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 + ζ^(-4) + 2/ζ^3 + 6/ζ^2 + 6/ζ + 6*ζ + 6*ζ^2 + 2*ζ^3 + ζ^4)
  +q(6/ζ^8 + 6*ζ^8)
  +q^2(ζ^(-12) + ζ^12)
  +q^3(2/ζ^14 + 2*ζ^14)
  +q^4(10/ζ^16 + 10*ζ^16)
• From the truncated singular part of ψ, the leading Jacobi coefficient of Borch(ψ) is the theta block

  	φ	= TB(9;1,1,1,1,1,1,2,2,2,2,2,2,3,3,4)
  		= 16263241
  		= η(τ)18(θ(τ,z)/η(τ))6(θ(τ,2z)/η(τ))6(θ(τ,3z)/η(τ))2(θ(τ,4z)/η(τ))

  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)	7
  (4,14)	3
  (9,3)	2
  (16,4)	1
  (16,12)	1

• From the singular part above, we compute that the valuation Ord(ψ) is -0.25, 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 + ζ^(-4) + 2/ζ^3 + 6/ζ^2 + 6/ζ + 6*ζ + 6*ζ^2 + 2*ζ^3 + ζ^4)
+q(132 + 6/ζ^8 - 4/ζ^7 - 10/ζ^6 - 10/ζ^5 - 72/ζ^4 - 2/ζ^3 + 10/ζ^2 + 16/ζ + 16*ζ + 10*ζ^2 - 2*ζ^3 - 72*ζ^4 - 10*ζ^5 - 10*ζ^6 - 4*ζ^7 + 6*ζ^8)
+q^2(888 + ζ^(-12) + 2/ζ^11 + 2/ζ^10 + 2/ζ^9 + 100/ζ^8 - 18/ζ^7 - 36/ζ^6 - 40/ζ^5 - 545/ζ^4 - 6/ζ^3 + 34/ζ^2 + 60/ζ + 60*ζ + 34*ζ^2 - 6*ζ^3 - 545*ζ^4 - 40*ζ^5 - 36*ζ^6 - 18*ζ^7 + 100*ζ^8 + 2*ζ^9 + 2*ζ^10 + 2*ζ^11 + ζ^12)
+q^3(4240 + 2/ζ^14 + 2/ζ^13 - 56/ζ^12 + 18/ζ^11 + 20/ζ^10 + 20/ζ^9 + 792/ζ^8 - 54/ζ^7 - 112/ζ^6 - 128/ζ^5 - 2856/ζ^4 - 28/ζ^3 + 90/ζ^2 + 170/ζ + 170*ζ + 90*ζ^2 - 28*ζ^3 - 2856*ζ^4 - 128*ζ^5 - 112*ζ^6 - 54*ζ^7 + 792*ζ^8 + 20*ζ^9 + 20*ζ^10 + 18*ζ^11 - 56*ζ^12 + 2*ζ^13 + 2*ζ^14)
+q^4(17100 + 10/ζ^16 - 4/ζ^15 - 2/ζ^14 + 6/ζ^13 - 481/ζ^12 + 64/ζ^11 + 80/ζ^10 + 66/ζ^9 + 3984/ζ^8 - 154/ζ^7 - 306/ζ^6 - 358/ζ^5 - 12063/ζ^4 - 76/ζ^3 + 228/ζ^2 + 456/ζ + 456*ζ + 228*ζ^2 - 76*ζ^3 - 12063*ζ^4 - 358*ζ^5 - 306*ζ^6 - 154*ζ^7 + 3984*ζ^8 + 66*ζ^9 + 80*ζ^10 + 64*ζ^11 - 481*ζ^12 + 6*ζ^13 - 2*ζ^14 - 4*ζ^15 + 10*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	0
[4 9 32]	47	0
[16 -55 192]	47	0
[2 4 32]	48	0
[26 76 224]	48	0
[6 12 32]	48	0
[14 36 96]	48	-1
[2 3 32]	55	0
[14 -29 64]	55	0
[14 -99 704]	55	0
[8 -35 160]	55	0
[2 2 32]	60	0
[30 -210 1472]	60	0
[16 -50 160]	60	-1
[16 -178 1984]	60	-1
[10 -30 96]	60	1
[10 -50 256]	60	-1
[8 -114 1632]	60	0
[2 1 32]	63	0
[16 -225 3168]	63	0
[4 33 288]	63	0
[12 -159 2112]	63	2
[8 -97 1184]	63	0
[2 0 32]	64	0
[2 8 64]	64	0
[2 16 160]	64	0
[4 8 32]	64	0
[20 56 160]	64	1
[10 -24 64]	64	-1
[10 -144 2080]	64	0
[36 -469 6112]	71	0
[18 -181 1824]	71	0
[18 -235 3072]	71	-2
