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# N_patches = 3
# origin = 0 0 0

### +z patch
# N_rho = 16
# N_sigma = 16
# ghosted_gfn=-1
# dpx = dsigma = dnu
# dpy = drho = dmu
#
# dpx	dpy	gridfn	global_x	global_y	global_z
0	0	1.93678738957900	0.000000000	0.000000000	1.936787390
3	0	1.93271511585415	0.1011504937	0.000000000	1.930066397
6	0	1.92050689283878	0.2007476342	0.000000000	1.909986155
9	0	1.90012673835448	0.2972453098	0.000000000	1.876733025
12	0	1.87153628167002	0.3891142727	0.000000000	1.830638724
15	0	1.83466565176916	0.4748464121	0.000000000	1.772150936
18	0	1.78940035726201	0.5529551201	0.000000000	1.701820870
21	0	1.73558049340673	0.6219764227	0.000000000	1.620303977
24	0	1.67297799742564	0.6804614546	0.000000000	1.528341450
27	0	1.60125669348170	0.7269553265	0.000000000	1.426730161
30	0	1.51993615006868	0.7599680750	0.000000000	1.316303318
33	0	1.42830062491488	0.7779082741	0.000000000	1.197873696
36	0	1.32537691878237	0.7790370066	0.000000000	1.072252451
39	0	1.20986525500807	0.7613928754	0.000000000	0.9402418968
42	0	1.08048464645938	0.7229853466	0.000000000	0.8029565740
45	0	0.938244105069595	0.6634387691	0.000000000	0.6634387691

0	3	1.93271511585415	0.000000000	0.1011504937	1.930066397
3	3	1.92865944607656	0.1008002822	0.1008002822	1.923383962
6	3	1.91649077565929	0.2000562869	0.09975340863	1.903408425
9	3	1.89617941321218	0.2962312223	0.09801985904	1.870330328
12	3	1.86767956206765	0.3878032060	0.09561645457	1.824470639
15	3	1.83092236495247	0.4732715657	0.09256647327	1.766273529
18	3	1.78579047675440	0.5511554125	0.08889836948	1.696281939
21	3	1.73212129788190	0.6199951171	0.08464603164	1.615142500
24	3	1.66968358353600	0.6783444913	0.07984779407	1.523586673
27	3	1.59813750594018	0.7247495222	0.07454487903	1.422401026
30	3	1.51699628363273	0.7577181196	0.06878029870	1.312406281
33	3	1.42554609741145	0.7756591822	0.06259639654	1.194410399
36	3	1.32280427869491	0.7768269261	0.05603494980	1.069210536
39	3	1.20747168057022	0.7592570794	0.04913776489	0.9376044085
42	3	1.07828876925365	0.7209694292	0.04196383497	0.8007176709
45	3	0.936324258917764	0.6616270866	0.03467440632	0.6616270866

0	6	1.92050689283878	0.000000000	0.2007476342	1.909986155
3	6	1.91649077565929	0.09975340863	0.2000562869	1.903408425
6	6	1.90444259038829	0.1979897581	0.1979897581	1.883746716
9	6	1.88432722289295	0.2931981205	0.1945668664	1.851180078
12	6	1.85609917380422	0.3838813573	0.1898203291	1.806019792
15	6	1.81967826208706	0.4685588859	0.1837942594	1.748685569
18	6	1.77494449335612	0.5457681282	0.1765437504	1.679701583
21	6	1.72172653890021	0.6140625406	0.1681339429	1.599687610
24	6	1.65977874008462	0.6720022249	0.1586382061	1.509341709
27	6	1.58875589914666	0.7181379052	0.1481365365	1.409424997
30	6	1.50815332642102	0.7509721126	0.1367113758	1.300721854
33	6	1.41725444453037	0.7689106402	0.1244453648	1.184018555
36	6	1.31505650469649	0.7701914803	0.1114186485	1.060077629
39	6	1.20026305640083	0.7528427678	0.09771366209	0.9296833933
42	6	1.07167360882856	0.7149121568	0.08345175258	0.7939903884
45	6	0.930552768527182	0.6561904508	0.06896839552	0.6561904508

0	9	1.90012673835448	0.000000000	0.2972453098	1.876733025
3	9	1.89617941321218	0.09801985904	0.2962312223	1.870330328
6	9	1.88432722289295	0.1945668664	0.2931981205	1.851180078
9	9	1.86453749620037	0.2881731880	0.2881731880	1.819453902
12	9	1.83675618321841	0.3773811277	0.2812018515	1.775438616
15	9	1.80088945067544	0.4607437708	0.2723450801	1.719519162
18	9	1.75680945008233	0.5368277814	0.2616805589	1.652186025
21	9	1.70433369137910	0.6042090881	0.2493000373	1.574018488
24	9	1.64319713051451	0.6614603166	0.2353060921	1.485664196
27	9	1.57303504225336	0.7071362636	0.2198111624	1.387833060
30	9	1.49332749189432	0.7397373806	0.2029320800	1.281262727
33	9	1.40333269041303	0.7576547932	0.1847849203	1.166686071
36	9	1.30203767666593	0.7591120772	0.1654845200	1.044828139
39	9	1.18814866857932	0.7421254903	0.1451512077	0.9164486577
42	9	1.06055650986960	0.7047855997	0.1239744240	0.7827437073
45	9	0.920896392982711	0.6471263379	0.1024947428	0.6471263379

0	12	1.87153628167002	0.000000000	0.3891142727	1.830638724
3	12	1.86767956206765	0.09561645457	0.3878032060	1.824470639
6	12	1.85609917380423	0.1898203291	0.3838813573	1.806019792
9	12	1.83675618321841	0.2812018515	0.3773811277	1.775438616
12	12	1.80958333038767	0.3683562402	0.3683562402	1.732979859
15	12	1.77447936079669	0.4498847559	0.3568809295	1.678992767
18	12	1.73129828751415	0.5243929702	0.3430483532	1.613915611
21	12	1.67984015881256	0.5904870574	0.3269696746	1.538271376
24	12	1.61982000662593	0.6467596462	0.3087694283	1.452645949
27	12	1.55084484422538	0.6917717838	0.2885834887	1.357678570
30	12	1.47236709931029	0.7240189704	0.2665539295	1.254037642
33	12	1.38362660593326	0.7418813544	0.2428240007	1.142397105
36	12	1.28358368928980	0.7435578256	0.2175345403	1.023419548
39	12	1.17096680274997	0.7270604341	0.1908428169	0.8978448627
42	12	1.04480903299921	0.6905516461	0.1630171304	0.7669353002
45	12	0.907310523264660	0.6344394040	0.1348542583	0.6344394040

