/* Some constants and matrices that we'll need.
    */

static const double xi[33] = {
  -1., -0.99518472667219688624, -0.98078528040323044912,
  -0.95694033573220886493, -0.92387953251128675612,
  -0.88192126434835502970, -0.83146961230254523708,
  -0.77301045336273696082, -0.70710678118654752440,
  -0.63439328416364549822, -0.55557023301960222475,
  -0.47139673682599764857, -0.38268343236508977173,
  -0.29028467725446236764, -0.19509032201612826785,
  -0.098017140329560601995, 0., 0.098017140329560601995,
  0.19509032201612826785, 0.29028467725446236764, 0.38268343236508977173,
  0.47139673682599764857, 0.55557023301960222475, 0.63439328416364549822,
  0.70710678118654752440, 0.77301045336273696082, 0.83146961230254523708,
  0.88192126434835502970, 0.92387953251128675612, 0.95694033573220886493,
  0.98078528040323044912, 0.99518472667219688624, 1.
};

static const double bee[68] = {
  0.00000000000000e+00, 2.28868854108532e-01, 0.00000000000000e+00,
  -8.15740215243451e-01, 0.00000000000000e+00, 5.31212715259731e-01,
  0.00000000000000e+00, 1.38538036812454e-02, 0.00000000000000e+00,
  3.74405228908818e-02, 0.00000000000000e+00, 2.12224115039342e-01,
  0.00000000000000e+00, -8.16362644507898e-01, 0.00000000000000e+00,
  5.35648426691481e-01, 0.00000000000000e+00, 1.52417902753662e-03,
  0.00000000000000e+00, 2.63058840550873e-03, 0.00000000000000e+00,
  4.15292106318904e-03, 0.00000000000000e+00, 6.97106011119775e-03,
  0.00000000000000e+00, 1.35535708431058e-02, 0.00000000000000e+00,
  3.52132898424856e-02, 0.00000000000000e+00, 2.06946714741884e-01,
  0.00000000000000e+00, -8.15674251283876e-01, 0.00000000000000e+00,
  5.38841175520580e-01, 0.00000000000000e+00, 1.84909689577590e-04,
  0.00000000000000e+00, 2.90936325007499e-04, 0.00000000000000e+00,
  3.84877750950089e-04, 0.00000000000000e+00, 4.86436656735046e-04,
  0.00000000000000e+00, 6.08688640346879e-04, 0.00000000000000e+00,
  7.66732830740331e-04, 0.00000000000000e+00, 9.82753336104205e-04,
  0.00000000000000e+00, 1.29359957505615e-03, 0.00000000000000e+00,
  1.76616363801885e-03, 0.00000000000000e+00, 2.53323433039089e-03,
  0.00000000000000e+00, 3.88872172121956e-03, 0.00000000000000e+00,
  6.58635106468291e-03, 0.00000000000000e+00, 1.30326736343254e-02,
  0.00000000000000e+00, 3.44353850696714e-02, 0.00000000000000e+00,
  2.05025409531915e-01, 0.00000000000000e+00, -8.14985893995401e-01,
  0.00000000000000e+00, 5.40679930965238e-01
};

static const double Lalpha[33] = {
  5.77350269189626e-01, 5.16397779494322e-01, 5.07092552837110e-01,
  5.03952630678970e-01, 5.02518907629606e-01, 5.01745206004255e-01,
  5.01280411827603e-01, 5.00979432868120e-01, 5.00773395667191e-01,
  5.00626174321759e-01, 5.00517330712619e-01, 5.00434593736979e-01,
  5.00370233297676e-01, 5.00319182924304e-01, 5.00278009473803e-01,
  5.00244319584578e-01, 5.00216403386025e-01, 5.00193012939056e-01,
  5.00173220168024e-01, 5.00156323280355e-01, 5.00141783641018e-01,
  5.00129182278347e-01, 5.00118189340972e-01, 5.00108542278496e-01,
  5.00100030010004e-01, 5.00092481273333e-01, 5.00085755939229e-01,
  5.00079738458365e-01, 5.00074332862969e-01, 5.00069458915387e-01,
  5.00065049112355e-01, 5.00061046334395e-01, 5.00057401986298e-01
};

static const double Lgamma[33] = {
  0.0, 0.0, 5.16397779494322e-01, 5.07092552837110e-01, 5.03952630678970e-01,
  5.02518907629606e-01, 5.01745206004255e-01, 5.01280411827603e-01,
  5.00979432868120e-01, 5.00773395667191e-01, 5.00626174321759e-01,
  5.00517330712619e-01, 5.00434593736979e-01, 5.00370233297676e-01,
  5.00319182924304e-01, 5.00278009473803e-01, 5.00244319584578e-01,
  5.00216403386025e-01, 5.00193012939056e-01, 5.00173220168024e-01,
  5.00156323280355e-01, 5.00141783641018e-01, 5.00129182278347e-01,
  5.00118189340972e-01, 5.00108542278496e-01, 5.00100030010003e-01,
  5.00092481273333e-01, 5.00085755939229e-01, 5.00079738458365e-01,
  5.00074332862969e-01, 5.00069458915387e-01, 5.00065049112355e-01,
  5.00061046334395e-01
};

