A Borcherds Product in S₉(K(16))⁻

properties |

c vector |

θ vector |

ψ expansion |

Borch(ψ) coefficients

• The singular part of ψ truncated up to q^(16/4) is
  (18 + 5/ζ^3 + 3/ζ^2 + 7/ζ + 7*ζ + 3*ζ^2 + 5*ζ^3)
  +q(ζ^(-9) + 3/ζ^8 + 3*ζ^8 + ζ^9)
  +q^2(ζ^(-12) + ζ^12)
  +q^3(ζ^(-14) + ζ^14)
  +q^4(-4/ζ^16 - 4*ζ^16)
• From the truncated singular part of ψ, the leading Jacobi coefficient of Borch(ψ) is the theta block

  	φ	= TB(9;1,1,1,1,1,1,1,2,2,2,3,3,3,3,3)
  		= 172335
  		= η(τ)18(θ(τ,z)/η(τ))7(θ(τ,2z)/η(τ))3(θ(τ,3z)/η(τ))5

  This theta block has q-order of vanishing 2. This theta block has index 2*16, and so Borch(ψ) begins with Jacobi coefficient #2.
• From the truncated singular part of ψ, we compute that Borch(ψ) is a symmetric form, and so the Fricke sign of Borch(ψ) is −1.
• We need to check that certain Fourier coefficients of Borch(ψ) are zero to determine that Borch(ψ) is a cusp form. For this weight and level and Fricke sign, an expansion of Borch(ψ) to 4 Fourier-Jacobi coefficients was needed to show that Borch(ψ) is a cusp form.
• From the truncated singular part of ψ, we can compute that all Humbert divisors of Borch(ψ) have nonnegative multiplicities, and hence Borch(ψ) is holomorphic.

  (D,r)	multiplicity of Hum(D,r)
  (1,1)	15
  (4,2)	3
  (4,14)	1
  (9,3)	5
  (16,12)	1
  (17,9)	1

• From the singular part above, we compute that the valuation Ord(ψ) is -0.265625, and hence we need to multiply ψ by Δ^1 to get a Jacobi cusp form. The definition of ψ is
      ψ = c · θ/ Δ^1.
  Here c is a vector of coefficients, θ is a basis of of J_12,16^cusp, and Δ is the weight 12 elliptic cusp form. Both c and θ will be given in tables.

The expansion of ψ up to q^(16/4) is

(18 + 5/ζ^3 + 3/ζ^2 + 7/ζ + 7*ζ + 3*ζ^2 + 5*ζ^3)
+q(170 + ζ^(-9) + 3/ζ^8 - ζ^(-7) - 25/ζ^6 - 29/ζ^5 - 24/ζ^4 + 47/ζ^3 - 39/ζ^2 - 18/ζ - 18*ζ - 39*ζ^2 + 47*ζ^3 - 24*ζ^4 - 29*ζ^5 - 25*ζ^6 - ζ^7 + 3*ζ^8 + ζ^9)
+q^2(1116 + ζ^(-12) + 16/ζ^11 + 21/ζ^10 - 46/ζ^9 + 50/ζ^8 + 12/ζ^7 - 142/ζ^6 - 173/ζ^5 - 97/ζ^4 + 439/ζ^3 - 391/ζ^2 - 248/ζ - 248*ζ - 391*ζ^2 + 439*ζ^3 - 97*ζ^4 - 173*ζ^5 - 142*ζ^6 + 12*ζ^7 + 50*ζ^8 - 46*ζ^9 + 21*ζ^10 + 16*ζ^11 + ζ^12)
+q^3(5416 + ζ^(-14) + 6/ζ^13 - 40/ζ^12 + 173/ζ^11 + 134/ζ^10 - 439/ζ^9 + 396/ζ^8 + 276/ζ^7 - 700/ζ^6 - 830/ζ^5 - 248/ζ^4 + 2359/ζ^3 - 2251/ζ^2 - 1545/ζ - 1545*ζ - 2251*ζ^2 + 2359*ζ^3 - 248*ζ^4 - 830*ζ^5 - 700*ζ^6 + 276*ζ^7 + 396*ζ^8 - 439*ζ^9 + 134*ζ^10 + 173*ζ^11 - 40*ζ^12 + 6*ζ^13 + ζ^14)
+q^4(22136 - 4/ζ^16 - 23/ζ^15 + 43/ζ^14 + 7/ζ^13 - 416/ζ^12 + 1066/ζ^11 + 684/ζ^10 - 2636/ζ^9 + 1992/ζ^8 + 1712/ζ^7 - 2861/ζ^6 - 3461/ζ^5 - 352/ζ^4 + 10366/ζ^3 - 10154/ζ^2 - 7031/ζ - 7031*ζ - 10154*ζ^2 + 10366*ζ^3 - 352*ζ^4 - 3461*ζ^5 - 2861*ζ^6 + 1712*ζ^7 + 1992*ζ^8 - 2636*ζ^9 + 684*ζ^10 + 1066*ζ^11 - 416*ζ^12 + 7*ζ^13 + 43*ζ^14 - 23*ζ^15 - 4*ζ^16)

