-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1658436477688738617018320602433', 'a10': [0.0, 0.0], 'a2': [-1.8019377358048383, 0.0], 'a3': [0.0, 0.0], 'a4': [2.246979603717467, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [-2.246979603717467, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5903939099448419, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [-1.0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [7, 13], 'central_character': '1183.846', 'coefficient_field': 'CDF', 'conductor': 1183, 'conductor_radical': 91, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.8019377358048383, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.246979603717467, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0.4450418679126288, 0], [1.0, 0]], [[1.0, 0], [1.8019377358048383, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0.4450418679126288, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.8019377358048383, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0.4450418679126288, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0.4450418679126288, 0], [1.0, 0]], [[1.0, 0], [0.4450418679126288, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.246979603717467, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.246979603717467, 0], [1.0, 0]], [[1.0, 0], [-1.246979603717467, 0], [1.0, 0]], [[1.0, 0], [-1.246979603717467, 0], [1.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-1183-7.6-c0-0-3', 'leading_term': '0.60320972305507102649034210645681', '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/1183/1/d/a/846/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.603209723055071, 0.6057834735352435, 0.6132157367044688, 0.6246836827400487, 0.638946345681001, 0.6544929057014288, 0.669684999944802, 0.6828706968875953, 0.6924655029912394, 0.697006559049134, 0.6951894663431499, 0.6858960274446434, 0.668218524693721, 0.6414835935814248, 0.6052768176922529, 0.5594678895933278, 0.5042353941222637, 0.44008981703403033, 0.36789314496025505, 0.28887332756698986, 0.20463187711188477, 0.11714296205749629, 0.02874249940039274, -0.05789403972568687, -0.1397861270884157, -0.21369566585869854, -0.2761877779041478, -0.3237047663840457, -0.352652657442214, -0.35949922019020447, -0.34088184028747337, -0.29372309434387645, -0.21535135738433658, -0.10362329281465109, 0.04295535593800649, 0.2251146097048608, 0.4427149338233102, 0.6946561026959042, 0.9788046131697703, 1.2919438800988836, 1.6297511575096257, 1.98680467314013, 2.3566238412054146, 2.731744632501883, 3.1038312433536857, 3.463824133149312, 3.8021233188753305, 4.10880455528297, 4.373864728369463, 4.587491490247534, 4.7403509119160505, 4.823885776424592, 4.830616129086509, 4.754432893679399, 4.590874801211901, 4.3373786032597454, 3.99349259060077, 3.5610438364845396, 3.044250348130061, 2.449770443320798, 1.7866831609722873, 1.066395340533259, 0.30247312553783307, -0.48960199243306335, -1.2927499392703445, -2.088676356090016, -2.858316521094819, -3.5823284494925525, -4.2416223810494005, -4.8179118148434785, -5.294269592120125, -5.655671349842936, -5.8895080464233995, -5.986049257865605, -5.9388395980324695, -5.745011948862284, -5.40550318778357, -4.9251607361509615, -4.312731462848067, -3.580728173236356, -2.745172982504568, -1.8252211794769964, -0.8426735796281796, 0.17861032059036916, 1.213382013526105, 2.2357364593694102, 3.2198843056061746, 4.140938459545502, 4.975688171177069, 5.703333290307618, 6.306151895476863, 6.77007607832162, 7.085153289349288, 7.245874249139574, 7.251352898823018, 7.105349059829968, 6.8161302125787575, 6.396174872892571, 5.861726205878113, 5.232210517844954, 4.529540851753915, 3.777330832006099, 3.0000479300200187, 2.2221382525389473, 1.4671566294635763, 0.7569360856553224, 0.11082966615455753, -0.4549449478060024, -0.927831474790303, -1.2993102604518973, -1.5651073571272474, -1.7252290195711546, -1.7838205769596824, -1.7488562113405286, -1.6316735786690582, -1.4463741095852685, -1.2091158953579964, -0.9373310012478803, -0.6489026006489684, -0.361339292709364, -0.09098422737642371, 0.14770483310299787, 0.34277160306015453, 0.485245416736231, 0.5694715479262098, 0.5932731712671355, 0.557938562094603, 0.468035666061166, 0.3310646912150374, 