[120 277 640]	71	0
[10 -43 192]	71	0
[10 -53 288]	71	2
[40 -441 4864]	79	0
[190 441 1024]	79	0
[10 -121 1472]	79	0
[44 -397 3584]	87	0
[22 -45 96]	87	0
[22 -243 2688]	87	6
[134 307 704]	87	0
[46 -138 416]	92	0
[46 -230 1152]	92	0
[4 6 32]	92	0
[24 -218 1984]	92	6
[26 70 192]	92	4
[162 374 864]	92	0
[6 26 128]	92	-5
[26 -86 288]	92	-5
[12 -26 64]	92	6
[12 -38 128]	92	-5
[12 -122 1248]	92	4
[12 -134 1504]	92	-5
[48 -337 2368]	95	0
[24 -337 4736]	95	0
[4 17 96]	95	-4
[16 -81 416]	95	4
[60 145 352]	95	2
[10 15 32]	95	0
[52 -261 1312]	103	0
[4 5 32]	103	0
[56 -169 512]	111	0
[120 297 736]	111	-6
[6 9 32]	111	0
[14 -183 2400]	111	-8
[10 23 64]	111	6
[2 4 64]	112	0
[58 172 512]	112	0
[4 4 32]	112	0
[28 -84 256]	112	-5
[28 -140 704]	112	9
[28 -196 1376]	112	14
[14 -28 64]	112	-14
[8 12 32]	112	0
[16 -84 448]	112	-5
[16 -212 2816]	112	3
[2 3 64]	119	0
[30 -451 6784]	119	0
[20 -61 192]	119	-14
[90 221 544]	119	4
[12 -61 320]	119	-14
[12 -125 1312]	119	-4
[2 2 64]	124	0
[62 -434 3040]	124	0
[4 2 32]	124	0
[32 -226 1600]	124	-14
[16 -226 3200]	124	-14
[8 34 160]	124	1
[28 -94 320]	124	1
[10 14 32]	124	0
[14 -158 1792]	124	1
[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	3
[6 8 32]	128	0
[22 -112 576]	128	-3
[22 -288 3776]	128	-9
[18 -40 96]	128	12
[18 -256 3648]	128	0
[12 16 32]	128	0
[12 -64 352]	128	9
[68 -885 11520]	135	0
[34 -171 864]	135	14
[24 -267 2976]	135	-38
[8 11 32]	135	0
[72 -793 8736]	143	0
[42 121 352]	143	2
[6 7 32]	143	0
[6 25 128]	143	26
[18 -199 2208]	143	26
[12 -25 64]	143	-2
[76 -685 6176]	151	0
[38 -115 352]	151	-6
[8 19 64]	151	6
[10 13 32]	151	0
[78 -234 704]	156	0
[78 -390 1952]	156	0
[40 -202 1024]	156	-49
[40 -522 6816]	156	-31
[6 6 32]	156	0
[8 10 32]	156	0
[20 -42 96]	156	-44
[10 22 64]	156	-31
[10 42 192]	156	30
[30 -102 352]	156	30
[16 -182 2080]	156	30
[80 -561 3936]	159	0
[46 -143 448]	159	-2
[28 -143 736]	159	-2
[12 15 32]	159	0
[84 -421 2112]	167	0
[42 -379 3424]	167	22
[28 -421 6336]	167	0
[36 101 288]	167	16
[22 -69 224]	167	28
[14 -155 1728]	167	-28
[14 -197 2784]	167	-22
[16 -37 96]	167	-16
[88 -265 800]	175	0
[4 9 64]	175	-12
[8 9 32]	175	0
[2 4 96]	176	0
[90 268 800]	176	0
[30 -92 288]	176	34
[30 -332 3680]	176	67
[30 -452 6816]	176	0
[22 -44 96]	176	101
[10 12 32]	176	0
[18 -92 480]	176	34
[2 3 96]	183	0
[46 -323 2272]	183	12