2u	det(2u)	a(u, Borch(ψ))
[4 -53 704]	7	0
[8 -89 992]	15	0
[4 -25 160]	15	0
[12 -109 992]	23	0
[6 -13 32]	23	0
[6 -19 64]	23	0
[14 -42 128]	28	0
[14 -70 352]	28	0
[8 -42 224]	28	0
[8 -106 1408]	28	0
[16 -113 800]	31	0
[8 -113 1600]	31	0
[14 -47 160]	31	0
[20 -101 512]	39	0
[10 -91 832]	39	0
[10 -101 1024]	39	0
[8 -27 96]	39	0
[24 -73 224]	47	0
[12 -73 448]	47	1
[4 9 32]	47	0
[16 -55 192]	47	-1
[2 4 32]	48	0
[26 76 224]	48	0
[6 12 32]	48	0
[14 36 96]	48	0
[2 3 32]	55	0
[14 -29 64]	55	-1
[14 -99 704]	55	1
[8 -35 160]	55	1
[2 2 32]	60	0
[30 -210 1472]	60	0
[16 -50 160]	60	0
[16 -178 1984]	60	-1
[10 -30 96]	60	0
[10 -50 256]	60	0
[8 -114 1632]	60	0
[2 1 32]	63	0
[16 -225 3168]	63	-3
[4 33 288]	63	3
[12 -159 2112]	63	0
[8 -97 1184]	63	-3
[2 0 32]	64	0
[2 8 64]	64	0
[2 16 160]	64	0
[4 8 32]	64	0
[20 56 160]	64	0
[10 -24 64]	64	0
[10 -144 2080]	64	0
[36 -469 6112]	71	0
[18 -181 1824]	71	2
[18 -235 3072]	71	0
[120 277 640]	71	0
[10 -43 192]	71	-2
[10 -53 288]	71	0
[40 -441 4864]	79	0
[190 441 1024]	79	0
[10 -121 1472]	79	7
[44 -397 3584]	87	0
[22 -45 96]	87	-4
[22 -243 2688]	87	7
[134 307 704]	87	0
[46 -138 416]	92	0
[46 -230 1152]	92	0
[4 6 32]	92	0
[24 -218 1984]	92	5
[26 70 192]	92	4
[162 374 864]	92	0
[6 26 128]	92	-4
[26 -86 288]	92	4
[12 -26 64]	92	5
[12 -38 128]	92	-5
[12 -122 1248]	92	4
[12 -134 1504]	92	-4
[48 -337 2368]	95	0
[24 -337 4736]	95	-15
[4 17 96]	95	5
[16 -81 416]	95	-5
[60 145 352]	95	5
[10 15 32]	95	0
[52 -261 1312]	103	0
[4 5 32]	103	0
[56 -169 512]	111	0
[120 297 736]	111	-10
[6 9 32]	111	0
[14 -183 2400]	111	-10
[10 23 64]	111	10
[2 4 64]	112	0
[58 172 512]	112	0
[4 4 32]	112	0
[28 -84 256]	112	10
[28 -140 704]	112	18
[28 -196 1376]	112	8
[14 -28 64]	112	-8
[8 12 32]	112	0
[16 -84 448]	112	10
[16 -212 2816]	112	10
[2 3 64]	119	0
[30 -451 6784]	119	0
[20 -61 192]	119	-5
[90 221 544]	119	5
[12 -61 320]	119	-5
[12 -125 1312]	119	-5
[2 2 64]	124	0
[62 -434 3040]	124	0
[4 2 32]	124	0
[32 -226 1600]	124	-1
[16 -226 3200]	124	-1
[8 34 160]	124	4
[28 -94 320]	124	-15
[10 14 32]	124	0
[14 -158 1792]	124	4
[2 1 64]	127	0
[4 1 32]	127	0
[2 0 64]	128	0
[2 8 96]	128	0
[2 16 192]	128	0
[4 0 32]	128	0
[4 16 96]	128	-32
[6 8 32]	128	0
[22 -112 576]	128	32
[22 -288 3776]	128	0
[18 -40 96]	128	16
[18 -256 3648]	128	0
[12 16 32]	128	0
[12 -64 352]	128	0
[68 -885 11520]	135	0
[34 -171 864]	135	-19
[24 -267 2976]	135	-4
[8 11 32]	135	0
[72 -793 8736]	143	0
[42 121 352]	143	5
[6 7 32]	143	0
[6 25 128]	143	26
[18 -199 2208]	143	26
[12 -25 64]	143	-5
[76 -685 6176]	151	0
