l1, l2, and integral data for the 8 phat 4 extra dirichelt
[0, 1, 0, 0, 1, 2, 2, 1, 2]:L1=2.1655131614201146037 	L2=110.78630811200598329   	integral=1.0005459307857768983 
[0, 0, 0, 1, 0, 2, 1, 0, 2]:L1=2.0083400266430330652 	L2=108.58505006464986765   	integral=1.0375372461854649345 
[1, 2, 2, 2, 2, 2, 1, 0, 2]:L1=2.4627967877590480763 	L2=147.14896349121599819   	integral=.99998631313552291912
[2, 2, 0, 0, 1, 2, 0, 1]:L1=2.3892939128106120745 	L2=119.07800498194408406   	integral=.99827342165293964221
[2, 2, 0, 1, 2, 2, 1, 2]:L1=2.6393425553796261607 	L2=129.64861867611065053   	integral=1.0046746346322437895 
[1, 1, 2, 2, 0, 0, 2, 1, 2]:L1=2.5881803203212927366 	L2=126.61946943085610702   	integral=.99730549530592605406
[1, 2, 2, 1, 1, 0, 2, 1, 2]:L1=2.1740096319762052376 	L2=122.47094333966350528   	integral=.99996893329915101656
[1, 1, 2, 2, 1, 2, 0, 1]:L1=2.2641284691191521872 	L2=113.16393601485843605   	integral=1.0022863797902423321 
[1, 2, 2, 2, 2, 1, 1, 0, 1]:L1=2.2614449884389863920 	L2=107.20988624124673635   	integral=.99999859909786662699
[1, 1, 1, 1, 2, 2, 0, 1, 2]:L1=2.3115979315747039588 	L2=123.34379687445285113   	integral=1.1131560000986709501 
[2, 2, 1, 0, 2, 2, 1, 0, 2]:L1=2.6353432521510788404 	L2=130.76829251255802487   	integral=1.0043385080670759312 
[1, 1, 0, 2, 0, 1, 1, 1, 2]:L1=2.1517275710702407069 	L2=110.46201078292740800   	integral=.99972749404694099695
[2, 0, 1, 1, 1, 2, 1, 2]:L1=2.2692077649045288139 	L2=116.81731837370539189   	integral=.99999488172037599886
[2, 0, 0, 2, 2, 0, 2, 0, 1]:L1=2.2231775863394393596 	L2=124.77350747869867022   	integral=.99996462864050122212
[1, 0, 0, 1, 1, 2, 0, 1]:L1=2.2321029360167725641 	L2=124.71306807921715444   	integral=.99996585360018566177
[0, 2, 0, 1, 1, 2, 0, 1]:L1=2.2289608055234589989 	L2=124.71320204691596990   	integral=.99986496719897607212
[1, 2, 1, 2, 2, 1, 2, 0, 2]:L1=2.2317723074099436782 	L2=128.46334892890798978   	integral=.99994640474564289682
[1, 2, 2, 1, 0, 1, 1, 2]:L1=2.2301547640608486976 	L2=106.54069969178953836   	integral=1.0000190604334814447 
[1, 2, 1, 2, 1, 0, 0, 0, 1]:L1=2.1633242211722894007 	L2=110.76400960042457455   	integral=1.0000853833139323944 
[1, 0, 0, 2, 0, 1, 1, 1, 2]:L1=2.1557446247123707969 	L2=110.46137924667177550   	integral=.99999859909786662762
[0, 0, 1, 1, 0, 2, 1, 0, 2]:L1=2.3072072121350801345 	L2=116.49973066009101646   	integral=1.0018617527947214286 
[1, 1, 0, 2, 1, 0, 0, 2]:L1=2.2122233857768685769 	L2=113.86751025964542076   	integral=1.0021176805535422055 
[2, 1, 0, 0, 0, 0, 1, 1, 2]:L1=2.4300930907662214521 	L2=144.38233732530459158   	integral=.99998506924504084256
[1, 2, 0, 2, 2, 1, 2]:L1=2.3367750151876605483 	L2=135.57188711650315622   	integral=.99998924121951079073
[0, 0, 1, 0, 2, 1, 0, 2]:L1=2.3565063278466004220 	L2=119.35112585214488738   	integral=1.0066779855909377388 