[6 3 32]	183	0
[38 -125 416]	183	-38
[16 -227 3232]	183	12
[2 2 96]	188	0
[94 -658 4608]	188	0
[48 -146 448]	188	27
[48 -530 5856]	188	15
[6 2 32]	188	0
[6 14 64]	188	15
[142 350 864]	188	-37
[24 -338 4768]	188	104
[8 18 64]	188	-27
[12 14 32]	188	0
[14 34 96]	188	37
[102 242 576]	188	5
[2 1 96]	191	0
[6 1 32]	191	0
[32 -417 5440]	191	-38
[8 33 160]	191	-26
[20 -223 2496]	191	-26
[18 -95 512]	191	38
[18 -257 3680]	191	28
[2 0 96]	192	0
[2 8 128]	192	0
[2 16 224]	192	0
[4 8 64]	192	-76
[52 152 448]	192	36
[6 0 32]	192	0
[6 24 128]	192	-26
[8 8 32]	192	0
[24 -72 224]	192	-22
[24 -120 608]	192	26
[26 -368 5216]	192	0
[12 24 64]	192	36
[14 16 32]	192	0
[14 -72 384]	192	-22
[100 -1301 16928]	199	0
[50 -651 8480]	199	34
[26 -341 4480]	199	22
[10 11 32]	199	0
[10 21 64]	199	34
[16 -213 2848]	199	22
[104 -1145 12608]	207	0
[478 1113 2592]	207	-44
[26 -391 5888]	207	0
[18 -39 96]	207	50
[108 -973 8768]	215	0
[54 -595 6560]	215	-50
[36 -397 4384]	215	108
[6 13 64]	215	-50
[12 13 32]	215	0
[110 -330 992]	220	0
[110 -550 2752]	220	0
[4 6 64]	220	57
[56 -506 4576]	220	-29
[28 -422 6368]	220	0
[10 10 32]	220	0
[170 390 896]	220	-29
[112 -785 5504]	223	0
[4 17 128]	223	26
[8 17 64]	223	26
[14 15 32]	223	0
[116 -581 2912]	231	0
[4 5 64]	231	2
[40 -123 384]	231	56
[30 -453 6848]	231	0
[24 -123 640]	231	56
[40 -133 448]	231	-210
[120 -361 1088]	239	0
[248 617 1536]	239	80
[48 -151 480]	239	12
[30 -151 768]	239	12
[24 -361 5440]	239	0
[10 41 192]	239	-164
[20 -41 96]	239	18
[198 457 1056]	239	80
[22 -247 2784]	239	-164
[2 4 128]	240	0
[122 364 1088]	240	0
[4 4 64]	240	-77
[60 -180 544]	240	-12
[60 -300 1504]	240	-22
[60 -420 2944]	240	-87
[6 12 64]	240	22
[46 132 384]	240	-66
[8 4 32]	240	0
[32 -100 320]	240	-55
[32 -356 3968]	240	-111
[10 20 64]	240	12
[12 12 32]	240	0
[20 -100 512]	240	-55
[16 -36 96]	240	66
[16 -228 3264]	240	-87
[2 3 128]	247	0
[62 -931 13984]	247	42
[8 3 32]	247	0
[2 2 128]	252	0
[126 -882 6176]	252	0
[4 2 64]	252	103
[42 -126 384]	252	-303
[42 -210 1056]	252	483
[8 2 32]	252	0
[24 -126 672]	252	-303
[14 14 32]	252	0
[18 -258 3712]	252	61
[2 1 128]	255	0
[4 1 64]	255	-8
[44 -575 7520]	255	-112
[8 1 32]	255	0
[14 33 96]	255	-112
[2 0 128]	256	0
[2 8 160]	256	0
[2 16 256]	256	0
[4 0 64]	256	0
[4 16 128]	256	-8
[8 0 32]	256	0
[8 16 64]	256	-8
[8 32 160]	256	52