0	15	1.83466565176916	0.000000000	0.4748464121	1.772150936
3	15	1.83092236495247	0.09256647327	0.4732715657	1.766273529
6	15	1.81967826208706	0.1837942594	0.4685588859	1.748685569
9	15	1.80088945067544	0.2723450801	0.4607437708	1.719519162
12	15	1.77447936079669	0.3568809295	0.4498847559	1.678992767
15	15	1.74032820541015	0.4360615204	0.4360615204	1.627403749
18	15	1.69827653969117	0.5085434250	0.4193768541	1.565135727
21	15	1.64809778505103	0.5729703110	0.3999513320	1.492638692
24	15	1.58947842118033	0.6279594184	0.3779208856	1.410419946
27	15	1.52199642671588	0.6720833317	0.3534351153	1.319037807
30	15	1.44507240201180	0.7038347587	0.3266508483	1.219077562
33	15	1.35791400544612	0.7215776816	0.2977269732	1.111132191
36	15	1.25946650060091	0.7234919580	0.2668241409	0.9958012506
39	15	1.14849660062526	0.7075937592	0.2341354837	0.8738055212
42	15	1.02425739029917	0.6721655620	0.2000282214	0.7465154851
45	15	0.889757058915978	0.6181556832	0.1656343161	0.6181556832

0	18	1.78940035726201	0.000000000	0.5529551201	1.701820870
3	18	1.78579047675441	0.08889836948	0.5511554125	1.696281939
6	18	1.77494449335612	0.1765437504	0.5457681282	1.679701583
9	18	1.75680945008233	0.2616805589	0.5368277814	1.652186025
12	18	1.73129828751415	0.3430483532	0.5243929702	1.613915611
15	18	1.69827653969117	0.4193768541	0.5085434250	1.565135727
18	18	1.65755862592164	0.4893806070	0.4893806070	1.506158638
21	18	1.60889364985637	0.5517499813	0.4670258736	1.437357843
24	18	1.55193724525141	0.6051340257	0.4416156692	1.359153275
27	18	1.48623018212099	0.6481202166	0.4133003054	1.272007546
30	18	1.41115962776821	0.6792025105	0.3822398381	1.176413257
33	18	1.32589835285184	0.6967307631	0.3485970141	1.072871291
36	18	1.22938167995317	0.6988703292	0.3125443127	0.9619124859
39	18	1.12044714659749	0.6836614353	0.2743139612	0.8442515625
42	18	0.998704242439854	0.6495948205	0.2344127096	0.7214481372
45	18	0.868230571209983	0.5983426243	0.1944133037	0.5983426243

0	21	1.73558049340673	0.000000000	0.6219764227	1.620303977
3	21	1.73212129788190	0.08464603164	0.6199951171	1.615142500
6	21	1.72172653890021	0.1681339429	0.6140625406	1.599687610
9	21	1.70433369137910	0.2493000373	0.6042090881	1.574018488
12	21	1.67984015881256	0.3269696746	0.5904870574	1.538271376
15	21	1.64809778505103	0.3999513320	0.5729703110	1.492638692
18	21	1.60889364985637	0.4670258736	0.5517499813	1.437357843
21	21	1.56195006405821	0.5269379282	0.5269379282	1.372720235
24	21	1.50688653704743	0.5783741836	0.4986584540	1.299049686
27	21	1.44320711174195	0.6199440053	0.4670506795	1.216708618
30	21	1.37026115080936	0.6501467401	0.4322643711	1.126087186
33	21	1.28719179411410	0.6673256676	0.3944553869	1.027591415
36	21	1.19294120154574	0.6696451370	0.3538026673	0.9216874597
39	21	1.08647207115415	0.6552056826	0.3105888568	0.8091116344
42	21	0.967965465694032	0.6228481673	0.2655352474	0.6917429694
45	21	0.842800018741895	0.5751391838	0.2207752478	0.5751391838

0	24	1.67297799742564	0.000000000	0.6804614546	1.528341450
3	24	1.66968358353600	0.07984779407	0.6783444913	1.523586673
6	24	1.65977874008462	0.1586382061	0.6720022249	1.509341709
9	24	1.64319713051451	0.2353060921	0.6614603166	1.485664196
12	24	1.61982000662593	0.3087694283	0.6467596462	1.452645949
15	24	1.58947842118033	0.3779208856	0.6279594184	1.410419946
18	24	1.55193724525141	0.4416156692	0.6051340257	1.359153275
21	24	1.50688653704743	0.4986584540	0.5783741836	1.299049686
24	24	1.45391201663248	0.5477816176	0.5477816176	1.230337657
27	24	1.39248013035606	0.5876236232	0.5134716891	1.153276296
30	24	1.32190418003945	0.6166973316	0.4755715150	1.068151111
33	24	1.24130487986001	0.6333500946	0.4342197919	0.9752736205
36	24	1.14966959215722	0.6357729361	0.3896046516	0.8750663748
39	24	1.04620500828531	0.6222051860	0.3420956522	0.7683594150
42	24	0.931938374931816	0.5920241420	0.2927420552	0.6575094212
45	24	0.813666615087718	0.5487949065	0.2443392347	0.5487949065

