T1 = 3 torsion corresponding to root of unity
T2 = [5,9]

[19A-8,1] = 2 [17/2, -1/2+69/4*2^(1/2)]
[19A-8,2] = 2 T1

[19A-13,1] = 2 [4, -1/2-3/2*13^(1/2)]
[19A-13,2] = 2 T1

[19A-29,2] = 2 [187766/50625, -1/2+17260511/22781250*29^(1/2)]
[19A-29,1] = 2 T1

[19A-37,2] = 2 [97/4, -1/2-159/8*37^(1/2)]
[19A-37,1] = T1

[19A-41,2] = 2 [328071349/100600900, -1/2-173802949917/1009027027000*41^(1/2)]
[19A-41,1] = T1

[19A-52,2] = []
[19A-52,1] = 2 T1

[19A-53,2] = 2 [171802/5929, -1/2+19788441/913066*53^(1/2)]
[19A-53,1] = 2 T1

[19A-89,2] = ????
[19A-89,1] = []

[19A-97,2] = 2 [78721/3136, -1/2+2270031/175616*97^(1/2)]
[19A-97,1] = []


[19A-12,1] + [19A-12,3] = 2 [31/4, -1/2+97/8*3^(1/2)]
[19A-12,1] - [19A-12,3] = []
[19A-12,1] = [31/4, -1/2+97/8*3^(1/2)]
[19A-12,3] = [31/4, -1/2+97/8*3^(1/2)]
---
[19A-12,2] + [19A-12,4] = T1
[19A-12,2] - [19A-12,4] = ????

[19A-21,2] = [19A-21,4] = [958/175, -1/2+30479/12250*21^(1/2)]
---
[19A-21,1] + [19A-21,3] = T1
[19A-21,1] - [19A-21,3] = ????

[19A-32,1] = [19A-32,4] = [17/2, -1/2-69/4*2^(1/2)]
---
[19A-32,2] + [19A-32,3] = T1
[19A-32,2] - [19A-32,3] = ????

[19A-33,3] = [19A-33,4] = [839/44, -1/2+14209/968*33^(1/2)]
---
[19A-33,1] + [19A-33,2] = 2 T1
[19A-33,1] - [19A-33,2] = ????

[19A-40,2] + [19A-40,3] = 2 [1201/10, -1/2-41781/100*10^(1/2)]
[19A-40,2] - [19A-40,3] = 6 [17/2, -1/2+69/4*2^(1/2)]
[19A-40,2] = [1201/10, -1/2-41781/100*10^(1/2)] + 3 [17/2, -1/2+69/4*2^(1/2)]
[19A-40,3] = [1201/10, -1/2-41781/100*10^(1/2)] + 3 [17/2, -1/2-69/4*2^(1/2)]
---
[19A-40,1] + [19A-40,4] = []
[19A-40,1] - [19A-40,4] = T1
3 [19A-40,1] = 3 [19A-40,4] = []

MISSING DATA FOR 48,56

[19A-48,2] = [31/4, -1/2-97/8*3^(1/2)]
---
[19A-48,1] + [19A-48,3] = T1
[19A-48,1] - [19A-48,3] = ????

[19A-56,3] = [81689740196849/3182668608350, -1/2-747294455075136103407/21244726707655335500*14^(1/2)]
---
[19A-56,1] + [19A-56,2] = 2 T1
[19A-56,1] - [19A-56,2] = ????

[19A-65,3] + [19A-65,4] = 2 [460138373/2979920, -1/2+2745872872863/11502491200*65^(1/2)]
[19A-65,3] - [19A-65,4] = 6 [4, -1/2-3/2*13^(1/2)]
[19A-65,3] = [460138373/2979920, -1/2+2745872872863/11502491200*65^(1/2)] + 3 [4, -1/2-3/2*13^(1/2)]
[19A-65,4] = [460138373/2979920, -1/2+2745872872863/11502491200*65^(1/2)] + 3 [4, -1/2+3/2*13^(1/2)]
---
[19A-65,1] + [19A-65,2] = T1
[19A-65,1] - [19A-65,2] = T1
3 [19A-65,1] = 3 [19A-65,2] = []

[19A-69,2] = [19A-69,4] = 2 [136/25, -1/2+339/250*69^(1/2)]
---
[19A-69,1] + [19A-69,3] = []
[19A-69,1] - [19A-69,3] = ????

[19A-72,1] = [19A-72,4] = 2 [17/2, -1/2-69/4*2^(1/2)]
---
[19A-72,2] + [19A-72,3] = T1
[19A-72,2] - [19A-72,3] = ????

[19A-84,3] = [19A-84,4] = []
---
[19A-84,1] + [19A-84,2] = T1
[19A-84,1] - [19A-84,2] = T1
3 [19A-84,1] = 3 [19A-84,2] = []

[19A-88,3] = [19A-88,4] = [3529/1078, -1/2+44589/166012*22^(1/2)]
---
[19A-88,1] + [19A-88,2] = []
[19A-88,1] - [19A-88,2] = ????


[19A-60,1] + [19A-60,3] + [19A-60,5] + [19A-60,7] = 2 [177592727/5304500, -1/2+1380972233981/27318175000*15^(1/2)]
[19A-60,1] - [19A-60,3] + [19A-60,5] - [19A-60,7] = []
[19A-60,1] - [19A-60,3] - [19A-60,5] + [19A-60,7] = []
[19A-60,1] - [19A-60,3] + [19A-60,5] - [19A-60,7] = 6 [31/4, -1/2+97/8*3^(1/2)]
2 [19A-60,1] = [177592727/5304500, -1/2+1380972233981/27318175000*15^(1/2)] + 3 [31/4, -1/2+97/8*3^(1/2)]
2 [19A-60,3] = [177592727/5304500, -1/2+1380972233981/27318175000*15^(1/2)] + 3 [31/4, -1/2+97/8*3^(1/2)]
2 [19A-60,5] = [177592727/5304500, -1/2+1380972233981/27318175000*15^(1/2)] + 3 [31/4, -1/2-97/8*3^(1/2)]
2 [19A-60,7] = [177592727/5304500, -1/2+1380972233981/27318175000*15^(1/2)] + 3 [31/4, -1/2-97/8*3^(1/2)]
---
DIDN'T BOTHER TRYING THE MINUS SIDE