static const double V1inv[5 * 5] = {
  .47140452079103168293e-1, .37712361663282534635, .56568542494923801952,
  .37712361663282534635, .47140452079103168293e-1,
  -.81649658092772603273e-1, -.46188021535170061160, 0,
  .46188021535170061160, .81649658092772603273e-1, .15058465048420853962,
  .12046772038736683169, -.54210474174315074262, .12046772038736683169,
  .15058465048420853962, -.21380899352993950775, .30237157840738178177, -0.,
  -.30237157840738178177, .21380899352993950775, .10774960475223581324,
  -.21549920950447162648, .21549920950447162648, -.21549920950447162648,
  .10774960475223581324
};

static const double V2inv[9 * 9] = {
  .11223917161691230546e-1, .10339219839658349826, .19754094204576565761,
  .25577315077753587922, .27835314560994251755, .25577315077753587922,
  .19754094204576565761, .10339219839658349826, .11223917161691230546e-1,
  -.19440394783993476970e-1, -.16544884625069155470, -.24193725566041460608,
  -.16953338808305493604, 0.0, .16953338808305493604, .24193725566041460608,
  .16544884625069155470, .19440394783993476970e-1, .26466393115406349388e-1,
  .17766815796285469394, .11316664642449611462, -.16306601003711325980,
  -.30847037493128779631, -.16306601003711325980, .11316664642449611462,
  .17766815796285469394, .26466393115406349388e-1,
  -.32395302049990834508e-1, -.15521142532414866547,
  .88573492664788602740e-1, .29570405784974857322, 0.0,
  -.29570405784974857322, -.88573492664788602740e-1, .15521142532414866547,
  .32395302049990834508e-1, .41442155673936851246e-1,
  .98186757907405608245e-1, -.23056908429499411784,
  -.68047008326360625520e-1, .31797435808002456774,
  -.68047008326360625520e-1, -.23056908429499411784,
  .98186757907405608245e-1, .41442155673936851246e-1,
  -.49981120317798783134e-1, -.24861810572835756217e-1,
  .23561326072010832539, -.24472785656448415351, 0.0, .24472785656448415351,
  -.23561326072010832539, .24861810572835756217e-1,
  .49981120317798783134e-1, .79691635865674781228e-1,
  -.95725617891693941833e-1, -.57957553356854386344e-1,
  .21164072460540271452, -.27529837844505833514, .21164072460540271452,
  -.57957553356854386344e-1, -.95725617891693941833e-1,
  .79691635865674781228e-1,
  -.10894869830716590913, .20131094491947531782, -.15407672674888869038,
  .83385723639789791384e-1, 0.0, -.83385723639789791384e-1,
  .15407672674888869038, -.20131094491947531782, .10894869830716590913,
  .54581057089643838221e-1, -.10916211417928767644, .10916211417928767644,
  -.10916211417928767644, .10916211417928767644, -.10916211417928767644,
  .10916211417928767644, -.10916211417928767644, .54581057089643838221e-1
};

