Database - gps_crep (Complex representations of finite groups)

Formats: - HTML - YAML - JSON - 2026-04-20T08:04:47.686138 - next page

Query: /api/gps_crep/?_offset=0

Column	Type
cyc_order_mat	integer
cyc_order_traces	integer
decomposition	jsonb
denominators	integer[]
dim	smallint
gens	jsonb
group	text
indicator	smallint
irreducible	boolean
label	text
order	numeric
schur_index	smallint
trace_field	integer[]
traces	jsonb

0. label: 1.1.1a
   {'cyc_order_mat': 1, 'cyc_order_traces': 1, 'decomposition': [['1.1.1a', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 0]]]]], 'group': '1.1', 'indicator': 1, 'irreducible': True, 'label': '1.1.1a', 'order': 1, 'schur_index': 1, 'trace_field': [0, 1], 'traces': [[[1, 0]]]}
1. label: 2.1.1b
   {'cyc_order_mat': 1, 'cyc_order_traces': 1, 'decomposition': [['2.1.1b', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[-1, 0]]]]], 'group': '2.1', 'indicator': 1, 'irreducible': True, 'label': '2.1.1b', 'order': 2, 'schur_index': 1, 'trace_field': [0, 1], 'traces': [[[-1, 0]]]}
2. label: 3.1.1b1
   {'cyc_order_mat': 3, 'cyc_order_traces': 3, 'decomposition': [['3.1.1b1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '3.1', 'indicator': 0, 'irreducible': True, 'label': '3.1.1b1', 'order': 3, 'schur_index': 1, 'trace_field': [1, -1, 1], 'traces': [[[1, 1]]]}
3. label: 4.1.1c1
   {'cyc_order_mat': 4, 'cyc_order_traces': 4, 'decomposition': [['4.1.1c1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '4.1', 'indicator': 0, 'irreducible': True, 'label': '4.1.1c1', 'order': 4, 'schur_index': 1, 'trace_field': [1, 0, 1], 'traces': [[[1, 1]]]}
4. label: 5.1.1b1
   {'cyc_order_mat': 5, 'cyc_order_traces': 5, 'decomposition': [['5.1.1b1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '5.1', 'indicator': 0, 'irreducible': True, 'label': '5.1.1b1', 'order': 5, 'schur_index': 1, 'trace_field': [1, -1, 1, -1, 1], 'traces': [[[1, 1]]]}
5. label: 6.2.1d1
   {'cyc_order_mat': 3, 'cyc_order_traces': 3, 'decomposition': [['6.2.1d1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[-1, 1]]]]], 'group': '6.2', 'indicator': 0, 'irreducible': True, 'label': '6.2.1d1', 'order': 6, 'schur_index': 1, 'trace_field': [1, -1, 1], 'traces': [[[-1, 1]]]}
6. label: 7.1.1b1
   {'cyc_order_mat': 7, 'cyc_order_traces': 7, 'decomposition': [['7.1.1b1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '7.1', 'indicator': 0, 'irreducible': True, 'label': '7.1.1b1', 'order': 7, 'schur_index': 1, 'trace_field': [1, -1, 1, -1, 1, -1, 1], 'traces': [[[1, 1]]]}
7. label: 8.1.1d1
   {'cyc_order_mat': 8, 'cyc_order_traces': 8, 'decomposition': [['8.1.1d1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '8.1', 'indicator': 0, 'irreducible': True, 'label': '8.1.1d1', 'order': 8, 'schur_index': 1, 'trace_field': [1, 0, 0, 0, 1], 'traces': [[[1, 1]]]}
8. label: 9.1.1c1
   {'cyc_order_mat': 9, 'cyc_order_traces': 9, 'decomposition': [['9.1.1c1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '9.1', 'indicator': 0, 'irreducible': True, 'label': '9.1.1c1', 'order': 9, 'schur_index': 1, 'trace_field': [1, 0, 0, -1, 0, 0, 1], 'traces': [[[1, 1]]]}
9. label: 10.2.1d1
   {'cyc_order_mat': 5, 'cyc_order_traces': 5, 'decomposition': [['10.2.1d1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[-1, 1]]]]], 'group': '10.2', 'indicator': 0, 'irreducible': True, 'label': '10.2.1d1', 'order': 10, 'schur_index': 1, 'trace_field': [1, -1, 1, -1, 1], 'traces': [[[-1, 1]]]}
10. label: 11.1.1b1
    {'cyc_order_mat': 11, 'cyc_order_traces': 11, 'decomposition': [['11.1.1b1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '11.1', 'indicator': 0, 'irreducible': True, 'label': '11.1.1b1', 'order': 11, 'schur_index': 1, 'trace_field': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 'traces': [[[1, 1]]]}
11. label: 12.2.1f1
    {'cyc_order_mat': 12, 'cyc_order_traces': 12, 'decomposition': [['12.2.1f1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '12.2', 'indicator': 0, 'irreducible': True, 'label': '12.2.1f1', 'order': 12, 'schur_index': 1, 'trace_field': [1, 0, 1], 'traces': [[[1, 1]]]}
12. label: 13.1.1b1
    {'cyc_order_mat': 13, 'cyc_order_traces': 13, 'decomposition': [['13.1.1b1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '13.1', 'indicator': 0, 'irreducible': True, 'label': '13.1.1b1', 'order': 13, 'schur_index': 1, 'trace_field': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 'traces': [[[1, 1]]]}
