class ThetaModel():
		def init(self,q,u,c): ##assuming q is prime
		self.F=FiniteField(q,'a')
		self.q=q
		self.u=u
		self.c=c
		def verificationParameters(self):
		F=self.F
		q=self.q
		u=self.u
		c=self.c
		if F.characteristic()==2:
		print 'Error: The characteristic is egal to', F.characteristic()
		return False
		else:
		if (F(c).is_zero() is True) or (F(1-c^4).is_zero() is True) or (F(1+c^4).is_zero() is True):
		print 'Error: bad value for c'
		return False
		else:
		if (F(u).is_zero() is True) or (F(u).is_square() is True):
		print 'Error: u={} is zero or is a square'.format(u)+' in the finite field of {} elements'.format(F.order())
		return False
		else:
		return True
		def setOfDefinition(self,value):
		F=self.F
		c=self.c
		u=self.u
		r=F(value)
		if (F(4*u*r*r*(c^6)-(1-c^4)*(1+3*c^4)).is_zero() is True) or
		( F(4*u*r*r*(c^6)+(1-c^4)^4).is_zero() is True ) or ( F(4*u*r*r*(c^6)*(1+3*(c^4))-(1-c^4)^3).is_zero() is True):
		print 'r={} is not in the set of definition'.format(r)
		return False
		else:
		return True
		def quadraticCharacter(self,value):
		F=self.F
		try:
		residu=value.is_square()
		except:
		residu=F(value).is_square()
		if residu is True:
		return 1
		else:
		return -1
		def encodeTheta(self,value):
		if self.verificationParameters() is True:
		if self.setOfDefinition(value) is True:
		F=self.F
		r=F(value)
		c=self.c
		u=self.u
		v=F(  c*(4*u*r*r*(c^6)+(1-c^4)*(3+c^4))/(4*u*r*r*(c^6)+(1-c^4)*(-3*(c^4)-1))  );
		e=self.quadraticCharacter((c*c-v*v)*(1-c*c*v*v));
		X=F(  v*(e+1)/2  + (((-c^4-1)*(v+c)-c*(1-c^4))/(2*(c^3)*(v+c)+1-c^4))*(e-1)/2 );
		try:
		a=F((c*c-X*X)/(1-c*c*X*X))
		root=a.square_root()
		Y=-e*root
		x=(X+1)/(X-1)
		y=(Y-1)/(Y+1)
		return (F(x),F(y))
		except:
		print 'Error when computing the square root of f(x)'
		return {}
		\end{verbatim}
		%\end{tiny}
		%\end{appendix}
		%%Example with $q=31,u=3,c=2$:
		%Example with $q=503,u=-1,c=3$:
		%\begin{appendix}
		%\begin{tiny}
		\begin{multicols}{3}[\section{Example with $q=503,u=-1,c=3$:.}]
			\begin{verbatim}
			t=ThetaModel()
			t.init(501,-1,3)
			if t.verificationParameters() is True:
			for i in t.F:
			if t.setOfDefinition(i) is True:
			print 'r=',i,'=====>(x,y)=',
			t.encodeTheta(i)
			
			
			r= 0 =====>(x,y)= (430, 121)
			r= 1 =====>(x,y)= (441, 382)
			r= 2 =====>(x,y)= (386, 240)
			r= 3 =====>(x,y)= (283, 274)
			r= 4 =====>(x,y)= (212, 73)
			r= 5 =====>(x,y)= (307, 100)
			r= 6 =====>(x,y)= (23, 298)
			r= 7 =====>(x,y)= (42, 171)
			r= 8 =====>(x,y)= (311, 239)
			r= 9 =====>(x,y)= (491, 332)
			r= 10 =====>(x,y)= (415, 385)
			r= 11 =====>(x,y)= (125, 490)
			r= 12 =====>(x,y)= (330, 470)
			r= 13 =====>(x,y)= (328, 205)
			r= 14 =====>(x,y)= (315, 483)
