# lfunc_search downloaded from the LMFDB on 12 July 2026. # Search link: https://www.lmfdb.org/L/1/5600/5600.5221/r1-0 # Query "{'degree': 1, 'conductor': 5600, 'spectral_label': 'r1-0'}" returned 320 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. "1-5600-5600.1019-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1019" [[1, 0.0]] [] 0 true true false false 0.2728301901396936 0 1.01607861286 ["Character/Dirichlet/5600/1019"] "1-5600-5600.1021-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1021" [[1, 0.0]] [] 0 true true false false -0.3662500000000001 0 0.374076947717 ["Character/Dirichlet/5600/1021"] "1-5600-5600.1027-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1027" [[1, 0.0]] [] 0 true true false false 0.04357704694605388 0 0.769078644022 ["Character/Dirichlet/5600/1027"] "1-5600-5600.1059-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1059" [[1, 0.0]] [] 0 true true false false -0.2828301901396936 0 0.521493652945 ["Character/Dirichlet/5600/1059"] "1-5600-5600.1067-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1067" [[1, 0.0]] [] 0 true true false false 0.38642295305394614 0 0.953473194419 ["Character/Dirichlet/5600/1067"] "1-5600-5600.1069-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1069" [[1, 0.0]] [] 0 true true false false -0.21642295305394613 0 0.491682465438 ["Character/Dirichlet/5600/1069"] "1-5600-5600.1083-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1083" [[1, 0.0]] [] 0 true true false false -0.40392295305394615 0 0.180912074859 ["Character/Dirichlet/5600/1083"] "1-5600-5600.11-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.11" [[1, 0.0]] [] 0 true true false false -0.2171698098603064 0 0.210329071177 ["Character/Dirichlet/5600/11"] "1-5600-5600.1109-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1109" [[1, 0.0]] [] 0 true true false false -0.29357704694605385 0 0.459667230035 ["Character/Dirichlet/5600/1109"] "1-5600-5600.1117-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1117" [[1, 0.0]] [] 0 true true false false -0.2896698098603064 0 0.299825513302 ["Character/Dirichlet/5600/1117"] "1-5600-5600.1123-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1123" [[1, 0.0]] [] 0 true true false false -0.4160770469460539 0 0.342977668897 ["Character/Dirichlet/5600/1123"] "1-5600-5600.1131-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1131" [[1, 0.0]] [] 0 true true false false 0.022830190139693604 0 0.614566637986 ["Character/Dirichlet/5600/1131"] "1-5600-5600.1147-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1147" [[1, 0.0]] [] 0 true true false false -0.30375 0 0.208990102977 ["Character/Dirichlet/5600/1147"] "1-5600-5600.1171-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1171" [[1, 0.0]] [] 0 true true false false -0.2728301901396936 0 0.56361466669 ["Character/Dirichlet/5600/1171"] "1-5600-5600.1173-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1173" [[1, 0.0]] [] 0 true true false false 0.032830190139693606 0 0.487160338453 ["Character/Dirichlet/5600/1173"] "1-5600-5600.1181-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1181" [[1, 0.0]] [] 0 true true false false 0.03357704694605387 0 0.557363837614 ["Character/Dirichlet/5600/1181"] "1-5600-5600.1189-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1189" [[1, 0.0]] [] 0 true true false false -0.12375000000000001 0 0.620339584204 ["Character/Dirichlet/5600/1189"] "1-5600-5600.1203-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1203" [[1, 0.0]] [] 0 true true false false -0.11625000000000002 0 0.167914021623 ["Character/Dirichlet/5600/1203"] "1-5600-5600.1213-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1213" [[1, 0.0]] [] 0 true true false false 0.46716980986030643 0 0.98657638054 ["Character/Dirichlet/5600/1213"] "1-5600-5600.1221-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1221" [[1, 0.0]] [] 0 true true false false 0.21642295305394613 0 0.179847290588 ["Character/Dirichlet/5600/1221"] "1-5600-5600.1339-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1339" [[1, 0.0]] [] 0 true true false false -0.2803301901396936 0 0.991354337009 ["Character/Dirichlet/5600/1339"] "1-5600-5600.1347-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1347" [[1, 0.0]] [] 0 true true false false -0.34607704694605385 0 0.161406259354 ["Character/Dirichlet/5600/1347"] "1-5600-5600.1363-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1363" [[1, 0.0]] [] 0 true true false false 0.3535770469460539 0 0.0972715489893 ["Character/Dirichlet/5600/1363"] "1-5600-5600.1389-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1389" [[1, 0.0]] [] 0 true true false false 0.08392295305394612 0 0.744143905808 ["Character/Dirichlet/5600/1389"] "1-5600-5600.1397-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1397" [[1, 0.0]] [] 0 true true false false 0.1028301901396936 0 0.317040422969 ["Character/Dirichlet/5600/1397"] "1-5600-5600.1403-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1403" [[1, 0.0]] [] 0 true true false false 