A Borcherds Product in S₆(K(16))⁺

poperties |

c vector |

θ vector |

ψ expansion |

Borch(ψ) coefficients

• The singular part of ψ truncated up to q^(16/4) is
  (12 + ζ^(-4) + 2/ζ^3 + 5/ζ^2 + 10/ζ + 10*ζ + 5*ζ^2 + 2*ζ^3 + ζ^4)
  +q(3/ζ^8 + 3*ζ^8)
  +q^3(-ζ^(-14) - ζ^14)
  +q^4(2/ζ^16 + 2*ζ^16)
• From the truncated singular part of ψ, the leading Jacobi coefficient of Borch(ψ) is the theta block

  	φ	= TB(6;1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,4)
  		= 110253241
  		= η(τ)12(θ(τ,z)/η(τ))10(θ(τ,2z)/η(τ))5(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 3 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)	18
  (4,2)	6
  (9,3)	2
  (16,4)	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

(12 + ζ^(-4) + 2/ζ^3 + 5/ζ^2 + 10/ζ + 10*ζ + 5*ζ^2 + 2*ζ^3 + ζ^4)
+q(74 + 3/ζ^8 - 7/ζ^6 - 26/ζ^5 - 40/ζ^4 - 30/ζ^3 + 7/ζ^2 + 56/ζ + 56*ζ + 7*ζ^2 - 30*ζ^3 - 40*ζ^4 - 26*ζ^5 - 7*ζ^6 + 3*ζ^8)
+q^2(476 - 2/ζ^11 + 3/ζ^10 + 22/ζ^9 + 50/ζ^8 + 46/ζ^7 - 34/ζ^6 - 180/ζ^5 - 288/ζ^4 - 226/ζ^3 + 31/ζ^2 + 340/ζ + 340*ζ + 31*ζ^2 - 226*ζ^3 - 288*ζ^4 - 180*ζ^5 - 34*ζ^6 + 46*ζ^7 + 50*ζ^8 + 22*ζ^9 + 3*ζ^10 - 2*ζ^11)
+q^3(2216 - ζ^(-14) - 6/ζ^13 - 24/ζ^12 - 34/ζ^11 + 26/ζ^10 + 192/ζ^9 + 396/ζ^8 + 366/ζ^7 - 100/ζ^6 - 912/ζ^5 - 1480/ζ^4 - 1176/ζ^3 + 75/ζ^2 + 1570/ζ + 1570*ζ + 75*ζ^2 - 1176*ζ^3 - 1480*ζ^4 - 912*ζ^5 - 100*ζ^6 + 366*ζ^7 + 396*ζ^8 + 192*ζ^9 + 26*ζ^10 - 34*ζ^11 - 24*ζ^12 - 6*ζ^13 - ζ^14)
+q^4(8812 + 2/ζ^16 + 8/ζ^15 - 3/ζ^14 - 78/ζ^13 - 225/ζ^12 - 280/ζ^11 + 84/ζ^10 + 1010/ζ^9 + 1992/ζ^8 + 1850/ζ^7 - 299/ζ^6 - 3790/ζ^5 - 6175/ζ^4 - 4900/ζ^3 + 218/ζ^2 + 6180/ζ + 6180*ζ + 218*ζ^2 - 4900*ζ^3 - 6175*ζ^4 - 3790*ζ^5 - 299*ζ^6 + 1850*ζ^7 + 1992*ζ^8 + 1010*ζ^9 + 84*ζ^10 - 280*ζ^11 - 225*ζ^12 - 78*ζ^13 - 3*ζ^14 + 8*ζ^15 + 2*ζ^16)

2u	det(2u)	a(u, Borch(ψ))
[4 -53 704]	7	0
[8 -89 992]	15	0
[4 -25 160]	15	-1
[12 -109 992]	23	0
[6 -13 32]	23	0
[6 -19 64]	23	-1
[14 -42 128]	28	0
[14 -70 352]	28	0
[8 -42 224]	28	0
[8 -106 1408]	28	2
[16 -113 800]	31	0
[8 -113 1600]	31	0
[14 -47 160]	31	1
[20 -101 512]	39	0
[10 -91 832]	39	5
[10 -101 1024]	39	5
[8 -27 96]	39	3
[24 -73 224]	47	0
[12 -73 448]	47	7
[4 9 32]	47	0
[8 -73 672]	47	7
[16 -55 192]	47	-2
[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	-9
[14 -99 704]	55	-9
[8 -35 160]	55	-1
[2 2 32]	60	0
[30 -210 1472]	60	0
[16 -50 160]	60	8
[16 -178 1984]	60	-10
[10 -30 96]	60	-8
[10 -50 256]	60	8