static const double V3inv[17 * 17] = {
  .27729677693590098996e-2, .26423663180333065153e-1,
  .53374068493933898312e-1, .77007854739523195947e-1,
  .98257061072911596869e-1, .11538049741786835604, .12832134344120884559,
  .13612785914022865001, .13888293186236181317, .13612785914022865001,
  .12832134344120884559, .11538049741786835604, .98257061072911596869e-1,
  .77007854739523195947e-1, .53374068493933898312e-1,
  .26423663180333065153e-1, .27729677693590098996e-2,
  -.48029210642807413690e-2, -.44887724635478800254e-1,
  -.85409520147301089416e-1, -.11090267822061423050, -.12033983162705862441,
  -.11102786862182788886, -.85054870109799336515e-1,
  -.45998467987742225160e-1, 0.0, .45998467987742225160e-1,
  .85054870109799336515e-1, .11102786862182788886, .12033983162705862441,
  .11090267822061423050, .85409520147301089416e-1, .44887724635478800254e-1,
  .48029210642807413690e-2, .62758546879582030087e-2,
  .55561297093529155869e-1,
  .93281491021051539742e-1, .92320151237493695139e-1,
  .55077987469605684531e-1,
  -.96998141716497488255e-2, -.80285961895427405567e-1,
  -.13496839655913850224,
  -.15512521776684524331, -.13496839655913850224, -.80285961895427405567e-1,
  -.96998141716497488255e-2, .55077987469605684531e-1,
  .92320151237493695139e-1, .93281491021051539742e-1,
  .55561297093529155869e-1, .62758546879582030087e-2,
  -.74850969394858555939e-2, -.61751608943839234096e-1,
  -.82974150437304275958e-1, -.38437763431942633378e-1,
  .45745502025779701366e-1, .12369235652734542162, .14720439712852868239,
  .98768034347019704401e-1, 0.0,
  -.98768034347019704401e-1, -.14720439712852868239, -.12369235652734542162,
  -.45745502025779701366e-1, .38437763431942633378e-1,
  .82974150437304275958e-1, .61751608943839234096e-1,
  .74850969394858555939e-2, .86710099994384056338e-2,
  .64006230103659573344e-1, .58517426396091675690e-1,
  -.29743410528985802680e-1,
  -.11934127779157114754, -.12686773515361299409, -.30729137153877447035e-1,
  .97307836256600731568e-1, .15635811574451401023, .97307836256600731568e-1,
  -.30729137153877447035e-1, -.12686773515361299409, -.11934127779157114754,
  -.29743410528985802680e-1, .58517426396091675690e-1,
  .64006230103659573344e-1, .86710099994384056338e-2,
  -.97486395666294840165e-2, -.62995604908060224672e-1,
  -.24373234450275529219e-1, .87760984413626872730e-1,
  .12205204576993351394,
  .16216004196864002088e-1, -.12422320942156845775, -.13682714580929614678,
  0.0, .13682714580929614678, .12422320942156845775,
  -.16216004196864002088e-1, -.12205204576993351394,
  -.87760984413626872730e-1, .24373234450275529219e-1,
  .62995604908060224672e-1, .97486395666294840165e-2,
  .10956271233750488468e-1, .58613204255294358939e-1,
  -.13306063940736618859e-1, -.11606666444978454399,
  -.52059598001115805639e-1, .10868540217796151849, .12594452879014618005,
  -.44678658254872910434e-1, -.15617684362128533405,
  -.44678658254872910434e-1, .12594452879014618005, .10868540217796151849,
  -.52059598001115805639e-1, -.11606666444978454399,
  -.13306063940736618859e-1, .58613204255294358939e-1,
  .10956271233750488468e-1, -.12098893000863087230e-1,
  -.51626244709126208453e-1, .48919433304746979330e-1,
  .10467644465949427090,
  -.48729879523084673782e-1, -.13668732103524749234, .28190838706814496438e-1,
  .15434223333238741600, 0.0, -.15434223333238741600,
  -.28190838706814496438e-1, .13668732103524749234,
  .48729879523084673782e-1, -.10467644465949427090,
  -.48919433304746979330e-1, .51626244709126208453e-1,
  .12098893000863087230e-1, .13542668300437944822e-1,
  .41712033418258689308e-1,
  -.76190463272803434388e-1, -.58303943170068132010e-1, .12158068748245606853,
  .42121099930651007882e-1, -.14684425840766337756,
  -.16108203535058647043e-1, .15698075850757976092,
  -.16108203535058647043e-1, -.14684425840766337756,
  .42121099930651007882e-1, .12158068748245606853,
  -.58303943170068132010e-1, -.76190463272803434388e-1,
  .41712033418258689308e-1, .13542668300437944822e-1,
  -.14939634995117694417e-1, -.30047246373341564039e-1,
  .91624635082546425678e-1, -.79133374319110026377e-2,
  -.12292558212072233355, .90013382617762643524e-1,
  .84013717196539593395e-1, -.14813033309980695856, 0.0,
  .14813033309980695856, -.84013717196539593395e-1,
  -.90013382617762643524e-1,
  .12292558212072233355, .79133374319110026377e-2, -.91624635082546425678e-1,
  .30047246373341564039e-1, .14939634995117694417e-1,
  .16986031342807474208e-1,
  .15760203882617033601e-1, -.91494054040950941996e-1,
  .70082459207876130806e-1,
  .53390713710144539104e-1, -.14340746778352039430, .84048122493418898508e-1,
  .72456667788091316868e-1, -.15564535320096811360,
  .72456667788091316868e-1, .84048122493418898508e-1,
  -.14340746778352039430, .53390713710144539104e-1,
  .70082459207876130806e-1, -.91494054040950941996e-1,
  .15760203882617033601e-1,
  .16986031342807474208e-1, -.18994065631858742028e-1,
  -.82901821370405592927e-3, .77239669773015192888e-1,
  -.10850735431039424680, .47524484622086496464e-1,
  .69148184871588737021e-1, -.14829314646228194928, .11992057742398672066,
  0.0, -.11992057742398672066, .14829314646228194928,
  -.69148184871588737021e-1, -.47524484622086496464e-1,
  .10850735431039424680, -.77239669773015192888e-1,
  .82901821370405592927e-3, .18994065631858742028e-1,
  .22761703826371535132e-1, -.17728848711449643358e-1,
  -.47496371572480503788e-1, .10659958402328690063, -.11696013966166296514,
  .63073750910894244526e-1, .32928881123602721303e-1,
  -.12280950532497593683, .15926189077282729505, -.12280950532497593683,
  .32928881123602721303e-1, .63073750910894244526e-1,
  -.11696013966166296514, .10659958402328690063, -.47496371572480503788e-1,
  -.17728848711449643358e-1, .22761703826371535132e-1,
  -.26493215276042203434e-1, .35579780856128386192e-1,
  .10447309718398935122e-1, -.68616154085314996709e-1,
  .11775363082763954214, -.13918901977011837274, .12312819418827395690,
  -.72053565748259077905e-1, 0.0, .72053565748259077905e-1,
  -.12312819418827395690, .13918901977011837274, -.11775363082763954214,
  .68616154085314996709e-1, -.10447309718398935122e-1,
  -.35579780856128386192e-1,
  .26493215276042203434e-1, .40742523354399706918e-1,
  -.73124912999529117195e-1, .49317266444153837821e-1,
  -.13686605413876015320e-1, -.28342624942191100464e-1,
  .70371855298258216249e-1, -.10600251632853603875, .12981016288391131812,
  -.13817029659318161476, .12981016288391131812, -.10600251632853603875,
  .70371855298258216249e-1, -.28342624942191100464e-1,
  -.13686605413876015320e-1,
  .49317266444153837821e-1, -.73124912999529117195e-1,
  .40742523354399706918e-1, -.54944368958699908688e-1,
  .10777725663147408190, -.10152395581538265428, .91369146312596428468e-1,
  -.77703071757424700773e-1, .61050911730999815031e-1,
  -.42052599404498348871e-1, .21438229266251454773e-1, 0.0,
  -.21438229266251454773e-1, .42052599404498348871e-1,
  -.61050911730999815031e-1, .77703071757424700773e-1,
  -.91369146312596428468e-1,
  .10152395581538265428, -.10777725663147408190, .54944368958699908688e-1,
  .27485608464748840573e-1, -.54971216929497681146e-1,
  .54971216929497681146e-1,
  -.54971216929497681146e-1, .54971216929497681146e-1,
  -.54971216929497681146e-1, .54971216929497681146e-1,
  -.54971216929497681146e-1, .54971216929497681146e-1,
  -.54971216929497681146e-1, .54971216929497681146e-1,
  -.54971216929497681146e-1, .54971216929497681146e-1,
  -.54971216929497681146e-1, .54971216929497681146e-1,
  -.54971216929497681146e-1, .27485608464748840573e-1
};