0	27	1.60125669348170	0.000000000	0.7269553265	1.426730161
3	27	1.59813750594018	0.07454487903	0.7247495222	1.422401026
6	27	1.58875589914665	0.1481365365	0.7181379052	1.409424997
9	27	1.57303504225336	0.2198111624	0.7071362636	1.387833060
12	27	1.55084484422538	0.2885834887	0.6917717838	1.357678570
15	27	1.52199642671588	0.3534351153	0.6720833317	1.319037807
18	27	1.48623018212099	0.4133003054	0.6481202166	1.272007546
21	27	1.44320711174195	0.4670506795	0.6199440053	1.216708618
24	27	1.39248013035606	0.5134716891	0.5876236232	1.153276296
27	27	1.33348291296993	0.5512406468	0.5512406468	1.081870684
30	27	1.26549319711940	0.5788928442	0.5108868089	1.002671818
33	27	1.18764646559214	0.5948068249	0.4666856655	0.9159221899
36	27	1.09904154276812	0.5972477551	0.4188508162	0.8220410121
39	27	0.999332718114488	0.5847273225	0.3679171725	0.7220781079
42	27	0.890718841175799	0.5573870304	0.3154171497	0.6190410116
45	27	0.781231926396665	0.5197118806	0.2648064296	0.5197118806

0	30	1.51993615006868	0.000000000	0.7599680750	1.316303318
3	30	1.51699628363272	0.06878029870	0.7577181196	1.312406281
6	30	1.50815332642101	0.1367113758	0.7509721126	1.300721854
9	30	1.49332749189432	0.2029320800	0.7397373806	1.281262727
12	30	1.47236709931028	0.2665539295	0.7240189704	1.254037642
15	30	1.44507240201180	0.3266508483	0.7038347587	1.219077562
18	30	1.41115962776821	0.3822398381	0.6792025105	1.176413257
21	30	1.37026115080936	0.4322643711	0.6501467401	1.126087186
24	30	1.32190418003945	0.4755715150	0.6166973316	1.068151111
27	30	1.26549319711940	0.5108868089	0.5788928442	1.002671818
30	30	1.20030807997668	0.5367940922	0.5367940922	0.9297546408
33	30	1.12554816418640	0.5517407009	0.4905203535	0.8496061744
36	30	1.04056621098249	0.5541591955	0.4403650831	0.7627346977
39	30	0.945783252123765	0.5430431249	0.3871724824	0.6706024108
42	30	0.844782651099089	0.5194740739	0.3330932355	0.5769344076
45	30	0.746162497542092	0.4884780180	0.2820229152	0.4884780180

0	33	1.42830062491487	0.000000000	0.7779082741	1.197873696
3	33	1.42554609741145	0.06259639654	0.7756591822	1.194410399
6	33	1.41725444453037	0.1244453648	0.7689106402	1.184018555
9	33	1.40333269041303	0.1847849203	0.7576547932	1.166686071
12	33	1.38362660593325	0.2428240007	0.7418813544	1.142397105
15	33	1.35791400544611	0.2977269732	0.7215776816	1.111132191
18	33	1.32589835285184	0.3485970141	0.6967307631	1.072871291
21	33	1.28719179411410	0.3944553869	0.6673256676	1.027591415
24	33	1.24130487986000	0.4342197919	0.6333500946	0.9752736205
27	33	1.18764646559214	0.4666856655	0.5948068249	0.9159221899
30	33	1.12554816418640	0.4905203535	0.5517407009	0.8496061744
33	33	1.05439381321441	0.5043166419	0.5043166419	0.7765795276
36	33	0.974064792305153	0.5068468680	0.4530363908	0.6976148655
39	33	0.886076224363195	0.4978194092	0.3992270669	0.6147557729
42	33	0.795196516780308	0.4792038406	0.3456210740	0.5322097826
45	33	0.709412452576115	0.4558646611	0.2960419724	0.4558646611

0	36	1.32537691878236	0.000000000	0.7790370066	1.072252451
3	36	1.32280427869491	0.05603494980	0.7768269261	1.069210536
6	36	1.31505650469649	0.1114186485	0.7701914803	1.060077629
9	36	1.30203767666593	0.1654845200	0.7591120772	1.044828139
12	36	1.28358368928979	0.2175345403	0.7435578256	1.023419548
15	36	1.25946650060091	0.2668241409	0.7234919580	0.9958012506
18	36	1.22938167995317	0.3125443127	0.6988703292	0.9619124859
21	36	1.19294120154573	0.3538026673	0.6696451370	0.9216874597
24	36	1.14966959215721	0.3896046516	0.6357729361	0.8750663748
27	36	1.09904154276811	0.4188508162	0.5972477551	0.8220410121
30	36	1.04056621098249	0.4403650831	0.5541591955	0.7627346977
33	36	0.974064792305152	0.4530363908	0.5068468680	0.6976148655
36	36	0.900269377933935	0.4561951710	0.4561951710	0.6278987855
39	36	0.821810957639548	0.4503531239	0.4040592105	0.5561397921
42	36	0.743746141748925	0.4379101188	0.3533528384	0.4863484583
45	36	0.672152730627211	0.4227572955	0.3071511542	0.4227572955

0	39	1.20986525500806	0.000000000	0.7613928754	0.9402418968
3	39	1.20747168057021	0.04913776489	0.7592570794	0.9376044085
6	39	1.20026305640082	0.09771366209	0.7528427678	0.9296833933
9	39	1.18814866857931	0.1451512077	0.7421254903	0.9164486577
12	39	1.17096680274996	0.1908428169	0.7270604341	0.8978448627
15	39	1.14849660062525	0.2341354837	0.7075937592	0.8738055212
18	39	1.12044714659748	0.2743139612	0.6836614353	0.8442515625
21	39	1.08647207115413	0.3105888568	0.6552056826	0.8091116344
24	39	1.04620500828530	0.3420956522	0.6222051860	0.7683594150
27	39	0.999332718114482	0.3679171725	0.5847273225	0.7220781079
30	39	0.945783252123760	0.3871724824	0.5430431249	0.6706024108
33	39	0.886076224363192	0.3992270669	0.4978194092	0.6147557729
36	39	0.821810957639547	0.4040592105	0.4503531239	0.5561397921
39	39	0.756030238142827	0.4026812355	0.4026812355	0.4972699127
42	39	0.692772586334411	0.3971819842	0.3572081124	0.4411152823
45	39	0.635596277966610	0.3900207701	0.3158325923	0.3900207701