[8 -50 320]	60	-2
[8 -114 1632]	60	0
[2 1 32]	63	0
[16 -225 3168]	63	5
[4 33 288]	63	5
[12 -159 2112]	63	6
[8 -97 1184]	63	-2
[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 -64 416]	64	0
[10 -144 2080]	64	0
[36 -469 6112]	71	0
[18 -181 1824]	71	-20
[18 -235 3072]	71	-14
[120 277 640]	71	0
[10 -43 192]	71	-3
[10 -53 288]	71	-14
[40 -441 4864]	79	0
[20 -121 736]	79	-25
[190 441 1024]	79	0
[10 -121 1472]	79	3
[44 -397 3584]	87	0
[22 -45 96]	87	28
[22 -243 2688]	87	40
[12 -51 224]	87	9
[134 307 704]	87	0
[46 -138 416]	92	0
[46 -230 1152]	92	0
[4 6 32]	92	0
[24 -218 1984]	92	-22
[26 70 192]	92	0
[162 374 864]	92	0
[6 26 128]	92	-24
[26 -86 288]	92	24
[12 -26 64]	92	-22
[12 -38 128]	92	2
[12 -122 1248]	92	0
[12 -134 1504]	92	-24
[48 -337 2368]	95	0
[24 -337 4736]	95	-14
[4 17 96]	95	-25
[16 -81 416]	95	-25
[12 -145 1760]	95	-4
[60 145 352]	95	7
[10 15 32]	95	0
[52 -261 1312]	103	0
[4 5 32]	103	0
[26 -261 2624]	103	20
[14 -59 256]	103	-25
[56 -169 512]	111	0
[28 -169 1024]	111	35
[120 297 736]	111	26
[6 9 32]	111	0
[14 -169 2048]	111	17
[14 -183 2400]	111	2
[10 23 64]	111	26
[2 4 64]	112	0
[58 172 512]	112	0
[4 4 32]	112	0
[28 -84 256]	112	40
[28 -140 704]	112	-72
[28 -196 1376]	112	32
[14 -28 64]	112	32
[14 -84 512]	112	-32
[8 12 32]	112	0
[16 -84 448]	112	40
[16 -148 1376]	112	-32
[16 -212 2816]	112	-8
[2 3 64]	119	0
[30 -61 128]	119	20
[30 -451 6784]	119	0
[20 -61 192]	119	63
[90 221 544]	119	-12
[16 -67 288]	119	13
[12 -61 320]	119	63
[24 61 160]	119	-65
[12 -125 1312]	119	-12
[2 2 64]	124	0
[62 -434 3040]	124	0
[4 2 32]	124	0
[32 -226 1600]	124	20
[16 -98 608]	124	0
[16 -226 3200]	124	20
[8 34 160]	124	24
[28 -94 320]	124	-4
[10 14 32]	124	0
[14 -46 160]	124	-24
[14 -130 1216]	124	0
[14 -158 1792]	124	24
[2 1 64]	127	0
[4 1 32]	127	0
[32 -449 6304]	127	-22
[16 -193 2336]	127	11
[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	-32
[18 -40 96]	128	0
[18 -112 704]	128	64
[18 -256 3648]	128	-64
[12 16 32]	128	0
[12 -64 352]	128	-32
[68 -885 11520]	135	0
[34 -171 864]	135	14
[34 -341 3424]	135	25
[24 -267 2976]	135	-99
[8 11 32]	135	0
[12 -75 480]	135	-84
[72 -793 8736]	143	0
[36 -217 1312]	143	63
[42 121 352]	143	42
[6 7 32]	143	0
[6 25 128]	143	55
[18 -199 2208]	143	55
[12 -25 64]	143	42
[14 -89 576]	143	-7
[76 -685 6176]	151	0
[38 -77 160]	151	-110
[38 -115 352]	151	-63
[8 19 64]	151	-63
[10 13 32]	151	0
[78 -234 704]	156	0