[26 -288 3200]	256	52
[26 -392 5920]	256	0
[16 16 32]	256	0
[20 -288 4160]	256	0
[132 -1717 22336]	263	0
[66 -331 1664]	263	-158
[408 949 2208]	263	-158
[22 -309 4352]	263	216
[22 -331 4992]	263	0
[136 -1497 16480]	271	0
[74 217 640]	271	-40
[34 -103 320]	271	-32
[28 -423 6400]	271	0
[20 -103 544]	271	-32
[212 487 1120]	271	40
[140 -1261 11360]	279	0
[70 -211 640]	279	104
[268 621 1440]	279	104
[24 -339 4800]	279	-124
[20 -301 4544]	279	0
[20 -109 608]	279	-210
[142 -426 1280]	284	0
[142 -710 3552]	284	0
[72 -362 1824]	284	372
[72 -938 12224]	284	198
[450 1046 2432]	284	372
[6 26 160]	284	62
[58 -182 576]	284	-62
[36 -182 928]	284	-62
[36 -470 6144]	284	-196
[30 -154 800]	284	-62
[30 -454 6880]	284	0
[24 -362 5472]	284	0
[240 554 1280]	284	-198
[18 -38 96]	284	24
[20 -106 576]	284	196
[144 -1009 7072]	287	0
[78 -239 736]	287	-4
[48 -241 1216]	287	-524
[338 785 1824]	287	-4
[26 -369 5248]	287	-286
[18 -271 4096]	287	0
[148 -741 3712]	295	0
[74 -667 6016]	295	-242
[38 -421 4672]	295	-214
[10 5 32]	295	0
[226 517 1184]	295	-242
[152 -457 1376]	303	0
[4 9 96]	303	94
[6 9 64]	303	94
[26 -393 5952]	303	0
[2 4 160]	304	0
[154 460 1376]	304	0
[10 4 32]	304	0
[50 -164 544]	304	314
[22 -332 5024]	304	0
[2 3 160]	311	0
[52 -157 480]	311	358
[218 541 1344]	311	-484
[8 35 192]	311	170
[10 3 32]	311	0
[26 -131 672]	311	-170
[12 29 96]	311	-358
[16 35 96]	311	484
[240 547 1248]	311	106
[2 2 160]	316	0
[158 -1106 7744]	316	0
[80 -242 736]	316	-185
[80 -882 9728]	316	-83
[380 882 2048]	316	83
[10 2 32]	316	0
[310 718 1664]	316	-185
[20 -302 4576]	316	0
[2 1 160]	319	0
[50 -159 512]	319	2
[10 1 32]	319	0
[32 -353 3904]	319	-2
[20 -289 4192]	319	-284
[2 0 160]	320	0
[2 8 192]	320	0
[4 8 96]	320	650
[84 248 736]	320	-274
[6 8 64]	320	650
[54 -272 1376]	320	-72
[54 -704 9184]	320	-96
[10 0 32]	320	0
[10 40 192]	320	166
[28 -312 3488]	320	166
[28 -424 6432]	320	0
[14 32 96]	320	-96
[254 584 1344]	320	274
[20 -40 96]	320	-482
[18 -272 4128]	320	0
[164 -2133 27744]	327	0
[82 -1067 13888]	327	-186
[56 -619 6848]	327	-536
[42 -213 1088]	327	536
[282 651 1504]	327	186
[24 -363 5504]	327	0
[168 -1849 20352]	335	0
[766 1785 4160]	335	506
[6 7 64]	335	-506
[6 25 160]	335	516
[36 -185 960]	335	-516
[30 -455 6912]	335	0
[172 -1549 13952]	343	0
[86 -947 10432]	343	112
[422 979 2272]	343	-112
