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 + 2/ζ^3 + 11/ζ^2 + 2/ζ + 2*ζ + 11*ζ^2 + 2*ζ^3)
  +q(-5/ζ^8 - 5*ζ^8)
  +q^2(ζ^(-12) + ζ^12)
  +q^3(9/ζ^14 + 9*ζ^14)
  +q^4(12/ζ^16 + 12*ζ^16)
• From the truncated singular part of ψ, the leading Jacobi coefficient of Borch(ψ) is the theta block

  	φ	= TB(9;1,1,2,2,2,2,2,2,2,2,2,2,2,3,3)
  		= 1221132
  		= η(τ)18(θ(τ,z)/η(τ))2(θ(τ,2z)/η(τ))11(θ(τ,3z)/η(τ))2

  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)	11
  (4,14)	9
  (9,3)	2
  (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 + 2/ζ^3 + 11/ζ^2 + 2/ζ + 2*ζ + 11*ζ^2 + 2*ζ^3)
+q(90 - 5/ζ^8 - 8/ζ^7 - 17/ζ^6 + 6/ζ^5 - 40/ζ^4 + 26/ζ^3 + 17/ζ^2 - 24/ζ - 24*ζ + 17*ζ^2 + 26*ζ^3 - 40*ζ^4 + 6*ζ^5 - 17*ζ^6 - 8*ζ^7 - 5*ζ^8)
+q^2(508 + ζ^(-12) + 6/ζ^11 - 3/ζ^10 - 18/ζ^9 + 34/ζ^8 - 82/ζ^7 - 46/ζ^6 + 100/ζ^5 - 289/ζ^4 + 214/ζ^3 + 49/ζ^2 - 220/ζ - 220*ζ + 49*ζ^2 + 214*ζ^3 - 289*ζ^4 + 100*ζ^5 - 46*ζ^6 - 82*ζ^7 + 34*ζ^8 - 18*ζ^9 - 3*ζ^10 + 6*ζ^11 + ζ^12)
+q^3(2280 + 9/ζ^14 + 10/ζ^13 - 24/ζ^12 + 70/ζ^11 + 6/ζ^10 - 152/ζ^9 + 364/ζ^8 - 474/ζ^7 - 140/ζ^6 + 656/ζ^5 - 1480/ζ^4 + 1120/ζ^3 + 125/ζ^2 - 1230/ζ - 1230*ζ + 125*ζ^2 + 1120*ζ^3 - 1480*ζ^4 + 656*ζ^5 - 140*ζ^6 - 474*ζ^7 + 364*ζ^8 - 152*ζ^9 + 6*ζ^10 + 70*ζ^11 - 24*ζ^12 + 10*ζ^13 + 9*ζ^14)
+q^4(8920 + 12/ζ^16 - 16/ζ^15 + 3/ζ^14 + 90/ζ^13 - 224/ζ^12 + 408/ζ^11 + 60/ζ^10 - 878/ζ^9 + 1928/ζ^8 - 2158/ζ^7 - 341/ζ^6 + 3074/ζ^5 - 6176/ζ^4 + 4748/ζ^3 + 278/ζ^2 - 5268/ζ - 5268*ζ + 278*ζ^2 + 4748*ζ^3 - 6176*ζ^4 + 3074*ζ^5 - 341*ζ^6 - 2158*ζ^7 + 1928*ζ^8 - 878*ζ^9 + 60*ζ^10 + 408*ζ^11 - 224*ζ^12 + 90*ζ^13 + 3*ζ^14 - 16*ζ^15 + 12*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	1
[20 -101 512]	39	0
[10 -91 832]	39	0
[10 -101 1024]	39	0
[8 -27 96]	39	-1
[24 -73 224]	47	0
[12 -73 448]	47	0
[4 9 32]	47	0
[16 -55 192]	47	5
[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	0
[14 -99 704]	55	0
[8 -35 160]	55	-6
[2 2 32]	60	0
[30 -210 1472]	60	0
[16 -50 160]	60	-2
[16 -178 1984]	60	2
[10 -30 96]	60	2
[10 -50 256]	60	-2
[8 -114 1632]	60	0
[2 1 32]	63	0
[16 -225 3168]	63	0
[4 33 288]	63	0
[12 -159 2112]	63	1
[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	0
[18 -235 3072]	71	-1
[120 277 640]	71	0
[10 -43 192]	71	-8
[10 -53 288]	71	1
[40 -441 4864]	79	0
[190 441 1024]	79	0
[10 -121 1472]	79	19
[44 -397 3584]	87	0
