l1, l2, and integral data for the 8 phat 4 extra dirichelt
[0, 1, 0, 0, 1, 2, 2, 1, 2]:L1=2.1655131614201146270 	L2=110.78630811200597860   	integral=1.0005459307857768978 
[0, 0, 0, 1, 0, 2, 1, 0, 2]:L1=2.0083400266430335926 	L2=108.58505006464987368   	integral=1.0375372461854649348 
[1, 2, 2, 2, 2, 2, 1, 0, 2]:L1=2.4627967877590480015 	L2=147.14896349121599468   	integral=.99998631313552291955
[2, 2, 0, 0, 1, 2, 0, 1]:L1=2.3892939128106120447 	L2=119.07800498194408216   	integral=.99827342165293964223
[2, 2, 0, 1, 2, 2, 1, 2]:L1=2.6393425553796261769 	L2=129.64861867611064945   	integral=1.0046746346322437887 
[1, 1, 2, 2, 0, 0, 2, 1, 2]:L1=2.5881803203212920424 	L2=126.61946943085610962   	integral=.99730549530592605365
[1, 2, 2, 1, 1, 0, 2, 1, 2]:L1=2.1740096319762050086 	L2=122.47094333966350253   	integral=.99996893329915101662
[1, 1, 2, 2, 1, 2, 0, 1]:L1=2.2641284691191517519 	L2=113.16393601485843485   	integral=1.0022863797902423323 
[1, 2, 2, 2, 2, 1, 1, 0, 1]:L1=2.2614449884389863479 	L2=107.20988624124673395   	integral=.99999859909786662729
[1, 1, 1, 1, 2, 2, 0, 1, 2]:L1=2.3115979315747042053 	L2=123.34379687445285854   	integral=1.1131560000986709498 
[2, 2, 1, 0, 2, 2, 1, 0, 2]:L1=2.6353432521510790464 	L2=130.76829251255802501   	integral=1.0043385080670759312 
[1, 1, 0, 2, 0, 1, 1, 1, 2]:L1=2.1517275710702405058 	L2=110.46201078292741103   	integral=.99972749404694099716
[2, 0, 1, 1, 1, 2, 1, 2]:L1=2.2692077649045290454 	L2=116.81731837370539197   	integral=.99999488172037599888
[2, 0, 0, 2, 2, 0, 2, 0, 1]:L1=2.2231775863394387851 	L2=124.77350747869866897   	integral=.99996462864050122187
[1, 0, 0, 1, 1, 2, 0, 1]:L1=2.2321029360167729086 	L2=124.71306807921715522   	integral=.99996585360018566248
[0, 2, 0, 1, 1, 2, 0, 1]:L1=2.2289608055234591891 	L2=124.71320204691597265   	integral=.99986496719897607286
[1, 2, 1, 2, 2, 1, 2, 0, 2]:L1=2.2317723074099436936 	L2=128.46334892890799152   	integral=.99994640474564289679
[1, 2, 2, 1, 0, 1, 1, 2]:L1=2.2301547640608489422 	L2=106.54069969178954522   	integral=1.0000190604334814446 
[1, 2, 1, 2, 1, 0, 0, 0, 1]:L1=2.1633242211722893167 	L2=110.76400960042457471   	integral=1.0000853833139323945 
[1, 0, 0, 2, 0, 1, 1, 1, 2]:L1=2.1557446247123708896 	L2=110.46137924667177623   	integral=.99999859909786662788
[0, 0, 1, 1, 0, 2, 1, 0, 2]:L1=2.3072072121350800682 	L2=116.49973066009101252   	integral=1.0018617527947214287 
[1, 1, 0, 2, 1, 0, 0, 2]:L1=2.2122233857768684859 	L2=113.86751025964541869   	integral=1.0021176805535422054 
[2, 1, 0, 0, 0, 0, 1, 1, 2]:L1=2.4300930907662217751 	L2=144.38233732530458980   	integral=.99998506924504084266
[1, 2, 0, 2, 2, 1, 2]:L1=2.3367750151876604592 	L2=135.57188711650316050   	integral=.99998924121951079089
[0, 0, 1, 0, 2, 1, 0, 2]:L1=2.3565063278465999574 	L2=119.35112585214488290   	integral=1.0066779855909377382 
