-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1099815540976548352948988578256', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0.3230419109976908, 0.3230419109976908], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [-0.9017029603938982, -0.9017029603938982], 'a8': [0, 0], 'a9': [0, -2.79128784747792], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.783544222340847, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [1.79128784747792, -2.79128784747792]]]], 'bad_primes': [2, 5, 11], 'central_character': '1100.593', 'coefficient_field': 'CDF', 'conductor': 1100, 'conductor_radical': 110, 'conjugate': '1497223024460315339732971200996', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.3230419109976908, -0.3230419109976908], [0, 3.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.9017029603938982, 0.9017029603938982], [0, 7.0]], [[1.0, 0], [1.79128784747792, -2.79128784747792]], [[1.0, 0], [2.5169125153823524, -2.5169125153823524], [0, -13.0]], [[1.0, 0], [-5.222021396564047, -5.222021396564047], [0, 17.0]], [[1.0, 0], [-5.0, 0], [19.0, 0]], [[1.0, 0], [-2.8399544263800434, -2.8399544263800434], [0, 23.0]], [[1.0, 0], [-8.37386354243376, 0], [29.0, 0]], [[1.0, 0], [-4.58257569495584, 0], [31.0, 0]], [[1.0, 0], [-4.96640225816553, 4.96640225816553], [0, -37.0]], [[1.0, 0], [0, 5.0], [-41.0, 0]], [[1.0, 0], [6.837230951552501, -6.837230951552501], [0, -43.0]], [[1.0, 0], [0.5786610493962074, -0.5786610493962074], [0, -47.0]], [[1.0, 0], [-7.092850089951018, -7.092850089951018], [0, 53.0]], [[1.0, 0], [0, 8.58257569495584], [-59.0, 0]], [[1.0, 0], [0, -7.79128784747792], [-61.0, 0]], [[1.0, 0], [6.19114712955712, -6.19114712955712], [0, -67.0]], [[1.0, 0], [0.41742430504416, 0], [71.0, 0]], [[1.0, 0], [0.9017029603938982, -0.9017029603938982], [0, -73.0]], [[1.0, 0], [-7.20871215252208, 0], [79.0, 0]], [[1.0, 0], [5.222021396564047, -5.222021396564047], [0, -83.0]], [[1.0, 0], [0, -4.79128784747792], [-89.0, 0]], [[1.0, 0], [-3.3511927031770763, 3.3511927031770763], [0, -97.0]], [[1.0, 0], [0, 7.79128784747792], [-101.0, 0]], [[1.0, 0], [-9.609762605333371, -9.609762605333371], [0, 103.0]], [[1.0, 0], [-0.7135065945945559, -0.7135065945945559], [0, 107.0]], [[1.0, 0], [1.62613645756624, 0], [109.0, 0]], [[1.0, 0], [12.449717031713414, 12.449717031713414], [0, 113.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-1100-55.43-c1-0-4', 'leading_term': '1.635328935878246549125489567147827252449494339352598189', '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/1100/2/k/e/593/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [1.6353289358782466, 1.5911406716108654, 1.5382942458439837, 1.4762811100055664, 1.4043717083090417, 1.321683808954493, 1.227261427824544, 1.1201592176798478, 0.9995275738097341, 0.8646944567671362, 0.715240810964038, 0.5510672700781672, 0.37245047516570273, 0.18008775929259957, -0.02487079794007443, -0.24080381259263148, -0.4656143259029126, -0.6967405320422609, -0.9311820886546281, -1.165542394470571, -1.3960869312314559, -1.6188173919732118, -1.8295608620622374, -2.024072797713128, -2.1981519786497326, -2.3477650205697773, -2.469177445466962, -2.559087751930624, -2.6147604326052463, -2.6341534814527687, -2.6160356477416133, -2.5600885530759707, -2.466988815209264, -2.338465536180583, -2.17732892495972, -1.9874664417946626, -1.7738036703686566, -1.5422281335037944, -1.299475448095902, -1.0529785354919021, -0.8106820258120602, -0.5808254715873988, -0.3717004631167186, -0.19138815511951987, -0.04748500795697612, 0.05317434787013825, 0.10478736128405085, 0.10283661783727882, 0.04431521575310772, -0.07208580847815303, -0.24583762562692155, -0.4744898622261756, -0.7536499616800036, -1.0770307382848145, -1.4365689144088607, -1.8226148465510275, -2.2241908520256146, -2.629312646225468, -3.025365505936356, -3.3995240116185848, -3.7392017201662147, -4.032515007735303, -4.268743721269378, -4.438770295761112, -4.535478721326199, -4.554095244174243, -4.492453992928513, -4.351172836845135, -4.133727668905897, -3.846416890088648, -3.4982120394245446, -3.100495120645465, -2.666688042318031, -2.2117845115615316, -1.7517994819599902, -1.3031556265505402, -0.8820300618400219, -0.5036874773225732, -0.18182774040382527, 0.07202320193780258, 0.2490508214546515, 0.3435914427534058, 0.35345030100951774, 0.2800793036622209, 0.12860107330393614, -0.09232774846992668, -0.37081390288981253, -0.6921781853891249, -1.0395445354566, -1.3945456242439012, -1.7381166560898786, -2.051343790519553, -2.3163296494628542, -2.5170360640010747, -2.6400637322742284, -2.6753299203910395, -2.6166087644192038, -2.4619040484023222, -2.2136313651309587, -1.8785950404379452, -1.4677547572446754, -0.995787017353329, -0.48045693643314275, 0.058174142559927186, 0.5986706403357364, 1.1192320745227853, 1.5987416554346816, 2.0178024977741416, 2.3597087687247416, 