0	42	1.08048464645936	0.000000000	0.7229853466	0.8029565740
3	42	1.07828876925363	0.04196383497	0.7209694292	0.8007176709
6	42	1.07167360882854	0.08345175258	0.7149121568	0.7939903884
9	42	1.06055650986958	0.1239744240	0.7047855997	0.7827437073
12	42	1.04480903299920	0.1630171304	0.6905516461	0.7669353002
15	42	1.02425739029916	0.2000282214	0.6721655620	0.7465154851
18	42	0.998704242439843	0.2344127096	0.6495948205	0.7214481372
21	42	0.967965465694021	0.2655352474	0.6228481673	0.6917429694
24	42	0.931938374931806	0.2927420552	0.5920241420	0.6575094212
27	42	0.890718841175792	0.3154171497	0.5573870304	0.6190410116
30	42	0.844782651099083	0.3330932355	0.5194740739	0.5769344076
33	42	0.795196516780305	0.3456210740	0.4792038406	0.5322097826
36	42	0.743746141748923	0.3533528384	0.4379101188	0.4863484583
39	42	0.692772586334411	0.3572081124	0.3971819842	0.4411152823
42	42	0.644583318271383	0.3584638004	0.3584638004	0.3981143828
45	42	0.600761800164168	0.3583380640	0.3226490420	0.3583380640

0	45	0.938244105069553	0.000000000	0.6634387691	0.6634387691
3	45	0.936324258917721	0.03467440632	0.6616270866	0.6616270866
6	45	0.930552768527148	0.06896839552	0.6561904508	0.6561904508
9	45	0.920896392982686	0.1024947428	0.6471263379	0.6471263379
12	45	0.907310523264642	0.1348542583	0.6344394040	0.6344394040
15	45	0.889757058915963	0.1656343161	0.6181556832	0.6181556832
18	45	0.868230571209970	0.1944133037	0.5983426243	0.5983426243
21	45	0.842800018741884	0.2207752478	0.5751391838	0.5751391838
24	45	0.813666615087710	0.2443392347	0.5487949065	0.5487949065
27	45	0.781231926396658	0.2648064296	0.5197118806	0.5197118806
30	45	0.746162497542088	0.2820229152	0.4884780180	0.4884780180
33	45	0.709412452576112	0.2960419724	0.4558646611	0.4558646611
36	45	0.672152730627210	0.3071511542	0.4227572955	0.4227572955
39	45	0.635596277966609	0.3158325923	0.3900207701	0.3900207701
42	45	0.600761800164167	0.3226490420	0.3583380640	0.3583380640
45	45	0.568307554927430	0.3281125198	0.3281125198	0.3281125198


### +x patch
# N_rho = 16
# N_sigma = 16
# ghosted_gfn=-1
# dpx = drho = dnu
# dpy = dsigma = dphi
#
# dpx	dpy	gridfn	global_x	global_y	global_z
45	0	0.938183875770009	0.6633961806	0.000000000	0.6633961806
45	3	0.936260418683200	0.6615819757	0.03467204216	0.6615819757
45	6	0.930478832178349	0.6561383137	0.06896291569	0.6561383137
45	9	0.920808417863457	0.6470645166	0.1024849513	0.6470645166
45	12	0.907209802107648	0.6343689744	0.1348392880	0.6343689744
45	15	0.889653544002758	0.6180837665	0.1656150461	0.6180837665
45	18	0.868145690733316	0.5982841288	0.1943942974	0.5982841288
45	21	0.842766476988368	0.5751162944	0.2207664614	0.5751162944
45	24	0.813720783987920	0.5488314419	0.2443555013	0.5488314419
45	27	0.781395533016616	0.5198207193	0.2648618857	0.5198207193
45	30	0.746416976473315	0.4886446135	0.2821190992	0.4886446135
45	33	0.709683441597697	0.4560387972	0.2961550577	0.4560387972
45	36	0.672334746538795	0.4228717762	0.3072343293	0.4228717762
45	39	0.635622509223955	0.3900368664	0.3158456268	0.3900368664
45	42	0.600666493007285	0.3582812159	0.3225978558	0.3582812159
45	45	0.568205241288989	0.3280534490	0.3280534490	0.3280534490

48	0	0.794194134609080	0.5902012616	0.000000000	0.5314196029
48	3	0.792427822997967	0.5884425201	0.03083896572	0.5298360250
48	6	0.787147056083953	0.5831880076	0.06129552956	0.5251048407
48	9	0.778408309115445	0.5745042343	0.09099253162	0.5172859361
48	12	0.766316062520794	0.5625093399	0.1195650512	0.5064856846
48	15	0.751036758859212	0.5473824995	0.1466706987	0.4928654163
48	18	0.732810713393334	0.5293708604	0.1720030192	0.4766476636
48	21	0.711971684718799	0.5088005975	0.1953102504	0.4581261157
48	24	0.688957732611664	0.4860795651	0.2164165657	0.4376680063
48	27	0.664311058476203	0.4616897843	0.2352426949	0.4157073490
48	30	0.638659663654403	0.4361651298	0.2518200551	0.3927248469
48	33	0.612673528556373	0.4100506460	0.2662900031	0.3692112600
48	36	0.586996034526329	0.3838468536	0.2788810634	0.3456172594
48	39	0.562160514870234	0.3579494904	0.2898617820	0.3222991688
48	42	0.538528859360611	0.3326119035	0.2994851031	0.2994851031
48	45	0.516288228310610	0.3079518773	0.3079518773	0.2772811158

51	0	0.672884814487474	0.5229297161	0.000000000	0.4234601346
51	3	0.671563163208597	0.5214702693	0.02732909877	0.4222782978
51	6	0.667626508940487	0.5171210386	0.05435161130	0.4187563603
51	9	0.661160197037021	0.5099693255	0.08077120620	0.4129650172
51	12	0.652306694657580	0.5001595377	0.1063121916	0.4050212077
51	15	0.641264800675829	0.4878906242	0.1307298988	0.3950860374
51	18	0.628290347540971	0.4734137699	0.1538214583	0.3833629119
51	21	0.613687527295654	0.4570220730	0.1754343370	0.3700891775
51	24	0.597802203174134	0.4390410555	0.1954736719	0.3555284367
51	27	0.581004644419883	0.4198108665	0.2139043205	0.3399561367
51	30	0.563666559415099	0.3996646724	0.2307465062	0.3236420704
51	33	0.546136881332502	0.3789073573	0.2460653150	0.3068331280
51	36	0.528717607156118	0.3577962759	0.2599542108	0.2897377113
51	39	0.511648585657537	0.3365307824	0.2725172542	0.2725172542
51	42	0.495106956513147	0.3152538787	0.2838558673	0.2552875574
51	45	0.479220056915036	0.2940636724	0.2940636724	0.2381280666