			r= 15 =====>(x,y)= (77, 31)
			r= 16 =====>(x,y)= (352, 369)
			r= 17 =====>(x,y)= (283, 123)
			r= 18 =====>(x,y)= (327, 188)
			r= 19 =====>(x,y)= (411, 365)
			r= 20 =====>(x,y)= (480, 265)
			r= 21 =====>(x,y)= (25, 485)
			r= 22 =====>(x,y)= (386, 153)
			r= 23 =====>(x,y)= (176, 404)
			r= 24 =====>(x,y)= (368, 142)
			r= 25 =====>(x,y)= (121, 62)
			r= 26 =====>(x,y)= (40, 422)
			r= 27 =====>(x,y)= (461, 50)
			r= 28 =====>(x,y)= (318, 46)
			r= 29 =====>(x,y)= (170, 76)
			r= 30 =====>(x,y)= (217, 310)
			r= 31 =====>(x,y)= (171, 12)
			r= 32 =====>(x,y)= (187, 49)
			r= 33 =====>(x,y)= (436, 313)
			r= 34 =====>(x,y)= (31, 98)
			r= 35 =====>(x,y)= (43, 350)
			r= 36 =====>(x,y)= (382, 73)
			r= 37 =====>(x,y)= (490, 125)
			r= 38 =====>(x,y)= (338, 435)
			r= 39 =====>(x,y)= (124, 141)
			r= 40 =====>(x,y)= (378, 387)
			r= 41 =====>(x,y)= (416, 457)
			r= 42 =====>(x,y)= (63, 32)
			r= 43 =====>(x,y)= (86, 51)
			r=44 is not in the set of definition
			r= 45 =====>(x,y)= (470, 330)
			r= 46 =====>(x,y)= (259, 352)
			r= 47 =====>(x,y)= (153, 460)
			r= 48 =====>(x,y)= (318, 339)
			r= 49 =====>(x,y)= (237, 69)
			r= 50 =====>(x,y)= (220, 380)
			r= 51 =====>(x,y)= (442, 330)
			r= 52 =====>(x,y)= (213, 166)
			r= 53 =====>(x,y)= (495, 110)
			r= 54 =====>(x,y)= (393, 8)
			r= 55 =====>(x,y)= (185, 164)
			r= 56 =====>(x,y)= (287, 364)
			r= 57 =====>(x,y)= (378, 13)
			r= 58 =====>(x,y)= (472, 405)
			r= 59 =====>(x,y)= (232, 304)
			r= 60 =====>(x,y)= (51, 310)
			r= 61 =====>(x,y)= (216, 139)
			r= 62 =====>(x,y)= (258, 199)
			r= 63 =====>(x,y)= (60, 476)
			r= 64 =====>(x,y)= (258, 91)
			r= 65 =====>(x,y)= (382, 441)
			r= 66 =====>(x,y)= (352, 259)
			r= 67 =====>(x,y)= (350, 117)
			r= 68 =====>(x,y)= (109, 149)
			r= 69 =====>(x,y)= (102, 336)
			r= 70 =====>(x,y)= (467, 375)
			r= 71 =====>(x,y)= (425, 154)
			r= 72 =====>(x,y)= (339, 318)
			r= 73 =====>(x,y)= (231, 209)
			r= 74 =====>(x,y)= (379, 362)
			r= 75 =====>(x,y)= (116, 334)
			r= 76 =====>(x,y)= (252, 502)
			r= 77 =====>(x,y)= (149, 109)
			r= 78 =====>(x,y)= (235, 278)
			r= 79 =====>(x,y)= (466, 338)
			r= 80 =====>(x,y)= (457, 416)
			r= 81 =====>(x,y)= (16, 123)
			r= 82 =====>(x,y)= (495, 471)
			r= 83 =====>(x,y)= (141, 215)
			r= 84 =====>(x,y)= (470, 157)
			r= 85 =====>(x,y)= (127, 94)
			r= 86 =====>(x,y)= (334, 490)
			r= 87 =====>(x,y)= (311, 181)
			r= 88 =====>(x,y)= (301, 409)
			r= 89 =====>(x,y)= (458, 67)
			r= 90 =====>(x,y)= (440, 471)
			r= 91 =====>(x,y)= (360, 253)
			r= 92 =====>(x,y)= (350, 43)
			r= 93 =====>(x,y)= (304, 245)
			r= 94 =====>(x,y)= (322, 192)
			r= 95 =====>(x,y)= (173, 33)
			r= 96 =====>(x,y)= (18, 342)
			r= 97 =====>(x,y)= (410, 179)
			r= 98 =====>(x,y)= (485, 25)