[78 -390 1952]	156	0
[40 -202 1024]	156	178
[40 -522 6816]	156	-88
[6 6 32]	156	0
[8 10 32]	156	0
[20 -42 96]	156	0
[20 -202 2048]	156	90
[10 22 64]	156	-88
[82 198 480]	156	88
[10 42 192]	156	32
[30 -102 352]	156	-32
[16 -54 192]	156	58
[16 -182 2080]	156	32
[80 -561 3936]	159	0
[40 -561 7872]	159	70
[46 -143 448]	159	18
[28 -143 736]	159	18
[30 81 224]	159	83
[16 -49 160]	159	-59
[12 15 32]	159	0
[14 -143 1472]	159	83
[84 -421 2112]	167	0
[42 -379 3424]	167	-40
[42 -421 4224]	167	-140
[28 -421 6336]	167	0
[36 101 288]	167	-19
[22 -69 224]	167	-51
[14 -155 1728]	167	-51
[14 -197 2784]	167	-40
[16 -37 96]	167	-19
[88 -265 800]	175	0
[4 9 64]	175	-299
[8 9 32]	175	0
[20 -265 3520]	175	-97
[2 4 96]	176	0
[90 268 800]	176	0
[30 -92 288]	176	-160
[30 -332 3680]	176	160
[30 -452 6816]	176	0
[22 -44 96]	176	0
[22 -132 800]	176	0
[10 12 32]	176	0
[18 -92 480]	176	-160
[18 -236 3104]	176	160
[2 3 96]	183	0
[46 -93 192]	183	-8
[46 -323 2272]	183	-161
[6 3 32]	183	0
[38 -125 416]	183	109
[16 -227 3232]	183	-161
[2 2 96]	188	0
[94 -658 4608]	188	0
[48 -146 448]	188	68
[48 -530 5856]	188	-136
[6 2 32]	188	0
[6 14 64]	188	-136
[142 350 864]	188	136
[24 -146 896]	188	-68
[24 -338 4768]	188	0
[8 18 64]	188	68
[112 274 672]	188	-136
[12 14 32]	188	0
[12 50 224]	188	-104
[32 -110 384]	188	36
[14 34 96]	188	136
[102 242 576]	188	-136
[14 62 288]	188	104
[42 -146 512]	188	-104
[2 1 96]	191	0
[48 -673 9440]	191	70
[6 1 32]	191	0
[32 -417 5440]	191	-15
[8 33 160]	191	-101
[20 -223 2496]	191	-101
[36 95 256]	191	161
[16 -161 1632]	191	161
[18 -95 512]	191	-15
[18 -257 3680]	191	148
[2 0 96]	192	0
[2 8 128]	192	0
[2 16 224]	192	0
[4 8 64]	192	112
[52 152 448]	192	-112
[6 0 32]	192	0
[6 24 128]	192	0
[8 8 32]	192	0
[24 -72 224]	192	0
[24 -120 608]	192	0
[26 -56 128]	192	0
[26 -160 992]	192	0
[26 -368 5216]	192	0
[12 24 64]	192	-112
[28 72 192]	192	112
[14 16 32]	192	0
[14 -72 384]	192	0
[100 -1301 16928]	199	0
[50 -651 8480]	199	113
[26 -341 4480]	199	107
[10 11 32]	199	0
[10 21 64]	199	113
[16 -213 2848]	199	107
[104 -1145 12608]	207	0
[478 1113 2592]	207	179
[26 -391 5888]	207	0
[18 -39 96]	207	21
[18 -57 192]	207	36
[108 -973 8768]	215	0
[54 -595 6560]	215	208
[36 -397 4384]	215	-7
[6 13 64]	215	208
[24 -77 256]	215	179
[12 13 32]	215	0
[18 -109 672]	215	23
[20 -205 2112]	215	-126
[16 -179 2016]	215	179
[110 -330 992]	220	0
[110 -550 2752]	220	0