[38 -115 352]	151	-55
[8 19 64]	151	55
[10 13 32]	151	0
[78 -234 704]	156	0
[78 -390 1952]	156	0
[40 -202 1024]	156	10
[40 -522 6816]	156	-40
[6 6 32]	156	0
[8 10 32]	156	0
[20 -42 96]	156	-12
[10 22 64]	156	-40
[10 42 192]	156	-4
[30 -102 352]	156	4
[16 -182 2080]	156	-4
[80 -561 3936]	159	0
[46 -143 448]	159	-76
[28 -143 736]	159	-76
[12 15 32]	159	0
[84 -421 2112]	167	0
[42 -379 3424]	167	22
[28 -421 6336]	167	0
[36 101 288]	167	54
[22 -69 224]	167	-12
[14 -155 1728]	167	12
[14 -197 2784]	167	-22
[16 -37 96]	167	-54
[88 -265 800]	175	0
[4 9 64]	175	27
[8 9 32]	175	0
[2 4 96]	176	0
[90 268 800]	176	0
[30 -92 288]	176	72
[30 -332 3680]	176	-8
[30 -452 6816]	176	0
[22 -44 96]	176	-32
[10 12 32]	176	0
[18 -92 480]	176	72
[2 3 96]	183	0
[46 -323 2272]	183	-8
[6 3 32]	183	0
[38 -125 416]	183	-8
[16 -227 3232]	183	-8
[2 2 96]	188	0
[94 -658 4608]	188	0
[48 -146 448]	188	113
[48 -530 5856]	188	-72
[6 2 32]	188	0
[6 14 64]	188	-72
[142 350 864]	188	100
[24 -338 4768]	188	-56
[8 18 64]	188	-113
[12 14 32]	188	0
[14 34 96]	188	-100
[102 242 576]	188	-68
[2 1 96]	191	0
[6 1 32]	191	0
[32 -417 5440]	191	110
[8 33 160]	191	-20
[20 -223 2496]	191	-20
[18 -95 512]	191	-110
[18 -257 3680]	191	9
[2 0 96]	192	0
[2 8 128]	192	0
[2 16 224]	192	0
[4 8 64]	192	-44
[52 152 448]	192	20
[6 0 32]	192	0
[6 24 128]	192	-48
[8 8 32]	192	0
[24 -72 224]	192	16
[24 -120 608]	192	48
[26 -368 5216]	192	0
[12 24 64]	192	20
[14 16 32]	192	0
[14 -72 384]	192	16
[100 -1301 16928]	199	0
[50 -651 8480]	199	55
[26 -341 4480]	199	-30
[10 11 32]	199	0
[10 21 64]	199	55
[16 -213 2848]	199	-30
[104 -1145 12608]	207	0
[478 1113 2592]	207	19
[26 -391 5888]	207	0
[18 -39 96]	207	52
[108 -973 8768]	215	0
[54 -595 6560]	215	0
[36 -397 4384]	215	226
[6 13 64]	215	0
[12 13 32]	215	0
[110 -330 992]	220	0
[110 -550 2752]	220	0
[4 6 64]	220	72
[56 -506 4576]	220	-56
[28 -422 6368]	220	0
[10 10 32]	220	0
[170 390 896]	220	-56
[112 -785 5504]	223	0
[4 17 128]	223	80
[8 17 64]	223	80
[14 15 32]	223	0
[116 -581 2912]	231	0
[4 5 64]	231	-5
[40 -123 384]	231	-268
[30 -453 6848]	231	0
[24 -123 640]	231	-268
[40 -133 448]	231	211
[120 -361 1088]	239	0
[248 617 1536]	239	90
[48 -151 480]	239	-63
[30 -151 768]	239	-63
[24 -361 5440]	239	0
[10 41 192]	239	-200
[20 -41 96]	239	13
[198 457 1056]	239	90
[22 -247 2784]	239	-200
[2 4 128]	240	0
[122 364 1088]	240	0
[4 4 64]	240	14
[60 -180 544]	240	-16
[60 -300 1504]	240	-40
[60 -420 2944]	240	-10
[6 12 64]	240	40
[46 132 384]	240	-56
[8 4 32]	240	0
[32 -100 320]	240	102
[32 -356 3968]	240	-106