			r= 99 =====>(x,y)= (190, 488)
			r= 100 =====>(x,y)= (475, 161)
			r= 101 =====>(x,y)= (225, 122)
			r= 102 =====>(x,y)= (8, 393)
			r= 103 =====>(x,y)= (73, 382)
			r= 104 =====>(x,y)= (342, 18)
			r= 105 =====>(x,y)= (69, 237)
			r= 106 =====>(x,y)= (442, 157)
			r= 107 =====>(x,y)= (443, 27)
			r= 108 =====>(x,y)= (403, 290)
			r= 109 =====>(x,y)= (12, 453)
			r= 110 =====>(x,y)= (148, 214)
			r= 111 =====>(x,y)= (291, 430)
			r= 112 =====>(x,y)= (289, 486)
			r= 113 =====>(x,y)= (135, 361)
			r= 114 =====>(x,y)= (250, 401)
			r= 115 =====>(x,y)= (369, 493)
			r= 116 =====>(x,y)= (305, 376)
			r= 117 =====>(x,y)= (167, 143)
			r= 118 =====>(x,y)= (493, 369)
			r= 119 =====>(x,y)= (212, 441)
			r= 120 =====>(x,y)= (125, 116)
			r= 121 =====>(x,y)= (38, 235)
			r= 122 =====>(x,y)= (490, 334)
			r= 123 =====>(x,y)= (196, 337)
			r= 124 =====>(x,y)= (263, 43)
			r= 125 =====>(x,y)= (324, 93)
			r= 126 =====>(x,y)= (357, 77)
			r= 127 =====>(x,y)= (337, 290)
			r= 128 =====>(x,y)= (337, 196)
			r= 129 =====>(x,y)= (164, 185)
			r= 130 =====>(x,y)= (460, 153)
			r= 131 =====>(x,y)= (14, 224)
			r= 132 =====>(x,y)= (245, 412)
			r= 133 =====>(x,y)= (110, 495)
			r= 134 =====>(x,y)= (271, 91)
			r= 135 =====>(x,y)= (478, 18)
			r= 136 =====>(x,y)= (151, 134)
			r= 137 =====>(x,y)= (435, 189)
			r= 138 =====>(x,y)= (467, 279)
			r= 139 =====>(x,y)= (404, 483)
			r= 140 =====>(x,y)= (489, 279)
			r= 141 =====>(x,y)= (409, 301)
			r= 142 =====>(x,y)= (493, 259)
			r= 143 =====>(x,y)= (315, 176)
			r= 144 =====>(x,y)= (28, 478)
			r= 145 =====>(x,y)= (237, 226)
			r= 146 =====>(x,y)= (157, 442)
			r= 147 =====>(x,y)= (465, 268)
			r= 148 =====>(x,y)= (394, 354)
			r= 149 =====>(x,y)= (460, 240)
			r= 150 =====>(x,y)= (198, 202)
			r= 151 =====>(x,y)= (202, 198)
			r= 152 =====>(x,y)= (189, 466)
			r= 153 =====>(x,y)= (87, 339)
			r= 154 =====>(x,y)= (78, 454)
			r= 155 =====>(x,y)= (240, 386)
			r= 156 =====>(x,y)= (213, 100)
			r= 157 =====>(x,y)= (143, 250)
			r= 158 =====>(x,y)= (224, 36)
			r= 159 =====>(x,y)= (51, 86)
			r= 160 =====>(x,y)= (435, 338)
			r= 161 =====>(x,y)= (215, 132)
			r= 162 =====>(x,y)= (411, 390)
			r= 163 =====>(x,y)= (376, 305)
			r= 164 =====>(x,y)= (275, 355)
			r= 165 =====>(x,y)= (316, 349)
			r= 166 =====>(x,y)= (307, 166)
			r= 167 =====>(x,y)= (272, 294)
			r= 168 =====>(x,y)= (502, 252)
			r= 169 =====>(x,y)= (485, 161)
			r= 170 =====>(x,y)= (463, 118)
			r= 171 =====>(x,y)= (381, 38)
			r= 172 =====>(x,y)= (217, 86)
			r= 173 =====>(x,y)= (476, 60)
			r= 174 =====>(x,y)= (264, 317)
			r= 175 =====>(x,y)= (333, 427)
			r= 176 =====>(x,y)= (88, 81)
			r= 177 =====>(x,y)= (298, 175)
			r= 178 =====>(x,y)= (67, 458)
