# lfunc_search downloaded from the LMFDB on 13 July 2026. # Search link: https://www.lmfdb.org/L/1/1183/1183.1055/r0-0 # Query "{'degree': 1, 'conductor': 1183, 'spectral_label': 'r0-0'}" returned 360 lfunc_searchs, sorted by root analytic conductor. # Each entry in the following data list has the form: # [Label, $\alpha$, $A$, $d$, $N$, $\chi$, $\mu$, $\nu$, $w$, prim, arith, $\mathbb{Q}$, self-dual, $\operatorname{Arg}(\epsilon)$, $r$, First zero, Origin] # For more details, see the definitions at the bottom of the file. "1-1183-1183.100-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.100" [[0, 0.0]] [] 0 true true false false -0.21525869112588691 0 0.721326588533 ["Character/Dirichlet/1183/100"] "1-1183-1183.1005-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1005" [[0, 0.0]] [] 0 true true false false -0.12103322208910323 0 0.774608663327 ["Character/Dirichlet/1183/1005"] "1-1183-1183.1006-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1006" [[0, 0.0]] [] 0 true true false false 0.1149355282083813 0 0.661459298879 ["Character/Dirichlet/1183/1006"] "1-1183-1183.1007-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1007" [[0, 0.0]] [] 0 true true false false -0.3648915187376726 0 1.59732672713 ["Character/Dirichlet/1183/1007"] "1-1183-1183.1010-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1010" [[0, 0.0]] [] 0 true true false false 0.38434683155655885 0 1.53917142568 ["Character/Dirichlet/1183/1010"] "1-1183-1183.1017-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1017" [[0, 0.0]] [] 0 true true false false -0.21525869112588691 0 0.749006712667 ["Character/Dirichlet/1183/1017"] "1-1183-1183.1020-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1020" [[0, 0.0]] [] 0 true true false false 0.0039007637048336955 0 0.464922579225 ["Character/Dirichlet/1183/1020"] "1-1183-1183.1021-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1021" [[0, 0.0]] [] 0 true true false false 0.1351084812623274 0 0.935622268886 ["Character/Dirichlet/1183/1021"] "1-1183-1183.1024-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1024" [[0, 0.0]] [] 0 true true false false -0.20835533806868772 0 0.453028242796 ["Character/Dirichlet/1183/1024"] "1-1183-1183.1025-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1025" [[0, 0.0]] [] 0 true true false false -0.1188803013839237 0 1.14476782201 ["Character/Dirichlet/1183/1025"] "1-1183-1183.1026-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1026" [[0, 0.0]] [] 0 true true false false -0.36758154556050365 0 0.235205504233 ["Character/Dirichlet/1183/1026"] "1-1183-1183.1031-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1031" [[0, 0.0]] [] 0 true true false false 0.06186162445596714 0 0.836922312499 ["Character/Dirichlet/1183/1031"] "1-1183-1183.1032-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1032" [[0, 0.0]] [] 0 true true false false 0.06109997475019859 0 1.58606787338 ["Character/Dirichlet/1183/1032"] "1-1183-1183.1034-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1034" [[0, 0.0]] [] 0 true true false false 0.27223335858313474 0 0.225513457854 ["Character/Dirichlet/1183/1034"] "1-1183-1183.1035-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1035" [[0, 0.0]] [] 0 true true false false -0.30177514792899407 0 0.283073782652 ["Character/Dirichlet/1183/1035"] "1-1183-1183.1042-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1042" [[0, 0.0]] [] 0 true true false false -0.18293885601577908 0 0.83173700157 ["Character/Dirichlet/1183/1042"] "1-1183-1183.1046-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1046" [[0, 0.0]] [] 0 true true false false 0.33723409703816704 0 1.25277335917 ["Character/Dirichlet/1183/1046"] "1-1183-1183.1048-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1048" [[0, 0.0]] [] 0 true true false false -0.2460112173537489 0 0.509710742365 ["Character/Dirichlet/1183/1048"] "1-1183-1183.1052-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1052" [[0, 0.0]] [] 0 true true false false 0.06580639763150956 0 1.03652155959 ["Character/Dirichlet/1183/1052"] "1-1183-1183.1054-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1054" [[0, 0.0]] [] 0 true true false false 0.43419360236849047 0 1.33205896821 ["Character/Dirichlet/1183/1054"] "1-1183-1183.1055-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1055" [[0, 0.0]] [] 0 true true false false -0.07885145404013941 0 0.108030026254 ["Character/Dirichlet/1183/1055"] "1-1183-1183.1060-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1060" [[0, 0.0]] [] 0 true true false false -0.007440459174850723 0 0.0738683731099 ["Character/Dirichlet/1183/1060"] "1-1183-1183.107-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.107" [[0, 0.0]] [] 0 true true false false -0.01407525917322418 0 0.587618092032 ["Character/Dirichlet/1183/107"] "1-1183-1183.1074-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1074" [[0, 0.0]] [] 0 true true false false -0.32943256962849965 0 0.0605222146553 ["Character/Dirichlet/1183/1074"] "1-1183-1183.1075-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1075" [[0, 0.0]] [] 0 true true false false 0.10480504221069953 0 0.771249945714 ["Character/Dirichlet/1183/1075"] "1-1183-1183.1077-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1077" [[0, 0.0]] [] 0 true true false false -0.0591715976331361 0 0.606075923298 ["Character/Dirichlet/1183/1077"] "1-1183-1183.1080-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1080" [[0, 0.0]] [] 0 true true false false -0.21525869112588691 0 0.409705611003 ["Character/Dirichlet/1183/1080"] "1-1183-1183.1081-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1081" [[0, 0.0]] [] 0 true true false false -0.020754068642306348 0 1.0655197031 ["Character/Dirichlet/1183/1081"] "1-1183-1183.1082-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1082" [[0, 0.0]] [] 0 true true false false 0.14030800079058117 0 0.609429983431 ["Character/Dirichlet/1183/1082"] "1-1183-1183.1089-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1089" [[0, 0.0]] [] 0 true true false false 0.2675269357018238 0 0.540037466817 ["Character/Dirichlet/1183/1089"] "1-1183-1183.1090-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1090" [[0, 0.0]] [] 0 true true false false 0.3540874019756397 0 1.89006807529 ["Character/Dirichlet/1183/1090"] "1-1183-1183.1096-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1096" [[0, 0.0]] [] 0 true true false false 0.006185712822139365 0 1.39122096362 ["Character/Dirichlet/1183/1096"] "1-1183-1183.1097-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1097" [[0, 0.0]] [] 0 true true false false -0.2948277854010862 0 1.02422565455 ["Character/Dirichlet/1183/1097"] "1-1183-1183.1098-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1098" [[0, 0.0]] [] 0 true true false false -0.4723865877712031 0 0.376327625802 ["Character/Dirichlet/1183/1098"] "1-1183-1183.110-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.110" [[0, 0.0]] [] 0 true true false false -0.12766802208747668 0 0.733340430043 ["Character/Dirichlet/1183/110"] "1-1183-1183.1101-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1101" [[0, 0.0]] [] 0 true true false false -0.14030800079058117 0 0.94412947784 ["Character/Dirichlet/1183/1101"] "1-1183-1183.1108-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1108" [[0, 0.0]] [] 0 true true false false -0.3789667779108968 0 2.20156592013 ["Character/Dirichlet/1183/1108"] "1-1183-1183.111-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.111" [[0, 0.0]] [] 0 true true false false 0.20759368836291917 0 1.38722992482 ["Character/Dirichlet/1183/111"] "1-1183-1183.1111-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1111" [[0, 0.0]] [] 0 true true false false 0.2460112173537489 0 1.22899084637 ["Character/Dirichlet/1183/1111"] "1-1183-1183.1112-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1112" [[0, 0.0]] [] 0 true true false false 0.10798816568047337 0 0.873874201566 ["Character/Dirichlet/1183/1112"] "1-1183-1183.1115-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1115" [[0, 0.0]] [] 0 true true false false -0.006185712822139365 0 0.907150010237 ["Character/Dirichlet/1183/1115"] "1-1183-1183.1116-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1116" [[0, 0.0]] [] 0 true true false false -0.020754068642306348 0 0.602874811422 ["Character/Dirichlet/1183/1116"] "1-1183-1183.1117-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1117" [[0, 0.0]] [] 0 true true false false -0.06876497751316636 0 0.837585159908 ["Character/Dirichlet/1183/1117"] "1-1183-1183.1122-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1122" [[0, 0.0]] [] 0 true true false false 0.45831132859797896 0 1.95405632028 ["Character/Dirichlet/1183/1122"] "1-1183-1183.1123-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1123" [[0, 0.0]] [] 0 true true false false -0.32943256962849965 0 0.316756105035 ["Character/Dirichlet/1183/1123"] "1-1183-1183.1125-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1125" [[0, 0.0]] [] 0 true true false false 0.020754068642306348 0 0.725985956842 ["Character/Dirichlet/1183/1125"] "1-1183-1183.1126-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1126" [[0, 0.0]] [] 0 true true false false 0.10798816568047337 0 1.35913388504 ["Character/Dirichlet/1183/1126"] "1-1183-1183.1133-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1133" [[0, 0.0]] [] 0 true true false false -0.10798816568047337 0 0.889690574109 ["Character/Dirichlet/1183/1133"] "1-1183-1183.1137-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1137" [[0, 