54	0	0.585743873284628	0.4738767478	0.000000000	0.3442916103
54	3	0.584846797804723	0.4727262895	0.02477453504	0.3434557534
54	6	0.582176917897486	0.4692974974	0.04932515458	0.3409645902
54	9	0.577797667431753	0.4636572906	0.07343610047	0.3368667400
54	12	0.571812612378987	0.4559143359	0.09690758366	0.3312411542
54	15	0.564360766342507	0.4462136600	0.1195625899	0.3241932006
54	18	0.555612588135579	0.4347312918	0.1412527593	0.3158507718
54	21	0.545762863979849	0.4216660361	0.1618624260	0.3063583078
54	24	0.535021454178358	0.4072294227	0.1813102205	0.2958694943
54	27	0.523604174569181	0.3916358835	0.1995484496	0.2845401249
54	30	0.511722134163460	0.3750921596	0.2165595593	0.2725204059
54	33	0.499572889198673	0.3577888008	0.2323507640	0.2599487798
54	36	0.487333899146669	0.3398942260	0.2469476102	0.2469476102
54	39	0.475159524752687	0.3215521974	0.2603878353	0.2336213464
54	42	0.463181588747536	0.3028824473	0.2727165805	0.2200569790
54	45	0.451512384335634	0.2839833058	0.2839833058	0.2063259489

57	0	0.525243387845730	0.4405061704	0.000000000	0.2860680519
57	3	0.524636531910159	0.4395728278	0.02303703574	0.2854619321
57	6	0.522829244110578	0.4367878532	0.04590825328	0.2836533485
57	9	0.519860703670943	0.4321956196	0.06845306133	0.2806711171
57	12	0.515793876710229	0.4258673756	0.09052090509	0.2765615074
57	15	0.510713441159916	0.4178984401	0.1119755495	0.2713864202
57	18	0.504722594312601	0.4084041438	0.1326985503	0.2652207520
57	21	0.497938297480213	0.3975142803	0.1525914356	0.2581487920
57	24	0.490486593126512	0.3853675622	0.1715766931	0.2502606211
57	27	0.482498423546962	0.3721065363	0.1895977502	0.2416488102
57	30	0.474103992419897	0.3578715617	0.2066172425	0.2324045096
57	33	0.465429601938607	0.3427970611	0.2226150144	0.2226150144
57	36	0.456594315632378	0.3270080026	0.2375852209	0.2123614799
57	39	0.447708279073711	0.3106180276	0.2515335192	0.2017177057
57	42	0.438872174394747	0.2937287319	0.2644745382	0.1907496689
57	45	0.430177398679208	0.2764297037	0.2764297037	0.1795155486

60	0	0.481973757555632	0.4174015180	0.000000000	0.2409868788
60	3	0.481553809603477	0.4166089602	0.02183355043	0.2405292953
60	6	0.480301948227161	0.4142411980	0.04353850433	0.2391622671
60	9	0.478241811629648	0.4103275479	0.06498949902	0.2369027202
60	12	0.475411587001686	0.4049153407	0.08606741259	0.2337779810
60	15	0.471862688311664	0.3980680933	0.1066620241	0.2298247208
60	18	0.467658097020095	0.3898631836	0.1266742272	0.2250876140
60	21	0.462870183367821	0.3803889369	0.1460176322	0.2196176551
60	24	0.457577743935935	0.3697410017	0.1646193001	0.2134700669
60	27	0.451864051603776	0.3580195858	0.1824200904	0.2067027042
60	30	0.445814291927902	0.3453262656	0.1993742124	0.1993742124
60	33	0.439513280863307	0.3317611889	0.2154482352	0.1915424117
60	36	0.433043902440482	0.3174210411	0.2306198856	0.1832631235
60	39	0.426485682495002	0.3023973265	0.2448765267	0.1745891778
60	42	0.419914049921608	0.2867753774	0.2582137096	0.1655698414
60	45	0.413400050601356	0.2706338606	0.2706338606	0.1562505323

63	0	0.449873621157078	0.4008403315	0.000000000	0.2042383501
63	3	0.449577831423269	0.4001407678	0.02097048904	0.2038819046
63	6	0.448695379245687	0.3980488658	0.04183662163	0.2028160272
63	9	0.447240852958126	0.3945847516	0.06249608504	0.2010509729
63	12	0.445238065985494	0.3897812106	0.08285055393	0.1986034465
63	15	0.442719377211933	0.3836826331	0.1028074517	0.1954960661
63	18	0.439724501246542	0.3763433756	0.1222813753	0.1917565276
63	21	0.436299451176910	0.3678261407	0.1411952266	0.1874167797
63	24	0.432495430676575	0.3582002483	0.1594810256	0.1825121425
63	27	0.428367329203090	0.3475395531	0.1770802470	0.1770802470
63	30	0.423972252819613	0.3359204385	0.1939437556	0.1711600124
63	33	0.419368597979841	0.3234203239	0.2100316142	0.1647908859
63	36	0.414614529779368	0.3101158004	0.2253123176	0.1580118926
63	39	0.409767466185193	0.2960816866	0.2397622223	0.1508611545
63	42	0.404883230852652	0.2813899440	0.2533646436	0.1433753377
63	45	0.400015519547098	0.2661089632	0.2661089632	0.1355892891