2.6113007553184793, 2.7636572171983835, 2.812585375822056, 2.7588782134318754, 2.608320012375353, 2.371433732424553, 2.0629772755152653, 1.7012092284000537, 1.3069575734701684, 0.9025363894973003, 0.5105650446317723, 0.15275121552772536, -0.15129722726316455, -0.38516616840104745, -0.5365730627054375, -0.5980935143609035, -0.5676316679706606, -0.44860244014341377, -0.2498088045740491, 0.014986048027388621, 0.3277747123519289, 0.6672760523843995, 1.0101111604911448, 1.3321227789981687, 1.6097663118010557, 1.8214945170363783, 1.9490562381733714, 1.9786323464347462, 1.901739421395698, 1.7158433111698201, 1.42464004984502, 1.0379798893710483, 0.5714304449959609, 0.04549602488444696, -0.5154691067603293, -1.0845967401222387, -1.6340169900307917, -2.1364614739459986, -2.5668644516956878, -2.9038667366545567, -3.131130594677956, -3.238382872932613, -3.2221178706146363, -3.0859102693708054, -2.8403107737587163, -2.5023217123174883, -2.0944752781806195, -1.6435618074253369, -1.1790779609072501, -0.7314834392127928, -0.3303686531773729, -0.0026435970839034026, 0.22914062677587624, 0.3482318650954875, 0.3447851854019159, 0.2165645227571179, -0.030813482622186618, -0.38411720649493436, -0.823213488293537, -1.3222210585203447, -1.8510398398732413, -2.3771670557074227, -2.8676911953620494, -3.29134147699012, -3.6204645357990626, -3.832802214451242, -3.912954602178594, -3.8534303943436132, -3.655211249059983, -3.327786665271252, -2.8886491803758676, -2.3622742965036823, -1.77864326275674, -1.1713974378900722, -0.5757383554391909, -0.026206024529869892, 0.44552194317335386, 0.8126669326874116, 1.0550867996463895, 1.1605970452933274, 1.1257842892355872, 0.9562529439388662, 0.6662828070268195, 0.27791422117364284, -0.18048407479044792, -0.6760738751537423, -1.173712812255104, -1.6382834221571658, -2.0370304732716185, -2.3417485632778314, -2.5306702471118445, -2.589923606062379, -2.5144561151781195, -2.3083571559718425, -1.984552235309605, -1.563885177961665, -1.0736472963105845, -0.5456518132603324, -0.013984810474405042, 0.48741173708409746, 0.9271555657694066, 1.2786671142105523, 1.52207875808873, 1.645670847819495, 1.646727069104416, 1.5317417755132128, 1.3159575220356172, 1.0222588948606515, 0.6794954922553743, 0.3203491809267648, -0.02110459760980097, -0.3119673085597847, -0.5230332608789552, -0.6310658232149239, -0.6206633874283151, -0.48557186778786854, -0.22933876125637262, 0.13474964034521014, 0.5844546543352961, 1.0900489690555106, 1.6163609613384429, 2.1252584687747533, 2.5783962421887643, 2.9400289914330107, 3.1796838646876964, 3.2744932288194764, 3.2110105039489567, 2.9863671982891717, 2.608675806573726, 2.0966376176772603, 1.4783728136381709, 0.7895482501241209, 0.070931645303289, -0.6344545061119632, -1.2843736322010824, -1.8403872796528353, -2.2706146958396305, -2.5520315163419096, -2.6721310253843793, -2.6298169980206185, -2.4354532563609492, -2.1100577036470956, -1.6836930954712885, -1.1931682957221545, -0.6792175152706952, -0.18336681867697122, 0.25527637792127883, 0.6030662769272505], 'positive_zeros': ['0.867601483230896735814702437594710', '2.77599928629211002028491996623320', '3.02763377765856675825723540274566', '4.91781490046104132841559445725629', '5.28850876691964703120027854929794', '6.43080479709935565452880169689134', '7.52979600611865278945682643289701', '7.996779683301576404150993542776154', '8.880177568251259320951975009108985', '10.00058461472580234417997629462029'], 'prelabel': '2-1100-55.43-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9637044762156783, 'root_angle': -0.17422774316264047, 'root_number': '0.8539052961148079519010206717179898494842166346785400828 - 0.5204284247301276564703382733246779039809630126609186283*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.08711387158132025', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.867601483230896735814702437595', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.77599928629211002028491996623', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.02763377765856675825723540275', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 8.783544222340847, 'bad_primes': [2, 5, 11], 'central_character': '55.43', 'conductor': 1100, 'conductor_radical': 110, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1100/2/k/e/593/3'], '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': '2-1100-55.43-c1-0-4', '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': '2-1100-55.43-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9637044762156783, 'root_angle': -0.08711387158132024, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.867601483230896735814702437595', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1099815540976548352948988578256', 'Lhash_array': ['1099815540976548352948988578256'], 'label': '2-1100-55.43-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1100/2/k/e/593/3'}