# 1D spherical lattice sums S_lm (a chain of period a along z) off the axis and their
# first derivatives, `l m re(k) im(k) kpar a x y z: S dS/dk dS/dkpar dS/dx dS/dy dS/dz dS/da`
# as re im pairs (dS/dk holomorphic), kpar the Bloch wave number. Generated by
# scripts/generate_references.py lattice-chain with mpmath 1.3.0: the Ewald method at
# 30 digits with a real split chosen for the precision it needs, independent of the
# double-precision split and of the spectral series; derivatives by central
# differences at 55 digits. Agrees with the spectral series in mpmath to 1e-17 and
# with absolutely convergent image sums for Im k > 0.
0 0 1.0 0.0 0.3 1.7 4.0 0.0 0.3: -0.2063690592193077 0.048973812705497326 0.11114242745726421 -0.9476429892389406 0.043261266563123575 0.33151084654263285 -0.02166480041586807 -0.2044467017081145 0.0 0.0 0.014692627339168363 0.06191161510406648 0.12139542405171945 -0.02880965469112517
8 0 1.0 0.0 0.3 1.7 4.0 0.0 0.3: 0.6768481807734382 -0.5633322180361866 -4.245276100314063 5.179436130181997 2.7437404079423935 -1.3566327686999178 -1.4347755562850157 1.9902604275229112 0.0 0.0 1.0936831192724734 3.1896854990800905 1.169907830251162 -2.4385300354374415
8 5 1.0 0.0 0.3 1.7 4.0 0.0 0.3: -0.7027611153344308 -0.4500699054085486 2.841004004940111 3.126848492822763 0.8865591252249232 -0.08891121096066282 0.9356466315695908 1.515363439258539 0.5625873817606857 -0.8784513941680384 0.756941258386373 -0.6934569539358875 -0.5074689184039339 -1.619553847834603
16 0 1.0 0.0 0.3 1.7 4.0 0.0 0.3: -554990.1722823996 -2795822.581827585 9126053.05905639 45951670.71153616 -1725068.7526485024 1317810.5690474096 3667329.552864219 9912371.794891205 0.0 0.0 220931.85218242474 22553652.683443088 -3604156.078735156 -40334.7660866805
20 -13 1.0 0.0 0.3 1.7 4.0 0.0 0.3: 3111411422.9671803 38492896885.69295 -63914876424.86641 -791660319342.4453 9272057955.226933 -9755337907.496288 -10234974104.904884 -191466481091.14487 125101914878.50208 -10112087124.643335 14656777638.412933 63669630373.99872 -14464938770.707455 -28130520860.184887
0 0 1.0 0.0 0.3 1.7 4.25 0.0 0.3: -0.20584830818851846 -0.0014941332934472662 0.3241790409701788 -0.9212457185942405 -0.035946946537202755 0.338576160760113 0.025336374041283256 -0.19757465721205938 0.0 0.0 -0.0004480298130373187 0.061754875128874336 0.12108810369263254 0.0008782119096373486
12 4 1.0 0.0 0.3 1.7 4.25 0.0 0.3: 257.1846296940236 -414.1834818279892 -3120.684994535317 5060.133529976465 814.2780998546426 -262.3129992444645 -743.815794382432 1504.2993071367664 389.8197476028134 242.05612206496338 672.6807067812558 2758.4191606254867 48.8302055953149 -1317.269513715163
16 -16 1.0 0.0 0.3 1.7 4.25 0.0 0.3: -238962.164028849 -3639469.167363067 3908091.446268938 59645738.365044795 -723833.8975939875 624628.0717852197 776370.853701685 13364745.790703189 -13701530.9830139 899622.2645791962 -869307.7337798367 714894.0069499867 383622.0405250187 1657934.6905922433
20 0 1.0 0.0 0.3 1.7 4.25 0.0 0.3: -1987222130.5931506 -2608556497.3542585 40647180849.56725 53508241241.41278 -5939050877.016179 1781537012.1482306 8211849972.3875885 7826020908.434761 0.0 0.0 -3706763780.290862 31002329227.369522 2986548434.060241 6753773362.352152
0 0 6.0 0.0 0.3 1.7 6.0 0.0 0.3: 0.003657806258084767 -0.021962112005108128 0.15348512496361633 0.05549038615663608 0.02627060339516752 -0.06341604420887875 0.11267554326167345 0.003351345055118347 0.0 0.0 0.02729042529772016 -0.045835067228752975 0.1438538492005244 0.1809176197147463
3 -1 6.0 0.0 0.3 1.7 6.0 0.0 0.3: -0.004005716325518067 -0.025328217752042456 0.18929061080968548 -0.02610913244725561 -0.07344461603999158 -0.021232049186192797 0.13098781261474338 -0.009138401735045711 -0.00422136962534041 0.0006676193875863446 -0.055360622980566286 -0.012783097737612532 0.20258328897166175 -0.061387688063431464
12 6 6.0 0.0 0.3 1.7 6.0 0.0 0.3: -0.006674495858255443 0.022877805560000575 -0.17548214411088597 -0.07136795227837889 -0.01999636393937034 -0.02383998309537118 -0.12154685172902725 -0.02662469212110473 -0.022877805560000575 -0.006674495858255443 -0.046797572951817384 -0.02999322304426359 -0.18563023034554013 -0.15683152291704544
0 0 2.0 0.0 0.3 1.7 8.0 0.0 0.3: -0.03744733585055014 0.03647687567511763 -0.2670093729833929 -0.33071569989718935 0.053803018959733814 0.058105789989960174 -0.06982601191856141 -0.07636163088701649 0.0 0.0 0.010943062727403002 0.011234200795755638 0.0220278448537675 -0.021456985847050247