[22 -45 96]	87	0
[22 -243 2688]	87	10
[134 307 704]	87	0
[46 -138 416]	92	0
[46 -230 1152]	92	0
[4 6 32]	92	0
[24 -218 1984]	92	0
[26 70 192]	92	0
[162 374 864]	92	0
[6 26 128]	92	14
[26 -86 288]	92	-2
[12 -26 64]	92	0
[12 -38 128]	92	18
[12 -122 1248]	92	0
[12 -134 1504]	92	14
[48 -337 2368]	95	0
[24 -337 4736]	95	0
[4 17 96]	95	7
[16 -81 416]	95	-7
[60 145 352]	95	9
[10 15 32]	95	0
[52 -261 1312]	103	0
[4 5 32]	103	0
[56 -169 512]	111	0
[120 297 736]	111	-11
[6 9 32]	111	0
[14 -183 2400]	111	9
[10 23 64]	111	11
[2 4 64]	112	0
[58 172 512]	112	0
[4 4 32]	112	0
[28 -84 256]	112	20
[28 -140 704]	112	20
[28 -196 1376]	112	0
[14 -28 64]	112	0
[8 12 32]	112	0
[16 -84 448]	112	20
[16 -212 2816]	112	12
[2 3 64]	119	0
[30 -451 6784]	119	0
[20 -61 192]	119	15
[90 221 544]	119	2
[12 -61 320]	119	15
[12 -125 1312]	119	-2
[2 2 64]	124	0
[62 -434 3040]	124	0
[4 2 32]	124	0
[32 -226 1600]	124	0
[16 -226 3200]	124	0
[8 34 160]	124	42
[28 -94 320]	124	54
[10 14 32]	124	0
[14 -158 1792]	124	42
[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	-40
[6 8 32]	128	0
[22 -112 576]	128	40
[22 -288 3776]	128	8
[18 -40 96]	128	0
[18 -256 3648]	128	0
[12 16 32]	128	0
[12 -64 352]	128	-8
[68 -885 11520]	135	0
[34 -171 864]	135	48
[24 -267 2976]	135	45
[8 11 32]	135	0
[72 -793 8736]	143	0
[42 121 352]	143	-55
[6 7 32]	143	0
[6 25 128]	143	26
[18 -199 2208]	143	26
[12 -25 64]	143	55
[76 -685 6176]	151	0
[38 -115 352]	151	5
[8 19 64]	151	-5
[10 13 32]	151	0
[78 -234 704]	156	0
[78 -390 1952]	156	0
[40 -202 1024]	156	-90
[40 -522 6816]	156	90
[6 6 32]	156	0
[8 10 32]	156	0
[20 -42 96]	156	0
[10 22 64]	156	90
[10 42 192]	156	84
[30 -102 352]	156	196
[16 -182 2080]	156	84
[80 -561 3936]	159	0
[46 -143 448]	159	56
[28 -143 736]	159	56
[12 15 32]	159	0
[84 -421 2112]	167	0
[42 -379 3424]	167	-165
[28 -421 6336]	167	0
[36 101 288]	167	-32
[22 -69 224]	167	99
[14 -155 1728]	167	-99
[14 -197 2784]	167	165
[16 -37 96]	167	32
[88 -265 800]	175	0
[4 9 64]	175	153
[8 9 32]	175	0
[2 4 96]	176	0
[90 268 800]	176	0
[30 -92 288]	176	112
[30 -332 3680]	176	-16
[30 -452 6816]	176	0
[22 -44 96]	176	0
[10 12 32]	176	0
[18 -92 480]	176	112
[2 3 96]	183	0
[46 -323 2272]	183	-330
[6 3 32]	183	0
[38 -125 416]	183	34
[16 -227 3232]	183	-330
[2 2 96]	188	0
[94 -658 4608]	188	0
[48 -146 448]	188	-262
[48 -530 5856]	188	262
