.2360108691346838, -1.1750975499992329, -1.0696321144855496, -0.926034251648787, -0.7524473114259713, -0.5584202059883555, -0.3545302550032633, -0.15196050811471046, 0.03795294311510633, 0.20418670971875755, 0.33649111506896057, 0.42582849323307687, 0.46477128967471576, 0.4478436435412668, 0.37179194536426347, 0.23577227634345665, 0.04144556998554627, -0.2070253038766927, -0.503078665470334, -0.8379556515560451, -1.200994755431267, -1.5800099329327322, -1.9617394297201545, -2.3323493946067626, -2.6779737913969703, -2.9852702222947243, -3.241970122279009, -3.4374014424854487, -3.5629624484289706, -3.612526620507916, -3.582760830840915, -3.473341919847457, -3.2870604137171617, -3.0298042861935413, -2.710420225582412, -2.3404546508293103, -1.933781544841346, -1.5061288475163466, -1.0745194838195755, -0.6566469101552456, -0.2702081771567815, 0.06778021634928759, 0.341657080762174, 0.5377550187886009, 0.6449765353844491, 0.6552835359650488, 0.5640788618930813, 0.370462337773348, 0.07734843776931315, -0.3085620499553008, -0.7769582698657814, -1.3142394379536313, -1.9039689488637925, -2.5274468898177576, -3.1643802713057174, -3.7936258912838974, -4.393977293824533, -4.9449649331075465, -5.427637535560909, -5.825292844358144, -6.12412745530322, -6.313778279059904, -6.387732202813728, -6.343585631419294, -6.183141570606816, -5.912338536616304, -5.541012567425608, -5.082500677098649, -4.553100932289262, -3.9714106362971093, -3.357569594529365, -2.732439847734923, -2.1167563789404467, -1.5302849615383556, -0.9910234151749558, -0.5144810359300892, -0.11306790158276238, 0.20437877332378304, 0.43290987061548375, 0.5716066907771107, 0.6235434885885928, 0.5955713980243628, 0.497933043063098, 0.34372494942051, 0.148232021842772, -0.07183551171718572, -0.2991674693172711, -0.5167029289011914, -0.708463322022254, -0.8603298049422634, -0.9607275455841482, -1.00118361600563, -0.976730885296513, -0.8861374280957423, -0.7319491866298916, -0.5203425759608976, -0.2607929852911292, 0.03442574040328645, 0.35088720217228747, 0.6727725542220334, 0.9837074985689666, 1.2676344450281278, 1.5096757014956865, 1.69694330260788, 1.819253045864061, 1.8697044365573356, 1.84509439037545, 1.746140444588838, 1.5774985298534032, 1.3475706196464043, 1.0681083078827998, 0.7536290349991251, 0.4206717452123474, 0.08692768519881758, -0.2297106372788833, -0.5121340425265842, -0.7449836073758189, -0.9155483772651084, -1.0145446138890974, -1.0367322448116072, -0.9813315193892905, -0.8522123235191016, -0.6578397331346708, -0.4109716631126851, -0.12811728989709362, 0.171222357098043, 0.4654982911984905, 0.7321980675737434, 0.9490184584339648, 1.0950678286624667, 1.1520365662131944, 1.1052738734800185, 0.9447123867022598, 0.6655883817731193, 0.2689145016918028, -0.23832639980212317, -0.8432841068826128, -1.527643517960648, -2.2683142826483103, -3.0383799953810806, -3.8082652721388315, -4.547066801096564, -5.223984745818356, -5.809784264099817, -6.278213810134077, -6.6073075589875065, -6.780503782385974, -6.787519162801419, -6.624930508134602, -6.296429585019898, -5.812733126009556, -5.191147657390342, -4.4548067262467095, -3.631615424596347, -2.7529528738373905, -1.8521966667905922, -0.9631434028946239, -0.11840578805589089, 0.652131107350707, 1.3227141201894188, 1.8729131201122, 2.2885360152299965, 2.5622189131606685, 2.6936597831782487, 2.689482961476062, 2.5627417440131497, 2.332086030953577], 'positive_zeros': ['0.862352435567200284811564386942584', '1.96868755164358078898084477180431', '4.32609382258691849305233686412297', '6.20429793500670285818088259655844', '7.67456776352960356819391242948267', '9.167977499201536980806912934178899', '9.954600013816565025937707169425886', '12.26108969407100525314806707870643', '12.95815214936743837105449812231628', '15.59307211555801978871495730503393'], 'prelabel': '2-2e3-8.5-c29-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.528585904039761, 'root_angle': 0.05541936101415134, 'root_number': '0.93998495548213623201415828244713072987782252325846390692 + 0.3412158898223328140266016917172243876327424313722618289*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.05541936101415135', 'prec': 64}, 'spectral_label': 'c29-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.862352435567200284811564386943', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.96868755164358078898084477180', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.32609382258691849305233686412', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 42.62243390642666, 'bad_primes': [2], 'central_character': '8.5', 'conductor': 8, 'conductor_radical': 2, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8/30/b/a/5/1'], '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': '2-2e3-8.5-c29-0-13', 'motivic_weight': 29, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [29], 'order_of_vanishing': 0, 'prelabel': '2-2e3-8.5-c29-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.528585904039761, 'root_angle': 0.05541936101415134, 'self_dual': False, 'spectral_label': 'c29-0', 'z1': {'__RealLiteral__': 0, 'data': '0.862352435567200284811564386943', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1093161582555036961610276917206', 'Lhash_array': ['1093161582555036961610276917206'], 'factors': ['2-2e3-8.5-c29-0-13'], 'label': '2-2e3-8.5-c29-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8/30/b/a/5/1'}