66	0	0.425387824510991	0.3886111148	0.000000000	0.1730208157
66	3	0.425178346974097	0.3879753442	0.02033292621	0.1727377524
66	6	0.424553067626781	0.3860729369	0.04057790079	0.1718907461
66	9	0.423521272267865	0.3829183843	0.06064831399	0.1704862488
66	12	0.422098141882998	0.3785353641	0.08046017547	0.1685348025
66	15	0.420304405322540	0.3729561275	0.09993329318	0.1660507663
66	18	0.418165821393869	0.3662206364	0.1189922979	0.1630519325
66	21	0.415712602081796	0.3583755722	0.1375674932	0.1595590849
66	24	0.412978605735997	0.3494730936	0.1555954460	0.1555954460
66	27	0.410000510884440	0.3395695639	0.1730193347	0.1511861105
66	30	0.406817324731191	0.3287245657	0.1897892165	0.1463576062
66	33	0.403469298046654	0.3169994491	0.2058618493	0.1411372480
66	36	0.399997438776467	0.3044564378	0.2212005500	0.1355527395
66	39	0.396442795995084	0.2911576148	0.2357747876	0.1296317221
66	42	0.392846162070916	0.2771643057	0.2495598618	0.1234014994
66	45	0.389247261494016	0.2625361672	0.2625361672	0.1168886326

69	0	0.406385799811001	0.3793938283	0.000000000	0.1456356458
69	3	0.406238606768091	0.3788032857	0.01985223899	0.1454089577
69	6	0.405799042488216	0.3770353105	0.03962800798	0.1447302957
69	9	0.405073100831339	0.3741007720	0.05925174140	0.1436038319
69	12	0.404070634102768	0.3700175204	0.07864965190	0.1420364184
69	15	0.402805165756801	0.3648100137	0.09775054857	0.1400374439
69	18	0.401293630238245	0.3585088093	0.1164865734	0.1376186381
69	21	0.399555891273178	0.3511498027	0.1347937802	0.1347937802
69	24	0.397614427789602	0.3427735829	0.1526126317	0.1315784506
69	27	0.395494001959832	0.3334247431	0.1698883921	0.1279897673
69	30	0.393221075354495	0.3231509658	0.1865712971	0.1240460337
69	33	0.390823330987569	0.3120022218	0.2026166119	0.1197664318
69	36	0.388329385175843	0.3000301474	0.2179846618	0.1151707830
69	39	0.385768145778987	0.2872871777	0.2326405694	0.1102792152
69	42	0.383168804389666	0.2738262220	0.2465542377	0.1051120385
69	45	0.380560078976181	0.2596998201	0.2596998201	0.09968942083

72	0	0.391533409590947	0.3723704005	0.000000000	0.1209904774
72	3	0.391432275459934	0.3718126555	0.01948587559	0.1208092551
72	6	0.391130170583062	0.3701422604	0.03890351922	0.1202665108
72	9	0.390630969742938	0.3673676899	0.05818532596	0.1193649982
72	12	0.389941066790402	0.3635029156	0.07726492989	0.1181092569
72	15	0.389069269540656	0.3585671708	0.09607778385	0.1165055362
72	18	0.388026518049626	0.3525845075	0.1145616511	0.1145616511
72	21	0.386825795996222	0.3455834956	0.1326570751	0.1122868844
72	24	0.385481956856014	0.3375968105	0.1503077841	0.1096918531
72	27	0.384011505614878	0.3286607544	0.1674610186	0.1067883525
72	30	0.382432037964205	0.3188144774	0.1840676244	0.1035891032
72	33	0.380762301461013	0.3080997432	0.2000823127	0.1001076750
72	36	0.379021740666086	0.2965602552	0.2154636375	0.09635826804
72	39	0.377230275906383	0.2842412075	0.2301739914	0.09235556679
72	42	0.375408111681310	0.2711888779	0.2441795624	0.08811460783
72	45	0.373575375015710	0.2574501264	0.2574501264	0.08365061685

75	0	0.379962769279838	0.3670158519	0.000000000	0.09834160112
75	3	0.379896078531718	0.3664821623	0.01920651627	0.09819859943
75	6	0.379696827601616	0.3648833845	0.03835078908	0.09777020820
75	9	0.379367469621734	0.3622263617	0.05737101956	0.09705826108
75	12	0.378912061872071	0.3585224067	0.07620629005	0.09606578934
75	15	0.378336091524065	0.3537870454	0.09479695311	0.09479695311
75	18	0.377646484557875	0.3480399048	0.1130850201	0.09325701143
75	21	0.376851544772176	0.3413045038	0.1310145240	0.09145226617
75	24	0.375960827656494	0.3336079580	0.1485318325	0.08938998292
75	27	0.374984866893570	0.3249805374	0.1655858544	0.08707827255
75	30	0.373935042011182	0.3154553494	0.1821282309	0.08452600611
75	33	0.372823592599560	0.3050681365	0.1981135643	0.08174276081
75	36	0.371663180031399	0.2938566919	0.2134993838	0.07873866330
75	39	0.370466985913939	0.2818607365	0.2282463240	0.07552435672
75	42	0.369248348329664	0.2691214264	0.2423180207	0.07211086887
75	45	0.368020736877748	0.2556811522	0.2556811522	0.06850955826

78	0	0.371093067895508	0.3629837940	0.000000000	0.07715458720
78	3	0.371052006903900	0.3624676877	0.01899612657	0.07704488542
78	6	0.370929324868182	0.3609212868	0.03793435584	0.07671618775
78	9	0.370726467431185	0.3583502766	0.05675710800	0.07616970267
78	12	0.370445819902780	0.3547640685	0.07540743061	0.07540743061
78	15	0.370090659393746	0.3501756931	0.09382929418	0.07443214131
78	18	0.369665149699321	0.3446017133	0.1119678840	0.07324735532
78	21	0.369174322810781	0.3380621011	0.1297698822	0.07185731783
78	24	0.368623983274591	0.3305800237	0.1471837093	0.07026695319
78	27	0.368020420416135	0.3221814484	0.1641596473	0.06848178091
78	30	0.367370581673040	0.3128951593	0.1806501045	0.06650791923
78	33	0.366681968936416	0.3027525041	0.1966097750	0.06435203132
78	36	0.365962273673590	0.2917869305	0.2119956141	0.06202122668
78	39	0.365219659768955	0.2800340663	0.2267671156	0.05952307829
78	42	0.364462311586235	0.2675311981	0.2408861727	0.05686551160
78	45	0.363698625607495	0.2543172743	0.2543172743	0.05405680541