13. label: 14.2.1d1
    {'cyc_order_mat': 7, 'cyc_order_traces': 7, 'decomposition': [['14.2.1d1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[-1, 1]]]]], 'group': '14.2', 'indicator': 0, 'irreducible': True, 'label': '14.2.1d1', 'order': 14, 'schur_index': 1, 'trace_field': [1, -1, 1, -1, 1, -1, 1], 'traces': [[[-1, 1]]]}
14. label: 15.1.1d1
    {'cyc_order_mat': 15, 'cyc_order_traces': 15, 'decomposition': [['15.1.1d1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '15.1', 'indicator': 0, 'irreducible': True, 'label': '15.1.1d1', 'order': 15, 'schur_index': 1, 'trace_field': [1, -1, 1], 'traces': [[[1, 1]]]}
15. label: 16.1.1e1
    {'cyc_order_mat': 16, 'cyc_order_traces': 16, 'decomposition': [['16.1.1e1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '16.1', 'indicator': 0, 'irreducible': True, 'label': '16.1.1e1', 'order': 16, 'schur_index': 1, 'trace_field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'traces': [[[1, 1]]]}
16. label: 17.1.1b1
    {'cyc_order_mat': 17, 'cyc_order_traces': 17, 'decomposition': [['17.1.1b1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '17.1', 'indicator': 0, 'irreducible': True, 'label': '17.1.1b1', 'order': 17, 'schur_index': 1, 'trace_field': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 'traces': [[[1, 1]]]}
17. label: 18.2.1f1
    {'cyc_order_mat': 9, 'cyc_order_traces': 9, 'decomposition': [['18.2.1f1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[-1, 1]]]]], 'group': '18.2', 'indicator': 0, 'irreducible': True, 'label': '18.2.1f1', 'order': 18, 'schur_index': 1, 'trace_field': [1, 0, 0, -1, 0, 0, 1], 'traces': [[[-1, 1]]]}
18. label: 19.1.1b1
    {'cyc_order_mat': 19, 'cyc_order_traces': 19, 'decomposition': [['19.1.1b1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '19.1', 'indicator': 0, 'irreducible': True, 'label': '19.1.1b1', 'order': 19, 'schur_index': 1, 'trace_field': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 'traces': [[[1, 1]]]}
19. label: 20.2.1f1
    {'cyc_order_mat': 20, 'cyc_order_traces': 20, 'decomposition': [['20.2.1f1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '20.2', 'indicator': 0, 'irreducible': True, 'label': '20.2.1f1', 'order': 20, 'schur_index': 1, 'trace_field': [1, 0, 1], 'traces': [[[1, 1]]]}
20. label: 21.2.1d1
    {'cyc_order_mat': 21, 'cyc_order_traces': 21, 'decomposition': [['21.2.1d1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '21.2', 'indicator': 0, 'irreducible': True, 'label': '21.2.1d1', 'order': 21, 'schur_index': 1, 'trace_field': [1, -1, 1], 'traces': [[[1, 1]]]}
21. label: 22.2.1d1
    {'cyc_order_mat': 11, 'cyc_order_traces': 11, 'decomposition': [['22.2.1d1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[-1, 1]]]]], 'group': '22.2', 'indicator': 0, 'irreducible': True, 'label': '22.2.1d1', 'order': 22, 'schur_index': 1, 'trace_field': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 'traces': [[[-1, 1]]]}
22. label: 23.1.1b1
    {'cyc_order_mat': 23, 'cyc_order_traces': 23, 'decomposition': [['23.1.1b1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '23.1', 'indicator': 0, 'irreducible': True, 'label': '23.1.1b1', 'order': 23, 'schur_index': 1, 'trace_field': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 'traces': [[[1, 1]]]}
23. label: 24.2.1h1
    {'cyc_order_mat': 24, 'cyc_order_traces': 24, 'decomposition': [['24.2.1h1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '24.2', 'indicator': 0, 'irreducible': True, 'label': '24.2.1h1', 'order': 24, 'schur_index': 1, 'trace_field': [1, 0, 0, 0, 1], 'traces': [[[1, 1]]]}
24. label: 25.1.1c1
    {'cyc_order_mat': 25, 'cyc_order_traces': 25, 'decomposition': [['25.1.1c1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '25.1', 'indicator': 0, 'irreducible': True, 'label': '25.1.1c1', 'order': 25, 'schur_index': 1, 'trace_field': [1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1], 'traces': [[[1, 1]]]}
25. label: 26.2.1d1
    {'cyc_order_mat': 13, 'cyc_order_traces': 13, 'decomposition': [['26.2.1d1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[-1, 1]]]]], 'group': '26.2', 'indicator': 0, 'irreducible': True, 'label': '26.2.1d1', 'order': 26, 'schur_index': 1, 'trace_field': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 'traces': [[[-1, 1]]]}