			r= 179 =====>(x,y)= (281, 119)
			r= 180 =====>(x,y)= (338, 466)
			r= 181 =====>(x,y)= (199, 258)
			r= 182 =====>(x,y)= (362, 288)
			r= 183 =====>(x,y)= (128, 14)
			r= 184 =====>(x,y)= (384, 222)
			r= 185 =====>(x,y)= (98, 357)
			r= 186 =====>(x,y)= (290, 403)
			r= 187 =====>(x,y)= (466, 189)
			r= 188 =====>(x,y)= (186, 239)
			r= 189 =====>(x,y)= (104, 69)
			r= 190 =====>(x,y)= (36, 128)
			r= 191 =====>(x,y)= (132, 124)
			r= 192 =====>(x,y)= (46, 87)
			r= 193 =====>(x,y)= (225, 268)
			r= 194 =====>(x,y)= (263, 117)
			r= 195 =====>(x,y)= (475, 25)
			r= 196 =====>(x,y)= (487, 229)
			r= 197 =====>(x,y)= (404, 176)
			r= 198 =====>(x,y)= (328, 265)
			r= 199 =====>(x,y)= (82, 390)
			r= 200 =====>(x,y)= (104, 226)
			r= 201 =====>(x,y)= (229, 220)
			r= 202 =====>(x,y)= (488, 190)
			r= 203 =====>(x,y)= (342, 28)
			r= 204 =====>(x,y)= (161, 475)
			r= 205 =====>(x,y)= (334, 116)
			r= 206 =====>(x,y)= (489, 375)
			r= 207 =====>(x,y)= (480, 205)
			r= 208 =====>(x,y)= (403, 196)
			r= 209 =====>(x,y)= (380, 487)
			r= 210 =====>(x,y)= (278, 381)
			r= 211 =====>(x,y)= (175, 238)
			r= 212 =====>(x,y)= (375, 467)
			r= 213 =====>(x,y)= (401, 167)
			r= 214 =====>(x,y)= (288, 371)
			r= 215 =====>(x,y)= (87, 46)
			r= 216 =====>(x,y)= (271, 199)
			r= 217 =====>(x,y)= (371, 379)
			r= 218 =====>(x,y)= (50, 491)
			r= 219 =====>(x,y)= (186, 181)
			r= 220 =====>(x,y)= (10, 244)
			r= 221 =====>(x,y)= (146, 426)
			r= 222 =====>(x,y)= (31, 77)
			r= 223 =====>(x,y)= (117, 263)
			r= 224 =====>(x,y)= (440, 110)
			r= 225 =====>(x,y)= (189, 435)
			r= 226 =====>(x,y)= (502, 2)
			r= 227 =====>(x,y)= (441, 212)
			r= 228 =====>(x,y)= (465, 122)
			r= 229 =====>(x,y)= (279, 489)
			r= 230 =====>(x,y)= (483, 315)
			r= 231 =====>(x,y)= (17, 228)
			r= 232 =====>(x,y)= (91, 271)
			r= 233 =====>(x,y)= (94, 127)
			r= 234 =====>(x,y)= (169, 387)
			r= 235 =====>(x,y)= (453, 42)
			r= 236 =====>(x,y)= (15, 45)
			r= 237 =====>(x,y)= (116, 125)
			r= 238 =====>(x,y)= (20, 99)
			r= 239 =====>(x,y)= (357, 98)
			r= 240 =====>(x,y)= (310, 217)
			r= 241 =====>(x,y)= (346, 61)
			r= 242 =====>(x,y)= (226, 104)
			r= 243 =====>(x,y)= (73, 212)
			r= 244 =====>(x,y)= (471, 440)
			r= 245 =====>(x,y)= (169, 13)
			r= 246 =====>(x,y)= (412, 232)
			r= 247 =====>(x,y)= (32, 63)
			r= 248 =====>(x,y)= (332, 461)
			r= 249 =====>(x,y)= (478, 28)
			r= 250 =====>(x,y)= (82, 365)
			r= 251 =====>(x,y)= (16, 274)
			r= 252 =====>(x,y)= (16, 274)
			r= 253 =====>(x,y)= (82, 365)
			r= 254 =====>(x,y)= (478, 28)
			r= 255 =====>(x,y)= (332, 461)
			r= 256 =====>(x,y)= (32, 63)
			r= 257 =====>(x,y)= (412, 232)
			r= 258 =====>(x,y)= (169, 13)
			r= 259 =====>(x,y)= (471, 440)
			r= 260 =====>(x,y)= (73, 212)