static const double V4inv[33 * 33] = {
  .69120897476690862600e-3, .66419939766331555194e-2,
  .13600665164323186111e-1, .20122785860913684493e-1,
  .26583214101668429944e-1, .32712713318999268739e-1,
  .38576221976287138036e-1, .44033030938268925133e-1,
  .49092709529622799673e-1, .53657949874312515646e-1,
  .57724533144734311859e-1, .61219564530655179096e-1,
  .64138907503837875026e-1, .66427905189318792009e-1,
  .68088956652280022887e-1, .69083051391555695878e-1,
  .69422738116739271449e-1, .69083051391555695878e-1,
  .68088956652280022887e-1, .66427905189318792009e-1,
  .64138907503837875026e-1, .61219564530655179096e-1,
  .57724533144734311859e-1, .53657949874312515646e-1,
  .49092709529622799673e-1, .44033030938268925133e-1,
  .38576221976287138036e-1, .32712713318999268739e-1,
  .26583214101668429944e-1, .20122785860913684493e-1,
  .13600665164323186111e-1, .66419939766331555194e-2,
  .69120897476690862600e-3, -.11972090629438798134e-2,
  -.11448874821643225573e-1, -.23104401104002905904e-1,
  -.33352899418646530133e-1, -.42538626424075425908e-1,
  -.49969730733911825941e-1, -.55555454015360728353e-1,
  -.58955533624852604918e-1, -.60126044219122513907e-1,
  -.58959430451175833624e-1, -.55546925396227130606e-1,
  -.49984739749347973762e-1, -.42513009141170294365e-1,
  -.33399140950669746346e-1, -.23007690803851790829e-1,
  -.11728275717520066169e-1, 0.0, .11728275717520066169e-1,
  .23007690803851790829e-1, .33399140950669746346e-1,
  .42513009141170294365e-1, .49984739749347973762e-1,
  .55546925396227130606e-1, .58959430451175833624e-1,
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};

static const double Tleft[33 * 33] = {
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static const double Tright[33 * 33] = {
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