26. label: 27.1.1d1
    {'cyc_order_mat': 27, 'cyc_order_traces': 27, 'decomposition': [['27.1.1d1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '27.1', 'indicator': 0, 'irreducible': True, 'label': '27.1.1d1', 'order': 27, 'schur_index': 1, 'trace_field': [1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'traces': [[[1, 1]]]}
27. label: 28.2.1f1
    {'cyc_order_mat': 28, 'cyc_order_traces': 28, 'decomposition': [['28.2.1f1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '28.2', 'indicator': 0, 'irreducible': True, 'label': '28.2.1f1', 'order': 28, 'schur_index': 1, 'trace_field': [1, 0, 1], 'traces': [[[1, 1]]]}
28. label: 29.1.1b1
    {'cyc_order_mat': 29, 'cyc_order_traces': 29, 'decomposition': [['29.1.1b1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '29.1', 'indicator': 0, 'irreducible': True, 'label': '29.1.1b1', 'order': 29, 'schur_index': 1, 'trace_field': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 'traces': [[[1, 1]]]}
29. label: 30.4.1h1
    {'cyc_order_mat': 15, 'cyc_order_traces': 15, 'decomposition': [['30.4.1h1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[-1, 1]]]]], 'group': '30.4', 'indicator': 0, 'irreducible': True, 'label': '30.4.1h1', 'order': 30, 'schur_index': 1, 'trace_field': [1, -1, 1], 'traces': [[[-1, 1]]]}
30. label: 31.1.1b1
    {'cyc_order_mat': 31, 'cyc_order_traces': 31, 'decomposition': [['31.1.1b1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '31.1', 'indicator': 0, 'irreducible': True, 'label': '31.1.1b1', 'order': 31, 'schur_index': 1, 'trace_field': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 'traces': [[[1, 1]]]}
31. label: 32.1.1f1
    {'cyc_order_mat': 32, 'cyc_order_traces': 32, 'decomposition': [['32.1.1f1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '32.1', 'indicator': 0, 'irreducible': True, 'label': '32.1.1f1', 'order': 32, 'schur_index': 1, 'trace_field': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'traces': [[[1, 1]]]}
32. label: 33.1.1d1
    {'cyc_order_mat': 33, 'cyc_order_traces': 33, 'decomposition': [['33.1.1d1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '33.1', 'indicator': 0, 'irreducible': True, 'label': '33.1.1d1', 'order': 33, 'schur_index': 1, 'trace_field': [1, -1, 1], 'traces': [[[1, 1]]]}
33. label: 34.2.1d1
    {'cyc_order_mat': 17, 'cyc_order_traces': 17, 'decomposition': [['34.2.1d1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[-1, 1]]]]], 'group': '34.2', 'indicator': 0, 'irreducible': True, 'label': '34.2.1d1', 'order': 34, 'schur_index': 1, 'trace_field': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 'traces': [[[-1, 1]]]}
34. label: 35.1.1d1
    {'cyc_order_mat': 35, 'cyc_order_traces': 35, 'decomposition': [['35.1.1d1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '35.1', 'indicator': 0, 'irreducible': True, 'label': '35.1.1d1', 'order': 35, 'schur_index': 1, 'trace_field': [1, -1, 1, -1, 1], 'traces': [[[1, 1]]]}
35. label: 36.2.1i1
    {'cyc_order_mat': 36, 'cyc_order_traces': 36, 'decomposition': [['36.2.1i1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '36.2', 'indicator': 0, 'irreducible': True, 'label': '36.2.1i1', 'order': 36, 'schur_index': 1, 'trace_field': [1, 0, 1], 'traces': [[[1, 1]]]}
36. label: 37.1.1b1
    {'cyc_order_mat': 37, 'cyc_order_traces': 37, 'decomposition': [['37.1.1b1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '37.1', 'indicator': 0, 'irreducible': True, 'label': '37.1.1b1', 'order': 37, 'schur_index': 1, 'trace_field': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 'traces': [[[1, 1]]]}
37. label: 38.2.1d1
    {'cyc_order_mat': 19, 'cyc_order_traces': 19, 'decomposition': [['38.2.1d1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[-1, 1]]]]], 'group': '38.2', 'indicator': 0, 'irreducible': True, 'label': '38.2.1d1', 'order': 38, 'schur_index': 1, 'trace_field': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 'traces': [[[-1, 1]]]}
38. label: 39.2.1d1
    {'cyc_order_mat': 39, 'cyc_order_traces': 39, 'decomposition': [['39.2.1d1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '39.2', 'indicator': 0, 'irreducible': True, 'label': '39.2.1d1', 'order': 39, 'schur_index': 1, 'trace_field': [1, -1, 1], 'traces': [[[1, 1]]]}