[22 -333 5056]	343	0
[174 -522 1568]	348	0
[174 -870 4352]	348	0
[4 6 96]	348	-428
[88 -794 7168]	348	78
[6 6 64]	348	-428
[44 -134 416]	348	24
[44 -486 5376]	348	598
[12 6 32]	348	0
[26 -134 704]	348	24
[26 -394 5984]	348	0
[22 -310 4384]	348	-624
[268 614 1408]	348	78
[4 17 160]	351	6
[60 -303 1536]	351	1292
[352 815 1888]	351	-6
[20 -303 4608]	351	0
[180 -901 4512]	359	0
[4 5 96]	359	38
[60 -901 13536]	359	-38
[12 5 32]	359	0
[18 37 96]	359	-70
[184 -553 1664]	367	0
[376 937 2336]	367	-508
[46 -599 7808]	367	-152
[28 -425 6464]	367	0
[296 681 1568]	367	-508
[26 -137 736]	367	152
[2 4 192]	368	0
[186 556 1664]	368	0
[4 4 96]	368	670
[92 -276 832]	368	323
[92 -460 2304]	368	-295
[62 -188 576]	368	358
[62 -684 7552]	368	1042
[62 -932 14016]	368	-670
[8 12 64]	368	295
[48 -244 1248]	368	-1042
[12 4 32]	368	0
[12 28 96]	368	-358
[324 748 1728]	368	323
[24 -340 4832]	368	-730
[24 -364 5536]	368	0
[18 44 128]	368	-116
[282 644 1472]	368	-52
[2 3 192]	375	0
[94 -1411 21184]	375	-470
[6 3 64]	375	470
[40 -445 4960]	375	-342
[12 3 32]	375	0
[2 2 192]	380	0
[4 2 96]	380	-1066
[6 2 64]	380	-1066
[6 14 96]	380	2511
[270 670 1664]	380	1383
[8 34 192]	380	-1209
[60 -190 608]	380	-799
[38 -190 960]	380	-799
[12 2 32]	380	0
[32 -162 832]	380	1209
[16 34 96]	380	-1383
[26 -370 5280]	380	1742
[22 -334 5088]	380	0
[20 30 64]	380	338
[2 1 192]	383	0
[4 1 96]	383	46
[6 1 64]	383	46
[64 -833 10848]	383	320
[12 1 32]	383	0
[14 31 96]	383	320
[2 0 192]	384	0
[2 8 224]	384	0
[4 0 96]	384	0
[4 16 160]	384	-184
[6 0 64]	384	0
[6 24 160]	384	-604
[10 24 96]	384	-604
[394 912 2112]	384	184
[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	728
[8 11 64]	391	-728
[26 -395 6016]	391	0
[200 -2201 24224]	399	0
[106 313 928]	399	252
[50 -551 6080]	399	1036
[52 -167 544]	399	-168
[34 -377 4192]	399	168
[14 7 32]	399	0
[310 711 1632]	399	-252
[20 -281 3968]	399	-1502
[102 -307 928]	407	-664
[68 -749 8256]	407	304
[6 13 96]	407	-996
[8 19 96]	407	304
[366 845 1952]	407	-664
[24 -365 5568]	407	0
[206 -618 1856]	412	0
[206 -1030 5152]	412	0
[104 -522 2624]	412	-638
[104 -1354 17632]	412	-244
[8 10 64]	412	638
[14 6 32]	412	0
[338 778 1792]	412	244
[28 -426 6496]	412	0
[110 -335 1024]	415	166
[10 15 64]	415	-166
[22 -335 5120]	415	0
[212 -1061 5312]	423	0
[72 -219 672]	423	-910
[54 -165 512]	423	-160
