-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1501586376471108402778246731966', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.6234898018587335, 0.7818314824680298], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.8262387743159949, -0.5633200580636221], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.9807890351403867, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-0.8262387743159949, 0.5633200580636221]]]], 'bad_primes': [3, 7], 'central_character': '3969.3266', 'coefficient_field': 'CDF', 'conductor': 3969, 'conductor_radical': 21, 'conjugate': '1578296046213598152991215729854', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-0.6234898018587335, -0.7818314824680298]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-0.8262387743159949, -0.5633200580636221]], [[1.0, 0], [-0.8262387743159949, 0.5633200580636221]], [[1.0, 0], [0, 0], [0.9888308262251285, -0.14904226617617444]], [[1.0, 0], [0.1095620699710928, 1.4620042202389492], [-0.9888308262251285, 0.14904226617617444]], [[1.0, 0], [0, 0], [0.7330518718298263, -0.6801727377709194]], [[1.0, 0], [-0.9009688679024191, -1.5605238552448022], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-0.9555728057861407, 0.2947551744109042]], [[1.0, 0], [0, 0], [0.7330518718298263, -0.6801727377709194]], [[1.0, 0], [1.977661652450257, 0], [1.0, 0]], [[1.0, 0], [-1.9555728057861408, -0.2947551744109042], [0.9555728057861407, 0.2947551744109042]], [[1.0, 0], [0, 0], [-0.07473009358642425, 0.9972037971811801]], [[1.0, 0], [1.211351760181443, 1.123970178357998], [0.07473009358642425, 0.9972037971811801]], [[1.0, 0], [0, 0], [-0.6234898018587335, -0.7818314824680298]], [[1.0, 0], [0, 0], [-0.9555728057861407, 0.2947551744109042]], [[1.0, 0], [0, 0], [0.9009688679024191, 0.4338837391175581]], [[1.0, 0], [-0.45557280578614073, 0.5712702293735344], [-0.2225209339563144, -0.9749279121818236]], [[1.0, 0], [-1.9111456115722814, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0.2225209339563144, -0.9749279121818236]], [[1.0, 0], [-0.09318690248616854, 1.2434927958345414], [-0.9888308262251285, -0.14904226617617444]], [[1.0, 0], [-0.7306820487327901, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0.9888308262251285, 0.14904226617617444]], [[1.0, 0], [0, 0], [-0.36534102436639504, -0.9308737486442042]], [[1.0, 0], [0.8262387743159949, -1.4310875362987383], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-0.07473009358642425, 0.9972037971811801]], [[1.0, 0], [-0.14282009041008062, -0.04405416353761935], [0.8262387743159949, 0.5633200580636221]], [[1.0, 0], [0, 0], [-0.36534102436639504, -0.9308737486442042]], [[1.0, 0], [1.211351760181443, -0.8258856460056492], [0.36534102436639504, -0.9308737486442042]], [[1.0, 0], [0, 0], [-0.36534102436639504, -0.9308737486442042]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-63e2-441.326-c0-0-0', 'leading_term': '1.712605996570952439778888568154', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3969/1/cb/a/3266/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.7126059965709524, 1.705717295208486, 1.707573717133554, 1.7165273566645154, 1.7302064107442634, 1.7457536123187998, 1.760068402654714, 1.7700181393561791, 1.7726031581340427, 1.7650761258503191, 1.745024365622675, 1.710425850192815, 1.659688047847497, 1.5916760446534728, 1.5057336628493885, 1.4016991691829535, 1.279915701956021, 1.141235645095094, 0.9870177044910783, 0.8191152749026123, 0.6398547340372629, 0.452002500850687, 0.2587200047513606, 0.06350610150953208, -0.1298730818480927, -0.31746640516552227, -0.4952310999083583, -0.6591357893084933, -0.8052711480822591, -0.9299657288138964, -1.0299040502404493, -1.102243673895813, -1.1447277073223423, -1.1557889807785025, -1.134642064805623, -1.081359340503083, -0.9969275121225951, -0.8832812680742014, -0.7433112527192361, -0.5808441036453987, -0.4005930285321533, -0.2080782279280322, -0.009517395657779537, 0.18831247755028446, 0.3782397386182459, 0.5528858474057903, 0.7048719869406033, 0.8270392632728794, 0.91267641790217, 0.9557482900327621, 0.951117762251765, 0.894753633766529, 0.7839168168984049, 0.6173174650927932, 0.3952361261029342, 0.11960277480324645, -0.2059713912515021, -0.5762132320339957, -0.9842603603431076, -1.421787910854855, -1.8791882285170292, -2.3458004340162093, -2.810184925942823, -3.2604360404156987, -3.684524381343655, -4.070658830155764, -4.407657011756478, -4.685312096830599, -4.894743313840137, -5.028717469988674, -5.081929167917308, -5.051228266649236, -4.935784466313228, -4.737180672762707, -4.459428977730644, -4.108905611533262, -3.6942040103122187, -3.225908095074641, -2.716290879833988, -2.1789464967968986, -1.6283665290954263, -1.0794740574312691, -0.5471309425541981, -0.04563547707516313, 0.41177144111846214, 0.813373105079575, 1.1493986077364085, 1.4123821862988815, 1.5974450229134498, 1.7024866991515561, 1.728276587841241, 1.6784390623548473, 1.5593303861804044, 1.3798093676542496, 1.1509081622404667, 0.885413802865808, 0.597374958701407, 0.3015518890651392, 