39. label: 40.2.1h1
    {'cyc_order_mat': 40, 'cyc_order_traces': 40, 'decomposition': [['40.2.1h1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '40.2', 'indicator': 0, 'irreducible': True, 'label': '40.2.1h1', 'order': 40, 'schur_index': 1, 'trace_field': [1, 0, 0, 0, 1], 'traces': [[[1, 1]]]}
40. label: 41.1.1b1
    {'cyc_order_mat': 41, 'cyc_order_traces': 41, 'decomposition': [['41.1.1b1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '41.1', 'indicator': 0, 'irreducible': True, 'label': '41.1.1b1', 'order': 41, 'schur_index': 1, 'trace_field': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 'traces': [[[1, 1]]]}
41. label: 42.6.1h1
    {'cyc_order_mat': 21, 'cyc_order_traces': 21, 'decomposition': [['42.6.1h1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[-1, 1]]]]], 'group': '42.6', 'indicator': 0, 'irreducible': True, 'label': '42.6.1h1', 'order': 42, 'schur_index': 1, 'trace_field': [1, -1, 1], 'traces': [[[-1, 1]]]}
42. label: 43.1.1b1
    {'cyc_order_mat': 43, 'cyc_order_traces': 43, 'decomposition': [['43.1.1b1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '43.1', 'indicator': 0, 'irreducible': True, 'label': '43.1.1b1', 'order': 43, 'schur_index': 1, 'trace_field': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 'traces': [[[1, 1]]]}
43. label: 44.2.1f1
    {'cyc_order_mat': 44, 'cyc_order_traces': 44, 'decomposition': [['44.2.1f1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '44.2', 'indicator': 0, 'irreducible': True, 'label': '44.2.1f1', 'order': 44, 'schur_index': 1, 'trace_field': [1, 0, 1], 'traces': [[[1, 1]]]}
44. label: 45.1.1f1
    {'cyc_order_mat': 45, 'cyc_order_traces': 45, 'decomposition': [['45.1.1f1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '45.1', 'indicator': 0, 'irreducible': True, 'label': '45.1.1f1', 'order': 45, 'schur_index': 1, 'trace_field': [1, 0, 0, -1, 0, 0, 1], 'traces': [[[1, 1]]]}
45. label: 46.2.1d1
    {'cyc_order_mat': 23, 'cyc_order_traces': 23, 'decomposition': [['46.2.1d1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[-1, 1]]]]], 'group': '46.2', 'indicator': 0, 'irreducible': True, 'label': '46.2.1d1', 'order': 46, 'schur_index': 1, 'trace_field': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 'traces': [[[-1, 1]]]}
46. label: 47.1.1b1
    {'cyc_order_mat': 47, 'cyc_order_traces': 47, 'decomposition': [['47.1.1b1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '47.1', 'indicator': 0, 'irreducible': True, 'label': '47.1.1b1', 'order': 47, 'schur_index': 1, 'trace_field': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 'traces': [[[1, 1]]]}
47. label: 48.2.1j1
    {'cyc_order_mat': 48, 'cyc_order_traces': 48, 'decomposition': [['48.2.1j1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '48.2', 'indicator': 0, 'irreducible': True, 'label': '48.2.1j1', 'order': 48, 'schur_index': 1, 'trace_field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'traces': [[[1, 1]]]}
48. label: 49.1.1c1
    {'cyc_order_mat': 49, 'cyc_order_traces': 49, 'decomposition': [['49.1.1c1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '49.1', 'indicator': 0, 'irreducible': True, 'label': '49.1.1c1', 'order': 49, 'schur_index': 1, 'trace_field': [1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1], 'traces': [[[1, 1]]]}
49. label: 50.2.1f1
    {'cyc_order_mat': 25, 'cyc_order_traces': 25, 'decomposition': [['50.2.1f1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[-1, 1]]]]], 'group': '50.2', 'indicator': 0, 'irreducible': True, 'label': '50.2.1f1', 'order': 50, 'schur_index': 1, 'trace_field': [1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1], 'traces': [[[-1, 1]]]}
50. label: 51.1.1d1
    {'cyc_order_mat': 51, 'cyc_order_traces': 51, 'decomposition': [['51.1.1d1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '51.1', 'indicator': 0, 'irreducible': True, 'label': '51.1.1d1', 'order': 51, 'schur_index': 1, 'trace_field': [1, -1, 1], 'traces': [[[1, 1]]]}
51. label: 52.2.1f1
    {'cyc_order_mat': 52, 'cyc_order_traces': 52, 'decomposition': [['52.2.1f1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '52.2', 'indicator': 0, 'irreducible': True, 'label': '52.2.1f1', 'order': 52, 'schur_index': 1, 'trace_field': [1, 0, 1], 'traces': [[[1, 1]]]}