[6 2 32]	188	0
[6 14 64]	188	262
[142 350 864]	188	-10
[24 -338 4768]	188	0
[8 18 64]	188	262
[12 14 32]	188	0
[14 34 96]	188	10
[102 242 576]	188	90
[2 1 96]	191	0
[6 1 32]	191	0
[32 -417 5440]	191	106
[8 33 160]	191	35
[20 -223 2496]	191	35
[18 -95 512]	191	-106
[18 -257 3680]	191	462
[2 0 96]	192	0
[2 8 128]	192	0
[2 16 224]	192	0
[4 8 64]	192	-240
[52 152 448]	192	-240
[6 0 32]	192	0
[6 24 128]	192	-160
[8 8 32]	192	0
[24 -72 224]	192	-96
[24 -120 608]	192	160
[26 -368 5216]	192	0
[12 24 64]	192	-240
[14 16 32]	192	0
[14 -72 384]	192	-96
[100 -1301 16928]	199	0
[50 -651 8480]	199	-111
[26 -341 4480]	199	3
[10 11 32]	199	0
[10 21 64]	199	-111
[16 -213 2848]	199	3
[104 -1145 12608]	207	0
[478 1113 2592]	207	375
[26 -391 5888]	207	0
[18 -39 96]	207	-207
[108 -973 8768]	215	0
[54 -595 6560]	215	215
[36 -397 4384]	215	-283
[6 13 64]	215	215
[12 13 32]	215	0
[110 -330 992]	220	0
[110 -550 2752]	220	0
[4 6 64]	220	418
[56 -506 4576]	220	-418
[28 -422 6368]	220	0
[10 10 32]	220	0
[170 390 896]	220	-418
[112 -785 5504]	223	0
[4 17 128]	223	22
[8 17 64]	223	22
[14 15 32]	223	0
[116 -581 2912]	231	0
[4 5 64]	231	748
[40 -123 384]	231	-17
[30 -453 6848]	231	0
[24 -123 640]	231	-17
[40 -133 448]	231	578
[120 -361 1088]	239	0
[248 617 1536]	239	-556
[48 -151 480]	239	174
[30 -151 768]	239	174
[24 -361 5440]	239	0
[10 41 192]	239	323
[20 -41 96]	239	593
[198 457 1056]	239	-556
[22 -247 2784]	239	323
[2 4 128]	240	0
[122 364 1088]	240	0
[4 4 64]	240	-484
[60 -180 544]	240	880
[60 -300 1504]	240	880
[60 -420 2944]	240	-484
[6 12 64]	240	-880
[46 132 384]	240	-144
[8 4 32]	240	0
[32 -100 320]	240	92
[32 -356 3968]	240	516
[10 20 64]	240	-880
[12 12 32]	240	0
[20 -100 512]	240	92
[16 -36 96]	240	144
[16 -228 3264]	240	-484
[2 3 128]	247	0
[62 -931 13984]	247	1210
[8 3 32]	247	0
[2 2 128]	252	0
[126 -882 6176]	252	0
[4 2 64]	252	330
[42 -126 384]	252	-526
[42 -210 1056]	252	-274
[8 2 32]	252	0
[24 -126 672]	252	-526
[14 14 32]	252	0
[18 -258 3712]	252	330
[2 1 128]	255	0
[4 1 64]	255	1551
[44 -575 7520]	255	-493
[8 1 32]	255	0
[14 33 96]	255	-493
[2 0 128]	256	0
[2 8 160]	256	0
[2 16 256]	256	0
[4 0 64]	256	0
[4 16 128]	256	-1280
[8 0 32]	256	0
[8 16 64]	256	-1280
[8 32 160]	256	-32
[26 -288 3200]	256	-32
[26 -392 5920]	256	0
[16 16 32]	256	0
[20 -288 4160]	256	0