0.15696745858153263, -0.04248052156882384, -0.2543632828277796, -0.46536654356658536, -0.6625297343246157, -0.8339682556609511, -0.9695277302107038, -1.0613354505989594, -1.1042195377972215, -1.095973266765614, -1.0374502495078641, -0.9324852743279077, -0.7876451110812681, -0.61182299889849, -0.41569932135308074, -0.2110986510205813, -0.010279465628956475, 0.1748029696096157, 0.3332180687006233, 0.4557236271374633, 0.5353324109622617, 0.5677473404955559, 0.551638092052495, 0.4887407591384171, 0.3837722727892516, 0.24416203225300692, 0.0796140399353831, -0.09847685665871425, -0.27772185135941957, -0.44550797974001904, -0.5897953646434808, -0.6998937492525251, -0.7671702693824658, -0.7856433996404539, -0.7524237740884568, -0.6679708733869079, -0.5361449715544822, -0.3640456918496125, -0.16164136683413818, 0.0587936097305652, 0.2834038889813735, 0.49760021561328976, 0.686979046928506, 0.8382592326323459, 0.9401772974387371, 0.9842834048952314, 0.9655841983331547, 0.8829862974063193, 0.7395049461667514, 0.5422156281690202, 0.30194167404394456, 0.03268713258850848, -0.24915949438863685, -0.5258096362961685, -0.7791926164337261, -0.9921419290789453, -1.1495774175888613, -1.2396079537267195, -1.2544807554888155, -1.1913096417825568, -1.0525251309977215, -0.8460038924710439, -0.5848529385815141, -0.28684415446043443, 0.026483826341376953, 0.33101802823908083, 0.6014994347520363, 0.8131114048914843, 0.9431388268035779, 0.972599817085891, 0.8877484897882353, 0.6813500059295471, 0.35363787296442356, -0.08712196709296074, -0.6245159640618382, -1.234348416417912, -1.8854923113821376, -2.541201845363476, -3.1608346061374077, -3.701904912288382, -4.122366796844679, -4.383007094911201, -4.449817314577184, -4.29620837740181, -3.904935457583083, -3.2696111356646513, -2.395703559074897, -1.300941456070155, -0.0150784450398959, 1.4209964843881464, 2.956779051968384, 4.534240778539173, 6.090397481319831, 7.560231791982627, 8.8798226923963, 9.98951914489683, 10.83698782837361, 11.379967432901767, 11.588574023718898, 11.447023203108271, 10.954664164989579, 10.126256732570681, 8.991463145740221, 7.593569450891967, 5.987494377186575, 4.237184046502145, 2.412526347928905, 0.5859471499582187, -1.1711300511069271, -2.791770213637668, -4.216769373385593, -5.397477178892917, -6.298045585392569, -6.896981896636474, -7.187923555004408, -7.1795962939117866, -6.894963889391595, -6.369624012290534, -5.6495478159113555, -4.7882982893748265, -3.843891787447238, -2.875486711093407, -1.9400918499294182, -1.08948387218931, -0.367509037414293, 0.1920807021804462, 0.5671409097841444, 0.7479215894429619], 'positive_zeros': ['1.30827570104108469382417681350729', '1.97640951424038817062552751330361', '3.65536776975584169137223988452689', '4.85313061377590386662183590434890', '6.22174566889859470914756399726416', '7.05251752677127003818424448919304', '7.60513379721912829456053608685880', '8.499191145247006009455017776762916', '9.108537370802856126684910944867348', '9.828384687608852769845120182048069'], 'prelabel': '2-1183-7.6-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7683709455366216, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.30827570104108469382417681351', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.97640951424038817062552751330', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.65536776975584169137223988453', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.5903939099448419, 'bad_primes': [7, 13], 'central_character': '7.6', 'conductor': 1183, 'conductor_radical': 91, 'degree': 2, 'index': 3, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1183/1/d/a/846/1', 'ArtinRepresentation/2.1183.7t2.a.a'], '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': '2-1183-7.6-c0-0-3', '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': '2-1183-7.6-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7683709455366216, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.30827570104108469382417681351', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 24597876
{'Lhash': '1658436477688738617018320602433', 'Lhash_array': ['1658436477688738617018320602433'], 'label': '2-1183-7.6-c0-0-3', 'type': 'Artin', 'url': 'ArtinRepresentation/2.1183.7t2.a.a'}
-
id: 19818693
{'Lhash': '1658436477688738617018320602433', 'Lhash_array': ['1658436477688738617018320602433'], 'label': '2-1183-7.6-c0-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1183/1/d/a/846/1'}