[0, 2, 1, 2, 2, 0, 0, 2]:L1=2.2344364781097310132 	L2=116.75542067346558349   	integral=.99999488172037599893
[0, 2, 2, 0, 2, 2, 0, 1, 2]:L1=2.6856392060996252693 	L2=128.80384396834889727   	integral=1.0000361834302616316 
[1, 1, 2, 2, 1, 0, 0, 0, 2]:L1=2.1357797522682604615 	L2=110.45088859654408751   	integral=1.0010357780235481568 
[2, 2, 0, 2, 2, 2, 0, 1]:L1=2.2923596619901180972 	L2=146.13746844209884205   	integral=.9884736560289676578 
[1, 0, 2, 2, 2, 1, 0, 1]:L1=2.2231638009082559922 	L2=114.79553991860293668   	integral=.99999488172037599947
[2, 0, 2, 2, 1, 1, 2, 0, 2]:L1=2.6180157624853780219 	L2=126.71264351702523155   	integral=1.0004341142463753696 
[0, 1, 1, 2, 2, 0, 1, 0, 2]:L1=2.1903019236289851919 	L2=121.04692997293541225   	integral=.99999242843148461198
[1, 2, 2, 2, 0, 1, 1, 0, 1]:L1=2.1733832627353244634 	L2=110.79010756203015172   	integral=.99999859909786662732
[0, 0, 1, 2, 0, 0, 0, 1]:L1=2.6488293845816650127 	L2=130.77370361799484539   	integral=1.0046634370881544010 
[0, 0, 0, 1, 2, 1, 1, 2]:L1=1.9661880657073011950 	L2=101.09908958302527622   	integral=.95993696573357163141
[0, 1, 1, 1, 0, 2, 2, 0, 1]:L1=2.2418159674357125773 	L2=112.89441118896768638   	integral=1.0000116851362540465 
[1, 0, 0, 0, 2, 1, 0, 1]:L1=2.2725068588363961320 	L2=113.66291933670029871   	integral=.999994881720376     
[2, 2, 2, 0, 2, 0, 0, 1]:L1=1.8952817575540485810 	L2=97.584194700401670622  	integral=1.0369040844760068998 
[2, 1, 0, 0, 0, 0, 2, 0, 2]:L1=2.4322050705641557740 	L2=144.50565650986374037   	integral=.99998700840679577097
[0, 0, 1, 2, 0, 0, 1, 1, 2]:L1=2.6058379790369121374 	L2=129.51729186188655148   	integral=1.0041233992339136574 
[0, 2, 1, 1, 1, 1, 1, 0, 1]:L1=2.4538333361913012218 	L2=149.68631568224236136   	integral=.99998506924504084235
[0, 1, 0, 0, 0, 2, 0, 1]:L1=2.2344496611079117109 	L2=124.71848861883247133   	integral=.99955978910765218709
[1, 2, 1, 0, 0, 0, 0, 0, 1]:L1=2.4099011992169925808 	L2=149.84661167910224387   	integral=.99990511130547279838
[1, 1, 1, 1, 0, 0, 0, 1, 2]:L1=2.3441202608312044351 	L2=120.90096446619775159   	integral=1.1055284926313414327 
[1, 2, 2, 2, 1, 1, 1, 2]:L1=2.6928407977599631921 	L2=129.14888230273318289   	integral=1.0000279675634881417 
[1, 2, 0, 0, 2, 2, 1, 2]:L1=2.7045733973208043149 	L2=130.26248286888096768   	integral=.99998578061776651992
[2, 2, 0, 2, 2, 1, 0, 0, 2]:L1=2.0729271539530000430 	L2=121.95994412547414746   	integral=.99386139928951463027
[1, 1, 0, 1, 1, 0, 1, 2]:L1=2.0902197205788184589 	L2=124.35571554583810838   	integral=.99322732237884666108
[1, 0, 1, 1, 0, 0, 2, 0, 2]:L1=2.6595131776884836196 	L2=129.03073911967405460   	integral=1.0004956584398323050 
[0, 1, 2, 0, 0, 1, 0, 0, 2]:L1=2.2762935586150784106 	L2=128.22914452726271310   	integral=.99996054488263437248