0.21642295305394613 0 0.513247989246 ["Character/Dirichlet/5600/1403"] "1-5600-5600.1411-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1411" [[1, 0.0]] [] 0 true true false false 0.4703301901396936 0 0.40418363506 ["Character/Dirichlet/5600/1411"] "1-5600-5600.1427-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1427" [[1, 0.0]] [] 0 true true false false 0.31375 0 0.835890262657 ["Character/Dirichlet/5600/1427"] "1-5600-5600.1437-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1437" [[1, 0.0]] [] 0 true true false false -0.032830190139693606 0 0.487780334429 ["Character/Dirichlet/5600/1437"] "1-5600-5600.1453-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1453" [[1, 0.0]] [] 0 true true false false 0.04033019013969361 0 0.0486850015987 ["Character/Dirichlet/5600/1453"] "1-5600-5600.1461-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1461" [[1, 0.0]] [] 0 true true false false -0.39392295305394615 0 1.0107384818 ["Character/Dirichlet/5600/1461"] "1-5600-5600.1469-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1469" [[1, 0.0]] [] 0 true true false false -0.44625000000000004 0 0.0494667263994 ["Character/Dirichlet/5600/1469"] "1-5600-5600.1483-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1483" [[1, 0.0]] [] 0 true true false false -0.13375 0 0.900829978881 ["Character/Dirichlet/5600/1483"] "1-5600-5600.1579-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1579" [[1, 0.0]] [] 0 true true false false 0.1028301901396936 0 0.818452974306 ["Character/Dirichlet/5600/1579"] "1-5600-5600.1581-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1581" [[1, 0.0]] [] 0 true true false false 0.30375 0 0.964870935684 ["Character/Dirichlet/5600/1581"] "1-5600-5600.1587-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1587" [[1, 0.0]] [] 0 true true false false -0.14642295305394615 0 0.15708314597 ["Character/Dirichlet/5600/1587"] "1-5600-5600.1619-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1619" [[1, 0.0]] [] 0 true true false false -0.3528301901396936 0 0.141207119734 ["Character/Dirichlet/5600/1619"] "1-5600-5600.1627-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1627" [[1, 0.0]] [] 0 true true false false -0.3535770469460539 0 0.978844483682 ["Character/Dirichlet/5600/1627"] "1-5600-5600.1629-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1629" [[1, 0.0]] [] 0 true true false false 0.11357704694605389 0 0.699157580367 ["Character/Dirichlet/5600/1629"] "1-5600-5600.1669-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1669" [[1, 0.0]] [] 0 true true false false 0.13642295305394614 0 0.677677195156 ["Character/Dirichlet/5600/1669"] "1-5600-5600.1677-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1677" [[1, 0.0]] [] 0 true true false false 0.4703301901396936 0 0.0979545939651 ["Character/Dirichlet/5600/1677"] "1-5600-5600.1683-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1683" [[1, 0.0]] [] 0 true true false false -0.17607704694605386 0 0.25690824098 ["Character/Dirichlet/5600/1683"] "1-5600-5600.1691-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1691" [[1, 0.0]] [] 0 true true false false -0.40716980986030643 0 0.368298471904 ["Character/Dirichlet/5600/1691"] "1-5600-5600.1717-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1717" [[1, 0.0]] [] 0 true true false false -0.29033019013969363 0 0.454125676449 ["Character/Dirichlet/5600/1717"] "1-5600-5600.1731-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1731" [[1, 0.0]] [] 0 true true false false -0.1028301901396936 0 0.683033173868 ["Character/Dirichlet/5600/1731"] "1-5600-5600.1733-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1733" [[1, 0.0]] [] 0 true true false false -0.22716980986030638 0 0.353118591543 ["Character/Dirichlet/5600/1733"] "1-5600-5600.1741-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1741" [[1, 0.0]] [] 0 true true false false 0.10357704694605388 0 0.945784080722 ["Character/Dirichlet/5600/1741"] "1-5600-5600.1763-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1763" [[1, 0.0]] [] 0 true true false false 0.12375000000000001 0 0.585734275697 ["Character/Dirichlet/5600/1763"] "1-5600-5600.1773-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1773" [[1, 0.0]] [] 0 true true false false 0.1571698098603064 0 0.0588151903189 ["Character/Dirichlet/5600/1773"] "1-5600-5600.1781-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1781" [[1, 0.0]] [] 0 true true false false -0.11357704694605389 0 0.417937130201 ["Character/Dirichlet/5600/1781"] "1-5600-5600.179-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.179" [[1, 0.0]] [] 0 true true false false -0.4596698098603064 0 0.00318590553269 ["Character/Dirichlet/5600/179"] "1-5600-5600.181-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.181" [[1, 0.0]] [] 0 true true false false 0.3662500000000001 0 0.712290568671 ["Character/Dirichlet/5600/181"] "1-5600-5600.1859-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1859" [[1, 0.0]] [] 0 true true false false -0.46966980986030643 0 