[132 -1717 22336]	263	0
[66 -331 1664]	263	593
[408 949 2208]	263	593
[22 -309 4352]	263	1012
[22 -331 4992]	263	0
[136 -1497 16480]	271	0
[74 217 640]	271	-1368
[34 -103 320]	271	-489
[28 -423 6400]	271	0
[20 -103 544]	271	-489
[212 487 1120]	271	1368
[140 -1261 11360]	279	0
[70 -211 640]	279	-605
[268 621 1440]	279	-605
[24 -339 4800]	279	-1166
[20 -301 4544]	279	0
[20 -109 608]	279	350
[142 -426 1280]	284	0
[142 -710 3552]	284	0
[72 -362 1824]	284	-1760
[72 -938 12224]	284	1760
[450 1046 2432]	284	-1760
[6 26 160]	284	1124
[58 -182 576]	284	-620
[36 -182 928]	284	-620
[36 -470 6144]	284	-340
[30 -154 800]	284	-1124
[30 -454 6880]	284	0
[24 -362 5472]	284	0
[240 554 1280]	284	-1760
[18 -38 96]	284	-560
[20 -106 576]	284	340
[144 -1009 7072]	287	0
[78 -239 736]	287	7
[48 -241 1216]	287	-1196
[338 785 1824]	287	7
[26 -369 5248]	287	1089
[18 -271 4096]	287	0
[148 -741 3712]	295	0
[74 -667 6016]	295	-2089
[38 -421 4672]	295	-237
[10 5 32]	295	0
[226 517 1184]	295	-2089
[152 -457 1376]	303	0
[4 9 96]	303	1403
[6 9 64]	303	1403
[26 -393 5952]	303	0
[2 4 160]	304	0
[154 460 1376]	304	0
[10 4 32]	304	0
[50 -164 544]	304	-1616
[22 -332 5024]	304	0
[2 3 160]	311	0
[52 -157 480]	311	736
[218 541 1344]	311	-1620
[8 35 192]	311	-21
[10 3 32]	311	0
[26 -131 672]	311	21
[12 29 96]	311	-736
[16 35 96]	311	1620
[240 547 1248]	311	2189
[2 2 160]	316	0
[158 -1106 7744]	316	0
[80 -242 736]	316	-3138
[80 -882 9728]	316	3138
[380 882 2048]	316	-3138
[10 2 32]	316	0
[310 718 1664]	316	-3138
[20 -302 4576]	316	0
[2 1 160]	319	0
[50 -159 512]	319	-346
[10 1 32]	319	0
[32 -353 3904]	319	346
[20 -289 4192]	319	1892
[2 0 160]	320	0
[2 8 192]	320	0
[4 8 96]	320	-2224
[84 248 736]	320	-2224
[6 8 64]	320	-2224
[54 -272 1376]	320	1792
[54 -704 9184]	320	-1792
[10 0 32]	320	0
[10 40 192]	320	256
[28 -312 3488]	320	256
[28 -424 6432]	320	0
[14 32 96]	320	-1792
[254 584 1344]	320	2224
[20 -40 96]	320	1552
[18 -272 4128]	320	0
[164 -2133 27744]	327	0
[82 -1067 13888]	327	-2137
[56 -619 6848]	327	857
[42 -213 1088]	327	-857
[282 651 1504]	327	2137
[24 -363 5504]	327	0
[168 -1849 20352]	335	0
[766 1785 4160]	335	2729
[6 7 64]	335	-2729
[6 25 160]	335	-111
[36 -185 960]	335	111
[30 -455 6912]	335	0
[172 -1549 13952]	343	0
[86 -947 10432]	343	240
[422 979 2272]	343	-240
[22 -333 5056]	343	0
[174 -522 1568]	348	0