			r= 261 =====>(x,y)= (226, 104)
			r= 262 =====>(x,y)= (346, 61)
			r= 263 =====>(x,y)= (310, 217)
			r= 264 =====>(x,y)= (357, 98)
			r= 265 =====>(x,y)= (20, 99)
			r= 266 =====>(x,y)= (116, 125)
			r= 267 =====>(x,y)= (15, 45)
			r= 268 =====>(x,y)= (453, 42)
			r= 269 =====>(x,y)= (169, 387)
			r= 270 =====>(x,y)= (94, 127)
			r= 271 =====>(x,y)= (91, 271)
			r= 272 =====>(x,y)= (17, 228)
			r= 273 =====>(x,y)= (483, 315)
			r= 274 =====>(x,y)= (279, 489)
			r= 275 =====>(x,y)= (465, 122)
			r= 276 =====>(x,y)= (441, 212)
			r= 277 =====>(x,y)= (502, 2)
			r= 278 =====>(x,y)= (189, 435)
			r= 279 =====>(x,y)= (440, 110)
			r= 280 =====>(x,y)= (117, 263)
			r= 281 =====>(x,y)= (31, 77)
			r= 282 =====>(x,y)= (146, 426)
			r= 283 =====>(x,y)= (10, 244)
			r= 284 =====>(x,y)= (186, 181)
			r= 285 =====>(x,y)= (50, 491)
			r= 286 =====>(x,y)= (371, 379)
			r= 287 =====>(x,y)= (271, 199)
			r= 288 =====>(x,y)= (87, 46)
			r= 289 =====>(x,y)= (288, 371)
			r= 290 =====>(x,y)= (401, 167)
			r= 291 =====>(x,y)= (375, 467)
			r= 292 =====>(x,y)= (175, 238)
			r= 293 =====>(x,y)= (278, 381)
			r= 294 =====>(x,y)= (380, 487)
			r= 295 =====>(x,y)= (403, 196)
			r= 296 =====>(x,y)= (480, 205)
			r= 297 =====>(x,y)= (489, 375)
			r= 298 =====>(x,y)= (334, 116)
			r= 299 =====>(x,y)= (161, 475)
			r= 300 =====>(x,y)= (342, 28)
			r= 301 =====>(x,y)= (488, 190)
			r= 302 =====>(x,y)= (229, 220)
			r= 303 =====>(x,y)= (104, 226)
			r= 304 =====>(x,y)= (82, 390)
			r= 305 =====>(x,y)= (328, 265)
			r= 306 =====>(x,y)= (404, 176)
			r= 307 =====>(x,y)= (487, 229)
			r= 308 =====>(x,y)= (475, 25)
			r= 309 =====>(x,y)= (263, 117)
			r= 310 =====>(x,y)= (225, 268)
			r= 311 =====>(x,y)= (46, 87)
			r= 312 =====>(x,y)= (132, 124)
			r= 313 =====>(x,y)= (36, 128)
			r= 314 =====>(x,y)= (104, 69)
			r= 315 =====>(x,y)= (186, 239)
			r= 316 =====>(x,y)= (466, 189)
			r= 317 =====>(x,y)= (290, 403)
			r= 318 =====>(x,y)= (98, 357)
			r= 319 =====>(x,y)= (384, 222)
			r= 320 =====>(x,y)= (128, 14)
			r= 321 =====>(x,y)= (362, 288)
			r= 322 =====>(x,y)= (199, 258)
			r= 323 =====>(x,y)= (338, 466)
			r= 324 =====>(x,y)= (281, 119)
			r= 325 =====>(x,y)= (67, 458)
			r= 326 =====>(x,y)= (298, 175)
			r= 327 =====>(x,y)= (88, 81)
			r= 328 =====>(x,y)= (333, 427)
			r= 329 =====>(x,y)= (264, 317)
			r= 330 =====>(x,y)= (476, 60)
			r= 331 =====>(x,y)= (217, 86)
			r= 332 =====>(x,y)= (381, 38)
			r= 333 =====>(x,y)= (463, 118)
			r= 334 =====>(x,y)= (485, 161)
			r= 335 =====>(x,y)= (502, 252)
			r= 336 =====>(x,y)= (272, 294)
			r= 337 =====>(x,y)= (307, 166)
			r= 338 =====>(x,y)= (316, 349)
			r= 339 =====>(x,y)= (275, 355)
			r= 340 =====>(x,y)= (376, 305)
			r= 341 =====>(x,y)= (411, 390)