[4 6 64]	220	-218
[56 -506 4576]	220	88
[28 -58 128]	220	-130
[28 -282 2848]	220	0
[28 -422 6368]	220	0
[10 10 32]	220	0
[34 86 224]	220	-88
[170 390 896]	220	88
[14 58 256]	220	48
[34 -118 416]	220	-48
[16 -70 320]	220	-178
[16 -198 2464]	220	48
[112 -785 5504]	223	0
[4 17 128]	223	-55
[8 17 64]	223	-55
[14 15 32]	223	0
[116 -581 2912]	231	0
[4 5 64]	231	174
[40 -123 384]	231	139
[30 -453 6848]	231	0
[24 -123 640]	231	139
[40 -133 448]	231	36
[20 -123 768]	231	43
[104 251 608]	231	-110
[120 -361 1088]	239	0
[248 617 1536]	239	323
[48 -151 480]	239	-122
[30 -151 768]	239	-122
[24 -361 5440]	239	0
[10 41 192]	239	-103
[20 -41 96]	239	133
[198 457 1056]	239	323
[22 -247 2784]	239	-103
[2 4 128]	240	0
[122 364 1088]	240	0
[4 4 64]	240	-312
[60 -180 544]	240	0
[60 -300 1504]	240	-32
[60 -420 2944]	240	344
[6 12 64]	240	-32
[46 132 384]	240	32
[30 -60 128]	240	32
[30 -180 1088]	240	-32
[8 4 32]	240	0
[32 -100 320]	240	280
[32 -356 3968]	240	-312
[10 20 64]	240	0
[34 92 256]	240	0
[12 12 32]	240	0
[20 -60 192]	240	-248
[20 -100 512]	240	280
[16 -36 96]	240	32
[16 -164 1696]	240	0
[16 -228 3264]	240	344
[2 3 128]	247	0
[62 -931 13984]	247	316
[8 3 32]	247	0
[2 2 128]	252	0
[126 -882 6176]	252	0
[4 2 64]	252	50
[42 -126 384]	252	264
[42 -210 1056]	252	-264
[8 2 32]	252	0
[32 -194 1184]	252	0
[32 -450 6336]	252	42
[24 -126 672]	252	264
[24 -318 4224]	252	264
[14 14 32]	252	0
[16 -194 2368]	252	130
[18 -222 2752]	252	-88
[18 -258 3712]	252	-8
[2 1 128]	255	0
[4 1 64]	255	-425
[44 -575 7520]	255	-393
[8 1 32]	255	0
[22 -223 2272]	255	-56
[22 -289 3808]	255	-35
[20 -65 224]	255	-305
[14 33 96]	255	-393
[2 0 128]	256	0
[2 8 160]	256	0
[2 16 256]	256	0
[4 0 64]	256	544
[4 16 128]	256	0
[8 0 32]	256	0
[8 16 64]	256	0
[8 32 160]	256	0
[34 -72 160]	256	0
[34 -480 6784]	256	0
[26 -80 256]	256	0
[26 -288 3200]	256	0
[26 -392 5920]	256	0
[16 16 32]	256	0
[16 -48 160]	256	0
[20 -48 128]	256	0
[20 -288 4160]	256	-544
[132 -1717 22336]	263	0
[66 -331 1664]	263	-317
[408 949 2208]	263	-317
[22 -309 4352]	263	-231
[22 -331 4992]	263	0
[24 -53 128]	263	-217
[12 53 256]	263	-190
[18 -203 2304]	263	-190
[136 -1497 16480]	271	0
[74 217 640]	271	-175
[34 -103 320]	271	-151
[28 -423 6400]	271	0
[134 327 800]	271	-136
[20 -103 544]	271	-151
[212 487 1120]	271	-175
[124 295 704]	271	-136
[140 -1261 11360]	279	0
[70 -211 640]	279	-274
[28 -365 4768]	279	-308
[268 621 1440]	279	-274