52. label: 53.1.1b1
    {'cyc_order_mat': 53, 'cyc_order_traces': 53, 'decomposition': [['53.1.1b1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '53.1', 'indicator': 0, 'irreducible': True, 'label': '53.1.1b1', 'order': 53, 'schur_index': 1, 'trace_field': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 'traces': [[[1, 1]]]}
53. label: 54.2.1h1
    {'cyc_order_mat': 27, 'cyc_order_traces': 27, 'decomposition': [['54.2.1h1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[-1, 1]]]]], 'group': '54.2', 'indicator': 0, 'irreducible': True, 'label': '54.2.1h1', 'order': 54, 'schur_index': 1, 'trace_field': [1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'traces': [[[-1, 1]]]}
54. label: 55.2.1d1
    {'cyc_order_mat': 55, 'cyc_order_traces': 55, 'decomposition': [['55.2.1d1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '55.2', 'indicator': 0, 'irreducible': True, 'label': '55.2.1d1', 'order': 55, 'schur_index': 1, 'trace_field': [1, -1, 1, -1, 1], 'traces': [[[1, 1]]]}
55. label: 56.2.1h1
    {'cyc_order_mat': 56, 'cyc_order_traces': 56, 'decomposition': [['56.2.1h1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '56.2', 'indicator': 0, 'irreducible': True, 'label': '56.2.1h1', 'order': 56, 'schur_index': 1, 'trace_field': [1, 0, 0, 0, 1], 'traces': [[[1, 1]]]}
56. label: 57.2.1d1
    {'cyc_order_mat': 57, 'cyc_order_traces': 57, 'decomposition': [['57.2.1d1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '57.2', 'indicator': 0, 'irreducible': True, 'label': '57.2.1d1', 'order': 57, 'schur_index': 1, 'trace_field': [1, -1, 1], 'traces': [[[1, 1]]]}
57. label: 58.2.1d1
    {'cyc_order_mat': 29, 'cyc_order_traces': 29, 'decomposition': [['58.2.1d1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[-1, 1]]]]], 'group': '58.2', 'indicator': 0, 'irreducible': True, 'label': '58.2.1d1', 'order': 58, 'schur_index': 1, 'trace_field': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 'traces': [[[-1, 1]]]}
58. label: 59.1.1b1
    {'cyc_order_mat': 59, 'cyc_order_traces': 59, 'decomposition': [['59.1.1b1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '59.1', 'indicator': 0, 'irreducible': True, 'label': '59.1.1b1', 'order': 59, 'schur_index': 1, 'trace_field': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 'traces': [[[1, 1]]]}
59. label: 60.4.1l1
    {'cyc_order_mat': 60, 'cyc_order_traces': 60, 'decomposition': [['60.4.1l1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '60.4', 'indicator': 0, 'irreducible': True, 'label': '60.4.1l1', 'order': 60, 'schur_index': 1, 'trace_field': [1, 0, 1], 'traces': [[[1, 1]]]}
60. label: 61.1.1b1
    {'cyc_order_mat': 61, 'cyc_order_traces': 61, 'decomposition': [['61.1.1b1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '61.1', 'indicator': 0, 'irreducible': True, 'label': '61.1.1b1', 'order': 61, 'schur_index': 1, 'trace_field': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 'traces': [[[1, 1]]]}
61. label: 62.2.1d1
    {'cyc_order_mat': 31, 'cyc_order_traces': 31, 'decomposition': [['62.2.1d1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[-1, 1]]]]], 'group': '62.2', 'indicator': 0, 'irreducible': True, 'label': '62.2.1d1', 'order': 62, 'schur_index': 1, 'trace_field': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 'traces': [[[-1, 1]]]}
62. label: 63.2.1f1
    {'cyc_order_mat': 63, 'cyc_order_traces': 63, 'decomposition': [['63.2.1f1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '63.2', 'indicator': 0, 'irreducible': True, 'label': '63.2.1f1', 'order': 63, 'schur_index': 1, 'trace_field': [1, 0, 0, -1, 0, 0, 1], 'traces': [[[1, 1]]]}
63. label: 64.1.1g1
    {'cyc_order_mat': 64, 'cyc_order_traces': 64, 'decomposition': [['64.1.1g1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '64.1', 'indicator': 0, 'irreducible': True, 'label': '64.1.1g1', 'order': 64, 'schur_index': 1, 'trace_field': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'traces': [[[1, 1]]]}
64. label: 65.1.1d1
    {'cyc_order_mat': 65, 'cyc_order_traces': 65, 'decomposition': [['65.1.1d1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '65.1', 'indicator': 0, 'irreducible': True, 'label': '65.1.1d1', 'order': 65, 'schur_index': 1, 'trace_field': [1, -1, 1, -1, 1], 'traces': [[[1, 1]]]}
65. label: 66.4.1h1