[10 20 64]	240	16
[12 12 32]	240	0
[20 -100 512]	240	102
[16 -36 96]	240	56
[16 -228 3264]	240	-10
[2 3 128]	247	0
[62 -931 13984]	247	153
[8 3 32]	247	0
[2 2 128]	252	0
[126 -882 6176]	252	0
[4 2 64]	252	97
[42 -126 384]	252	484
[42 -210 1056]	252	568
[8 2 32]	252	0
[24 -126 672]	252	484
[14 14 32]	252	0
[18 -258 3712]	252	32
[2 1 128]	255	0
[4 1 64]	255	74
[44 -575 7520]	255	360
[8 1 32]	255	0
[14 33 96]	255	360
[2 0 128]	256	0
[2 8 160]	256	0
[2 16 256]	256	0
[4 0 64]	256	0
[4 16 128]	256	136
[8 0 32]	256	0
[8 16 64]	256	136
[8 32 160]	256	192
[26 -288 3200]	256	192
[26 -392 5920]	256	0
[16 16 32]	256	0
[20 -288 4160]	256	0
[132 -1717 22336]	263	0
[66 -331 1664]	263	23
[408 949 2208]	263	23
[22 -309 4352]	263	-253
[22 -331 4992]	263	0
[136 -1497 16480]	271	0
[74 217 640]	271	-110
[34 -103 320]	271	-318
[28 -423 6400]	271	0
[20 -103 544]	271	-318
[212 487 1120]	271	110
[140 -1261 11360]	279	0
[70 -211 640]	279	331
[268 621 1440]	279	331
[24 -339 4800]	279	492
[20 -301 4544]	279	0
[20 -109 608]	279	-325
[142 -426 1280]	284	0
[142 -710 3552]	284	0
[72 -362 1824]	284	-104
[72 -938 12224]	284	315
[450 1046 2432]	284	-104
[6 26 160]	284	-292
[58 -182 576]	284	152
[36 -182 928]	284	152
[36 -470 6144]	284	-403
[30 -154 800]	284	292
[30 -454 6880]	284	0
[24 -362 5472]	284	0
[240 554 1280]	284	-315
[18 -38 96]	284	-12
[20 -106 576]	284	403
[144 -1009 7072]	287	0
[78 -239 736]	287	472
[48 -241 1216]	287	-387
[338 785 1824]	287	472
[26 -369 5248]	287	-181
[18 -271 4096]	287	0
[148 -741 3712]	295	0
[74 -667 6016]	295	-80
[38 -421 4672]	295	-234
[10 5 32]	295	0
[226 517 1184]	295	-80
[152 -457 1376]	303	0
[4 9 96]	303	-378
[6 9 64]	303	-378
[26 -393 5952]	303	0
[2 4 160]	304	0
[154 460 1376]	304	0
[10 4 32]	304	0
[50 -164 544]	304	-776
[22 -332 5024]	304	0
[2 3 160]	311	0
[52 -157 480]	311	-488
[218 541 1344]	311	-48
[8 35 192]	311	-471
[10 3 32]	311	0
[26 -131 672]	311	471
[12 29 96]	311	488
[16 35 96]	311	48
[240 547 1248]	311	60
[2 2 160]	316	0
[158 -1106 7744]	316	0
[80 -242 736]	316	-864
[80 -882 9728]	316	540
[380 882 2048]	316	-540
[10 2 32]	316	0
[310 718 1664]	316	-864
[20 -302 4576]	316	0
[2 1 160]	319	0
[50 -159 512]	319	728
[10 1 32]	319	0
[32 -353 3904]	319	-728
[20 -289 4192]	319	-35
[2 0 160]	320	0
[2 8 192]	320	0
[4 8 96]	320	480
[84 248 736]	320	-32
[6 8 64]	320	480
[54 -272 1376]	320	96
[54 -704 9184]	320	-320
[10 0 32]	320	0
[10 40 192]	320	1024
[28 -312 3488]	320	1024
[28 -424 6432]	320	0
[14 32 96]	320	-320
[254 584 1344]	320	32
[20 -40 96]	320	-928
[18 -272 4128]	320	0