[24 -339 4800]	279	54
[42 -141 480]	279	-42
[20 -301 4544]	279	0
[98 237 576]	279	317
[18 -237 3136]	279	-308
[20 -109 608]	279	248
[142 -426 1280]	284	0
[142 -710 3552]	284	0
[72 -362 1824]	284	304
[72 -938 12224]	284	-454
[450 1046 2432]	284	304
[6 26 160]	284	-64
[58 -182 576]	284	64
[36 -74 160]	284	0
[36 -182 928]	284	64
[36 -362 3648]	284	-150
[36 -470 6144]	284	-214
[30 -154 800]	284	-64
[30 -394 5184]	284	64
[30 -454 6880]	284	0
[24 -362 5472]	284	0
[240 554 1280]	284	-454
[18 -38 96]	284	-304
[18 -182 1856]	284	304
[20 -106 576]	284	-214
[20 -266 3552]	284	64
[144 -1009 7072]	287	0
[78 -239 736]	287	124
[48 -241 1216]	287	295
[338 785 1824]	287	124
[24 -241 2432]	287	-123
[12 49 224]	287	281
[26 -369 5248]	287	48
[24 -271 3072]	287	281
[18 -271 4096]	287	0
[148 -741 3712]	295	0
[74 -667 6016]	295	-575
[38 -421 4672]	295	122
[10 5 32]	295	0
[226 517 1184]	295	-575
[152 -457 1376]	303	0
[4 9 96]	303	89
[6 9 64]	303	89
[26 -55 128]	303	291
[26 -393 5952]	303	0
[22 -73 256]	303	-94
[2 4 160]	304	0
[154 460 1376]	304	0
[38 -76 160]	304	0
[10 4 32]	304	0
[10 44 224]	304	-480
[50 -164 544]	304	480
[22 -68 224]	304	480
[22 -244 2720]	304	-480
[22 -332 5024]	304	0
[2 3 160]	311	0
[52 -157 480]	311	-256
[218 541 1344]	311	44
[8 35 192]	311	-398
[10 3 32]	311	0
[26 -131 672]	311	-398
[26 -157 960]	311	-31
[28 -285 2912]	311	-263
[12 29 96]	311	-256
[16 35 96]	311	44
[20 -227 2592]	311	-169
[240 547 1248]	311	-163
[2 2 160]	316	0
[158 -1106 7744]	316	0
[80 -242 736]	316	552
[80 -882 9728]	316	-292
[40 -562 7904]	316	0
[380 882 2048]	316	-292
[10 2 32]	316	0
[310 718 1664]	316	552
[20 -302 4576]	316	0
[22 -50 128]	316	552
[22 -226 2336]	316	-552
[2 1 160]	319	0
[50 -159 512]	319	498
[10 1 32]	319	0
[32 -353 3904]	319	498
[38 97 256]	319	221
[20 -289 4192]	319	564
[2 0 160]	320	0
[2 8 192]	320	0
[4 8 96]	320	64
[84 248 736]	320	-64
[6 8 64]	320	64
[54 -272 1376]	320	-448
[54 -704 9184]	320	448
[42 -88 192]	320	0
[42 -592 8352]	320	0
[10 0 32]	320	0
[10 40 192]	320	0
[28 -312 3488]	320	0
[28 -424 6432]	320	0
[14 32 96]	320	448
[126 304 736]	320	-448
[254 584 1344]	320	-64
[20 -40 96]	320	-64
[20 -120 736]	320	64
[18 -56 192]	320	0
[18 -272 4128]	320	0
[164 -2133 27744]	327	0
[82 -1067 13888]	327	123
[56 -619 6848]	327	-45
[42 -213 1088]	327	-45
[282 651 1504]	327	123
[24 -363 5504]	327	0
[44 -149 512]	327	201
[168 -1849 20352]	335	0