[12 27 96]	423	910
[14 5 32]	423	0
[32 -165 864]	423	-160
[18 27 64]	423	-1010
[216 -649 1952]	431	0
[4 9 128]	431	-90
[80 -247 768]	431	834
[8 9 64]	431	-90
[10 23 96]	431	-834
[30 -457 6976]	431	0
[22 -311 4416]	431	1066
[2 4 224]	432	0
[6 12 96]	432	-2927
[14 4 32]	432	0
[18 36 96]	432	1174
[26 -396 6048]	432	0
[2 3 224]	439	0
[70 -221 704]	439	1914
[44 -221 1120]	439	1914
[14 3 32]	439	0
[20 29 64]	439	218
[2 2 224]	444	0
[112 -338 1024]	444	453
[112 -1234 13600]	444	387
[74 -222 672]	444	-341
[74 -370 1856]	444	1789
[8 18 96]	444	-1789
[10 14 64]	444	387
[46 -510 5664]	444	179
[12 18 64]	444	-453
[14 2 32]	444	0
[14 30 96]	444	341
[24 -366 5600]	444	0
[2 1 224]	447	0
[76 -991 12928]	447	1446
[8 33 192]	447	1180
[38 -193 992]	447	-1180
[14 1 32]	447	0
[16 33 96]	447	1446
[22 31 64]	447	920
[2 0 224]	448	0
[2 8 256]	448	0
[4 8 128]	448	-1584
[116 344 1024]	448	208
[8 8 64]	448	-1584
[56 -168 512]	448	-944
[56 -280 1408]	448	2544
[14 0 32]	448	0
[16 8 32]	448	0
[16 24 64]	448	208
[32 -168 896]	448	-944
[22 -336 5152]	448	0
[114 -1483 19296]	455	268
[696 1621 3776]	455	-2982
[14 21 64]	455	268
[28 -427 6528]	455	0
[18 43 128]	455	840
[24 -341 4864]	455	2306
[232 -2553 28096]	463	0
[1054 2457 5728]	463	-2174
[58 -871 13088]	463	-2174
[16 7 32]	463	0
[118 -1299 14304]	471	104
[10 13 64]	471	104
[26 -371 5312]	471	-2146
[26 -397 6080]	471	0
[238 -1190 5952]	476	0
[4 6 128]	476	574
[738 1718 4000]	476	-71
[6 26 192]	476	-1500
[90 -278 864]	476	-2172
[60 -902 13568]	476	-574
[10 22 96]	476	2172
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[40 -442 4896]	476	341
[12 26 96]	476	-1500
[16 6 32]	476	0
[18 26 64]	476	868
[30 -458 7008]	476	0
[248 570 1312]	476	-1517
[4 17 192]	479	-430
[80 -401 2016]	479	-780
[8 17 96]	479	780
[12 17 64]	479	-430
[28 -401 5760]	479	-2498
[24 -367 5632]	479	0
[244 -1221 6112]	487	0
[4 5 128]	487	-558
[62 -933 14048]	487	558
[16 5 32]	487	0
[504 1257 3136]	495	1934
[6 9 96]	495	1200
[62 -311 1568]	495	-224
[16 23 64]	495	-1934
[18 9 32]	495	0
[2 4 256]	496	0
[4 4 128]	496	-1806
[124 -372 1120]	496	-896
[124 -620 3104]	496	1540
[8 4 64]	496	-1806
[64 -196 608]	496	-288
[64 -708 7840]	496	-636
[10 12 64]	496	-1540
[50 -252 1280]	496	636
[14 20 64]	496	896
[38 -196 1024]	496	-288
[16 4 32]	496	0
[20 28 64]	496	630
[28 -428 6560]	496	0