[174 -870 4352]	348	0
[4 6 96]	348	1808
[88 -794 7168]	348	-1808
[6 6 64]	348	1808
[44 -134 416]	348	-320
[44 -486 5376]	348	-1344
[12 6 32]	348	0
[26 -134 704]	348	-320
[26 -394 5984]	348	0
[22 -310 4384]	348	3264
[268 614 1408]	348	-1808
[4 17 160]	351	-1516
[60 -303 1536]	351	3288
[352 815 1888]	351	1516
[20 -303 4608]	351	0
[180 -901 4512]	359	0
[4 5 96]	359	3923
[60 -901 13536]	359	-3923
[12 5 32]	359	0
[18 37 96]	359	-3724
[184 -553 1664]	367	0
[376 937 2336]	367	-3322
[46 -599 7808]	367	-1343
[28 -425 6464]	367	0
[296 681 1568]	367	-3322
[26 -137 736]	367	1343
[2 4 192]	368	0
[186 556 1664]	368	0
[4 4 96]	368	-944
[92 -276 832]	368	4060
[92 -460 2304]	368	4060
[62 -188 576]	368	4048
[62 -684 7552]	368	-1840
[62 -932 14016]	368	944
[8 12 64]	368	-4060
[48 -244 1248]	368	1840
[12 4 32]	368	0
[12 28 96]	368	-4048
[324 748 1728]	368	4060
[24 -340 4832]	368	-4688
[24 -364 5536]	368	0
[18 44 128]	368	720
[282 644 1472]	368	944
[2 3 192]	375	0
[94 -1411 21184]	375	4037
[6 3 64]	375	-4037
[40 -445 4960]	375	1243
[12 3 32]	375	0
[2 2 192]	380	0
[4 2 96]	380	308
[6 2 64]	380	308
[6 14 96]	380	5574
[270 670 1664]	380	-4314
[8 34 192]	380	14
[60 -190 608]	380	2258
[38 -190 960]	380	2258
[12 2 32]	380	0
[32 -162 832]	380	-14
[16 34 96]	380	4314
[26 -370 5280]	380	3740
[22 -334 5088]	380	0
[20 30 64]	380	308
[2 1 192]	383	0
[4 1 96]	383	3421
[6 1 64]	383	3421
[64 -833 10848]	383	3812
[12 1 32]	383	0
[14 31 96]	383	3812
[2 0 192]	384	0
[2 8 224]	384	0
[4 0 96]	384	0
[4 16 160]	384	-4640
[6 0 64]	384	0
[6 24 160]	384	-3584
[10 24 96]	384	-3584
[394 912 2112]	384	4640
[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	1484
[8 11 64]	391	-1484
[26 -395 6016]	391	0
[200 -2201 24224]	399	0
[106 313 928]	399	-2398
[50 -551 6080]	399	2086
[52 -167 544]	399	-2132
[34 -377 4192]	399	2132
[14 7 32]	399	0
[310 711 1632]	399	2398
[20 -281 3968]	399	5877
[102 -307 928]	407	-2640
[68 -749 8256]	407	-3401
[6 13 96]	407	6495
[8 19 96]	407	-3401
[366 845 1952]	407	-2640
[24 -365 5568]	407	0
[206 -618 1856]	412	0
[206 -1030 5152]	412	0
[104 -522 2624]	412	-2320
[104 -1354 17632]	412	2320
[8 10 64]	412	2320
[14 6 32]	412	0
[338 778 1792]	412	-2320
[28 -426 6496]	412	0
[110 -335 1024]	415	-844
[10 15 64]	415	844
[22 -335 5120]	415	0
[212 -1061 5312]	423	0
[72 -219 672]	423	-3021
