T1 <-> 4th root of unity, 4 + 2*17 + 10*17^2 + 5*17^3 + 12*17^4 + ... T2 = [7,13] [17A-5,1]: [3, -2-5^(1/2)] [17A-5,2]: [] [17A-20,1]: 2*T1 + [3, -2+5^(1/2)] [17A-20,2]: 3*T1 [17A-29,1]: 2*T1 + [5091/1225, -3158/1225-52207/42875*29^(1/2)] [17A-29,2]: 3*T1 [17A-37,1]: 0*T1 + 2*T2 + [88251563/6497401, -47374482/6497401+131903494275/16561875149*37^(1/2)] [17A-37,2]: 2*T1 [17A-41,1]: 2*T1 + [27/4, -31/8-5/2*41^(1/2)] [17A-41,2]: 3*T1 [17A-61,1]: 2*T1 + [67/9, -38/9+65/27*61^(1/2)] [17A-61,2]: 1*T1 [17A-73,1]: [1543/36, -1579/72-3515/108*73^(1/2)] [17A-73,2]: [] [17A-97,1]: 2*T1 + [49765/17424, -67189/34848-330455/2299968*97^(1/2)] [17A-97,2]: 3*T1 [17A-12,1] + [17A-12,2] = [29/6, -35/12-185/36*3^(1/2)] [17A-12,1] = [17A-12,2] = 2*T2 + [-4/3-5/6*I*2^(1/2), 1/6+5/12*I*2^(1/2)+49/36*I*6^(1/2)-5/18*6^(1/2)*2^(1/2)] 2 [17A-12,1] = 2 [17A-12,2] = [29/6, -35/12-185/36*3^(1/2)] [17A-12,3] + [17A-12,4] = 2*T1 2 [17A-12,3] - 2 [17A-12,4] = [1/2, -3/4 - 15/4*I] [17A-24,1] + [17A-24,2] = [131/12, -143/24-1015/72*6^(1/2)] [17A-24,1] = [17A-24,2] = [-7/6-7/6*I*2^(1/2), 1/12+7/12*I*2^(1/2)+47/36*I*3^(1/2)-7/18*3^(1/2)*2^(1/2)] 2 [17A-24,1] = 2 [17A-24,2] = [131/12, -143/24-1015/72*6^(1/2)] [17A-24,3] + [17A-24,4] = 2*T1 [17A-24,3] - [17A-24,4] = 2*T1 + 3*T2 + [5/8, -13/16+85/32*I*2^(1/2)] [17A-24,3] = 2*T1 + [1-2^(1/2)+7*I+4*I*2^(1/2), -19-11*2^(1/2)+9*I+10*I*2^(1/2)] [17A-24,4] = - [1-2^(1/2)+7*I+4*I*2^(1/2), -19-11*2^(1/2)+9*I+10*I*2^(1/2)] 8 [17A-24,3] = 4 [5/8, -13/16+85/32*I*2^(1/2)] 8 [17A-24,4] = 4 [5/8, -13/16-85/32*I*2^(1/2)] [17A-28,1] + [17A-28,2] = 2*T1 + [5231/1134, -6365/2268-439205/142884*7^(1/2)] [17A-28,1] - [17A-28,2] = 2*T1 [17A-28,1] = [-109/81-65/81*I*2^(1/2), 14/81+65/162*I*2^(1/2)+1327/1458*I*14^(1/2)-130/729*14^(1/2)*2^(1/2)] 2 [17A-28,1] = 2 [17A-28,2] = [5231/1134, -6365/2268-439205/142884*7^(1/2)] 8 [17A-28,3] = 2 [1/2, -3/4 + 15/4*I] 8 [17A-28,4] = 2 [1/2, -3/4 - 15/4*I] 2 [17A-40,1] = 2 [5, -3+3*10^(1/2)] + 4 [3, -2 - 5^(1/2)] 2 [17A-40,2] = 2 [5, -3+3*10^(1/2)] + 4 [3, -2 + 5^(1/2)] 8 [17A-40,3] = 8 [17A-40,4] = [] 2 [17A-44,1] = 2 [17A-44,2] = [27101/9702, -36803/19404+1206545/4482324*11^(1/2)] 8 [17A-44,3] = 2 [1/2, -3/4 - 15/4*I] 8 [17A-44,4] = 2 [1/2, -3/4 + 15/4*I] 2 [17A-45,1] = 2 [17A-45,2] = [] 4 [17A-45,3] = - 4 [17A-45,4] = 8 [4/3, -7/6+17/18*I*15^(1/2)] 2 [17A-48,1] = 2 [17A-48,2] = [29/6, -35/12+185/36*3^(1/2)] 4 [17A-48,3] = 4 [17A-48,4] = [] 2 [17A-56,1] = 2 [17A-56,2] = [10469/3388, -13857/6776+46275/65219*14^(1/2)] 8 [17A-56,3] = 4 [5/8, -13/16-85/32*I*2^(1/2)] 8 [17A-56,4] = 4 [5/8, -13/16+85/32*I*2^(1/2)] 2 [17A-57,1] = 2 [17A-57,2] = [8522141/1554124, -10076265/3108248-6274142315/4222554908*57^(1/2)] 8 [17A-57,3] = 4 [-63/76, -13/152-629/722*I*19^(1/2)] 8 [17A-57,4] = 4 [-63/76, -13/152+629/722*I*19^(1/2)] [17A-65,1] + [17A-65,2] = 2 T1 + 2 [15, -8-7*65^(1/2)] [17A-65,1] - [17A-65,2] = 2 T1 + 4 [3, -2+5^(1/2)] 2 [17A-65,1] = 2 [15, -8-7*65^(1/2)] + 4 [3, -2+5^(1/2)] 2 [17A-65,2] = 2 [15, -8-7*65^(1/2)] - 4 [3, -2-5^(1/2)] 4 [17A-65,3] = 4 [17A-65,4] = [] 2 [17A-80,1] = 2 [17A-80,2] = 2 [3, -2+5^(1/2)] 8 [17A-80,3] = 4 [1/2, -3/4-15/4*I] 8 [17A-80,4] = 4 [1/2, -3/4+15/4*I] 2 [17A-88,1] = 2 [17A-88,2] = [1168375625699/393455082636, -1561830708335/786910165272+363441210673276055/818538445544777496*22^(1/2)] 8 [17A-88,3] = 4 [5/8, -13/16+85/32*I*2^(1/2)] 8 [17A-88,4] = 4 [5/8, -13/16-85/32*I*2^(1/2) 2 [17A-92,1] = 2 [17A-92,2] = [1621831557551/2873040814, -1624704598365/5746081628-2919003154601635125/1044459511439932*23^(1/2)] 8 [17A-92,3] = 2 [1/2, -3/4-15/4*I] 8 [17A-92,4] = 2 [1/2, -3/4+15/4*I] [17A-96,1] + [17A-96,2] + [17A-96,4] + [17A-96,5] = 2 T1 + 2 [131/12, -143/24+1015/72*6^(1/2)] [17A-96,1] - [17A-96,2] + [17A-96,4] - [17A-96,5] = 2 T1 + 4 [29/6, -35/12-185/36*3^(1/2)] [17A-96,1] - [17A-96,2] - [17A-96,4] + [17A-96,5] = 2 T1 [17A-96,1] + [17A-96,2] - [17A-96,4] - [17A-96,5] = 2 T1 2 [17A-96,1] = 2 [17A-96,4] = [131/12, -143/24+1015/72*6^(1/2)] + 2 [29/6, -35/12-185/36*3^(1/2)] 2 [17A-96,2] = 2 [17A-96,5] = [131/12, -143/24+1015/72*6^(1/2)] + 2 [29/6, -35/12+185/36*3^(1/2)] --- 2 [17A-96,3] + 2 [17A-96,6] + 2 [17A-96,7] + 2 [17A-96,8] = 2 T1 2 [17A-96,3] - 2 [17A-96,6] + 2 [17A-96,7] - 2 [17A-96,8] = 2 T1 2 [17A-96,3] + 2 [17A-96,6] - 2 [17A-96,7] - 2 [17A-96,8] = 2 T1 + 2 [1/2, -3/4+15/4*I] 2 [17A-96,3] + 2 [17A-96,6] - 2 [17A-96,7] - 2 [17A-96,8] = 2 T1 8 [17A-96,3] = 2 [1/2, -3/4+15/4*I] 8 [17A-96,6] = 2 [1/2, -3/4-15/4*I] 8 [17A-96,7] = 2 [1/2, -3/4-15/4*I] 8 [17A-96,8] = 2 [1/2, -3/4+15/4*I]