[164 -2133 27744]	327	0
[82 -1067 13888]	327	-522
[56 -619 6848]	327	18
[42 -213 1088]	327	-18
[282 651 1504]	327	522
[24 -363 5504]	327	0
[168 -1849 20352]	335	0
[766 1785 4160]	335	-60
[6 7 64]	335	60
[6 25 160]	335	-858
[36 -185 960]	335	858
[30 -455 6912]	335	0
[172 -1549 13952]	343	0
[86 -947 10432]	343	-270
[422 979 2272]	343	270
[22 -333 5056]	343	0
[174 -522 1568]	348	0
[174 -870 4352]	348	0
[4 6 96]	348	-408
[88 -794 7168]	348	87
[6 6 64]	348	-408
[44 -134 416]	348	288
[44 -486 5376]	348	785
[12 6 32]	348	0
[26 -134 704]	348	288
[26 -394 5984]	348	0
[22 -310 4384]	348	-324
[268 614 1408]	348	87
[4 17 160]	351	-930
[60 -303 1536]	351	-1028
[352 815 1888]	351	930
[20 -303 4608]	351	0
[180 -901 4512]	359	0
[4 5 96]	359	-261
[60 -901 13536]	359	261
[12 5 32]	359	0
[18 37 96]	359	-433
[184 -553 1664]	367	0
[376 937 2336]	367	-189
[46 -599 7808]	367	1748
[28 -425 6464]	367	0
[296 681 1568]	367	-189
[26 -137 736]	367	-1748
[2 4 192]	368	0
[186 556 1664]	368	0
[4 4 96]	368	72
[92 -276 832]	368	-402
[92 -460 2304]	368	-554
[62 -188 576]	368	-1208
[62 -684 7552]	368	408
[62 -932 14016]	368	-72
[8 12 64]	368	554
[48 -244 1248]	368	-408
[12 4 32]	368	0
[12 28 96]	368	1208
[324 748 1728]	368	-402
[24 -340 4832]	368	-664
[24 -364 5536]	368	0
[18 44 128]	368	-1552
[282 644 1472]	368	80
[2 3 192]	375	0
[94 -1411 21184]	375	-1410
[6 3 64]	375	1410
[40 -445 4960]	375	-596
[12 3 32]	375	0
[2 2 192]	380	0
[4 2 96]	380	-840
[6 2 64]	380	-840
[6 14 96]	380	-1256
[270 670 1664]	380	936
[8 34 192]	380	2290
[60 -190 608]	380	-1588
[38 -190 960]	380	-1588
[12 2 32]	380	0
[32 -162 832]	380	-2290
[16 34 96]	380	-936
[26 -370 5280]	380	-436
[22 -334 5088]	380	0
[20 30 64]	380	-66
[2 1 192]	383	0
[4 1 96]	383	-915
[6 1 64]	383	-915
[64 -833 10848]	383	343
[12 1 32]	383	0
[14 31 96]	383	343
[2 0 192]	384	0
[2 8 224]	384	0
[4 0 96]	384	0
[4 16 160]	384	320
[6 0 64]	384	0
[6 24 160]	384	3056
[10 24 96]	384	3056
[394 912 2112]	384	-320
[12 0 32]	384	0
[30 -456 6944]	384	0
[28 -400 5728]	384	0
[20 -304 4640]	384	0
[22 32 64]	384	0
[196 -2549 33152]	391	0
[98 -491 2464]	391	1022
[8 11 64]	391	-1022
[26 -395 6016]	391	0
[200 -2201 24224]	399	0
[106 313 928]	399	496
[50 -551 6080]	399	2036
[52 -167 544]	399	1667
[34 -377 4192]	399	-1667
[14 7 32]	399	0
[310 711 1632]	399	-496
[20 -281 3968]	399	-2766
[102 -307 928]	407	-62
[68 -749 8256]	407	174
[6 13 96]	407	-1646
[8 19 96]	407	174
[366 845 1952]	407	-62
[24 -365 5568]	407	0
[206 -618 1856]	412	0
[206 -1030 5152]	412	0
[104 -522 2624]	412	193