			r= 342 =====>(x,y)= (215, 132)
			r= 343 =====>(x,y)= (435, 338)
			r= 344 =====>(x,y)= (51, 86)
			r= 345 =====>(x,y)= (224, 36)
			r= 346 =====>(x,y)= (143, 250)
			r= 347 =====>(x,y)= (213, 100)
			r= 348 =====>(x,y)= (240, 386)
			r= 349 =====>(x,y)= (78, 454)
			r= 350 =====>(x,y)= (87, 339)
			r= 351 =====>(x,y)= (189, 466)
			r= 352 =====>(x,y)= (202, 198)
			r= 353 =====>(x,y)= (198, 202)
			r= 354 =====>(x,y)= (460, 240)
			r= 355 =====>(x,y)= (394, 354)
			r= 356 =====>(x,y)= (465, 268)
			r= 357 =====>(x,y)= (157, 442)
			r= 358 =====>(x,y)= (237, 226)
			r= 359 =====>(x,y)= (28, 478)
			r= 360 =====>(x,y)= (315, 176)
			r= 361 =====>(x,y)= (493, 259)
			r= 362 =====>(x,y)= (409, 301)
			r= 363 =====>(x,y)= (489, 279)
			r= 364 =====>(x,y)= (404, 483)
			r= 365 =====>(x,y)= (467, 279)
			r= 366 =====>(x,y)= (435, 189)
			r= 367 =====>(x,y)= (151, 134)
			r= 368 =====>(x,y)= (478, 18)
			r= 369 =====>(x,y)= (271, 91)
			r= 370 =====>(x,y)= (110, 495)
			r= 371 =====>(x,y)= (245, 412)
			r= 372 =====>(x,y)= (14, 224)
			r= 373 =====>(x,y)= (460, 153)
			r= 374 =====>(x,y)= (164, 185)
			r= 375 =====>(x,y)= (337, 196)
			r= 376 =====>(x,y)= (337, 290)
			r= 377 =====>(x,y)= (357, 77)
			r= 378 =====>(x,y)= (324, 93)
			r= 379 =====>(x,y)= (263, 43)
			r= 380 =====>(x,y)= (196, 337)
			r= 381 =====>(x,y)= (490, 334)
			r= 382 =====>(x,y)= (38, 235)
			r= 383 =====>(x,y)= (125, 116)
			r= 384 =====>(x,y)= (212, 441)
			r= 385 =====>(x,y)= (493, 369)
			r= 386 =====>(x,y)= (167, 143)
			r= 387 =====>(x,y)= (305, 376)
			r= 388 =====>(x,y)= (369, 493)
			r= 389 =====>(x,y)= (250, 401)
			r= 390 =====>(x,y)= (135, 361)
			r= 391 =====>(x,y)= (289, 486)
			r= 392 =====>(x,y)= (291, 430)
			r= 393 =====>(x,y)= (148, 214)
			r= 394 =====>(x,y)= (12, 453)
			r= 395 =====>(x,y)= (403, 290)
			r= 396 =====>(x,y)= (443, 27)
			r= 397 =====>(x,y)= (442, 157)
			r= 398 =====>(x,y)= (69, 237)
			r= 399 =====>(x,y)= (342, 18)
			r= 400 =====>(x,y)= (73, 382)
			r= 401 =====>(x,y)= (8, 393)
			r= 402 =====>(x,y)= (225, 122)
			r= 403 =====>(x,y)= (475, 161)
			r= 404 =====>(x,y)= (190, 488)
			r= 405 =====>(x,y)= (485, 25)
			r= 406 =====>(x,y)= (410, 179)
			r= 407 =====>(x,y)= (18, 342)
			r= 408 =====>(x,y)= (173, 33)
			r= 409 =====>(x,y)= (322, 192)
			r= 410 =====>(x,y)= (304, 245)
			r= 411 =====>(x,y)= (350, 43)
			r= 412 =====>(x,y)= (360, 253)
			r= 413 =====>(x,y)= (440, 471)
			r= 414 =====>(x,y)= (458, 67)
			r= 415 =====>(x,y)= (301, 409)
			r= 416 =====>(x,y)= (311, 181)
			r= 417 =====>(x,y)= (334, 490)
			r= 418 =====>(x,y)= (127, 94)
			r= 419 =====>(x,y)= (470, 157)
			r= 420 =====>(x,y)= (141, 215)
			r= 421 =====>(x,y)= (495, 471)
