l1, l2, and integral data for the 8 phat 5 extra dirichelt
[0, 1, 0, 0, 1, 2, 0, 0, 1]:L1=2.2528693065903716341 	L2=341.92162993510951928   	integral=.99999909267335338945
[2, 1, 2, 0, 2, 1, 0, 2]:L1=2.2910441815529464094 	L2=341.57845112644033618   	integral=1.0000002680962579342 
[2, 1, 1, 2, 2, 0, 1, 1, 2]:L1=2.2668569071879258037 	L2=341.00375708117849147   	integral=1.0000000304345866894 
[2, 1, 0, 0, 1, 0, 0, 1]:L1=2.5119195117273380268 	L2=360.09653943616847691   	integral=.99999999900180764528
[0, 1, 1, 1, 0, 0, 2]:L1=2.2426938166450687397 	L2=299.51150497495713179   	integral=.99999999985052522347
[2, 2, 1, 0, 2, 0, 0, 1]:L1=2.5703944187573768247 	L2=374.23884583686308617   	integral=1.0000414580272347630 
[1, 1, 2, 1, 1, 2, 0, 1, 2]:L1=2.4032322532181257803 	L2=357.32374991607289742   	integral=1.0005128599591099109 
[2, 2, 0, 2, 0, 1, 1, 2]:L1=2.5657055867466061566 	L2=376.13332548508140873   	integral=.9998029084851262018 
[0, 1, 1, 1, 1, 0, 2, 1, 2]:L1=2.2703673794334347939 	L2=341.00241794585753313   	integral=1.0000000008153259341 
[1, 1, 2, 2, 1, 0, 2, 0, 1]:L1=2.4034982892788016376 	L2=358.63482631704370851   	integral=1.0000422289660242114 
[2, 1, 0, 0, 1, 0, 1, 2]:L1=2.3011791525300595484 	L2=340.58467142264237665   	integral=.99999999928590195666
[0, 2, 2, 2, 1, 2, 1, 0, 2]:L1=2.3466725772157175279 	L2=340.28465690850674125   	integral=.99999999905995421361
[2, 0, 2, 1, 0, 1, 1, 2]:L1=2.5713500479370239267 	L2=374.23902096450117927   	integral=.99999989791152621092
[2, 0, 2, 0, 2, 0, 2]:L1=2.2524920083299610537 	L2=300.32053195911900460   	integral=.99999997472223517249
[1, 1, 0, 2, 1, 1, 2]:L1=2.2516350196936435686 	L2=300.32046018829113684   	integral=.99999609500229833537
[0, 0, 0, 0, 2, 0, 0, 2]:L1=2.0545321473544498142 	L2=315.44702226932852108   	integral=1.0602551332352435154 
[1, 2, 1, 0, 2, 0, 0, 0, 1]:L1=2.7090077113642221564 	L2=390.85174021407049312   	integral=.99999986576323305017
[1, 0, 1, 2, 0, 2, 0, 2]:L1=2.5089048305818381583 	L2=360.09806091211254758   	integral=.99999986350475816771
[0, 0, 0, 2, 2, 2, 2, 1, 2]:L1=2.4538184745192536355 	L2=445.45405595574349185   	integral=.99862935354847949304
[2, 1, 2, 0, 0, 0, 1, 0, 2]:L1=2.2469478177149676406 	L2=374.20083799920771244   	integral=.99999991012169816799
[0, 0, 1, 2, 2, 0, 0, 1, 2]:L1=2.6724450767359013573 	L2=388.65566246903483659   	integral=1.0000256028503885239 
[1, 2, 0, 0, 0, 2, 2, 0, 2]:L1=2.6927106650251142633 	L2=387.47172730982052675   	integral=.99999999900180764467
[2, 0, 0, 1, 1, 2, 0, 2]:L1=2.5698266493138451918 	L2=374.31438380211460756   	integral=1.0000000013873786925 
[1, 0, 1, 1, 0, 2, 0, 1]:L1=2.2933470059619969711 	L2=341.57972338762667584   	integral=.9999986166784272379 
[0, 2, 0, 0, 0, 0, 0, 2]:L1=2.3449375024521494084 	L2=406.65760331114732340   	integral=.99999582194702858317