0.0]] [] 0 true true false false 0.49255954082514936 0 0.176888986518 ["Character/Dirichlet/1183/1137"] "1-1183-1183.1139-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1139" [[0, 0.0]] [] 0 true true false false -0.047786365282742965 0 0.961259530514 ["Character/Dirichlet/1183/1139"] "1-1183-1183.114-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.114" [[0, 0.0]] [] 0 true true false false -0.47364133412391457 0 0.407984931902 ["Character/Dirichlet/1183/114"] "1-1183-1183.1143-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1143" [[0, 0.0]] [] 0 true true false false -0.2123001112442301 0 0.583993132936 ["Character/Dirichlet/1183/1143"] "1-1183-1183.1145-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1145" [[0, 0.0]] [] 0 true true false false -0.2876998887557699 0 1.58771887904 ["Character/Dirichlet/1183/1145"] "1-1183-1183.1146-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1146" [[0, 0.0]] [] 0 true true false false -0.33723409703816704 0 0.0437552003994 ["Character/Dirichlet/1183/1146"] "1-1183-1183.115-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.115" [[0, 0.0]] [] 0 true true false false -0.2460112173537489 0 0.312390725026 ["Character/Dirichlet/1183/115"] "1-1183-1183.1151-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1151" [[0, 0.0]] [] 0 true true false false 0.33723409703816704 0 1.61471057732 ["Character/Dirichlet/1183/1151"] "1-1183-1183.116-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.116" [[0, 0.0]] [] 0 true true false false -0.12497799526464563 0 0.885754770138 ["Character/Dirichlet/1183/116"] "1-1183-1183.1165-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1165" [[0, 0.0]] [] 0 true true false false 0.06109997475019859 0 0.840453448833 ["Character/Dirichlet/1183/1165"] "1-1183-1183.1166-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1166" [[0, 0.0]] [] 0 true true false false -0.29164466193131233 0 0.621324789231 ["Character/Dirichlet/1183/1166"] "1-1183-1183.1168-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1168" [[0, 0.0]] [] 0 true true false false 0.46844181459566075 0 1.11641798327 ["Character/Dirichlet/1183/1168"] "1-1183-1183.1171-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1171" [[0, 0.0]] [] 0 true true false false -0.01407525917322418 0 0.898388073275 ["Character/Dirichlet/1183/1171"] "1-1183-1183.1172-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1172" [[0, 0.0]] [] 0 true true false false 0.38111969861607625 0 1.64283114064 ["Character/Dirichlet/1183/1172"] "1-1183-1183.1173-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1173" [[0, 0.0]] [] 0 true true false false 0.43813837554403284 0 0.348904723817 ["Character/Dirichlet/1183/1173"] "1-1183-1183.1175-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1175" [[0, 0.0]] [] 0 true true false false 0.30177514792899407 0 1.55109384376 ["Character/Dirichlet/1183/1175"] "1-1183-1183.1180-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1180" [[0, 0.0]] [] 0 true true false false -0.06876497751316636 0 0.761411730867 ["Character/Dirichlet/1183/1180"] "1-1183-1183.1181-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.1181" [[0, 0.0]] [] 0 true true false false 0.2855469680505904 0 0.940280001641 ["Character/Dirichlet/1183/1181"] "1-1183-1183.121-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.121" [[0, 0.0]] [] 0 true true false false 0.1358261214973873 0 1.48210537759 ["Character/Dirichlet/1183/121"] "1-1183-1183.122-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.122" [[0, 0.0]] [] 0 true true false false 0.31257926469102704 0 0.950511913245 ["Character/Dirichlet/1183/122"] "1-1183-1183.124-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.124" [[0, 0.0]] [] 0 true true false false -0.15528143431627356 0 0.717232369094 ["Character/Dirichlet/1183/124"] "1-1183-1183.125-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.125" [[0, 0.0]] [] 0 true true false false 0.13905325443786984 0 1.13838192817 ["Character/Dirichlet/1183/125"] "1-1183-1183.132-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.132" [[0, 0.0]] [] 0 true true false false -0.15039447731755423 0 0.637569958408 ["Character/Dirichlet/1183/132"] "1-1183-1183.136-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.136" [[0, 0.0]] [] 0 true true false false 0.07885145404013941 0 0.555296143883 ["Character/Dirichlet/1183/136"] "1-1183-1183.138-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.138" [[0, 0.0]] [] 0 true true false false 0.32943256962849965 0 1.00349555736 ["Character/Dirichlet/1183/138"] "1-1183-1183.142-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.142" [[0, 0.0]] [] 0 true true false false 0.19302533254275214 0 1.18672184181 ["Character/Dirichlet/1183/142"] "1-1183-1183.144-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.144" [[0, 0.0]] [] 0 true true false false -0.19302533254275214 0 1.40051005111 ["Character/Dirichlet/1183/144"] "1-1183-1183.145-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.145" [[0, 0.0]] [] 0 true true false false -0.3219481009829402 0 0.876151564203 ["Character/Dirichlet/1183/145"] "1-1183-1183.16-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.16" [[0, 0.0]] [] 0 true true false false -0.13241845443949637 0 1.12173816434 ["Character/Dirichlet/1183/16"] "1-1183-1183.164-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.164" [[0, 0.0]] [] 0 true true false false -0.2460112173537489 0 0.746055096763 ["Character/Dirichlet/1183/164"] "1-1183-1183.165-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.165" [[0, 0.0]] [] 0 true true false false -0.46915945483072063 0 0.251802823728 ["Character/Dirichlet/1183/165"] "1-1183-1183.167-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.167" [[0, 0.0]] [] 0 true true false false 0.4723865877712031 0 1.46959900294 ["Character/Dirichlet/1183/167"] "1-1183-1183.171-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.171" [[0, 0.0]] [] 0 true true false false 0.15922620749181596 0 1.37450897209 ["Character/Dirichlet/1183/171"] "1-1183-1183.172-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.172" [[0, 0.0]] [] 0 true true false false -0.06876497751316636 0 0.113113034734 ["Character/Dirichlet/1183/172"] "1-1183-1183.174-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.174" [[0, 0.0]] [] 0 true true false false 0.0591715976331361 0 1.32092411983 ["Character/Dirichlet/1183/174"] "1-1183-1183.179-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.179" [[0, 0.0]] [] 0 true true false false -0.06186162445596714 0 0.704056097618 ["Character/Dirichlet/1183/179"] "1-1183-1183.180-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.180" [[0, 0.0]] [] 0 true true false false -0.49255954082514936 0 1.59706682624 ["Character/Dirichlet/1183/180"] "1-1183-1183.186-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.186" [[0, 0.0]] [] 0 true true false false 0.20835533806868772 0 1.13767208184 ["Character/Dirichlet/1183/186"] "1-1183-1183.187-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.187" [[0, 0.0]] [] 0 true true false false -0.31257926469102704 0 0.366808590208 ["Character/Dirichlet/1183/187"] "1-1183-1183.198-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.198" [[0, 0.0]] [] 0 true true false false -0.1008602690351571 0 1.20832791461 ["Character/Dirichlet/1183/198"] "1-1183-1183.20-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.20" [[0, 0.0]] [] 0 true true false false 0.45907297830374755 0 1.93190003747 ["Character/Dirichlet/1183/20"] "1-1183-1183.201-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.201" [[0, 0.0]] [] 0 true true false false -0.036445142403058545 0 0.878638368116 ["Character/Dirichlet/1183/201"] "1-1183-1183.202-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.202" [[0, 0.0]] [] 0 true true false false -0.10798816568047337 0 0.96099360933 ["Character/Dirichlet/1183/202"] "1-1183-1183.205-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.205" [[0, 0.0]] [] 0 true true false false 0.3951949577893005 0 1.45119546909 ["Character/Dirichlet/1183/205"] "1-1183-1183.206-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.206" [[0, 0.0]] [] 0 true true false false 0.036445142403058545 0 0.268036893479 ["Character/Dirichlet/1183/206"] "1-1183-1183.207-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.207" [[0, 0.0]] [] 0 true true false false 0.2123001112442301 0 1.66696366116 ["Character/Dirichlet/1183/207"] "1-1183-1183.212-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.212" [[0, 0.0]] [] 0 true true false false 0.32714762051119395 0 0.904457353332 ["Character/Dirichlet/1183/212"] "1-1183-1183.213-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.213" [[0, 0.0]] [] 0 true true false false -0.17410712584151739 0 1.01485468661 ["Character/Dirichlet/1183/213"] "1-1183-1183.215-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.215" [[0, 0.0]] [] 0 true true false false -0.38111969861607625 0 0.527245249623 ["Character/Dirichlet/1183/215"] "1-1183-1183.216-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.216" [[0, 0.0]] [] 0 true true false false 0.1257396449704142 0 0.747831363468 ["Character/Dirichlet/1183/216"] "1-1183-1183.223-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.223" [[0, 0.0]] [] 0 true true false false 0.0591715976331361 0 1.02528471244 ["Character/Dirichlet/1183/223"] "1-1183-1183.227-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.227" [[0, 0.0]] [] 0 true true false false 0.39443330808353194 0 0.12930348535 ["Character/Dirichlet/1183/227"] "1-1183-1183.229-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.229" [[0, 0.0]] [] 0 true true false false 0.2968881909302748 0 1.44613984368 ["Character/Dirichlet/1183/229"] "1-1183-1183.233-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.233" [[0, 0.0]] [] 0 true true false false 0.06876497751316636 0 1.4197033966 ["Character/Dirichlet/1183/233"] "1-1183-1183.235-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.235" [[0, 0.0]] [] 0 true true false false -0.06876497751316636 0 1.21132454059 ["Character/Dirichlet/1183/235"] "1-1183-1183.236-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.236" [[0, 0.0]] [] 0 true true false false -0.39443330808353194 0 0.165875308668 ["Character/Dirichlet/1183/236"] "1-1183-1183.24-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.24" [[0, 0.0]] [] 0 true true false false -0.44826886154171464 0 2.02280915009 ["Character/Dirichlet/1183/24"] "1-1183-1183.241-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.241" [[0, 0.0]] [] 0 true true false false 0.12766802208747668 0 1.38691536479 ["Character/Dirichlet/1183/241"] "1-1183-1183.25-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.25" [[0, 0.0]] [] 0 true true false false -0.19302533254275214 0 0.396840930199 ["Character/Dirichlet/1183/25"] "1-1183-1183.255-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.255" [[0, 0.0]] [] 0 true true false false 0.07885145404013941 0 1.30586352764 ["Character/Dirichlet/1183/255"] "1-1183-1183.256-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.256" [[0, 0.0]] [] 0 true true false false 0.006185712822139365 0 1.02218085965 ["Character/Dirichlet/1183/256"] "1-1183-1183.261-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.261" [[0, 0.0]] [] 0 true true false false 0.051013498223225526 0 0.4746809061 ["Character/Dirichlet/1183/261"] "1-1183-1183.262-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.262" [[0, 0.0]] [] 0 true true false false -0.27223335858313474 0 1.46287178184 ["Character/Dirichlet/1183/262"] "1-1183-1183.263-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.263" [[0, 0.0]] [] 0 true true false false -0.23247306429817624 0 0.830917114659 ["Character/Dirichlet/1183/263"] "1-1183-1183.265-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.265" [[0, 0.0]] [] 0 true true false false -0.13905325443786984 0 1.39280259745 ["Character/Dirichlet/1183/265"] "1-1183-1183.270-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.270" [[0, 0.0]] [] 0 true true false false 0.14030800079058117 0 0.954922033792 ["Character/Dirichlet/1183/270"] "1-1183-1183.271-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.271" [[0, 0.0]] [] 0 true true false false -0.39443330808353194 0 1.48335433651 ["Character/Dirichlet/1183/271"] "1-1183-1183.277-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.277" [[0, 0.0]] [] 0 true true false false -0.3951949577893005 0 0.83581983136 ["Character/Dirichlet/1183/277"] "1-1183-1183.278-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.278" [[0, 0.0]] [] 0 true true false false 0.2968881909302748 0 1.60163661103 ["Character/Dirichlet/1183/278"] "1-1183-1183.279-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.279" [[0, 0.0]] [] 0 true true false false 0.0591715976331361 0 0.966999333229 ["Character/Dirichlet/1183/279"] "1-1183-1183.282-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.282" [[0, 0.0]] [] 0 true true false false 0.06876497751316636 0 1.21230506672 ["Character/Dirichlet/1183/282"] "1-1183-1183.289-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.289" [[0, 0.0]] [] 0 true true false false 0.06876497751316636 0 0.651398142665 ["Character/Dirichlet/1183/289"] "1-1183-1183.292-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.292" [[0, 0.0]] [] 0 true true false false 0.1188803013839237 0 1.76329555364 ["Character/Dirichlet/1183/292"] "1-1183-1183.293-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.293" [[0, 0.0]] [] 0 true true false false 0.03155818540433925 0 1.0353972012 ["Character/Dirichlet/1183/293"] "1-1183-1183.296-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.296" [[0, 0.0]] [] 0 true true false false 0.46915945483072063 0 0.419706782962 ["Character/Dirichlet/1183/296"] "1-1183-1183.297-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.297" [[0, 0.0]] [] 0 true true false false 0.2948277854010862 0 1.09028298657 ["Character/Dirichlet/1183/297"] "1-1183-1183.298-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.298" [[0, 0.0]] [] 0 true true false false -0.06580639763150956 0 0.903846028067 ["Character/Dirichlet/1183/298"] "1-1183-1183.30-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.30" [[0, 0.0]] [] 0 true true false false 0.36758154556050365 0 0.0404931554418 ["Character/Dirichlet/1183/30"] "1-1183-1183.303-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.303" [[0, 0.0]] [] 0 true true false false 0.4543665554224366 0 0.384055539544 ["Character/Dirichlet/1183/303"] "1-1183-1183.304-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.304" [[0, 0.0]] [] 0 true true false false -0.37233197791252337 0 0.780481849378 ["Character/Dirichlet/1183/304"] "1-1183-1183.306-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.306" [[0, 0.0]] [] 0 true true false false -0.036445142403058545 0 0.806843143274 ["Character/Dirichlet/1183/306"] "1-1183-1183.307-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.307" [[0, 0.0]] [] 0 true true false false -0.4837278106508876 0 1.84589782552 ["Character/Dirichlet/1183/307"] "1-1183-1183.31-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.31" [[0, 0.0]] [] 0 true true false false -0.2968881909302748 0 0.559866637243 ["Character/Dirichlet/1183/31"] "1-1183-1183.314-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.314" [[0, 0.0]] [] 0 true true false false -0.1351084812623274 0 0.0286433228374 ["Character/Dirichlet/1183/314"] "1-1183-1183.318-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.318" [[0, 0.0]] [] 0 true true false false -0.3540874019756397 0 0.967645927483 ["Character/Dirichlet/1183/318"] "1-1183-1183.320-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.320" [[0, 0.0]] [] 0 true true false false -0.31257926469102704 0 0.897460525614 ["Character/Dirichlet/1183/320"] "1-1183-1183.324-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.324" [[0, 0.0]] [] 0 true true false false 0.36758154556050365 0 1.74981593722 ["Character/Dirichlet/1183/324"] "1-1183-1183.326-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.326" [[0, 0.0]] [] 0 true true false false 0.13241845443949637 0 1.43012509825 ["Character/Dirichlet/1183/326"] "1-1183-1183.327-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.327" [[0, 0.0]] [] 0 true true false false 0.007440459174850723 0 1.09960094484 ["Character/Dirichlet/1183/327"] "1-1183-1183.33-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.33" [[0, 0.0]] [] 0 true true false false -0.2948277854010862 0 2.20271110427 ["Character/Dirichlet/1183/33"] "1-1183-1183.332-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.332" [[0, 0.0]] [] 0 true true false false 0.3697784757363919 0 0.0697292488503 ["Character/Dirichlet/1183/332"] "1-1183-1183.34-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.34" [[0, 0.0]] [] 0 true true false false -0.0591715976331361 0 1.07328862316 ["Character/Dirichlet/1183/34"] "1-1183-1183.346-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.346" [[0, 0.0]] [] 0 true true false false -0.01138523235039313 0 0.727199432964 ["Character/Dirichlet/1183/346"] "1-1183-1183.347-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.347" [[0, 0.0]] [] 0 true true false false 0.3789667779108968 0 0.459626772639 ["Character/Dirichlet/1183/347"] "1-1183-1183.349-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.349" [[0, 0.0]] [] 0 true true false false -0.3057199211045365 0 0.267474215233 ["Character/Dirichlet/1183/349"] "1-1183-1183.352-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.352" [[0, 0.0]] [] 0 true true false false -0.13241845443949637 0 0.323062657778 ["Character/Dirichlet/1183/352"] "1-1183-1183.353-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.353" [[0, 0.0]] [] 0 true true false false 0.15528143431627356 0 0.854596861024 ["Character/Dirichlet/1183/353"] "1-1183-1183.354-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.354" [[0, 0.0]] [] 0 true true false false 0.01407525917322418 0 0.774863910717 ["Character/Dirichlet/1183/354"] "1-1183-1183.356-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.356" [[0, 0.0]] [] 0 true true false false -0.1257396449704142 0 0.59980338779 ["Character/Dirichlet/1183/356"] "1-1183-1183.362-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.362" [[0, 0.0]] [] 0 true true false false 0.1780518990170598 0 0.991797156449 ["Character/Dirichlet/1183/362"] "1-1183-1183.368-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.368" [[0, 0.0]] [] 0 true true false false -0.48592474082677584 0 1.66675534173 ["Character/Dirichlet/1183/368"] "1-1183-1183.369-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.369" [[0, 0.0]] [] 0 true true false false 0.32943256962849965 0 1.33219689962 ["Character/Dirichlet/1183/369"] "1-1183-1183.370-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.370" [[0, 0.0]] [] 0 true true false false 0.15039447731755423 0 1.24753618176 ["Character/Dirichlet/1183/370"] "1-1183-1183.373-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.373" [[0, 0.0]] [] 0 true true false false -0.04563344457756344 0 0.543607654393 ["Character/Dirichlet/1183/373"] "1-1183-1183.380-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.380" [[0, 0.0]] [] 0 true true false false 0.46915945483072063 0 1.68201577654 ["Character/Dirichlet/1183/380"] "1-1183-1183.383-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.383" [[0, 0.0]] [] 0 true true false false 0.3447185656837265 0 1.37788087877 ["Character/Dirichlet/1183/383"] "1-1183-1183.384-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.384" [[0, 0.0]] [] 0 true true false false -0.1942800788954635 0 1.00467661902 ["Character/Dirichlet/1183/384"] "1-1183-1183.387-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.387" [[0, 0.0]] [] 0 true true false false 0.06876497751316636 0 1.0003797961 ["Character/Dirichlet/1183/387"] "1-1183-1183.388-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.388" [[0, 0.0]] [] 0 true true false false 0.07885145404013941 0 0.777014663065 ["Character/Dirichlet/1183/388"] "1-1183-1183.389-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.389" [[0, 0.0]] [] 0 true true false false 0.2714717088773662 0 1.40271911459 ["Character/Dirichlet/1183/389"] "1-1183-1183.394-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.394" [[0, 0.0]] [] 0 true true false false 0.06876497751316636 0 1.13702316764 ["Character/Dirichlet/1183/394"] "1-1183-1183.395-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.395" [[0, 0.0]] [] 0 true true false false 0.2948277854010862 0 0.932754859722 ["Character/Dirichlet/1183/395"] "1-1183-1183.397-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.397" [[0, 0.0]] [] 0 true true false false 0.37233197791252337 0 0.177677118722 ["Character/Dirichlet/1183/397"] "1-1183-1183.398-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.398" [[0, 0.0]] [] 0 true true false false 0.4837278106508876 0 0.484997422753 ["Character/Dirichlet/1183/398"] "1-1183-1183.4-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.4" [[0, 0.0]] [] 0 true true false false -0.46915945483072063 0 1.09129630193 ["Character/Dirichlet/1183/4"] "1-1183-1183.405-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.405" [[0, 0.0]] [] 0 true true false false -0.20759368836291917 0 0.412199460407 ["Character/Dirichlet/1183/405"] "1-1183-1183.409-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.409" [[0, 0.0]] [] 0 true true false false 0.2948277854010862 0 1.20612204684 ["Character/Dirichlet/1183/409"] "1-1183-1183.41-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.41" [[0, 0.0]] [] 0 true true false false 0.10798816568047337 0 1.03008777666 ["Character/Dirichlet/1183/41"] "1-1183-1183.411-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.411" [[0, 0.0]] [] 0 true true false false 0.17410712584151739 0 1.35242154334 ["Character/Dirichlet/1183/411"] "1-1183-1183.415-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.415" [[0, 0.0]] [] 0 true true false false 0.051013498223225526 0 1.10272049531 ["Character/Dirichlet/1183/415"] "1-1183-1183.417-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.417" [[0, 0.0]] [] 0 true true false false -0.051013498223225526 0 0.841358750439 ["Character/Dirichlet/1183/417"] "1-1183-1183.423-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.423" [[0, 0.0]] [] 0 true true false false 0.21445303194940962 0 0.809630723877 ["Character/Dirichlet/1183/423"] "1-1183-1183.438-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.438" [[0, 0.0]] [] 0 true true false false -0.06876497751316636 0 0.553898819428 ["Character/Dirichlet/1183/438"] "1-1183-1183.440-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.440" [[0, 0.0]] [] 0 true true false false -0.20759368836291917 0 1.11937174475 ["Character/Dirichlet/1183/440"] "1-1183-1183.443-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.443" [[0, 0.0]] [] 0 true true false false 0.06876497751316636 0 0.514823909123 ["Character/Dirichlet/1183/443"] "1-1183-1183.444-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.444" [[0, 0.0]] [] 0 true true false false -0.37233197791252337 0 1.71070727663 ["Character/Dirichlet/1183/444"] "1-1183-1183.445-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.445" [[0, 0.0]] [] 0 true true false false 0.13241845443949637 0 1.56596582458 ["Character/Dirichlet/1183/445"] "1-1183-1183.447-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.447" [[0, 0.0]] [] 0 true true false false 0.4837278106508876 0 0.240760465482 ["Character/Dirichlet/1183/447"] "1-1183-1183.45-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.45" [[0, 0.0]] [] 0 true true false false -0.28160219487504795 0 0.51481364785 ["Character/Dirichlet/1183/45"] "1-1183-1183.452-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.452" [[0, 0.0]] [] 0 true true false false -0.32714762051119395 0 0.28122142894 ["Character/Dirichlet/1183/452"] "1-1183-1183.453-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.453" [[0, 0.0]] [] 0 true true false false 0.37233197791252337 0 1.25239310067 ["Character/Dirichlet/1183/453"] "1-1183-1183.459-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.459" [[0, 0.0]] [] 0 true true false false 0.28231983511010783 0 1.08119160619 ["Character/Dirichlet/1183/459"] "1-1183-1183.460-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.460" [[0, 0.0]] [] 0 true true false false -0.06109997475019859 0 0.879145841442 ["Character/Dirichlet/1183/460"] "1-1183-1183.461-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.461" [[0, 0.0]] [] 0 true true false false 0.3057199211045365 0 0.979554078517 ["Character/Dirichlet/1183/461"] "1-1183-1183.464-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.464" [[0, 0.0]] [] 0 true true false false 0.32714762051119395 0 1.63688037291 ["Character/Dirichlet/1183/464"] "1-1183-1183.47-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.47" [[0, 0.0]] [] 0 true true false false -0.06109997475019859 0 1.2109556299 ["Character/Dirichlet/1183/47"] "1-1183-1183.471-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.471" [[0, 0.0]] [] 0 true true false false -0.10480504221069953 0 1.0733668577 ["Character/Dirichlet/1183/471"] "1-1183-1183.474-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.474" [[0, 0.0]] [] 0 true true false false -0.2948277854010862 0 0.3892798004 ["Character/Dirichlet/1183/474"] "1-1183-1183.475-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.475" [[0, 0.0]] [] 0 true true false false 0.15039447731755423 0 0.850058289196 ["Character/Dirichlet/1183/475"] "1-1183-1183.478-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.478" [[0, 0.0]] [] 0 true true false false 0.3991397309648429 0 1.18172994345 ["Character/Dirichlet/1183/478"] "1-1183-1183.479-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.479" [[0, 0.0]] [] 0 true true false false 0.0039007637048336955 0 1.10387216915 ["Character/Dirichlet/1183/479"] "1-1183-1183.480-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.480" [[0, 0.0]] [] 0 true true false false 0.33951904615547274 0 0.710698038301 ["Character/Dirichlet/1183/480"] "1-1183-1183.486-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.486" [[0, 0.0]] [] 0 true true false false 0.38506447179161873 0 0.0580104630273 ["Character/Dirichlet/1183/486"] "1-1183-1183.489-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.489" [[0, 0.0]] [] 0 true true false false -0.1257396449704142 0 0.169814378482 ["Character/Dirichlet/1183/489"] "1-1183-1183.496-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.496" [[0, 0.0]] [] 0 true true false false 0.1942800788954635 0 0.764098570682 ["Character/Dirichlet/1183/496"] "1-1183-1183.5-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.5" [[0, 0.0]] [] 0 true true false false -0.12766802208747668 0 1.17226119159 ["Character/Dirichlet/1183/5"] "1-1183-1183.500-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.500" [[0, 0.0]] [] 0 true true false false -0.1780518990170598 0 0.25561047486 ["Character/Dirichlet/1183/500"] "1-1183-1183.502-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.502" [[0, 0.0]] [] 0 true true false false 0.37233197791252337 0 1.42417424999 ["Character/Dirichlet/1183/502"] "1-1183-1183.509-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.509" [[0, 0.0]] [] 0 true true false false -0.21445303194940962 0 0.645534056941 ["Character/Dirichlet/1183/509"] "1-1183-1183.51-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.51" [[0, 0.0]] [] 0 true true false false 0.12497799526464563 0 0.998729852352 ["Character/Dirichlet/1183/51"] "1-1183-1183.514-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.514" [[0, 0.0]] [] 0 true true false false 0.3219481009829402 0 2.05379974565 ["Character/Dirichlet/1183/514"] "1-1183-1183.528-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.528" [[0, 0.0]] [] 0 true true false false -0.1149355282083813 0 1.25958310082 ["Character/Dirichlet/1183/528"] "1-1183-1183.53-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.53" [[0, 0.0]] [] 0 true true false false 0.3750220047353544 0 1.83919988631 ["Character/Dirichlet/1183/53"] "1-1183-1183.531-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.531" [[0, 0.0]] [] 0 true true false false 0.3648915187376726 0 0.262323705012 ["Character/Dirichlet/1183/531"] "1-1183-1183.534-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.534" [[0, 0.0]] [] 0 true true false false 0.19302533254275214 0 1.83967008794 ["Character/Dirichlet/1183/534"] "1-1183-1183.535-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.535" [[0, 0.0]] [] 0 true true false false 