			r= 422 =====>(x,y)= (16, 123)
			r= 423 =====>(x,y)= (457, 416)
			r= 424 =====>(x,y)= (466, 338)
			r= 425 =====>(x,y)= (235, 278)
			r= 426 =====>(x,y)= (149, 109)
			r= 427 =====>(x,y)= (252, 502)
			r= 428 =====>(x,y)= (116, 334)
			r= 429 =====>(x,y)= (379, 362)
			r= 430 =====>(x,y)= (231, 209)
			r= 431 =====>(x,y)= (339, 318)
			r= 432 =====>(x,y)= (425, 154)
			r= 433 =====>(x,y)= (467, 375)
			r= 434 =====>(x,y)= (102, 336)
			r= 435 =====>(x,y)= (109, 149)
			r= 436 =====>(x,y)= (350, 117)
			r= 437 =====>(x,y)= (352, 259)
			r= 438 =====>(x,y)= (382, 441)
			r= 439 =====>(x,y)= (258, 91)
			r= 440 =====>(x,y)= (60, 476)
			r= 441 =====>(x,y)= (258, 199)
			r= 442 =====>(x,y)= (216, 139)
			r= 443 =====>(x,y)= (51, 310)
			r= 444 =====>(x,y)= (232, 304)
			r= 445 =====>(x,y)= (472, 405)
			r= 446 =====>(x,y)= (378, 13)
			r= 447 =====>(x,y)= (287, 364)
			r= 448 =====>(x,y)= (185, 164)
			r= 449 =====>(x,y)= (393, 8)
			r= 450 =====>(x,y)= (495, 110)
			r= 451 =====>(x,y)= (213, 166)
			r= 452 =====>(x,y)= (442, 330)
			r= 453 =====>(x,y)= (220, 380)
			r= 454 =====>(x,y)= (237, 69)
			r= 455 =====>(x,y)= (318, 339)
			r= 456 =====>(x,y)= (153, 460)
			r= 457 =====>(x,y)= (259, 352)
			r= 458 =====>(x,y)= (470, 330)
			r=459 is not in the set of definition
			r= 460 =====>(x,y)= (86, 51)
			r= 461 =====>(x,y)= (63, 32)
			r= 462 =====>(x,y)= (416, 457)
			r= 463 =====>(x,y)= (378, 387)
			r= 464 =====>(x,y)= (124, 141)
			r= 465 =====>(x,y)= (338, 435)
			r= 466 =====>(x,y)= (490, 125)
			r= 467 =====>(x,y)= (382, 73)
			r= 468 =====>(x,y)= (43, 350)
			r= 469 =====>(x,y)= (31, 98)
			r= 470 =====>(x,y)= (436, 313)
			r= 471 =====>(x,y)= (187, 49)
			r= 472 =====>(x,y)= (171, 12)
			r= 473 =====>(x,y)= (217, 310)
			r= 474 =====>(x,y)= (170, 76)
			r= 475 =====>(x,y)= (318, 46)
			r= 476 =====>(x,y)= (461, 50)
			r= 477 =====>(x,y)= (40, 422)
			r= 478 =====>(x,y)= (121, 62)
			r= 479 =====>(x,y)= (368, 142)
			r= 480 =====>(x,y)= (176, 404)
			r= 481 =====>(x,y)= (386, 153)
			r= 482 =====>(x,y)= (25, 485)
			r= 483 =====>(x,y)= (480, 265)
			r= 484 =====>(x,y)= (411, 365)
			r= 485 =====>(x,y)= (327, 188)
			r= 486 =====>(x,y)= (283, 123)
			r= 487 =====>(x,y)= (352, 369)
			r= 488 =====>(x,y)= (77, 31)
			r= 489 =====>(x,y)= (315, 483)
			r= 490 =====>(x,y)= (328, 205)
			r= 491 =====>(x,y)= (330, 470)
			r= 492 =====>(x,y)= (125, 490)
			r= 493 =====>(x,y)= (415, 385)
			r= 494 =====>(x,y)= (491, 332)
			r= 495 =====>(x,y)= (311, 239)
			r= 496 =====>(x,y)= (42, 171)
			r= 497 =====>(x,y)= (23, 298)
			r= 498 =====>(x,y)= (307, 100)
			r= 499 =====>(x,y)= (212, 73)
			r= 500 =====>(x,y)= (283, 274)
			r= 501 =====>(x,y)= (386, 240)
			r= 502 =====>(x,y)= (441, 382)