[54 -165 512]	423	1128
[12 27 96]	423	3021
[14 5 32]	423	0
[32 -165 864]	423	1128
[18 27 64]	423	659
[216 -649 1952]	431	0
[4 9 128]	431	2671
[80 -247 768]	431	-26
[8 9 64]	431	2671
[10 23 96]	431	26
[30 -457 6976]	431	0
[22 -311 4416]	431	-6367
[2 4 224]	432	0
[6 12 96]	432	-9648
[14 4 32]	432	0
[18 36 96]	432	-7632
[26 -396 6048]	432	0
[2 3 224]	439	0
[70 -221 704]	439	739
[44 -221 1120]	439	739
[14 3 32]	439	0
[20 29 64]	439	-1409
[2 2 224]	444	0
[112 -338 1024]	444	-470
[112 -1234 13600]	444	470
[74 -222 672]	444	-9498
[74 -370 1856]	444	-5718
[8 18 96]	444	5718
[10 14 64]	444	470
[46 -510 5664]	444	-4602
[12 18 64]	444	470
[14 2 32]	444	0
[14 30 96]	444	9498
[24 -366 5600]	444	0
[2 1 224]	447	0
[76 -991 12928]	447	-10353
[8 33 192]	447	-352
[38 -193 992]	447	352
[14 1 32]	447	0
[16 33 96]	447	-10353
[22 31 64]	447	3894
[2 0 224]	448	0
[2 8 256]	448	0
[4 8 128]	448	256
[116 344 1024]	448	256
[8 8 64]	448	256
[56 -168 512]	448	2240
[56 -280 1408]	448	-1088
[14 0 32]	448	0
[16 8 32]	448	0
[16 24 64]	448	256
[32 -168 896]	448	2240
[22 -336 5152]	448	0
[114 -1483 19296]	455	1055
[696 1621 3776]	455	10297
[14 21 64]	455	1055
[28 -427 6528]	455	0
[18 43 128]	455	3692
[24 -341 4864]	455	5199
[232 -2553 28096]	463	0
[1054 2457 5728]	463	29
[58 -871 13088]	463	29
[16 7 32]	463	0
[118 -1299 14304]	471	2243
[10 13 64]	471	2243
[26 -371 5312]	471	-4481
[26 -397 6080]	471	0
[238 -1190 5952]	476	0
[4 6 128]	476	-928
[738 1718 4000]	476	-10262
[6 26 192]	476	9232
[90 -278 864]	476	-5872
[60 -902 13568]	476	928
[10 22 96]	476	5872
[62 -198 640]	476	7038
[40 -442 4896]	476	-7038
[12 26 96]	476	9232
[16 6 32]	476	0
[18 26 64]	476	-928
[30 -458 7008]	476	0
[248 570 1312]	476	-11354
[4 17 192]	479	3366
[80 -401 2016]	479	-8808
[8 17 96]	479	8808
[12 17 64]	479	3366
[28 -401 5760]	479	4885
[24 -367 5632]	479	0
[244 -1221 6112]	487	0
[4 5 128]	487	-6039
[62 -933 14048]	487	6039
[16 5 32]	487	0
[504 1257 3136]	495	7579
[6 9 96]	495	12853
[62 -311 1568]	495	6717
[16 23 64]	495	-7579
[18 9 32]	495	0
[2 4 256]	496	0
[4 4 128]	496	504
[124 -372 1120]	496	-7280
[124 -620 3104]	496	-7280
[8 4 64]	496	504
[64 -196 608]	496	-752
[64 -708 7840]	496	8432
[10 12 64]	496	7280
[50 -252 1280]	496	-8432
[14 20 64]	496	7280
[38 -196 1024]	496	-752
[16 4 32]	496	0
[20 28 64]	496	504
[28 -428 6560]	496	0