    {'cyc_order_mat': 33, 'cyc_order_traces': 33, 'decomposition': [['66.4.1h1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[-1, 1]]]]], 'group': '66.4', 'indicator': 0, 'irreducible': True, 'label': '66.4.1h1', 'order': 66, 'schur_index': 1, 'trace_field': [1, -1, 1], 'traces': [[[-1, 1]]]}
66. label: 67.1.1b1
    {'cyc_order_mat': 67, 'cyc_order_traces': 67, 'decomposition': [['67.1.1b1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '67.1', 'indicator': 0, 'irreducible': True, 'label': '67.1.1b1', 'order': 67, 'schur_index': 1, 'trace_field': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 'traces': [[[1, 1]]]}
67. label: 68.2.1f1
    {'cyc_order_mat': 68, 'cyc_order_traces': 68, 'decomposition': [['68.2.1f1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '68.2', 'indicator': 0, 'irreducible': True, 'label': '68.2.1f1', 'order': 68, 'schur_index': 1, 'trace_field': [1, 0, 1], 'traces': [[[1, 1]]]}
68. label: 69.1.1d1
    {'cyc_order_mat': 69, 'cyc_order_traces': 69, 'decomposition': [['69.1.1d1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '69.1', 'indicator': 0, 'irreducible': True, 'label': '69.1.1d1', 'order': 69, 'schur_index': 1, 'trace_field': [1, -1, 1], 'traces': [[[1, 1]]]}
69. label: 70.4.1h1
    {'cyc_order_mat': 35, 'cyc_order_traces': 35, 'decomposition': [['70.4.1h1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[-1, 1]]]]], 'group': '70.4', 'indicator': 0, 'irreducible': True, 'label': '70.4.1h1', 'order': 70, 'schur_index': 1, 'trace_field': [1, -1, 1, -1, 1], 'traces': [[[-1, 1]]]}
70. label: 71.1.1b1
    {'cyc_order_mat': 71, 'cyc_order_traces': 71, 'decomposition': [['71.1.1b1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '71.1', 'indicator': 0, 'irreducible': True, 'label': '71.1.1b1', 'order': 71, 'schur_index': 1, 'trace_field': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 'traces': [[[1, 1]]]}
71. label: 72.2.1l1
    {'cyc_order_mat': 72, 'cyc_order_traces': 72, 'decomposition': [['72.2.1l1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '72.2', 'indicator': 0, 'irreducible': True, 'label': '72.2.1l1', 'order': 72, 'schur_index': 1, 'trace_field': [1, 0, 0, 0, 1], 'traces': [[[1, 1]]]}
72. label: 73.1.1b1
    {'cyc_order_mat': 73, 'cyc_order_traces': 73, 'decomposition': [['73.1.1b1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '73.1', 'indicator': 0, 'irreducible': True, 'label': '73.1.1b1', 'order': 73, 'schur_index': 1, 'trace_field': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 'traces': [[[1, 1]]]}
73. label: 74.2.1d1
    {'cyc_order_mat': 37, 'cyc_order_traces': 37, 'decomposition': [['74.2.1d1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[-1, 1]]]]], 'group': '74.2', 'indicator': 0, 'irreducible': True, 'label': '74.2.1d1', 'order': 74, 'schur_index': 1, 'trace_field': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 'traces': [[[-1, 1]]]}
74. label: 75.1.1f1
    {'cyc_order_mat': 75, 'cyc_order_traces': 75, 'decomposition': [['75.1.1f1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '75.1', 'indicator': 0, 'irreducible': True, 'label': '75.1.1f1', 'order': 75, 'schur_index': 1, 'trace_field': [1, -1, 1], 'traces': [[[1, 1]]]}
75. label: 76.2.1f1
    {'cyc_order_mat': 76, 'cyc_order_traces': 76, 'decomposition': [['76.2.1f1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '76.2', 'indicator': 0, 'irreducible': True, 'label': '76.2.1f1', 'order': 76, 'schur_index': 1, 'trace_field': [1, 0, 1], 'traces': [[[1, 1]]]}
76. label: 77.1.1d1
    {'cyc_order_mat': 77, 'cyc_order_traces': 77, 'decomposition': [['77.1.1d1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '77.1', 'indicator': 0, 'irreducible': True, 'label': '77.1.1d1', 'order': 77, 'schur_index': 1, 'trace_field': [1, -1, 1, -1, 1, -1, 1], 'traces': [[[1, 1]]]}
77. label: 78.6.1h1
    {'cyc_order_mat': 39, 'cyc_order_traces': 39, 'decomposition': [['78.6.1h1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[-1, 1]]]]], 'group': '78.6', 'indicator': 0, 'irreducible': True, 'label': '78.6.1h1', 'order': 78, 'schur_index': 1, 'trace_field': [1, -1, 1], 'traces': [[[-1, 1]]]}
78. label: 79.1.1b1