81	0	0.364530375655256	0.3600424018	0.000000000	0.05702511431
81	3	0.364507873707455	0.3595388318	0.01884263174	0.05694535665
81	6	0.364440627303655	0.3580297628	0.03763044443	0.05670634361
81	9	0.364329405019431	0.3555201003	0.05630885211	0.05630885211
81	12	0.364175476751650	0.3520179817	0.07482373183	0.05575417101
81	15	0.363980608484709	0.3475347311	0.09312165053	0.05504409387
81	18	0.363747070263649	0.3420848096	0.1111500924	0.05418091111
81	21	0.363477635529277	0.3356857411	0.1288576831	0.05316739823
81	24	0.363175448168912	0.3283579006	0.1461943564	0.05200678232
81	27	0.362843888252520	0.3201243012	0.1631114785	0.05070270828
81	30	0.362486780482046	0.3110106815	0.1795621007	0.04925925273
81	33	0.362108226624140	0.3010452382	0.1955010636	0.04768088157
81	36	0.361712400931186	0.2902583400	0.2108850281	0.04597240472
81	39	0.361303829227563	0.2786826414	0.2256727533	0.04413899418
81	42	0.360886951266678	0.2663526059	0.2398249636	0.04218610842
81	45	0.360466432466471	0.2533046325	0.2533046325	0.04011951244

84	0	0.360009578317542	0.3580374082	0.000000000	0.03763124798
84	3	0.359999667541620	0.3575422376	0.01873799467	0.03757920346
84	6	0.359970044924929	0.3560581944	0.03742322424	0.03742322424
84	9	0.359921041314670	0.3535896808	0.05600310369	0.03716377299
84	12	0.359853208047799	0.3501440145	0.07442540780	0.03680161887
84	15	0.359767326717836	0.3457314106	0.09263845226	0.03633783551
84	18	0.359664429071626	0.3403649597	0.1105912793	0.03577379880
84	21	0.359545803606971	0.3340605805	0.1282338424	0.03511118185
84	24	0.359412822883060	0.3268367954	0.1455171167	0.03435193143
84	27	0.359266962846905	0.3187146864	0.1623932438	0.03349826338
84	30	0.359109967528978	0.3097179674	0.1788157519	0.03255267011
84	33	0.358943654171070	0.2998727211	0.1947396221	0.03151789303
84	36	0.358769844716038	0.2892072583	0.2101213726	0.03039690772
84	39	0.358590600377448	0.2777522181	0.2249193114	0.02919293447
84	42	0.358407815292942	0.2655401403	0.2390934163	0.02790939338
84	45	0.358223599549863	0.2526056697	0.2526056697	0.02654992574

87	0	0.357360405267004	0.3568706553	0.000000000	0.01870279853
87	3	0.357357803783324	0.3563803189	0.01867710109	0.01867710109
87	6	0.357350026159438	0.3549106832	0.03730261594	0.01860008075
87	9	0.357337157235138	0.3524658679	0.05582510923	0.01847195341
87	12	0.357319343758161	0.3490527309	0.07419344832	0.01829307848
87	15	0.357296810540613	0.3446808617	0.09235695854	0.01806395852
87	18	0.357269886694284	0.3393625760	0.1102655851	0.01778523898
87	21	0.357239015070586	0.3331128810	0.1278700546	0.01745770635
87	24	0.357204557010090	0.3259492445	0.1451219536	0.01708227606
87	27	0.357166903921003	0.3178916512	0.1619738865	0.01665999549
87	30	0.357126604679984	0.3089626548	0.1783796719	0.01619204662
87	33	0.357084163987901	0.2991871251	0.1942943908	0.01567973282
87	36	0.357040048152653	0.2885921882	0.2096744980	0.01512447570
87	39	0.356994891009009	0.2772073159	0.2244780583	0.01452781983
87	42	0.356949107839082	0.2650639295	0.2386646341	0.01389141191
87	45	0.356903317693017	0.2521956470	0.2521956470	0.01321701380

90	0	0.356487575650383	0.3564875757	0.000000000	0.000000000
90	3	0.356487371609989	0.3559988181	0.01865710748	0.000000000
90	6	0.356486759649984	0.3545338879	0.03726301316	0.000000000
90	9	0.356485745177247	0.3520968141	0.05576665684	0.000000000
90	12	0.356484344125301	0.3486943059	0.07411726274	0.000000000
90	15	0.356482600958066	0.3443357509	0.09226448638	0.000000000
90	18	0.356480616823767	0.3390332136	0.1101585688	0.000000000
90	21	0.356478559782466	0.3328014059	0.1277504905	0.000000000
90	24	0.356476462443946	0.3256574530	0.1449920397	0.000000000
90	27	0.356474363415298	0.3176209835	0.1618359744	0.000000000
90	30	0.356472421770091	0.3087141730	0.1782362109	0.000000000
90	33	0.356470713973128	0.2989614961	0.1941478657	0.000000000
90	36	0.356469263196345	0.2883896919	0.2095273758	0.000000000
90	39	0.356468235783862	0.2770278498	0.2243327295	0.000000000
90	42	0.356467561862015	0.2649070240	0.2385233558	0.000000000
90	45	0.356467370147728	0.2520604947	0.2520604947	0.000000000


### +y patch
# N_rho = 16
# N_sigma = 16
# ghosted_gfn=-1
# dpx = 90 - dsigma = 90 - dphi
# dpy = drho = dmu
#
# dpx	dpy	gridfn	global_x	global_y	global_z
45	45	0.568205241288990	0.3280534490	0.3280534490	0.3280534490
42	45	0.600666493007285	0.3225978558	0.3582812159	0.3582812159
39	45	0.635622509223955	0.3158456268	0.3900368664	0.3900368664
36	45	0.672334746538795	0.3072343293	0.4228717762	0.4228717762
33	45	0.709683441597696	0.2961550577	0.4560387972	0.4560387972
30	45	0.746416976473312	0.2821190992	0.4886446135	0.4886446135
27	45	0.781395533016612	0.2648618857	0.5198207193	0.5198207193
24	45	0.813720783987915	0.2443555013	0.5488314419	0.5488314419
21	45	0.842766476988363	0.2207664614	0.5751162944	0.5751162944
18	45	0.868145690733311	0.1943942974	0.5982841288	0.5982841288
15	45	0.889653544002753	0.1656150461	0.6180837665	0.6180837665
12	45	0.907209802107644	0.1348392880	0.6343689744	0.6343689744
9	45	0.920808417863448	0.1024849513	0.6470645166	0.6470645166
6	45	0.930478832178337	0.06896291569	0.6561383137	0.6561383137
3	45	0.936260418683185	0.03467204216	0.6615819757	0.6615819757
0	45	0.938183875769994	0.000000000	0.6633961806	0.6633961806