0.0039007637048336955 0 1.36044319086 ["Character/Dirichlet/1183/535"] "1-1183-1183.536-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.536" [[0, 0.0]] [] 0 true true false false 0.04563344457756344 0 0.944348680647 ["Character/Dirichlet/1183/536"] "1-1183-1183.538-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.538" [[0, 0.0]] [] 0 true true false false -0.4837278106508876 0 1.59262783072 ["Character/Dirichlet/1183/538"] "1-1183-1183.54-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.54" [[0, 0.0]] [] 0 true true false false -0.12766802208747668 0 0.407451176089 ["Character/Dirichlet/1183/54"] "1-1183-1183.543-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.543" [[0, 0.0]] [] 0 true true false false -0.45831132859797896 0 0.393558094161 ["Character/Dirichlet/1183/543"] "1-1183-1183.544-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.544" [[0, 0.0]] [] 0 true true false false -0.33723409703816704 0 0.92709409397 ["Character/Dirichlet/1183/544"] "1-1183-1183.550-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.550" [[0, 0.0]] [] 0 true true false false 0.47364133412391457 0 1.51343488356 ["Character/Dirichlet/1183/550"] "1-1183-1183.551-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.551" [[0, 0.0]] [] 0 true true false false 0.452213634717257 0 1.01609473704 ["Character/Dirichlet/1183/551"] "1-1183-1183.552-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.552" [[0, 0.0]] [] 0 true true false false -0.46844181459566075 0 0.380163285125 ["Character/Dirichlet/1183/552"] "1-1183-1183.555-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.555" [[0, 0.0]] [] 0 true true false false 0.1358261214973873 0 1.26610122113 ["Character/Dirichlet/1183/555"] "1-1183-1183.562-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.562" [[0, 0.0]] [] 0 true true false false -0.47364133412391457 0 1.3220959465 ["Character/Dirichlet/1183/562"] "1-1183-1183.565-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.565" [[0, 0.0]] [] 0 true true false false 0.020754068642306348 0 0.896791733947 ["Character/Dirichlet/1183/565"] "1-1183-1183.566-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.566" [[0, 0.0]] [] 0 true true false false -0.44082840236686394 0 1.11259120615 ["Character/Dirichlet/1183/566"] "1-1183-1183.569-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.569" [[0, 0.0]] [] 0 true true false false 0.48592474082677584 0 0.922589424053 ["Character/Dirichlet/1183/569"] "1-1183-1183.570-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.570" [[0, 0.0]] [] 0 true true false false 0.12766802208747668 0 0.782787004464 ["Character/Dirichlet/1183/570"] "1-1183-1183.571-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.571" [[0, 0.0]] [] 0 true true false false 0.21525869112588691 0 0.704522544836 ["Character/Dirichlet/1183/571"] "1-1183-1183.576-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.576" [[0, 0.0]] [] 0 true true false false -0.21525869112588691 0 1.70986097007 ["Character/Dirichlet/1183/576"] "1-1183-1183.579-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.579" [[0, 0.0]] [] 0 true true false false -0.2460112173537489 0 0.116659344101 ["Character/Dirichlet/1183/579"] "1-1183-1183.580-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.580" [[0, 0.0]] [] 0 true true false false 0.3609467455621302 0 1.10548313564 ["Character/Dirichlet/1183/580"] "1-1183-1183.59-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.59" [[0, 0.0]] [] 0 true true false false -0.2460112173537489 0 0.827537461703 ["Character/Dirichlet/1183/59"] "1-1183-1183.591-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.591" [[0, 0.0]] [] 0 true true false false -0.2855469680505904 0 0.335467325539 ["Character/Dirichlet/1183/591"] "1-1183-1183.593-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.593" [[0, 0.0]] [] 0 true true false false -0.2948277854010862 0 0.146979454009 ["Character/Dirichlet/1183/593"] "1-1183-1183.597-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.597" [[0, 0.0]] [] 0 true true false false -0.19750721183594608 0 0.231485390437 ["Character/Dirichlet/1183/597"] "1-1183-1183.599-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.599" [[0, 0.0]] [] 0 true true false false 0.19750721183594608 0 1.00171379932 ["Character/Dirichlet/1183/599"] "1-1183-1183.6-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.6" [[0, 0.0]] [] 0 true true false false 0.18293885601577908 0 0.209507204928 ["Character/Dirichlet/1183/6"] "1-1183-1183.600-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.600" [[0, 0.0]] [] 0 true true false false 0.3540874019756397 0 1.42373900952 ["Character/Dirichlet/1183/600"] "1-1183-1183.605-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.605" [[0, 0.0]] [] 0 true true false false 0.2948277854010862 0 1.69396605879 ["Character/Dirichlet/1183/605"] "1-1183-1183.619-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.619" [[0, 0.0]] [] 0 true true false false 0.2948277854010862 0 1.33862948054 ["Character/Dirichlet/1183/619"] "1-1183-1183.620-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.620" [[0, 0.0]] [] 0 true true false false 0.21525869112588691 0 1.2159901387 ["Character/Dirichlet/1183/620"] "1-1183-1183.622-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.622" [[0, 0.0]] [] 0 true true false false -0.44082840236686394 0 0.589933493015 ["Character/Dirichlet/1183/622"] "1-1183-1183.625-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.625" [[0, 0.0]] [] 0 true true false false -0.3750220047353544 0 1.02123600425 ["Character/Dirichlet/1183/625"] "1-1183-1183.626-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.626" [[0, 0.0]] [] 0 true true false false 0.07885145404013941 0 0.988358969923 ["Character/Dirichlet/1183/626"] "1-1183-1183.627-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.627" [[0, 0.0]] [] 0 true true false false 0.21525869112588691 0 0.99549002066 ["Character/Dirichlet/1183/627"] "1-1183-1183.629-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.629" [[0, 0.0]] [] 0 true true false false 0.1257396449704142 0 1.35330944261 ["Character/Dirichlet/1183/629"] "1-1183-1183.634-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.634" [[0, 0.0]] [] 0 true true false false -0.38434683155655885 0 1.79620958001 ["Character/Dirichlet/1183/634"] "1-1183-1183.635-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.635" [[0, 0.0]] [] 0 true true false false -0.07885145404013941 0 0.679075445937 ["Character/Dirichlet/1183/635"] "1-1183-1183.641-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.641" [[0, 0.0]] [] 0 true true false false -0.3991397309648429 0 0.538844572955 ["Character/Dirichlet/1183/641"] "1-1183-1183.642-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.642" [[0, 0.0]] [] 0 true true false false 0.2460112173537489 0 1.35756265756 ["Character/Dirichlet/1183/642"] "1-1183-1183.643-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.643" [[0, 0.0]] [] 0 true true false false -0.10798816568047337 0 1.43023046859 ["Character/Dirichlet/1183/643"] "1-1183-1183.646-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.646" [[0, 0.0]] [] 0 true true false false -0.13241845443949637 0 1.22929477473 ["Character/Dirichlet/1183/646"] "1-1183-1183.656-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.656" [[0, 0.0]] [] 0 true true false false 0.27223335858313474 0 0.837420827129 ["Character/Dirichlet/1183/656"] "1-1183-1183.660-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.660" [[0, 0.0]] [] 0 true true false false 0.36758154556050365 0 0.816355051898 ["Character/Dirichlet/1183/660"] "1-1183-1183.661-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.661" [[0, 0.0]] [] 0 true true false false -0.3447185656837265 0 0.904234004433 ["Character/Dirichlet/1183/661"] "1-1183-1183.662-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.662" [[0, 0.0]] [] 0 true true false false -0.48592474082677584 0 0.0396048910423 ["Character/Dirichlet/1183/662"] "1-1183-1183.667-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.667" [[0, 0.0]] [] 0 true true false false -0.2675269357018238 0 0.313024174019 ["Character/Dirichlet/1183/667"] "1-1183-1183.668-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.668" [[0, 0.0]] [] 0 true true false false 0.4886147676496069 0 0.379028131187 ["Character/Dirichlet/1183/668"] "1-1183-1183.670-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.670" [[0, 0.0]] [] 0 true true false false 0.0039007637048336955 0 1.18414740163 ["Character/Dirichlet/1183/670"] "1-1183-1183.671-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.671" [[0, 0.0]] [] 0 true true false false -0.44082840236686394 0 0.255224159289 ["Character/Dirichlet/1183/671"] "1-1183-1183.678-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.678" [[0, 0.0]] [] 0 true true false false -0.027613412228796843 0 0.680300308745 ["Character/Dirichlet/1183/678"] "1-1183-1183.682-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.682" [[0, 0.0]] [] 0 true true false false 0.3697784757363919 0 1.37817975381 ["Character/Dirichlet/1183/682"] "1-1183-1183.684-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.684" [[0, 0.0]] [] 0 true true false false -0.38506447179161873 0 1.91958219306 ["Character/Dirichlet/1183/684"] "1-1183-1183.688-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.688" [[0, 0.0]] [] 0 true true false false 0.48592474082677584 0 1.37343230256 ["Character/Dirichlet/1183/688"] "1-1183-1183.690-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.690" [[0, 