[0, 2, 1, 2, 2, 0, 0, 2]:L1=2.2344364781097308726 	L2=116.75542067346558433   	integral=.99999488172037599916
[0, 2, 2, 0, 2, 2, 0, 1, 2]:L1=2.6856392060996243497 	L2=128.80384396834888360   	integral=1.0000361834302616315 
[1, 1, 2, 2, 1, 0, 0, 0, 2]:L1=2.1357797522682605967 	L2=110.45088859654408852   	integral=1.0010357780235481566 
[2, 2, 0, 2, 2, 2, 0, 1]:L1=2.2923596619901179068 	L2=146.13746844209884153   	integral=.98847365602896765747
[1, 0, 2, 2, 2, 1, 0, 1]:L1=2.2231638009082561624 	L2=114.79553991860293559   	integral=.99999488172037599939
[2, 0, 2, 2, 1, 1, 2, 0, 2]:L1=2.6180157624853772339 	L2=126.71264351702523284   	integral=1.0004341142463753697 
[0, 1, 1, 2, 2, 0, 1, 0, 2]:L1=2.1903019236289850745 	L2=121.04692997293541369   	integral=.9999924284314846121 
[1, 2, 2, 2, 0, 1, 1, 0, 1]:L1=2.1733832627353244622 	L2=110.79010756203015368   	integral=.99999859909786662755
[0, 0, 1, 2, 0, 0, 0, 1]:L1=2.6488293845816655683 	L2=130.77370361799485557   	integral=1.0046634370881544006 
[0, 0, 0, 1, 2, 1, 1, 2]:L1=1.9661880657073011989 	L2=101.09908958302527900   	integral=.9599369657335716311 
[0, 1, 1, 1, 0, 2, 2, 0, 1]:L1=2.2418159674357122664 	L2=112.89441118896767837   	integral=1.0000116851362540454 
[1, 0, 0, 0, 2, 1, 0, 1]:L1=2.2725068588363962883 	L2=113.66291933670029927   	integral=.99999488172037599949
[2, 2, 2, 0, 2, 0, 0, 1]:L1=1.8952817575540487870 	L2=97.584194700401670553  	integral=1.0369040844760068995 
[2, 1, 0, 0, 0, 0, 2, 0, 2]:L1=2.4322050705641554320 	L2=144.50565650986373891   	integral=.99998700840679577102
[0, 0, 1, 2, 0, 0, 1, 1, 2]:L1=2.6058379790369126538 	L2=129.51729186188656060   	integral=1.0041233992339136572 
[0, 2, 1, 1, 1, 1, 1, 0, 1]:L1=2.4538333361913004422 	L2=149.68631568224235946   	integral=.99998506924504084273
[0, 1, 0, 0, 0, 2, 0, 1]:L1=2.2344496611079114724 	L2=124.71848861883247439   	integral=.99955978910765218691
[1, 2, 1, 0, 0, 0, 0, 0, 1]:L1=2.4099011992169929833 	L2=149.84661167910224621   	integral=.9999051113054727996 
[1, 1, 1, 1, 0, 0, 0, 1, 2]:L1=2.3441202608312041710 	L2=120.90096446619774308   	integral=1.1055284926313414322 
[1, 2, 2, 2, 1, 1, 1, 2]:L1=2.6928407977599633907 	L2=129.14888230273319828   	integral=1.0000279675634881419 
[1, 2, 0, 0, 2, 2, 1, 2]:L1=2.7045733973208046078 	L2=130.26248286888095674   	integral=.9999857806177665201 
[2, 2, 0, 2, 2, 1, 0, 0, 2]:L1=2.0729271539529999335 	L2=121.95994412547414691   	integral=.99386139928951463123
[1, 1, 0, 1, 1, 0, 1, 2]:L1=2.0902197205788185365 	L2=124.35571554583810938   	integral=.99322732237884666062
[1, 0, 1, 1, 0, 0, 2, 0, 2]:L1=2.6595131776884831212 	L2=129.03073911967406262   	integral=1.0004956584398323051 
[0, 1, 2, 0, 0, 1, 0, 0, 2]:L1=2.2762935586150776424 	L2=128.22914452726270756   	integral=.99996054488263437187
average:L1=2.3196677169144320528 	L2=122.79747607137278021   	integral=1.0051277916841691154 
minL1=1.8952817575540487870 	maxL1=2.7045733973208046078