1.01932637003 ["Character/Dirichlet/5600/1859"] "1-5600-5600.1861-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1861" [[1, 0.0]] [] 0 true true false false 0.37625 0 0.0365105278941 ["Character/Dirichlet/5600/1861"] "1-5600-5600.1867-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1867" [[1, 0.0]] [] 0 true true false false 0.34607704694605385 0 0.94070474925 ["Character/Dirichlet/5600/1867"] "1-5600-5600.187-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.187" [[1, 0.0]] [] 0 true true false false -0.3339229530539461 0 0.583936328709 ["Character/Dirichlet/5600/187"] "1-5600-5600.1909-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1909" [[1, 0.0]] [] 0 true true false false -0.3339229530539461 0 0.0299603062534 ["Character/Dirichlet/5600/1909"] "1-5600-5600.1923-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1923" [[1, 0.0]] [] 0 true true false false -0.45642295305394615 0 0.69691727555 ["Character/Dirichlet/5600/1923"] "1-5600-5600.1963-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1963" [[1, 0.0]] [] 0 true true false false -0.04357704694605388 0 0.370385105437 ["Character/Dirichlet/5600/1963"] "1-5600-5600.1971-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1971" [[1, 0.0]] [] 0 true true false false -0.4596698098603064 0 0.132433498031 ["Character/Dirichlet/5600/1971"] "1-5600-5600.1987-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1987" [[1, 0.0]] [] 0 true true false false -0.37625 0 0.256886578886 ["Character/Dirichlet/5600/1987"] "1-5600-5600.1997-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.1997" [[1, 0.0]] [] 0 true true false false 0.22716980986030638 0 0.994556443034 ["Character/Dirichlet/5600/1997"] "1-5600-5600.2011-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2011" [[1, 0.0]] [] 0 true true false false 0.2196698098603064 0 0.92344445861 ["Character/Dirichlet/5600/2011"] "1-5600-5600.2013-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2013" [[1, 0.0]] [] 0 true true false false 0.2803301901396936 0 0.791657775746 ["Character/Dirichlet/5600/2013"] "1-5600-5600.2021-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2021" [[1, 0.0]] [] 0 true true false false 0.17607704694605386 0 0.546622039218 ["Character/Dirichlet/5600/2021"] "1-5600-5600.2029-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2029" [[1, 0.0]] [] 0 true true false false 0.38375000000000004 0 0.0606717004478 ["Character/Dirichlet/5600/2029"] "1-5600-5600.2053-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2053" [[1, 0.0]] [] 0 true true false false -0.4603301901396936 0 0.93812453614 ["Character/Dirichlet/5600/2053"] "1-5600-5600.2061-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2061" [[1, 0.0]] [] 0 true true false false -0.4160770469460539 0 0.9807834962 ["Character/Dirichlet/5600/2061"] "1-5600-5600.2139-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2139" [[1, 0.0]] [] 0 true true false false -0.46716980986030643 0 0.152121717503 ["Character/Dirichlet/5600/2139"] "1-5600-5600.2141-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2141" [[1, 0.0]] [] 0 true true false false -0.12625 0 0.473590989366 ["Character/Dirichlet/5600/2141"] "1-5600-5600.2147-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2147" [[1, 0.0]] [] 0 true true false false -0.38642295305394614 0 0.898813524135 ["Character/Dirichlet/5600/2147"] "1-5600-5600.2179-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2179" [[1, 0.0]] [] 0 true true false false -0.022830190139693604 0 0.280454387745 ["Character/Dirichlet/5600/2179"] "1-5600-5600.2187-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2187" [[1, 0.0]] [] 0 true true false false 0.45642295305394615 0 0.100897145574 ["Character/Dirichlet/5600/2187"] "1-5600-5600.2189-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2189" [[1, 0.0]] [] 0 true true false false 0.04357704694605388 0 0.407525436912 ["Character/Dirichlet/5600/2189"] "1-5600-5600.219-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.219" [[1, 0.0]] [] 0 true true false false 0.4596698098603064 0 0.961824359771 ["Character/Dirichlet/5600/219"] "1-5600-5600.2203-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2203" [[1, 0.0]] [] 0 true true false false 0.17607704694605386 0 0.771477051287 ["Character/Dirichlet/5600/2203"] "1-5600-5600.2229-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2229" [[1, 0.0]] [] 0 true true false false -0.03357704694605387 0 0.708952126314 ["Character/Dirichlet/5600/2229"] "1-5600-5600.2237-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2237" [[1, 0.0]] [] 0 true true false false -0.2196698098603064 0 0.507085076654 ["Character/Dirichlet/5600/2237"] "1-5600-5600.2267-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2267" [[1, 0.0]] [] 0 true true false false 0.11625000000000002 0 0.602030910784 ["Character/Dirichlet/5600/2267"] "1-5600-5600.227-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.227" [[1, 0.0]] [] 0 true true false false 0.08392295305394612 0 0.604406670261 ["Character/Dirichlet/5600/227"] "1-5600-5600.2277-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2277" [[1, 0.0]] [] 0 true true false false -0.030330190139693607 0 0.523891104217 ["Character/Dirichlet/5600/2277"] "1-5600-5600.229-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.229" [[1, 0.0]] [] 0 true true false false 0.17607704694605386 0 0.622359666541 ["Character/Dirichlet/5600/229"] "1-5600-5600.2291-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2291" [[1, 0.0]] [] 0 true true false false -0.032830190139693606 0 0.621743375726 ["Character/Dirichlet/5600/2291"] "1-5600-5600.2309-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2309" [[1, 0.0]] [] 0 true true false false 0.43625 0 0.213485235472 ["Character/Dirichlet/5600/2309"] "1-5600-5600.2323-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2323" [[1, 0.0]] [] 0 true true false false -0.18625 0 0.420589055318 ["Character/Dirichlet/5600/2323"] "1-5600-5600.2333-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2333" [[1, 0.0]] [] 0 true true false false -0.1028301901396936 0 0.251920021805 ["Character/Dirichlet/5600/2333"] "1-5600-5600.2341-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2341" [[1, 0.0]] [] 0 true true false false 0.45642295305394615 0 1.15465923565 ["Character/Dirichlet/5600/2341"] "1-5600-5600.2419-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2419" [[1, 0.0]] [] 0 true true false false 0.4603301901396936 0 1.26250720684 ["Character/Dirichlet/5600/2419"] "1-5600-5600.2421-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2421" [[1, 0.0]] [] 0 true true false false 0.44625000000000004 0 0.0226832222597 ["Character/Dirichlet/5600/2421"] "1-5600-5600.2427-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2427" [[1, 0.0]] [] 0 true true false false -0.39392295305394615 0 1.36102048502 ["Character/Dirichlet/5600/2427"] "1-5600-5600.2459-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2459" [[1, 0.0]] [] 0 true true false false 0.27966980986030643 0 0.714349207722 ["Character/Dirichlet/5600/2459"] "1-5600-5600.2467-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2467" [[1, 0.0]] [] 0 true true false false 0.07392295305394612 0 0.233198745157 ["Character/Dirichlet/5600/2467"] "1-5600-5600.2469-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2469" [[1, 0.0]] [] 0 true true false false 0.09607704694605386 0 0.5212374685 ["Character/Dirichlet/5600/2469"] "1-5600-5600.2483-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2483" [[1, 0.0]] [] 0 true true false false -0.21642295305394613 0 0.265641461417 ["Character/Dirichlet/5600/2483"] "1-5600-5600.2509-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2509" [[1, 0.0]] [] 0 true true false false 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["Character/Dirichlet/5600/2571"] "1-5600-5600.2573-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2573" [[1, 0.0]] [] 0 true true false false -0.029669809860306394 0 0.299505633994 ["Character/Dirichlet/5600/2573"] "1-5600-5600.2581-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2581" [[1, 0.0]] [] 0 true true false false -0.15392295305394613 0 0.461393260699 ["Character/Dirichlet/5600/2581"] "1-5600-5600.2589-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2589" [[1, 0.0]] [] 0 true true false false -0.18625 0 0.694467070252 ["Character/Dirichlet/5600/2589"] "1-5600-5600.2603-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2603" [[1, 0.0]] [] 0 true true false false 0.44625000000000004 0 0.547361824499 ["Character/Dirichlet/5600/2603"] "1-5600-5600.2613-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2613" [[1, 0.0]] [] 0 true true false false 0.27966980986030643 0 0.861621541156 ["Character/Dirichlet/5600/2613"] 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"5600.2763" [[1, 0.0]] [] 0 true true false false -0.08392295305394612 0 0.750264222739 ["Character/Dirichlet/5600/2763"] "1-5600-5600.277-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.277" [[1, 0.0]] [] 0 true true false false -0.46716980986030643 0 0.30898930619 ["Character/Dirichlet/5600/277"] "1-5600-5600.2789-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2789" [[1, 0.0]] [] 0 true true false false 0.3964229530539462 0 1.07022354573 ["Character/Dirichlet/5600/2789"] "1-5600-5600.2797-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2797" [[1, 0.0]] [] 0 true true false false 0.04033019013969361 0 0.290100745212 ["Character/Dirichlet/5600/2797"] "1-5600-5600.2803-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2803" [[1, 0.0]] [] 0 true true false false 0.40392295305394615 0 1.134036601 ["Character/Dirichlet/5600/2803"] "1-5600-5600.2811-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2811" [[1, 0.0]] [] 0 true true false false 0.032830190139693606 0 0.398527189161 ["Character/Dirichlet/5600/2811"] "1-5600-5600.2827-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2827" [[1, 0.0]] [] 0 true true false false -0.12375000000000001 0 0.119997275923 ["Character/Dirichlet/5600/2827"] "1-5600-5600.283-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.283" [[1, 0.0]] [] 0 true true false false -0.3635770469460539 0 1.32165188666 ["Character/Dirichlet/5600/283"] "1-5600-5600.2837-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2837" [[1, 0.0]] [] 0 true true false false -0.22033019013969363 0 0.317428462985 ["Character/Dirichlet/5600/2837"] "1-5600-5600.2853-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2853" [[1, 0.0]] [] 0 true true false false 0.3528301901396936 0 0.0424937706686 ["Character/Dirichlet/5600/2853"] "1-5600-5600.2861-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2861" [[1, 0.0]] [] 0 true true false false -0.45642295305394615 0 0.0729500213854 ["Character/Dirichlet/5600/2861"] "1-5600-5600.2869-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2869" [[1, 0.0]] [] 0 true true false false 0.3662500000000001 0 0.210402875549 ["Character/Dirichlet/5600/2869"] "1-5600-5600.2883-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2883" [[1, 0.0]] [] 0 true true false false -0.44625000000000004 0 1.05840084409 ["Character/Dirichlet/5600/2883"] "1-5600-5600.291-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.291" [[1, 0.0]] [] 0 true true false false 0.030330190139693607 0 0.489000295125 ["Character/Dirichlet/5600/291"] "1-5600-5600.2979-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2979" [[1, 0.0]] [] 0 true true false false -0.20966980986030642 0 0.302101568216 ["Character/Dirichlet/5600/2979"] "1-5600-5600.2981-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2981" [[1, 0.0]] [] 0 true true false false -0.38375000000000004 0 0.227623093884 ["Character/Dirichlet/5600/2981"] "1-5600-5600.2987-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.2987" [[1, 0.0]] [] 0 true true false false 0.4160770469460539 0 0.807747052886 ["Character/Dirichlet/5600/2987"] "1-5600-5600.3-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.3" [[1, 0.0]] [] 0 true true false false -0.34607704694605385 0 0.0731505227184 ["Character/Dirichlet/5600/3"] "1-5600-5600.3019-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.3019" [[1, 0.0]] [] 0 true true false false 0.20966980986030642 0 0.702280478792 ["Character/Dirichlet/5600/3019"] "1-5600-5600.3027-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.3027" [[1, 0.0]] [] 0 true true false false -0.1660770469460539 0 0.139535125599 ["Character/Dirichlet/5600/3027"] "1-5600-5600.3029-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.3029" [[1, 0.0]] [] 0 true true false false -0.07392295305394612 0 0.296257590877 ["Character/Dirichlet/5600/3029"] "1-5600-5600.3069-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.3069" [[1, 0.0]] [] 0 true true false false 0.07392295305394612 0 0.490354510312 ["Character/Dirichlet/5600/3069"] "1-5600-5600.3077-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.3077" [[1, 0.0]] [] 0 true true false false -0.2171698098603064 0 0.324173620447 ["Character/Dirichlet/5600/3077"] "1-5600-5600.3083-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.3083" [[1, 0.0]] [] 0 true true false false 0.38642295305394614 0 0.0966613956534 ["Character/Dirichlet/5600/3083"] "1-5600-5600.3091-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.3091" [[1, 0.0]] [] 0 true true false false -0.2196698098603064 0 0.259968529563 ["Character/Dirichlet/5600/3091"] "1-5600-5600.3117-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.3117" [[1, 0.0]] [] 0 true true false false -0.3528301901396936 0 1.11685188386 ["Character/Dirichlet/5600/3117"] "1-5600-5600.3131-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.3131" [[1, 0.0]] [] 0 true true false false 0.4596698098603064 0 1.37528697509 ["Character/Dirichlet/5600/3131"] "1-5600-5600.3133-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.3133" [[1, 0.0]] [] 0 true true false false -0.2896698098603064 0 0.418060363784 ["Character/Dirichlet/5600/3133"] "1-5600-5600.3141-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.3141" [[1, 0.0]] [] 0 true true false false 0.4160770469460539 0 0.00302447482096 ["Character/Dirichlet/5600/3141"] "1-5600-5600.3163-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.3163" [[1, 0.0]] [] 0 true true false false -0.31375 0 0.0503988793404 ["Character/Dirichlet/5600/3163"] "1-5600-5600.317-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.317" [[1, 0.0]] [] 0 true true false false -0.1028301901396936 0 0.533908386665 ["Character/Dirichlet/5600/317"] "1-5600-5600.3173-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.3173" [[1, 0.0]] [] 0 true true false false 0.46966980986030643 0 0.0921958444655 ["Character/Dirichlet/5600/3173"] "1-5600-5600.3181-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.3181" [[1, 0.0]] [] 0 true true false false -0.17607704694605386 0 0.253471527892 ["Character/Dirichlet/5600/3181"] "1-5600-5600.3259-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.3259" [[1, 0.0]] [] 0 true true false false 0.09283019013969361 0 0.502643557567 ["Character/Dirichlet/5600/3259"] "1-5600-5600.3261-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.3261" [[1, 0.0]] [] 0 true true false false 0.31375 0 0.502046441575 ["Character/Dirichlet/5600/3261"] "1-5600-5600.3267-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.3267" [[1, 0.0]] [] 0 true true false false 0.03357704694605387 0 0.637633865127 ["Character/Dirichlet/5600/3267"] "1-5600-5600.3309-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.3309" [[1, 0.0]] [] 0 true true false false -0.3964229530539462 0 0.153071710383 ["Character/Dirichlet/5600/3309"] "1-5600-5600.331-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.331" [[1, 0.0]] [] 0 true true false false 0.20966980986030642 0 0.676011926163 ["Character/Dirichlet/5600/331"] "1-5600-5600.3323-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.3323" [[1, 0.0]] [] 0 true true false false 0.10607704694605388 0 0.41102599771 ["Character/Dirichlet/5600/3323"] "1-5600-5600.333-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.333" [[1, 0.0]] [] 0 true true false false 0.4603301901396936 0 0.836288051834 ["Character/Dirichlet/5600/333"] "1-5600-5600.3363-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.3363" [[1, 0.0]] [] 0 true true false false -0.35607704694605385 0 1.21798696767 ["Character/Dirichlet/5600/3363"] "1-5600-5600.3371-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.3371" [[1, 0.0]] [] 0 true true false false 0.1028301901396936 0 0.659174558139 ["Character/Dirichlet/5600/3371"] "1-5600-5600.3387-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.3387" [[1, 0.0]] [] 0 true true false false 0.18625 0 0.797641607916 ["Character/Dirichlet/5600/3387"] "1-5600-5600.3397-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.3397" [[1, 0.0]] [] 0 true true false false -0.4603301901396936 0 0.234233359795 ["Character/Dirichlet/5600/3397"] "1-5600-5600.341-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.341" [[1, 0.0]] [] 0 true true false false 0.1660770469460539 0 0.65841175703 ["Character/Dirichlet/5600/341"] "1-5600-5600.3411-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.3411" [[1, 0.0]] [] 0 true true false false 0.40716980986030643 0 1.17592824628 ["Character/Dirichlet/5600/3411"] "1-5600-5600.3413-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.3413" [[1, 0.0]] [] 0 true true false false 0.09283019013969361 0 0.331208624359 ["Character/Dirichlet/5600/3413"] "1-5600-5600.3421-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.3421" [[1, 0.0]] [] 0 true true false false 0.11357704694605389 0 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["Character/Dirichlet/5600/4987"] "1-5600-5600.4989-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.4989" [[1, 0.0]] [] 0 true true false false 0.29357704694605385 0 1.08709626619 ["Character/Dirichlet/5600/4989"] "1-5600-5600.5003-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.5003" [[1, 0.0]] [] 0 true true false false -0.07392295305394612 0 0.348178471483 ["Character/Dirichlet/5600/5003"] "1-5600-5600.5029-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.5029" [[1, 0.0]] [] 0 true true false false 0.21642295305394613 0 0.585288942079 ["Character/Dirichlet/5600/5029"] "1-5600-5600.5037-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.5037" [[1, 0.0]] [] 0 true true false false -0.46966980986030643 0 0.863284718526 ["Character/Dirichlet/5600/5037"] "1-5600-5600.5067-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.5067" [[1, 0.0]] [] 0 true true false false -0.13375 0 0.161644400603 ["Character/Dirichlet/5600/5067"] "1-5600-5600.5077-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.5077" [[1, 0.0]] [] 0 true true false false -0.2803301901396936 0 0.246234586729 ["Character/Dirichlet/5600/5077"] "1-5600-5600.509-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.509" [[1, 0.0]] [] 0 true true false false -0.14642295305394615 0 0.13632078398 ["Character/Dirichlet/5600/509"] "1-5600-5600.5091-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.5091" [[1, 0.0]] [] 0 true true false false 0.2171698098603064 0 0.385385389479 ["Character/Dirichlet/5600/5091"] "1-5600-5600.5109-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.5109" [[1, 0.0]] [] 0 true true false false 0.18625 0 0.469565290958 ["Character/Dirichlet/5600/5109"] "1-5600-5600.5123-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.5123" [[1, 0.0]] [] 0 true true false false 0.06374999999999999 0 0.673734367411 ["Character/Dirichlet/5600/5123"] "1-5600-5600.5133-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.5133" [[1, 0.0]] [] 0 true true false false -0.3528301901396936 0 0.239328032634 ["Character/Dirichlet/5600/5133"] "1-5600-5600.5141-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.5141" [[1, 0.0]] [] 0 true true false false 0.20642295305394612 0 0.678852107218 ["Character/Dirichlet/5600/5141"] "1-5600-5600.5219-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.5219" [[1, 0.0]] [] 0 true true false false -0.2896698098603064 0 0.562718064546 ["Character/Dirichlet/5600/5219"] "1-5600-5600.5221-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.5221" [[1, 0.0]] [] 0 true true false false -0.30375 0 0.0807932819698 ["Character/Dirichlet/5600/5221"] "1-5600-5600.5227-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.5227" [[1, 0.0]] [] 0 true true false false 0.35607704694605385 0 0.0728379330095 ["Character/Dirichlet/5600/5227"] "1-5600-5600.523-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.523" [[1, 0.0]] [] 0 true true false false -0.14392295305394615 0 0.380259389439 ["Character/Dirichlet/5600/523"] "1-5600-5600.5259-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.5259" [[1, 0.0]] [] 0 true true false false 0.029669809860306394 0 0.517392598058 ["Character/Dirichlet/5600/5259"] "1-5600-5600.5267-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.5267" [[1, 0.0]] [] 0 true true false false -0.17607704694605386 0 0.679851879737 ["Character/Dirichlet/5600/5267"] "1-5600-5600.5269-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.5269" [[1, 0.0]] [] 0 true true false false -0.15392295305394613 0 0.59754542819 ["Character/Dirichlet/5600/5269"] "1-5600-5600.5283-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.5283" [[1, 0.0]] [] 0 true true false false 0.03357704694605387 0 0.527820078055 ["Character/Dirichlet/5600/5283"] "1-5600-5600.53-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.53" [[1, 0.0]] [] 0 true true false false 0.1028301901396936 0 0.804193905036 ["Character/Dirichlet/5600/53"] "1-5600-5600.5309-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.5309" [[1, 0.0]] [] 0 true true false false -0.10607704694605388 0 0.195482988219 ["Character/Dirichlet/5600/5309"] "1-5600-5600.5317-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.5317" [[1, 0.0]] [] 0 true true false false -0.22716980986030638 0 0.334673146146 ["Character/Dirichlet/5600/5317"] "1-5600-5600.5323-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.5323" [[1, 0.0]] [] 0 true true false false -0.10357704694605388 0 0.321096110381 ["Character/Dirichlet/5600/5323"] "1-5600-5600.5331-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.5331" [[1, 0.0]] [] 0 true true false false 0.4603301901396936 0 0.0355048105597 ["Character/Dirichlet/5600/5331"] "1-5600-5600.5347-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.5347" [[1, 0.0]] [] 0 true true false false 0.13375 0 0.87377524636 ["Character/Dirichlet/5600/5347"] "1-5600-5600.5371-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.5371" [[1, 0.0]] [] 0 true true false false -0.4603301901396936 0 0.848309227002 ["Character/Dirichlet/5600/5371"] "1-5600-5600.5373-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.5373" [[1, 0.0]] [] 0 true true false false 0.22033019013969363 0 0.765087164033 ["Character/Dirichlet/5600/5373"] "1-5600-5600.5381-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.5381" [[1, 0.0]] [] 0 true true false false 0.09607704694605386 0 0.710770138112 ["Character/Dirichlet/5600/5381"] "1-5600-5600.5389-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.5389" [[1, 0.0]] [] 0 true true false false -0.43625 0 0.996749435725 ["Character/Dirichlet/5600/5389"] "1-5600-5600.5403-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.5403" [[1, 0.0]] [] 0 true true false false -0.30375 0 0.434511596445 ["Character/Dirichlet/5600/5403"] "1-5600-5600.5413-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.5413" [[1, 0.0]] [] 0 true true false false -0.4703301901396936 0 0.920550699028 ["Character/Dirichlet/5600/5413"] "1-5600-5600.5421-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.5421" [[1, 0.0]] [] 0 true true false false -0.09607704694605386 0 0.574145843915 ["Character/Dirichlet/5600/5421"] "1-5600-5600.5539-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.5539" [[1, 0.0]] [] 0 true true false false 0.1571698098603064 0 0.605067494984 ["Character/Dirichlet/5600/5539"] "1-5600-5600.5547-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.5547" [[1, 0.0]] [] 0 true true false false -0.03357704694605387 0 0.576531219799 ["Character/Dirichlet/5600/5547"] "1-5600-5600.5563-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.5563" [[1, 0.0]] [] 0 true true false false 0.1660770469460539 0 0.286356958752 ["Character/Dirichlet/5600/5563"] "1-5600-5600.5589-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.5589" [[1, 0.0]] [] 0 true true false false 0.14642295305394615 0 0.219872813373 ["Character/Dirichlet/5600/5589"] "1-5600-5600.5597-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.5597" [[1, 0.0]] [] 0 true true false false 0.29033019013969363 0 0.92793736231 ["Character/Dirichlet/5600/5597"] "1-5600-5600.563-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.563" [[1, 0.0]] [] 0 true true false false 0.39392295305394615 0 0.142604470326 ["Character/Dirichlet/5600/563"] "1-5600-5600.571-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.571" [[1, 0.0]] [] 0 true true false false 0.3528301901396936 0 0.904534769367 ["Character/Dirichlet/5600/571"] "1-5600-5600.587-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.587" [[1, 0.0]] [] 0 true true false false -0.06374999999999999 0 0.517029405733 ["Character/Dirichlet/5600/587"] "1-5600-5600.597-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.597" [[1, 0.0]] [] 0 true true false false 0.2896698098603064 0 0.716901360258 ["Character/Dirichlet/5600/597"] "1-5600-5600.61-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.61" [[1, 0.0]] [] 0 true true false false -0.20642295305394612 0 0.32924453592 ["Character/Dirichlet/5600/61"] "1-5600-5600.611-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.611" [[1, 0.0]] [] 0 true true false false -0.3428301901396936 0 0.00744793648334 ["Character/Dirichlet/5600/611"] "1-5600-5600.613-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.613" [[1, 0.0]] [] 0 true true false false 0.3428301901396936 0 0.770994715218 ["Character/Dirichlet/5600/613"] "1-5600-5600.621-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.621" [[1, 0.0]] [] 0 true true false false -0.13642295305394614 0 0.438011152004 ["Character/Dirichlet/5600/621"] "1-5600-5600.629-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.629" [[1, 0.0]] [] 0 true true false false 0.44625000000000004 0 0.940112381992 ["Character/Dirichlet/5600/629"] "1-5600-5600.653-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.653" [[1, 0.0]] [] 0 true true false false 0.22716980986030638 0 0.559951896734 ["Character/Dirichlet/5600/653"] "1-5600-5600.661-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.661" [[1, 0.0]] [] 0 true true false false -0.3535770469460539 0 0.23890301419 ["Character/Dirichlet/5600/661"] "1-5600-5600.69-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.69" [[1, 0.0]] [] 0 true true false false -0.38375000000000004 0 1.0134827392 ["Character/Dirichlet/5600/69"] "1-5600-5600.739-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.739" [[1, 0.0]] [] 0 true true false false -0.029669809860306394 0 0.355639488946 ["Character/Dirichlet/5600/739"] "1-5600-5600.741-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.741" [[1, 0.0]] [] 0 true true false false -0.06374999999999999 0 0.414409287728 ["Character/Dirichlet/5600/741"] "1-5600-5600.747-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.747" [[1, 0.0]] [] 0 true true false false -0.07392295305394612 0 0.159469382337 ["Character/Dirichlet/5600/747"] "1-5600-5600.779-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.779" [[1, 0.0]] [] 0 true true false false 0.2896698098603064 0 0.705366558397 ["Character/Dirichlet/5600/779"] "1-5600-5600.787-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.787" [[1, 0.0]] [] 0 true true false false -0.10607704694605388 0 0.198794778575 ["Character/Dirichlet/5600/787"] "1-5600-5600.789-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.789" [[1, 0.0]] [] 0 true true false false 0.10607704694605388 0 0.627916290087 ["Character/Dirichlet/5600/789"] "1-5600-5600.803-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.803" [[1, 0.0]] [] 0 true true false false -0.38642295305394614 0 0.301541678829 ["Character/Dirichlet/5600/803"] "1-5600-5600.829-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.829" [[1, 0.0]] [] 0 true true false false 0.15392295305394613 0 0.99859151381 ["Character/Dirichlet/5600/829"] "1-5600-5600.83-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.83" [[1, 0.0]] [] 0 true true false false 0.30375 0 0.881607025513 ["Character/Dirichlet/5600/83"] "1-5600-5600.837-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.837" [[1, 0.0]] [] 0 true true false false -0.1571698098603064 0 1.41447619068 ["Character/Dirichlet/5600/837"] "1-5600-5600.867-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.867" [[1, 0.0]] [] 0 true true false false -0.44625000000000004 0 0.0335813248714 ["Character/Dirichlet/5600/867"] "1-5600-5600.877-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.877" [[1, 0.0]] [] 0 true true false false -0.3428301901396936 0 0.0330625615484 ["Character/Dirichlet/5600/877"] "1-5600-5600.891-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.891" [[1, 0.0]] [] 0 true true false false -0.22033019013969363 0 0.297586287124 ["Character/Dirichlet/5600/891"] "1-5600-5600.909-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.909" [[1, 0.0]] [] 0 true true false false 0.12375000000000001 0 0.893576362809 ["Character/Dirichlet/5600/909"] "1-5600-5600.923-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.923" [[1, 0.0]] [] 0 true true false false -0.37375 0 1.05140819508 ["Character/Dirichlet/5600/923"] "1-5600-5600.933-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.933" [[1, 0.0]] [] 0 true true false false -0.04033019013969361 0 0.506178227162 ["Character/Dirichlet/5600/933"] "1-5600-5600.941-r1-0-0" 601.8035788499001 601.8035788499001 1 5600 "5600.941" [[1, 0.0]] [] 0 true true false false 0.14392295305394615 0 0.374807285318 ["Character/Dirichlet/5600/941"] # 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).