[766 1785 4160]	335	-525
[6 7 64]	335	-525
[6 25 160]	335	203
[36 -185 960]	335	203
[28 -57 128]	335	7
[30 -455 6912]	335	0
[24 -313 4096]	335	-180
[14 57 256]	335	-138
[54 -185 640]	335	-138
[118 281 672]	335	-555
[172 -1549 13952]	343	0
[86 -947 10432]	343	346
[422 979 2272]	343	346
[28 -371 4928]	343	488
[22 -333 5056]	343	0
[174 -522 1568]	348	0
[174 -870 4352]	348	0
[4 6 96]	348	-176
[88 -794 7168]	348	862
[6 6 64]	348	-176
[44 -90 192]	348	686
[44 -134 416]	348	336
[44 -486 5376]	348	350
[12 6 32]	348	0
[26 -134 704]	348	336
[26 -342 4512]	348	-336
[26 -394 5984]	348	0
[22 -310 4384]	348	176
[268 614 1408]	348	862
[4 17 160]	351	-401
[60 -303 1536]	351	879
[36 -111 352]	351	314
[352 815 1888]	351	-401
[30 -303 3072]	351	237
[22 -111 576]	351	314
[20 -303 4608]	351	0
[20 -47 128]	351	-526
[180 -901 4512]	359	0
[4 5 96]	359	1137
[60 -901 13536]	359	1137
[30 -421 5920]	359	87
[12 5 32]	359	0
[32 -69 160]	359	473
[20 -261 3424]	359	891
[18 37 96]	359	737
[22 -229 2400]	359	452
[22 -251 2880]	359	1000
[184 -553 1664]	367	0
[376 937 2336]	367	390
[46 -599 7808]	367	148
[28 -425 6464]	367	0
[296 681 1568]	367	390
[26 -137 736]	367	148
[2 4 192]	368	0
[186 556 1664]	368	0
[4 4 96]	368	-480
[92 -276 832]	368	536
[92 -460 2304]	368	-184
[62 -188 576]	368	-352
[62 -684 7552]	368	352
[62 -932 14016]	368	-480
[46 -92 192]	368	-352
[8 12 64]	368	-184
[48 -244 1248]	368	352
[12 4 32]	368	0
[12 28 96]	368	-352
[324 748 1728]	368	536
[12 52 256]	368	520
[52 -172 576]	368	-168
[24 -52 128]	368	-168
[24 -76 256]	368	-872
[24 -244 2496]	368	-184
[24 -268 3008]	368	520
[24 -340 4832]	368	480
[24 -364 5536]	368	0
[18 44 128]	368	0
[146 348 832]	368	0
[282 644 1472]	368	128
[2 3 192]	375	0
[94 -1411 21184]	375	-323
[6 3 64]	375	-323
[40 -445 4960]	375	-1446
[12 3 32]	375	0
[32 -451 6368]	375	112
[46 -157 544]	375	-357
[2 2 192]	380	0
[4 2 96]	380	0
[6 2 64]	380	0
[6 14 96]	380	-104
[270 670 1664]	380	104
[48 -674 9472]	380	-466
[8 34 192]	380	-202
[60 -190 608]	380	-264
[38 -190 960]	380	-264
[12 2 32]	380	0
[32 -162 832]	380	-202
[16 34 96]	380	104
[120 290 704]	380	-570
[26 -370 5280]	380	0
[22 -114 608]	380	264
[22 -290 3840]	380	-264
[22 -334 5088]	380	0
[20 30 64]	380	-466
[2 1 192]	383	0
[4 1 96]	383	-261
[6 1 64]	383	-261
[64 -833 10848]	383	-472
[12 1 32]	383	0
[32 -321 3232]	383	-127
[34 -481 6816]	383	-244
[14 31 96]	383	-472