    {'cyc_order_mat': 79, 'cyc_order_traces': 79, 'decomposition': [['79.1.1b1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '79.1', 'indicator': 0, 'irreducible': True, 'label': '79.1.1b1', 'order': 79, 'schur_index': 1, 'trace_field': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 'traces': [[[1, 1]]]}
79. label: 80.2.1j1
    {'cyc_order_mat': 80, 'cyc_order_traces': 80, 'decomposition': [['80.2.1j1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '80.2', 'indicator': 0, 'irreducible': True, 'label': '80.2.1j1', 'order': 80, 'schur_index': 1, 'trace_field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'traces': [[[1, 1]]]}
80. label: 81.1.1e1
    {'cyc_order_mat': 81, 'cyc_order_traces': 81, 'decomposition': [['81.1.1e1', 1]], 'denominators': [1], 'dim': 1, 'gens': [[[[[1, 1]]]]], 'group': '81.1', 'indicator': 0, 'irreducible': True, 'label': '81.1.1e1', 'order': 81, 'schur_index': 1, 'trace_field': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'traces': [[[1, 1]]]}
81. label: 3.1.1b1-1b1
    {'cyc_order_mat': 1, 'cyc_order_traces': 1, 'decomposition': [['3.1.1b1', 1], ['3.1.1b1', 1]], 'denominators': [1], 'dim': 2, 'gens': [[[[[-1, 0]], [[-1, 0]]], [[[1, 0]], [[0, 0]]]]], 'group': '3.1', 'indicator': 0, 'irreducible': False, 'label': '3.1.1b1-1b1', 'order': 3, 'schur_index': 1, 'trace_field': [0, 1], 'traces': [[[-1, 0]]]}
82. label: 4.1.1c1-1c1
    {'cyc_order_mat': 1, 'cyc_order_traces': 1, 'decomposition': [['4.1.1c1', 1], ['4.1.1c1', 1]], 'denominators': [1, 1], 'dim': 2, 'gens': [[[[[0, 0]], [[1, 0]]], [[[-1, 0]], [[0, 0]]]]], 'group': '4.1', 'indicator': 0, 'irreducible': False, 'label': '4.1.1c1-1c1', 'order': 4, 'schur_index': 1, 'trace_field': [0, 1], 'traces': [[[0, 0]]]}
83. label: 6.1.2a
    {'cyc_order_mat': 3, 'cyc_order_traces': 1, 'decomposition': [['6.1.2a', 1]], 'denominators': [1, 1], 'dim': 2, 'gens': [[[[[1, -1]], [[0, 0]]], [[[0, 0]], [[1, 1]]]], [[[[0, 0]], [[1, 0]]], [[[1, 0]], [[0, 0]]]]], 'group': '6.1', 'indicator': 1, 'irreducible': True, 'label': '6.1.2a', 'order': 6, 'schur_index': 3, 'trace_field': [0, 1], 'traces': [[[-1, 0]], [[0, 0]]]}
84. label: 6.2.1d1-1d1
    {'cyc_order_mat': 1, 'cyc_order_traces': 1, 'decomposition': [['6.2.1d1', 1], ['6.2.1d1', 1]], 'denominators': [1, 1], 'dim': 2, 'gens': [[[[[1, 0]], [[1, 0]]], [[[-1, 0]], [[0, 0]]]]], 'group': '6.2', 'indicator': 0, 'irreducible': False, 'label': '6.2.1d1-1d1', 'order': 6, 'schur_index': 1, 'trace_field': [0, 1], 'traces': [[[1, 0]]]}
85. label: 8.3.2a
    {'cyc_order_mat': 4, 'cyc_order_traces': 1, 'decomposition': [['8.3.2a', 1]], 'denominators': [1, 1], 'dim': 2, 'gens': [[[[[0, 0]], [[1, 0]]], [[[1, 0]], [[0, 0]]]], [[[[0, 0]], [[1, 1]]], [[[-1, 1]], [[0, 0]]]]], 'group': '8.3', 'indicator': 1, 'irreducible': True, 'label': '8.3.2a', 'order': 8, 'schur_index': 4, 'trace_field': [0, 1], 'traces': [[[0, 0]], [[0, 0]]]}
86. label: 8.4.2a
    {'cyc_order_mat': 4, 'cyc_order_traces': 1, 'decomposition': [['8.4.2a', 1]], 'denominators': [1, 1], 'dim': 2, 'gens': [[[[[0, 0]], [[-1, 0]]], [[[1, 0]], [[0, 0]]]], [[[[0, 0]], [[-1, 1]]], [[[-1, 1]], [[0, 0]]]]], 'group': '8.4', 'indicator': -1, 'irreducible': True, 'label': '8.4.2a', 'order': 8, 'schur_index': 4, 'trace_field': [0, 1], 'traces': [[[0, 0]], [[0, 0]]]}
87. label: 10.1.2a1
    {'cyc_order_mat': 5, 'cyc_order_traces': 5, 'decomposition': [['10.1.2a1', 1]], 'denominators': [1, 1], 'dim': 2, 'gens': [[[[[1, 1]], [[0, 0]]], [[[0, 0]], [[1, -1]]]], [[[[0, 0]], [[1, -2]]], [[[1, 2]], [[0, 0]]]]], 'group': '10.1', 'indicator': 1, 'irreducible': True, 'label': '10.1.2a1', 'order': 10, 'schur_index': 1, 'trace_field': [-1, -1, 1], 'traces': [[[1, 1], [1, -1]], [[0, 0]]]}
88. label: 12.1.2b
    {'cyc_order_mat': 3, 'cyc_order_traces': 1, 'decomposition': [['12.1.2b', 1]], 'denominators': [1, 1], 'dim': 2, 'gens': [[[[[-1, 1]], [[0, 0]]], [[[0, 0]], [[-1, -1]]]], [[[[0, 0]], [[-1, 0]]], [[[1, 0]], [[0, 0]]]]], 'group': '12.1', 'indicator': -1, 'irreducible': True, 'label': '12.1.2b', 'order': 12, 'schur_index': 3, 'trace_field': [0, 1], 'traces': [[[1, 0]], [[0, 0]]]}
89. label: 12.4.2b
    {'cyc_order_mat': 3, 'cyc_order_traces': 1, 'decomposition': [['12.4.2b', 1]], 'denominators': [1, 1], 'dim': 2, 'gens': [[[[[0, 0]], [[1, 0]]], [[[1, 0]], [[0, 0]]]], [[[[0, 0]], [[-1, -1]]], [[[-1, 1]], [[0, 0]]]]], 'group': '12.4', 'indicator': 1, 'irreducible': True, 'label': '12.4.2b', 'order': 12, 'schur_index': 3, 'trace_field': [0, 1], 'traces': [[[0, 0]], [[0, 0]]]}