[2, 1, 2, 1, 1, 0, 2, 0, 1]:L1=2.4079359174558069399 	L2=357.33583488634169441   	integral=.99999990372561130519
[2, 1, 2, 1, 2, 2, 0, 0, 1]:L1=2.1878741779056097173 	L2=344.24674870115094175   	integral=.99999982940699951814
[0, 0, 0, 1, 2, 1, 0, 0, 2]:L1=2.2515921017003019594 	L2=340.87551661032121801   	integral=.99911031643604890619
[0, 2, 2, 1, 2, 2, 2, 0, 2]:L1=2.4359433255734528011 	L2=445.88433508804283547   	integral=.99999999905995421316
[2, 2, 1, 0, 2, 0, 2, 0, 2]:L1=2.2667708499992254898 	L2=321.98168842356410893   	integral=1.0000187069024968940 
[1, 1, 0, 1, 0, 2, 0, 0, 2]:L1=2.2584771044021354177 	L2=322.21080286333884698   	integral=.99977860023868617825
[2, 2, 2, 0, 1, 2, 0, 2]:L1=2.5135334945140252682 	L2=375.48574111165980257   	integral=1.0035937668585595224 
[2, 0, 0, 0, 1, 0, 2]:L1=2.0813571515819145073 	L2=322.76725556424261662   	integral=1.0000000002636556697 
[1, 1, 1, 0, 2, 0, 2, 1, 2]:L1=2.1904162201716599162 	L2=319.17813126453100127   	integral=.99769747037957711492
[0, 0, 0, 1, 2, 2, 0, 0, 1]:L1=2.1834988086904689459 	L2=344.24907420640945687   	integral=.99944968922724020117
[1, 1, 1, 0, 0, 0, 2, 0, 1]:L1=2.2316287841762314366 	L2=374.14465840541036991   	integral=.99832210990618341864
[2, 2, 1, 1, 0, 0, 1]:L1=2.2538764405650099683 	L2=300.32125002257415879   	integral=.99998436142313867063
[0, 1, 0, 1, 2, 0, 2, 0, 2]:L1=2.2656759048274123196 	L2=322.21662952509520452   	integral=1.0000001215248889039 
[2, 0, 0, 1, 1, 1, 0, 0, 2]:L1=2.2195034149297183080 	L2=344.40278119038618249   	integral=.99999999905995421341
[1, 1, 0, 1, 1, 0, 0, 0, 1]:L1=2.6830024769437335546 	L2=387.46003012132920086   	integral=1.0004464755675897554 
[0, 0, 0, 2, 2, 0, 1, 1, 2]:L1=2.2355442498352342187 	L2=340.81355180190020975   	integral=1.0015277186169949641 
[0, 2, 1, 2, 1, 2, 0, 1, 2]:L1=2.4089289760303227991 	L2=357.24950930882945453   	integral=.99999999945370313037
[0, 2, 2, 0, 2, 1, 0, 1, 2]:L1=2.4026230998229956933 	L2=358.63377045036432066   	integral=.99999999002193545527
[0, 0, 0, 1, 1, 0, 0, 0, 2]:L1=2.6505154970029396594 	L2=390.22665627295147777   	integral=1.0039980284947195561 
[0, 0, 1, 1, 1, 1, 2, 0, 2]:L1=2.2224404337628266230 	L2=344.40161706894902291   	integral=.99998782261761500452
[2, 1, 2, 1, 0, 1, 1, 2]:L1=2.5713542355674318521 	L2=374.23902096890021320   	integral=.99999989791152621176
[0, 1, 2, 1, 2, 2, 2, 0, 1]:L1=2.4240913071459620025 	L2=441.21570721459115206   	integral=.99999999905995421371
[2, 2, 1, 0, 1, 0, 1]:L1=2.2520107209119213851 	L2=300.32048792789758413   	integral=.99998491100265095367
[1, 1, 1, 0, 2, 1, 1, 0, 1]:L1=2.6466311859233912244 	L2=392.34680167741089709   	integral=1.0046635704984699421 
[0, 1, 2, 2, 0, 0, 2]:L1=2.2544273687090499911 	L2=300.32130490527273663   	integral=.99999999985052522306
average:L1=2.3709608317203384404 	L2=355.08908225419008950   	integral=1.0013572453567678002 
minL1=2.0545321473544498142 	maxL1=2.7090077113642221564