0.012830407698314015, -0.2543772416170802, -0.4867204932632273, -0.6724632112566848, -0.801977524146437, -0.8681569869816049, -0.8667301023173154, -0.7964589228532036, -0.6592119256253735, -0.45990542665354506, -0.2063132966531519, 0.0912495825780543, 0.4203590582037995, 0.7670122627649703, 1.1162358426835306, 1.4527467351586758, 1.761637380895487, 2.0290554308737194, 2.2428474588850036, 2.3931369973981322, 2.472809382985639, 2.4778793776081116, 2.4077222098752036, 2.2651543828858554, 2.0563570954522765, 1.790642149052175, 1.4800674568307888, 1.1389164049918636, 0.7830620056860205, 0.4292426973986674, 0.09428149169073528, -0.2057163284602398, -0.4561497921710705, -0.6446556661019424, -0.7617527641941146, -0.8013644083995798, -0.7611911763519321, -0.642912406769961, -0.45220247802960534, -0.1985563070501779, 0.1050725420566998, 0.4428087110933024, 0.7965457308179814, 1.146761464999683, 1.4734224831852665, 1.756936303877126, 1.9791070615569675, 2.1240488205538024, 2.1790116122891363, 2.1350783326875424, 1.9876958182142246, 1.7370105293338585, 1.387988014966376, 0.9503053264037933, 0.43801633593782663, -0.13099901738306916, -0.7357797257364528, -1.3531911227341227, -1.9589541958403927, -2.528749404560125, -3.039342905108061, -3.4696808555475482, -3.801897900456665, -4.022189057317363, -4.121499958644015, -4.095998519856299, -3.947301250939545, -3.6824391446770957, -3.3135607978134867, -2.8573835296803507, -2.3344160954225104, -1.7679884851399301, -1.1831346248517247, -0.6053819844963093, -0.059507683312058024, 0.43167668103586493, 0.8484497658549768, 1.175156766741268, 1.4009860015929163, 1.5205040818851894, 1.533919823508253, 1.4470606697656159, 1.271060092860194, 1.0217694541690656, 0.7189223510292388, 0.3850927795277643, 0.04449976952056332, -0.27828013944443414, -0.5596256269144465, -0.7781394666540198, -0.9158060420203256, -0.9589751845535134, -0.8991186274924783, -0.7333169871432638, -0.4644492392441004, -0.10107242088102782, 0.34300407047570547, 0.8494285865601944, 1.3962650601391853, 1.9591479894665915, 2.512572726410396, 3.031251209426334, 3.491459038410163, 3.872299605606611, 4.156814949191663, 4.332880927446484, 4.393835838661894, 4.338806142412857, 4.172709698390212, 3.9059350157855968, 3.553713393931509, 3.1352184919005537, 2.672443771924445, 2.188921480892284, 1.7083565646141101, 1.2532545353577949, 0.8436234436546364, 0.4958266019318633, 0.22165469699947657, 0.027673801250082952, -0.08510981443824929, -0.12124539812276017, -0.09049113866719716, -0.007142780819190703, 0.1109254747034365, 0.24345296822521453, 0.3691478860960739, 0.4671253933829861, 0.5183418179169813, 0.5069368663472154, 0.4213998316535495, 0.2554848154055872, 0.008813696327549967, -0.3128767953531751, -0.6978669627407078, -1.1289656948126354, -1.5843795541080041, -2.038895292600712, -2.4653119081443866, -2.8360419900992495, -3.1247901998524927, -3.3082100886525976, -3.3674395720745944, -3.289420423796788, -3.0679179363248394, -2.704172890712398, -2.207138326686973, -1.5932771768406633, -0.8859222766138002, -0.11422610041141458, 0.6882477333544487, 1.4852170956638195, 2.23956598396431, 2.915316142473117, 3.479573774839764, 3.904339114658116, 4.168072929227242, 4.256926722821364, 4.16556181494502], 'positive_zeros': ['1.18454278821053759701428743417331', '2.13523697470875816880840198874896', '2.81250637750135099199955592724196', '4.21967753728484473788519381885905', '4.97889113077939177761673598025903', '5.52024303783440960318875643685940', '6.51521970044423044261944261599410', '6.99101005944351128465239985722532', '7.75818706529117394426524195582977', '8.740198488078288056953886618706295'], 'prelabel': '2-63e2-441.326-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4074050714490078, 'root_angle': -0.10770975056689343, 'root_number': '0.94329362381992495149822560399728 - 0.33195954461451159508819176664634*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.053854875283446714', 'prec': 70}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.18454278821053759701428743417', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.13523697470875816880840198875', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.81250637750135099199955592724', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.9807890351403867, 'bad_primes': [3, 7], 'central_character': '441.326', 'conductor': 3969, 'conductor_radical': 21, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3969/1/cb/a/3266/1'], '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': '2-63e2-441.326-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-63e2-441.326-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4074050714490078, 'root_angle': -0.053854875283446714, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.18454278821053759701428743417', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1501586376471108402778246731966', 'Lhash_array': ['1501586376471108402778246731966'], 'label': '2-63e2-441.326-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3969/1/cb/a/3266/1'}