45	48	0.516288228310610	0.3079518773	0.3079518773	0.2772811158
42	48	0.538528859360611	0.2994851031	0.3326119035	0.2994851031
39	48	0.562160514870234	0.2898617820	0.3579494904	0.3222991688
36	48	0.586996034526329	0.2788810634	0.3838468536	0.3456172594
33	48	0.612673528556373	0.2662900031	0.4100506460	0.3692112600
30	48	0.638659663654403	0.2518200551	0.4361651298	0.3927248469
27	48	0.664311058476201	0.2352426949	0.4616897843	0.4157073490
24	48	0.688957732611661	0.2164165657	0.4860795651	0.4376680063
21	48	0.711971684718796	0.1953102504	0.5088005975	0.4581261157
18	48	0.732810713393330	0.1720030192	0.5293708604	0.4766476636
15	48	0.751036758859207	0.1466706987	0.5473824995	0.4928654163
12	48	0.766316062520789	0.1195650512	0.5625093399	0.5064856846
9	48	0.778408309115439	0.09099253162	0.5745042343	0.5172859361
6	48	0.787147056083945	0.06129552956	0.5831880076	0.5251048407
3	48	0.792427822997958	0.03083896572	0.5884425201	0.5298360250
0	48	0.794194134609072	0.000000000	0.5902012616	0.5314196029

45	51	0.479220056915036	0.2940636724	0.2940636724	0.2381280666
42	51	0.495106956513147	0.2838558673	0.3152538787	0.2552875574
39	51	0.511648585657537	0.2725172542	0.3365307824	0.2725172542
36	51	0.528717607156118	0.2599542108	0.3577962759	0.2897377113
33	51	0.546136881332502	0.2460653150	0.3789073573	0.3068331280
30	51	0.563666559415099	0.2307465062	0.3996646724	0.3236420704
27	51	0.581004644419883	0.2139043205	0.4198108665	0.3399561367
24	51	0.597802203174133	0.1954736719	0.4390410555	0.3555284367
21	51	0.613687527295651	0.1754343370	0.4570220730	0.3700891775
18	51	0.628290347540967	0.1538214583	0.4734137699	0.3833629119
15	51	0.641264800675825	0.1307298988	0.4878906242	0.3950860374
12	51	0.652306694657575	0.1063121916	0.5001595377	0.4050212077
9	51	0.661160197037016	0.08077120620	0.5099693255	0.4129650172
6	51	0.667626508940482	0.05435161130	0.5171210386	0.4187563603
3	51	0.671563163208592	0.02732909877	0.5214702693	0.4222782978
0	51	0.672884814487468	0.000000000	0.5229297161	0.4234601346

45	54	0.451512384335634	0.2839833058	0.2839833058	0.2063259489
42	54	0.463181588747537	0.2727165805	0.3028824473	0.2200569790
39	54	0.475159524752688	0.2603878353	0.3215521974	0.2336213464
36	54	0.487333899146670	0.2469476102	0.3398942260	0.2469476102
33	54	0.499572889198674	0.2323507640	0.3577888008	0.2599487798
30	54	0.511722134163460	0.2165595593	0.3750921596	0.2725204059
27	54	0.523604174569181	0.1995484496	0.3916358835	0.2845401249
24	54	0.535021454178358	0.1813102205	0.4072294227	0.2958694943
21	54	0.545762863979848	0.1618624260	0.4216660361	0.3063583078
18	54	0.555612588135577	0.1412527593	0.4347312918	0.3158507718
15	54	0.564360766342505	0.1195625899	0.4462136600	0.3241932006
12	54	0.571812612378984	0.09690758366	0.4559143359	0.3312411542
9	54	0.577797667431750	0.07343610047	0.4636572906	0.3368667400
6	54	0.582176917897482	0.04932515458	0.4692974974	0.3409645902
3	54	0.584846797804719	0.02477453504	0.4727262895	0.3434557534
0	54	0.585743873284624	0.000000000	0.4738767478	0.3442916103

45	57	0.430177398679208	0.2764297037	0.2764297037	0.1795155486
42	57	0.438872174394747	0.2644745382	0.2937287319	0.1907496689
39	57	0.447708279073711	0.2515335192	0.3106180276	0.2017177057
36	57	0.456594315632378	0.2375852209	0.3270080026	0.2123614799
33	57	0.465429601938607	0.2226150144	0.3427970611	0.2226150144
30	57	0.474103992419898	0.2066172425	0.3578715617	0.2324045096
27	57	0.482498423546962	0.1895977502	0.3721065363	0.2416488102
24	57	0.490486593126512	0.1715766931	0.3853675622	0.2502606211
21	57	0.497938297480212	0.1525914356	0.3975142803	0.2581487920
18	57	0.504722594312600	0.1326985503	0.4084041438	0.2652207520
15	57	0.510713441159914	0.1119755495	0.4178984401	0.2713864202
12	57	0.515793876710226	0.09052090509	0.4258673756	0.2765615074
9	57	0.519860703670939	0.06845306133	0.4321956196	0.2806711171
6	57	0.522829244110574	0.04590825328	0.4367878532	0.2836533485
3	57	0.524636531910156	0.02303703574	0.4395728278	0.2854619321
0	57	0.525243387845726	0.000000000	0.4405061704	0.2860680519

45	60	0.413400050601356	0.2706338606	0.2706338606	0.1562505323
42	60	0.419914049921608	0.2582137096	0.2867753774	0.1655698414
39	60	0.426485682495001	0.2448765267	0.3023973265	0.1745891778
36	60	0.433043902440482	0.2306198856	0.3174210411	0.1832631235
33	60	0.439513280863307	0.2154482352	0.3317611889	0.1915424117
30	60	0.445814291927902	0.1993742124	0.3453262656	0.1993742124
27	60	0.451864051603776	0.1824200904	0.3580195858	0.2067027042
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