2 1 2.0 0.0 0.3 1.7 8.0 0.0 0.3: 0.015684370459519748 -0.01434198060760295 0.096348690390573 0.14457747473896143 0.029997354076220634 -0.07097158824775199 0.02733396677454614 0.031866635406031366 0.0017927475759503687 0.0019605463074399685 -0.004302594445044888 -0.004705310974774415 -0.009226099328731457 0.008436460616340407
0 0 12.0 0.0 0.3 1.7 4.0 0.0 0.3: -0.013685164443495119 -0.00775564674020399 0.1405546482923128 -0.06675406922803438 -0.0545332593945696 -0.003633326572712988 -0.008697512377480234 -0.13403583219525345 0.0 0.0 -0.042423565343503084 -0.02376985655853555 1.0104781887072674 -0.1522732605645012
3 2 12.0 0.0 0.3 1.7 4.0 0.0 0.3: 0.005043644273706543 0.00750774216020385 -0.03199899035828956 0.02075700336282368 -0.035217532355351036 -0.04606706397026507 -0.08694989298056498 0.06529425393794157 -0.003753871080101925 0.0025218221368532713 -0.07665736876030069 -0.009518941761117746 -0.013974330268076441 -0.013563183565074306
1 1 3.3 0.0 0.3 1.7 3.4 1.0 0.0: -0.043932965319896614 -0.009660528466875406 0.05433655828417347 -0.17033798858334012 0.0032212810765076256 -0.0034998928643781625 0.030821094317812412 -0.13348466668228393 0.01190635964255524 -0.05218165647122957 0.0022131032807817686 0.014683201896217333 0.03739938019859253 -0.03360929823137702
3 1 4.36 0.0 1.1 0.88 -2.472 -1.38 0.437: 0.03935384015366352 0.008932983063329071 -0.030886563599568064 0.11375105869103658 -0.024135422494685962 -0.054011050539306035 0.03736970234213805 -0.1364202030068011 0.024475393323414068 -0.09207674769540819 0.009799296877385455 -0.04328941305125698 -0.04470764522455921 -0.010041727101583476
10 -7 4.36 0.0 1.1 0.88 -2.472 -1.38 0.437: -0.07092993027459747 0.015829111333147097 -0.021334155806990544 -0.17244596860801628 0.06583435131862657 0.06308705394306764 0.04884967440966578 0.30266929350979604 -0.017553086022124156 -0.03188749469201609 0.015580372705399564 0.07664002202281477 0.07855156896581061 -0.013371139245810215
0 0 0.8 0.0 0.3 1.7 5.5 0.0 0.3: -0.25641597259981214 -0.008233296705653705 0.553783789313301 -1.5156853874525187 -0.0899439140624468 0.64916616474152 0.029157973329663207 -0.19074712300639646 0.0 0.0 -0.002469986005663398 0.07692479693982227 0.15083294101203423 0.004843104066867539
6 2 0.8 0.0 0.3 1.7 5.5 0.0 0.3: -0.20646006828390825 -0.11732485482394323 1.697720527647811 -0.4810334803766475 -2.0333089738686803 -0.5294559685915889 0.09966477704359475 -0.12301567848087748 0.04266358357234299 -0.07507638846687573 -0.03453948671033271 0.06317605239993584 0.12375841307704318 0.06704108296826512
2 -1 2.3 0.4 0.3 1.7 5.0 1.0 0.2: -0.0016817838300328888 -0.0016139699243203492 0.010320473008611367 -0.007246483825118131 -0.006723812490253255 -0.0037432675774088375 0.004490913376801771 -0.003019678347069781 0.0005753886904962844 -0.0002675789034073784 -0.0004824239394960029 0.0005047759123836767 0.0009912158330420454 0.000943124463958673
16 9 2.3 0.4 0.3 1.7 5.0 1.0 0.2: -0.11942792128720378 -0.13028009908470553 0.8870601510124693 0.48909338088233345 -0.327952963606764 0.031086706428386738 0.390048739045045 0.4751540026472758 0.31251392616147894 -0.11993945778751164 0.012843343990575833 -0.6723848368063688 -0.30535952017123685 -0.37193455277924886
5 3 1.0 0.9 -2.0 1.0 3.0 -2.0 0.45: -0.017336610441912113 -0.011427688840518813 0.08834608901487227 -0.048319787984473464 -0.028418208368102327 -0.016315064887087734 0.041989125233714474 0.007471261915048937 -0.016565061315290838 -0.022317451718611405 0.02318109191772886 -0.03543309314119113 0.019141325242399962 0.012718024634253446
4 -2 1.5 0.0 10.871975511965978 1.2 3.5 2.0 -0.5: 0.01735109673709464 0.09092218958795255 -0.3534918456413838 0.10118770660848218 -0.040325410385015664 -0.4853512416780594 -0.1324052395240625 0.013986120462666318 -0.023704599963491394 -0.0019228435853876123 0.036372411322736574 -0.0069413853465992706 -0.366367415629479 -4.31126806786273
24 11 1.0 0.0 0.0 1.7 5.0 0.0 -0.6: -6.741332035724946e-73 -1834965139935.8394 -2.571756600851816e-70 44839195855390.51 1902920545411.331 -0.00478164103828657 -1.0171269069162824e-72 7622860629170.647 4036923307858.846 0.0 -1.751406449783974e-71 -5383877548030.458 -1.5446968485253177e-70 2055627165128.819
24 0 3.0 0.0 0.2 1.0 3.0 0.5 0.1: -86562.34668401026 -753805.4219550346 660685.4514503251 5813590.907744905 -425483.11613209825 27383.871880080744 545007.2324986513 4348169.698638288 90834.53874977521 724694.949773048 -739885.5875873097 3995177.9318345212 290509.3230124453 3639875.133625889