[104 -1354 17632]	412	-568
[8 10 64]	412	-193
[14 6 32]	412	0
[338 778 1792]	412	568
[28 -426 6496]	412	0
[110 -335 1024]	415	-296
[10 15 64]	415	296
[22 -335 5120]	415	0
[212 -1061 5312]	423	0
[72 -219 672]	423	2986
[54 -165 512]	423	312
[12 27 96]	423	-2986
[14 5 32]	423	0
[32 -165 864]	423	312
[18 27 64]	423	61
[216 -649 1952]	431	0
[4 9 128]	431	1981
[80 -247 768]	431	2725
[8 9 64]	431	1981
[10 23 96]	431	-2725
[30 -457 6976]	431	0
[22 -311 4416]	431	1671
[2 4 224]	432	0
[6 12 96]	432	2984
[14 4 32]	432	0
[18 36 96]	432	3656
[26 -396 6048]	432	0
[2 3 224]	439	0
[70 -221 704]	439	1303
[44 -221 1120]	439	1303
[14 3 32]	439	0
[20 29 64]	439	469
[2 2 224]	444	0
[112 -338 1024]	444	1610
[112 -1234 13600]	444	-624
[74 -222 672]	444	1788
[74 -370 1856]	444	1116
[8 18 96]	444	-1116
[10 14 64]	444	-624
[46 -510 5664]	444	-2380
[12 18 64]	444	-1610
[14 2 32]	444	0
[14 30 96]	444	-1788
[24 -366 5600]	444	0
[2 1 224]	447	0
[76 -991 12928]	447	1138
[8 33 192]	447	-2324
[38 -193 992]	447	2324
[14 1 32]	447	0
[16 33 96]	447	1138
[22 31 64]	447	535
[2 0 224]	448	0
[2 8 256]	448	0
[4 8 128]	448	-1616
[116 344 1024]	448	-592
[8 8 64]	448	-1616
[56 -168 512]	448	3696
[56 -280 1408]	448	7440
[14 0 32]	448	0
[16 8 32]	448	0
[16 24 64]	448	-592
[32 -168 896]	448	3696
[22 -336 5152]	448	0
[114 -1483 19296]	455	1623
[696 1621 3776]	455	-90
[14 21 64]	455	1623
[28 -427 6528]	455	0
[18 43 128]	455	1791
[24 -341 4864]	455	350
[232 -2553 28096]	463	0
[1054 2457 5728]	463	121
[58 -871 13088]	463	121
[16 7 32]	463	0
[118 -1299 14304]	471	586
[10 13 64]	471	586
[26 -371 5312]	471	3018
[26 -397 6080]	471	0
[238 -1190 5952]	476	0
[4 6 128]	476	-69
[738 1718 4000]	476	-1140
[6 26 192]	476	1544
[90 -278 864]	476	-592
[60 -902 13568]	476	69
[10 22 96]	476	592
[62 -198 640]	476	-1600
[40 -442 4896]	476	1600
[12 26 96]	476	1544
[16 6 32]	476	0
[18 26 64]	476	-568
[30 -458 7008]	476	0
[248 570 1312]	476	-1672
[4 17 192]	479	2890
[80 -401 2016]	479	35
[8 17 96]	479	-35
[12 17 64]	479	2890
[28 -401 5760]	479	-833
[24 -367 5632]	479	0
[244 -1221 6112]	487	0
[4 5 128]	487	2592
[62 -933 14048]	487	-2592
[16 5 32]	487	0
[504 1257 3136]	495	-306
[6 9 96]	495	-7180
[62 -311 1568]	495	-5085
[16 23 64]	495	306
[18 9 32]	495	0
[2 4 256]	496	0
[4 4 128]	496	-972
[124 -372 1120]	496	1920
[124 -620 3104]	496	2416
[8 4 64]	496	-972
[64 -196 608]	496	224
[64 -708 7840]	496	-1968
[10 12 64]	496	-2416
[50 -252 1280]	496	1968
[14 20 64]	496	-1920
[38 -196 1024]	496	224
[16 4 32]	496	0
[20 28 64]	496	-476
[28 -428 6560]	496	0