0.0]] [] 0 true true false false 0.01407525917322418 0 0.899308246834 ["Character/Dirichlet/1183/690"] "1-1183-1183.691-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.691" [[0, 0.0]] [] 0 true true false false -0.21839780512495205 0 0.547214200431 ["Character/Dirichlet/1183/691"] "1-1183-1183.696-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.696" [[0, 0.0]] [] 0 true true false false -0.3540874019756397 0 0.259787546183 ["Character/Dirichlet/1183/696"] "1-1183-1183.710-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.710" [[0, 0.0]] [] 0 true true false false 0.12766802208747668 0 0.765152948275 ["Character/Dirichlet/1183/710"] "1-1183-1183.711-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.711" [[0, 0.0]] [] 0 true true false false 0.1008602690351571 0 1.55795991917 ["Character/Dirichlet/1183/711"] "1-1183-1183.713-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.713" [[0, 0.0]] [] 0 true true false false -0.15039447731755423 0 0.763774658724 ["Character/Dirichlet/1183/713"] "1-1183-1183.716-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.716" [[0, 0.0]] [] 0 true true false false 0.2876998887557699 0 0.0444023717831 ["Character/Dirichlet/1183/716"] "1-1183-1183.717-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.717" [[0, 0.0]] [] 0 true true false false 0.2948277854010862 0 0.477452645006 ["Character/Dirichlet/1183/717"] "1-1183-1183.718-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.718" [[0, 0.0]] [] 0 true true false false -0.38434683155655885 0 0.732840984031 ["Character/Dirichlet/1183/718"] "1-1183-1183.720-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.720" [[0, 0.0]] [] 0 true true false false -0.3609467455621302 0 0.540758015751 ["Character/Dirichlet/1183/720"] "1-1183-1183.725-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.725" [[0, 0.0]] [] 0 true true false false 0.21525869112588691 0 0.227537689161 ["Character/Dirichlet/1183/725"] "1-1183-1183.726-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.726" [[0, 0.0]] [] 0 true true false false -0.2948277854010862 0 0.836505269389 ["Character/Dirichlet/1183/726"] "1-1183-1183.73-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.73" [[0, 0.0]] [] 0 true true false false -0.452213634717257 0 0.611784497459 ["Character/Dirichlet/1183/73"] "1-1183-1183.732-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.732" [[0, 0.0]] [] 0 true true false false 0.21525869112588691 0 1.56445145738 ["Character/Dirichlet/1183/732"] "1-1183-1183.733-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.733" [[0, 0.0]] [] 0 true true false false -0.07885145404013941 0 1.44926448095 ["Character/Dirichlet/1183/733"] "1-1183-1183.734-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.734" [[0, 0.0]] [] 0 true true false false 0.20759368836291917 0 1.08201529241 ["Character/Dirichlet/1183/734"] "1-1183-1183.737-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.737" [[0, 0.0]] [] 0 true true false false -0.041688671402021024 0 0.96669721529 ["Character/Dirichlet/1183/737"] "1-1183-1183.74-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.74" [[0, 0.0]] [] 0 true true false false 0.13241845443949637 0 0.775469543931 ["Character/Dirichlet/1183/74"] "1-1183-1183.744-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.744" [[0, 0.0]] [] 0 true true false false -0.006185712822139365 0 1.20927109012 ["Character/Dirichlet/1183/744"] "1-1183-1183.747-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.747" [[0, 0.0]] [] 0 true true false false -0.07885145404013941 0 1.06000603476 ["Character/Dirichlet/1183/747"] "1-1183-1183.748-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.748" [[0, 0.0]] [] 0 true true false false -0.0591715976331361 0 1.20969094299 ["Character/Dirichlet/1183/748"] "1-1183-1183.751-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.751" [[0, 0.0]] [] 0 true true false false 0.12103322208910323 0 1.11953775706 ["Character/Dirichlet/1183/751"] "1-1183-1183.752-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.752" [[0, 0.0]] [] 0 true true false false -0.27223335858313474 0 0.789693191714 ["Character/Dirichlet/1183/752"] "1-1183-1183.753-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.753" [[0, 0.0]] [] 0 true true false false 0.19750721183594608 0 1.04677807568 ["Character/Dirichlet/1183/753"] "1-1183-1183.758-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.758" [[0, 0.0]] [] 0 true true false false -0.14030800079058117 0 0.456499109769 ["Character/Dirichlet/1183/758"] "1-1183-1183.759-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.759" [[0, 0.0]] [] 0 true true false false 0.07885145404013941 0 1.07065003701 ["Character/Dirichlet/1183/759"] "1-1183-1183.76-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.76" [[0, 0.0]] [] 0 true true false false -0.45907297830374755 0 1.49544348036 ["Character/Dirichlet/1183/76"] "1-1183-1183.761-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.761" [[0, 0.0]] [] 0 true true false false -0.15922620749181596 0 0.879073823848 ["Character/Dirichlet/1183/761"] "1-1183-1183.762-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.762" [[0, 0.0]] [] 0 true true false false -0.10798816568047337 0 0.625998600955 ["Character/Dirichlet/1183/762"] "1-1183-1183.769-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.769" [[0, 0.0]] [] 0 true true false false -0.45907297830374755 0 0.91451789049 ["Character/Dirichlet/1183/769"] "1-1183-1183.773-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.773" [[0, 0.0]] [] 0 true true false false -0.37233197791252337 0 0.506961303626 ["Character/Dirichlet/1183/773"] "1-1183-1183.779-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.779" [[0, 0.0]] [] 0 true true false false -0.21525869112588691 0 0.364807692725 ["Character/Dirichlet/1183/779"] "1-1183-1183.781-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.781" [[0, 0.0]] [] 0 true true false false 0.21525869112588691 0 1.46953163221 ["Character/Dirichlet/1183/781"] "1-1183-1183.782-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.782" [[0, 0.0]] [] 0 true true false false 0.2460112173537489 0 1.4366037871 ["Character/Dirichlet/1183/782"] "1-1183-1183.787-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.787" [[0, 0.0]] [] 0 true true false false 0.39443330808353194 0 1.64628161706 ["Character/Dirichlet/1183/787"] "1-1183-1183.79-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.79" [[0, 0.0]] [] 0 true true false false -0.19750721183594608 0 0.747964699766 ["Character/Dirichlet/1183/79"] "1-1183-1183.801-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.801" [[0, 0.0]] [] 0 true true false false 0.3258928741584826 0 0.982204287795 ["Character/Dirichlet/1183/801"] "1-1183-1183.802-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.802" [[0, 0.0]] [] 0 true true false false 0.47364133412391457 0 0.498326472607 ["Character/Dirichlet/1183/802"] "1-1183-1183.804-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.804" [[0, 0.0]] [] 0 true true false false 0.10798816568047337 0 1.52230190664 ["Character/Dirichlet/1183/804"] "1-1183-1183.807-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.807" [[0, 0.0]] [] 0 true true false false -0.43419360236849047 0 0.518567193092 ["Character/Dirichlet/1183/807"] "1-1183-1183.808-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.808" [[0, 0.0]] [] 0 true true false false 0.036445142403058545 0 1.25234070107 ["Character/Dirichlet/1183/808"] "1-1183-1183.809-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.809" [[0, 0.0]] [] 0 true true false false 0.041688671402021024 0 0.443134696725 ["Character/Dirichlet/1183/809"] "1-1183-1183.81-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.81" [[0, 0.0]] [] 0 true true false false -0.1358261214973873 0 1.06561699941 ["Character/Dirichlet/1183/81"] "1-1183-1183.811-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.811" [[0, 0.0]] [] 0 true true false false 0.44082840236686394 0 0.882421782168 ["Character/Dirichlet/1183/811"] "1-1183-1183.816-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.816" [[0, 0.0]] [] 0 true true false false -0.4543665554224366 0 1.73517172428 ["Character/Dirichlet/1183/816"] "1-1183-1183.817-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.817" [[0, 0.0]] [] 0 true true false false -0.3697784757363919 0 0.754168758636 ["Character/Dirichlet/1183/817"] "1-1183-1183.824-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.824" [[0, 0.0]] [] 0 true true false false 0.01138523235039313 0 0.975341290641 ["Character/Dirichlet/1183/824"] "1-1183-1183.825-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.825" [[0, 0.0]] [] 0 true true false false 0.45907297830374755 0 0.0025227583405 ["Character/Dirichlet/1183/825"] "1-1183-1183.828-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.828" [[0, 0.0]] [] 0 true true false false -0.43813837554403284 0 1.4745355331 ["Character/Dirichlet/1183/828"] "1-1183-1183.83-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.83" [[0, 0.0]] [] 0 true true false false -0.10798816568047337 0 0.0923878319781 ["Character/Dirichlet/1183/83"] "1-1183-1183.835-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.835" [[0, 0.0]] [] 0 true true false false 0.29164466193131233 0 0.713494820139 ["Character/Dirichlet/1183/835"] "1-1183-1183.838-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.838" [[0, 0.0]] [] 0 true true false false 0.44826886154171464 0 0.686761575811 ["Character/Dirichlet/1183/838"] "1-1183-1183.839-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.839" [[0, 