90. label: 14.1.2a1
    {'cyc_order_mat': 7, 'cyc_order_traces': 7, 'decomposition': [['14.1.2a1', 1]], 'denominators': [1, 1], 'dim': 2, 'gens': [[[[[1, -1]], [[0, 0]]], [[[0, 0]], [[1, 1]]]], [[[[0, 0]], [[1, -1]]], [[[1, 1]], [[0, 0]]]]], 'group': '14.1', 'indicator': 1, 'irreducible': True, 'label': '14.1.2a1', 'order': 14, 'schur_index': 1, 'trace_field': [1, -2, -1, 1], 'traces': [[[1, 1], [1, -1]], [[0, 0]]]}
91. label: 16.13.2a1
    {'cyc_order_mat': 4, 'cyc_order_traces': 4, 'decomposition': [['16.13.2a1', 1]], 'denominators': [1, 1, 1], 'dim': 2, 'gens': [[[[[0, 0]], [[1, 1]]], [[[1, 1]], [[0, 0]]]], [[[[0, 0]], [[1, 1]]], [[[-1, 1]], [[0, 0]]]], [[[[-1, 1]], [[0, 0]]], [[[0, 0]], [[-1, 1]]]]], 'group': '16.13', 'indicator': 0, 'irreducible': True, 'label': '16.13.2a1', 'order': 16, 'schur_index': 1, 'trace_field': [1, 0, 1], 'traces': [[[0, 0]], [[0, 0]], [[-2, 1]]]}
92. label: 16.6.2a1
    {'cyc_order_mat': 8, 'cyc_order_traces': 4, 'decomposition': [['16.6.2a1', 1]], 'denominators': [1, 1], 'dim': 2, 'gens': [[[[[1, 1]], [[0, 0]]], [[[0, 0]], [[-1, 1]]]], [[[[0, 0]], [[-1, 0]]], [[[-1, 0]], [[0, 0]]]]], 'group': '16.6', 'indicator': 0, 'irreducible': True, 'label': '16.6.2a1', 'order': 16, 'schur_index': 2, 'trace_field': [1, 0, 1], 'traces': [[[0, 0]], [[0, 0]]]}
93. label: 16.7.2b1
    {'cyc_order_mat': 8, 'cyc_order_traces': 8, 'decomposition': [['16.7.2b1', 1]], 'denominators': [1, 1], 'dim': 2, 'gens': [[[[[1, 3]], [[0, 0]]], [[[0, 0]], [[-1, 1]]]], [[[[0, 0]], [[1, 2]]], [[[-1, 2]], [[0, 0]]]]], 'group': '16.7', 'indicator': 1, 'irreducible': True, 'label': '16.7.2b1', 'order': 16, 'schur_index': 1, 'trace_field': [-2, 0, 1], 'traces': [[[-1, 1], [-1, -1]], [[0, 0]]]}
94. label: 16.8.2b1
    {'cyc_order_mat': 8, 'cyc_order_traces': 8, 'decomposition': [['16.8.2b1', 1]], 'denominators': [1, 1], 'dim': 2, 'gens': [[[[[1, 1]], [[0, 0]]], [[[0, 0]], [[1, 3]]]], [[[[0, 0]], [[1, 2]]], [[[-1, 2]], [[0, 0]]]]], 'group': '16.8', 'indicator': 0, 'irreducible': True, 'label': '16.8.2b1', 'order': 16, 'schur_index': 1, 'trace_field': [2, 0, 1], 'traces': [[[1, 1], [1, 3]], [[0, 0]]]}
95. label: 16.9.2b1
    {'cyc_order_mat': 8, 'cyc_order_traces': 8, 'decomposition': [['16.9.2b1', 1]], 'denominators': [1, 1], 'dim': 2, 'gens': [[[[[-1, 3]], [[0, 0]]], [[[0, 0]], [[1, 1]]]], [[[[0, 0]], [[1, 2]]], [[[1, 2]], [[0, 0]]]]], 'group': '16.9', 'indicator': -1, 'irreducible': True, 'label': '16.9.2b1', 'order': 16, 'schur_index': 1, 'trace_field': [-2, 0, 1], 'traces': [[[1, 1], [1, -1]], [[0, 0]]]}
96. label: 18.1.2b1
    {'cyc_order_mat': 9, 'cyc_order_traces': 9, 'decomposition': [['18.1.2b1', 1]], 'denominators': [1, 1], 'dim': 2, 'gens': [[[[[1, -4]], [[0, 0]]], [[[0, 0]], [[1, 4]]]], [[[[0, 0]], [[1, 0]]], [[[1, 0]], [[0, 0]]]]], 'group': '18.1', 'indicator': 1, 'irreducible': True, 'label': '18.1.2b1', 'order': 18, 'schur_index': 1, 'trace_field': [-1, -3, 0, 1], 'traces': [[[1, 4], [1, -4]], [[0, 0]]]}
97. label: 18.3.2b1
    {'cyc_order_mat': 3, 'cyc_order_traces': 3, 'decomposition': [['18.3.2b1', 1]], 'denominators': [1, 1], 'dim': 2, 'gens': [[[[[1, 0]], [[0, 0]]], [[[0, 0]], [[1, -1]]]], [[[[0, 0]], [[1, 0]]], [[[1, -1]], [[0, 0]]]]], 'group': '18.3', 'indicator': 0, 'irreducible': True, 'label': '18.3.2b1', 'order': 18, 'schur_index': 1, 'trace_field': [1, -1, 1], 'traces': [[[-1, 1]], [[0, 0]]]}
98. label: 20.1.2b1
    {'cyc_order_mat': 5, 'cyc_order_traces': 5, 'decomposition': [['20.1.2b1', 1]], 'denominators': [1, 1], 'dim': 2, 'gens': [[[[[-1, 1]], [[0, 0]]], [[[0, 0]], [[-1, -1]]]], [[[[0, 0]], [[-1, 0]]], [[[1, 0]], [[0, 0]]]]], 'group': '20.1', 'indicator': -1, 'irreducible': True, 'label': '20.1.2b1', 'order': 20, 'schur_index': 1, 'trace_field': [-1, -1, 1], 'traces': [[[-1, 1], [-1, -1]], [[0, 0]]]}
99. label: 20.4.2b1
    {'cyc_order_mat': 5, 'cyc_order_traces': 5, 'decomposition': [['20.4.2b1', 1]], 'denominators': [1, 1], 'dim': 2, 'gens': [[[[[0, 0]], [[1, 0]]], [[[1, 0]], [[0, 0]]]], [[[[0, 0]], [[-1, -2]]], [[[-1, 2]], [[0, 0]]]]], 'group': '20.4', 'indicator': 1, 'irreducible': True, 'label': '20.4.2b1', 'order': 20, 'schur_index': 1, 'trace_field': [-1, -1, 1], 'traces': [[[0, 0]], [[0, 0]]]}