[24 -319 4256]	383	-165
[56 -193 672]	383	-316
[2 0 192]	384	0
[2 8 224]	384	0
[4 0 96]	384	832
[4 16 160]	384	-320
[6 0 64]	384	832
[6 24 160]	384	0
[50 -704 9920]	384	640
[10 24 96]	384	0
[394 912 2112]	384	-320
[12 0 32]	384	0
[12 48 224]	384	-320
[30 -336 3776]	384	-320
[30 -456 6944]	384	0
[28 -64 160]	384	320
[28 -400 5728]	384	-832
[20 -64 224]	384	320
[20 -304 4640]	384	0
[22 32 64]	384	-192
[22 -120 672]	384	0
[196 -2549 33152]	391	0
[98 -491 2464]	391	237
[8 11 64]	391	237
[10 43 224]	391	730
[28 -309 3424]	391	730
[26 -395 6016]	391	0
[20 -203 2080]	391	-18
[22 -117 640]	391	219
[200 -2201 24224]	399	0
[106 313 928]	399	-140
[50 -551 6080]	399	226
[52 -167 544]	399	139
[34 -71 160]	399	-237
[34 -377 4192]	399	139
[14 7 32]	399	0
[310 711 1632]	399	-140
[20 -281 3968]	399	297
[102 -307 928]	407	-933
[68 -749 8256]	407	-90
[6 13 96]	407	-1507
[8 19 96]	407	-90
[36 -365 3712]	407	721
[366 845 1952]	407	-933
[24 -365 5568]	407	0
[206 -618 1856]	412	0
[206 -1030 5152]	412	0
[104 -522 2624]	412	-398
[104 -1354 17632]	412	-80
[8 10 64]	412	-398
[14 6 32]	412	0
[338 778 1792]	412	-80
[26 -54 128]	412	-80
[26 -262 2656]	412	80
[28 -426 6496]	412	0
[110 -335 1024]	415	951
[10 15 64]	415	951
[26 -79 256]	415	624
[22 -49 128]	415	-300
[22 -335 5120]	415	0
[212 -1061 5312]	423	0
[72 -219 672]	423	621
[54 -165 512]	423	69
[12 27 96]	423	621
[14 5 32]	423	0
[32 -165 864]	423	69
[148 357 864]	423	-402
[18 27 64]	423	-325
[216 -649 1952]	431	0
[4 9 128]	431	-455
[80 -247 768]	431	-666
[8 9 64]	431	-455
[10 23 96]	431	-666
[36 -73 160]	431	-635
[30 -457 6976]	431	0
[24 -265 2944]	431	-848
[22 -311 4416]	431	-311
[24 -247 2560]	431	122
[2 4 224]	432	0
[6 12 96]	432	1056
[14 4 32]	432	0
[54 -180 608]	432	-160
[18 36 96]	432	-1056
[26 -292 3296]	432	160
[26 -396 6048]	432	0
[2 3 224]	439	0
[70 -221 704]	439	-896
[44 -221 1120]	439	-896
[14 3 32]	439	0
[22 -67 224]	439	-476
[20 29 64]	439	916
[26 -61 160]	439	613
[2 2 224]	444	0
[112 -338 1024]	444	426
[112 -1234 13600]	444	-696
[74 -222 672]	444	600
[74 -370 1856]	444	-600
[8 18 96]	444	-600
[10 14 64]	444	-696
[46 -142 448]	444	-760
[46 -510 5664]	444	760
[12 18 64]	444	426
[14 2 32]	444	0
[14 30 96]	444	600
[28 -142 736]	444	-760
[28 -366 4800]	444	490
[30 -66 160]	444	696
[30 -306 3136]	444	-696
[24 -366 5600]	444	0
[20 46 128]	444	330
[140 334 800]	444	-600
[2 1 224]	447	0
[76 -991 12928]	447	-429