0.0]] [] 0 true true false false 0.18293885601577908 0 1.10233333661 ["Character/Dirichlet/1183/839"] "1-1183-1183.842-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.842" [[0, 0.0]] [] 0 true true false false -0.21525869112588691 0 0.946109396455 ["Character/Dirichlet/1183/842"] "1-1183-1183.843-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.843" [[0, 0.0]] [] 0 true true false false -0.34077379250818407 0 0.777666082042 ["Character/Dirichlet/1183/843"] "1-1183-1183.849-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.849" [[0, 0.0]] [] 0 true true false false 0.38434683155655885 0 0.354467788651 ["Character/Dirichlet/1183/849"] "1-1183-1183.850-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.850" [[0, 0.0]] [] 0 true true false false 0.2460112173537489 0 0.5222196782 ["Character/Dirichlet/1183/850"] "1-1183-1183.852-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.852" [[0, 0.0]] [] 0 true true false false -0.05173113845828537 0 0.706773802846 ["Character/Dirichlet/1183/852"] "1-1183-1183.853-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.853" [[0, 0.0]] [] 0 true true false false -0.19822485207100593 0 1.03492168515 ["Character/Dirichlet/1183/853"] "1-1183-1183.860-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.860" [[0, 0.0]] [] 0 true true false false -0.03155818540433925 0 1.02595930636 ["Character/Dirichlet/1183/860"] "1-1183-1183.866-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.866" [[0, 0.0]] [] 0 true true false false -0.4886147676496069 0 1.14892050884 ["Character/Dirichlet/1183/866"] "1-1183-1183.870-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.870" [[0, 0.0]] [] 0 true true false false -0.33951904615547274 0 0.726815908477 ["Character/Dirichlet/1183/870"] "1-1183-1183.872-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.872" [[0, 0.0]] [] 0 true true false false 0.33951904615547274 0 1.29144546396 ["Character/Dirichlet/1183/872"] "1-1183-1183.873-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.873" [[0, 0.0]] [] 0 true true false false -0.3697784757363919 0 1.12280528748 ["Character/Dirichlet/1183/873"] "1-1183-1183.878-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.878" [[0, 0.0]] [] 0 true true false false 0.07885145404013941 0 1.1636582687 ["Character/Dirichlet/1183/878"] "1-1183-1183.88-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.88" [[0, 0.0]] [] 0 true true false false -0.1358261214973873 0 0.920568076662 ["Character/Dirichlet/1183/88"] "1-1183-1183.892-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.892" [[0, 0.0]] [] 0 true true false false 0.31257926469102704 0 1.27006607272 ["Character/Dirichlet/1183/892"] "1-1183-1183.893-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.893" [[0, 0.0]] [] 0 true true false false 0.28231983511010783 0 0.852059629 ["Character/Dirichlet/1183/893"] "1-1183-1183.895-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.895" [[0, 0.0]] [] 0 true true false false -0.10798816568047337 0 0.378815520892 ["Character/Dirichlet/1183/895"] "1-1183-1183.898-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.898" [[0, 0.0]] [] 0 true true false false 0.22852829112263381 0 0.0275665837127 ["Character/Dirichlet/1183/898"] "1-1183-1183.899-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.899" [[0, 0.0]] [] 0 true true false false 0.2460112173537489 0 1.35019062558 ["Character/Dirichlet/1183/899"] "1-1183-1183.9-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.9" [[0, 0.0]] [] 0 true true false false 0.23247306429817624 0 0.887891081104 ["Character/Dirichlet/1183/9"] "1-1183-1183.900-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.900" [[0, 0.0]] [] 0 true true false false -0.32714762051119395 0 0.538976265588 ["Character/Dirichlet/1183/900"] "1-1183-1183.902-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.902" [[0, 0.0]] [] 0 true true false false 0.10798816568047337 0 0.629617431614 ["Character/Dirichlet/1183/902"] "1-1183-1183.907-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.907" [[0, 0.0]] [] 0 true true false false -0.36758154556050365 0 1.65029031783 ["Character/Dirichlet/1183/907"] "1-1183-1183.908-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.908" [[0, 0.0]] [] 0 true true false false -0.2460112173537489 0 1.01808542878 ["Character/Dirichlet/1183/908"] "1-1183-1183.914-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.914" [[0, 0.0]] [] 0 true true false false -0.06876497751316636 0 1.19753806715 ["Character/Dirichlet/1183/914"] "1-1183-1183.916-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.916" [[0, 0.0]] [] 0 true true false false 0.10798816568047337 0 0.895549526314 ["Character/Dirichlet/1183/916"] "1-1183-1183.919-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.919" [[0, 0.0]] [] 0 true true false false -0.01407525917322418 0 0.673920597317 ["Character/Dirichlet/1183/919"] "1-1183-1183.926-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.926" [[0, 0.0]] [] 0 true true false false -0.28231983511010783 0 0.650968485205 ["Character/Dirichlet/1183/926"] "1-1183-1183.929-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.929" [[0, 0.0]] [] 0 true true false false 0.34077379250818407 0 1.35112843705 ["Character/Dirichlet/1183/929"] "1-1183-1183.930-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.930" [[0, 0.0]] [] 0 true true false false 0.027613412228796843 0 1.12481717747 ["Character/Dirichlet/1183/930"] "1-1183-1183.933-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.933" [[0, 0.0]] [] 0 true true false false -0.28231983511010783 0 0.332376181221 ["Character/Dirichlet/1183/933"] "1-1183-1183.935-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.935" [[0, 0.0]] [] 0 true true false false -0.051013498223225526 0 1.31951315885 ["Character/Dirichlet/1183/935"] "1-1183-1183.940-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.940" [[0, 0.0]] [] 0 true true false false 0.48592474082677584 0 1.88282354318 ["Character/Dirichlet/1183/940"] "1-1183-1183.941-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.941" [[0, 0.0]] [] 0 true true false false 0.047786365282742965 0 0.672858627486 ["Character/Dirichlet/1183/941"] "1-1183-1183.943-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.943" [[0, 0.0]] [] 0 true true false false -0.07885145404013941 0 0.89545935572 ["Character/Dirichlet/1183/943"] "1-1183-1183.95-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.95" [[0, 0.0]] [] 0 true true false false -0.36758154556050365 0 0.550551293342 ["Character/Dirichlet/1183/95"] "1-1183-1183.951-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.951" [[0, 0.0]] [] 0 true true false false 0.44082840236686394 0 0.505551864613 ["Character/Dirichlet/1183/951"] "1-1183-1183.955-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.955" [[0, 0.0]] [] 0 true true false false 0.2460112173537489 0 1.67789531785 ["Character/Dirichlet/1183/955"] "1-1183-1183.957-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.957" [[0, 0.0]] [] 0 true true false false -0.07885145404013941 0 0.473004204061 ["Character/Dirichlet/1183/957"] "1-1183-1183.96-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.96" [[0, 0.0]] [] 0 true true false false -0.3258928741584826 0 0.167707191665 ["Character/Dirichlet/1183/96"] "1-1183-1183.961-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.961" [[0, 0.0]] [] 0 true true false false -0.2714717088773662 0 1.00167177798 ["Character/Dirichlet/1183/961"] "1-1183-1183.963-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.963" [[0, 0.0]] [] 0 true true false false -0.22852829112263381 0 1.80587274615 ["Character/Dirichlet/1183/963"] "1-1183-1183.964-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.964" [[0, 0.0]] [] 0 true true false false -0.2948277854010862 0 0.336081036532 ["Character/Dirichlet/1183/964"] "1-1183-1183.969-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.969" [[0, 0.0]] [] 0 true true false false 0.21839780512495205 0 0.894791896585 ["Character/Dirichlet/1183/969"] "1-1183-1183.97-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.97" [[0, 0.0]] [] 0 true true false false 0.44082840236686394 0 1.83945519858 ["Character/Dirichlet/1183/97"] "1-1183-1183.983-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.983" [[0, 0.0]] [] 0 true true false false -0.2968881909302748 0 0.943037608346 ["Character/Dirichlet/1183/983"] "1-1183-1183.984-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.984" [[0, 0.0]] [] 0 true true false false 0.01407525917322418 0 0.788534603044 ["Character/Dirichlet/1183/984"] "1-1183-1183.986-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.986" [[0, 0.0]] [] 0 true true false false -0.18293885601577908 0 2.42917106918 ["Character/Dirichlet/1183/986"] "1-1183-1183.989-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.989" [[0, 0.0]] [] 0 true true false false -0.33951904615547274 0 0.0375451410764 ["Character/Dirichlet/1183/989"] "1-1183-1183.990-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.990" [[0, 0.0]] [] 0 true true false false 0.05173113845828537 0 1.14739864311 ["Character/Dirichlet/1183/990"] "1-1183-1183.993-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.993" [[0, 0.0]] [] 0 true true false false 0.19822485207100593 0 1.64961883657 ["Character/Dirichlet/1183/993"] "1-1183-1183.998-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.998" [[0, 0.0]] [] 0 true true false false -0.48592474082677584 0 0.709112340922 ["Character/Dirichlet/1183/998"] "1-1183-1183.999-r0-0-0" 5.493828903459774 5.493828903459774 1 1183 "1183.999" [[0, 0.0]] [] 0 true true false false 0.28160219487504795 0 1.35044864723 ["Character/Dirichlet/1183/999"] # Label -- # Each L-function $L$ has a label of the form d-N-q.k-x-y-i, where # * $d$ is the degree of $L$. # * $N$ is the conductor of $L$. When $N$ is a perfect power $m^n$ we write $N$ as $m$e$n$, since $N$ can be very large for some imprimitive L-functions. # * q.k is the label of the primitive Dirichlet character from which the central character is induced. # * x-y is the spectral label encoding the $\mu_j$ and $\nu_j$ in the analytically normalized functional equation. # * i is a non-negative integer disambiguating between L-functions that would otherwise have the same label. #$\alpha$ (root_analytic_conductor) -- # If $d$ is the degree of the L-function $L(s)$, the **root analytic conductor** $\alpha$ of $L$ is the $d$th root of the analytic conductor of $L$. It plays a role analogous to the root discriminant for number fields. #$A$ (analytic_conductor) -- # The **analytic conductor** of an L-function $L(s)$ with infinity factor $L_{\infty}(s)$ and conductor $N$ is the real number # \[ # A := \mathrm{exp}\left(2\mathrm{Re}\left(\frac{L_{\infty}'(1/2)}{L_{\infty}(1/2)}\right)\right)N. # \] #$d$ (degree) -- # The **degree** of an L-function is the number $J + 2K$ of Gamma factors occurring in its functional equation # \[ # \Lambda(s) := N^{s/2} # \prod_{j=1}^J \Gamma_{\mathbb R}(s+\mu_j) \prod_{k=1}^K \Gamma_{\mathbb C}(s+\nu_k) # \cdot L(s) = \varepsilon \overline{\Lambda}(1-s). # \] # The degree appears as the first component of the Selberg data of $L(s).$ In all known cases it is the degree of the polynomial of the inverse of the Euler factor at any prime not dividing the conductor. #$N$ (conductor) -- # The **conductor** of an L-function is the integer $N$ occurring in its functional equation # \[ # \Lambda(s) := N^{s/2} # \prod_{j=1}^J \Gamma_{\mathbb R}(s+\mu_j) \prod_{k=1}^K \Gamma_{\mathbb C}(s+\nu_k) # \cdot L(s) = \varepsilon \overline{\Lambda}(1-s). # \] # The conductor of an analytic L-function is the second component in the Selberg data. For a Dirichlet L-function # associated with a primitive Dirichlet character, the conductor of the L-function is the same as the conductor of the character. For a primitive L-function associated with a cusp form $\phi$ on $GL(2)/\mathbb Q$, the conductor of the L-function is the same as the level of $\phi$. # In the literature, the word _level_ is sometimes used instead of _conductor_. #$\chi$ (central_character) -- # An L-function has an Euler product of the form # $L(s) = \prod_p L_p(p^{-s})^{-1}$ # where $L_p(x) = 1 + a_p x + \ldots + (-1)^d \chi(p) x^d$. The character $\chi$ is a Dirichlet character mod $N$ and is called **central character** of the L-function. # Here, $N$ is the conductor of $L$. #$\mu$ (mus) -- # All known analytic L-functions have a **functional equation** that can be written in the form # \[ # \Lambda(s) := N^{s/2} # \prod_{j=1}^J \Gamma_{\mathbb R}(s+\mu_j) \prod_{k=1}^K \Gamma_{\mathbb C}(s+\nu_k) # \cdot L(s) = \varepsilon \overline{\Lambda}(1-s), # \] # where $N$ is an integer, $\Gamma_{\mathbb R}$ and $\Gamma_{\mathbb C}$ are defined in terms of the $\Gamma$-function, $\mathrm{Re}(\mu_j) = 0 \ \mathrm{or} \ 1$ (assuming Selberg's eigenvalue conjecture), and $\mathrm{Re}(\nu_k)$ is a positive integer # or half-integer, # \[ # \sum \mu_j + 2 \sum \nu_k \ \ \ \ \text{is real}, # \] # and $\varepsilon$ is the sign of the functional equation. # With those restrictions on the spectral parameters, the # data in the functional equation is specified uniquely. The integer $d = J + 2 K$ # is the degree of the L-function. The integer $N$ is the conductor (or level) # of the L-function. The pair $[J,K]$ is the signature of the L-function. The parameters # in the functional equation can be used to make up the 4-tuple called the Selberg data. # The axioms of the Selberg class are less restrictive than # given above. # Note that the functional equation above has the central point at $s=1/2$, and relates $s\leftrightarrow 1-s$. # For many L-functions there is another normalization which is natural. The corresponding functional equation relates $s\leftrightarrow w+1-s$ for some positive integer $w$, # called the motivic weight of the L-function. The central point is at $s=(w+1)/2$, and the arithmetically normalized Dirichlet coefficients $a_n n^{w/2}$ are algebraic integers. #$\nu$ (nus) -- # All known analytic L-functions have a **functional equation** that can be written in the form # \[ # \Lambda(s) := N^{s/2} # \prod_{j=1}^J \Gamma_{\mathbb R}(s+\mu_j) \prod_{k=1}^K \Gamma_{\mathbb C}(s+\nu_k) # \cdot L(s) = \varepsilon \overline{\Lambda}(1-s), # \] # where $N$ is an integer, $\Gamma_{\mathbb R}$ and $\Gamma_{\mathbb C}$ are defined in terms of the $\Gamma$-function, $\mathrm{Re}(\mu_j) = 0 \ \mathrm{or} \ 1$ (assuming Selberg's eigenvalue conjecture), and $\mathrm{Re}(\nu_k)$ is a positive integer # or half-integer, # \[ # \sum \mu_j + 2 \sum \nu_k \ \ \ \ \text{is real}, # \] # and $\varepsilon$ is the sign of the functional equation. # With those restrictions on the spectral parameters, the # data in the functional equation is specified uniquely. The integer $d = J + 2 K$ # is the degree of the L-function. The integer $N$ is the conductor (or level) # of the L-function. The pair $[J,K]$ is the signature of the L-function. The parameters # in the functional equation can be used to make up the 4-tuple called the Selberg data. # The axioms of the Selberg class are less restrictive than # given above. # Note that the functional equation above has the central point at $s=1/2$, and relates $s\leftrightarrow 1-s$. # For many L-functions there is another normalization which is natural. The corresponding functional equation relates $s\leftrightarrow w+1-s$ for some positive integer $w$, # called the motivic weight of the L-function. The central point is at $s=(w+1)/2$, and the arithmetically normalized Dirichlet coefficients $a_n n^{w/2}$ are algebraic integers. #$w$ (motivic_weight) -- # The **motivic weight** (or **arithmetic weight**) of an arithmetic L-function with analytic normalization $L_{an}(s)=\sum_{n=1}^\infty a_nn^{-s}$ is the least nonnegative integer $w$ for which $a_nn^{w/2}$ is an algebraic integer for all $n\ge 1$. # If the L-function arises from a motive, then the weight of the motive has the # same parity as the motivic weight of the L-function, but the weight of the motive # could be larger. This apparent discrepancy comes from the fact that a Tate twist # increases the weight of the motive. This corresponds to the change of variables # $s \mapsto s + j$ in the L-function of the motive. #prim (primitive) -- # An L-function is primitive if it cannot be written as a product of nontrivial L-functions. The "trivial L-function" is the constant function $1$. #arith (algebraic) -- # An L-function $L(s) = \sum_{n=1}^{\infty} a_n n^{-s}$ is called **arithmetic** if its Dirichlet coefficients $a_n$ are algebraic numbers. #$\mathbb{Q}$ (rational) -- # A **rational** L-function $L(s)$ is an arithmetic L-function with coefficient field $\Q$; equivalently, its Euler product in the arithmetic normalization can be written as a product over rational primes # \[ # L(s)=\prod_pL_p(p^{-s})^{-1} # \] # with $L_p\in \Z[T]$. #self-dual (self_dual) -- # An L-function $L(s) = \sum_{n=1}^{\infty} \frac{a_n}{n^s}$ is called **self-dual** if its Dirichlet coefficients $a_n$ are real. #$\operatorname{Arg}(\epsilon)$ (root_angle) -- # The **root angle** of an L-function is the argument of its root number, as a real number $\alpha$ with $-0.5 < \alpha \le 0.5$. #$r$ (order_of_vanishing) -- # The **analytic rank** of an L-function $L(s)$ is its order of vanishing at its central point. # When the analytic rank $r$ is positive, the value listed in the LMFDB is typically an upper bound that is believed to be tight (in the sense that there are known to be $r$ zeroes located very near to the central point). #First zero (z1) -- # The **zeros** of an L-function $L(s)$ are the complex numbers $\rho$ for which $L(\rho)=0$. # Under the Riemann Hypothesis, every non-trivial zero $\rho$ lies on the critical line $\Re(s)=1/2$ (in the analytic normalization). # The **lowest zero** of an L-function $L(s)$ is the least $\gamma>0$ for which $L(1/2+i\gamma)=0$. Note that even when $L(1/2)=0$, the lowest zero is by definition a positive real number. #Origin (instance_urls) -- # L-functions arise from many different sources. Already in degree 2 we have examples of # L-functions associated with holomorphic cusp forms, with Maass forms, with elliptic curves, with characters of number fields (Hecke characters), and with 2-dimensional representations of the Galois group of a number field (Artin L-functions). # Sometimes an L-function may arise from more than one source. For example, the L-functions associated with elliptic curves are also associated with weight 2 cusp forms. A goal of the Langlands program ostensibly is to prove that any degree $d$ L-function is associated with an automorphic form on $\mathrm{GL}(d)$. Because of this representation theoretic genesis, one can associate an L-function not only to an automorphic representation but also to symmetric powers, or exterior powers of that representation, or to the tensor product of two representations (the Rankin-Selberg product of two L-functions).