[8 33 192]	447	222
[38 -193 992]	447	222
[38 -383 3872]	447	-455
[14 1 32]	447	0
[16 33 96]	447	-429
[22 31 64]	447	-693
[2 0 224]	448	0
[2 8 256]	448	0
[4 8 128]	448	1152
[116 344 1024]	448	-1152
[8 8 64]	448	1152
[56 -168 512]	448	-448
[56 -280 1408]	448	-576
[14 0 32]	448	0
[14 56 256]	448	0
[28 -56 128]	448	-128
[16 8 32]	448	0
[16 24 64]	448	-1152
[32 -168 896]	448	-448
[32 -360 4064]	448	0
[32 -424 5632]	448	1472
[22 -72 256]	448	0
[22 -336 5152]	448	0
[114 -1483 19296]	455	-73
[696 1621 3776]	455	-47
[38 -533 7488]	455	806
[40 -85 192]	455	-269
[62 -203 672]	455	1161
[14 21 64]	455	-73
[30 -395 5216]	455	-323
[28 -427 6528]	455	0
[18 43 128]	455	295
[24 -341 4864]	455	-1382
[232 -2553 28096]	463	0
[1054 2457 5728]	463	-61
[58 -871 13088]	463	-61
[16 7 32]	463	0
[118 -1299 14304]	471	-466
[10 13 64]	471	-466
[40 -563 7936]	471	612
[12 51 256]	471	-487
[30 -333 3712]	471	-487
[24 -51 128]	471	-7
[26 -371 5312]	471	-393
[26 -397 6080]	471	0
[238 -1190 5952]	476	0
[4 6 128]	476	188
[738 1718 4000]	476	1592
[6 26 192]	476	-672
[90 -278 864]	476	672
[60 -902 13568]	476	188
[10 22 96]	476	672
[10 42 224]	476	-280
[62 -198 640]	476	280
[40 -442 4896]	476	280
[12 26 96]	476	-672
[34 -170 864]	476	-280
[30 -422 5952]	476	-688
[16 6 32]	476	0
[18 26 64]	476	-688
[30 -458 7008]	476	0
[24 -122 640]	476	-780
[24 -314 4128]	476	280
[248 570 1312]	476	-1592
[24 -58 160]	476	-672
[24 -250 2624]	476	172
[4 17 192]	479	432
[80 -401 2016]	479	330
[8 17 96]	479	330
[54 -175 576]	479	-401
[12 17 64]	479	432
[42 -593 8384]	479	-801
[36 -401 4480]	479	-401
[28 -145 768]	479	-176
[28 -401 5760]	479	1350
[168 401 960]	479	464
[24 -367 5632]	479	0
[244 -1221 6112]	487	0
[4 5 128]	487	-1739
[62 -933 14048]	487	-1739
[16 5 32]	487	0
[504 1257 3136]	495	378
[6 9 96]	495	-1950
[62 -311 1568]	495	-1211
[42 -87 192]	495	-1086
[16 23 64]	495	378
[18 9 32]	495	0
[26 -265 2720]	495	-703
[26 -343 4544]	495	-293
[28 -151 832]	495	113
[2 4 256]	496	0
[4 4 128]	496	144
[124 -372 1120]	496	-576
[124 -620 3104]	496	896
[8 4 64]	496	144
[64 -196 608]	496	-320
[64 -708 7840]	496	0
[10 12 64]	496	896
[50 -252 1280]	496	0
[14 20 64]	496	-576
[38 -196 1024]	496	-320
[16 4 32]	496	0
[32 -68 160]	496	-896
[32 -324 3296]	496	576
[32 -452 6400]	496	176
[56 -188 640]	496	880
[20 28 64]	496	-464
[28 -148 800]	496	0
[28 -316 3584]	496	-560
[28 -372 4960]	496	320
[28 -428 6560]	496	0