Sigma: ((0 7 10 4) (1 9 6 3 11 8 5 2))
Alpha: ((0 1) (2 3) (4 5) (6 7) (8 9) (10 11))
Phi:   ((0 2 6) (1 4 8) (3 5 10) (7 9 11))

     Order number:    1
     Passport:        8(1) 4(1)
     Modulus:          I
        root of  z + - I
     Klein invariant: 1728
        root of  z + -1728
     g2 coefficient:  189.07272012923385229306139653492131339873116127089114630823242144305559026096476730
        root of 7044337878 z^7 + -1333484949081 z^6 + 306000047134 z^5 + -915575303111 z^4 + 84099611022 z^3 + -1333748748539 z^2 + -579792679928 z + -437712119250
     g3 coefficient:  0
        root of  z

Sigma: ((0 5 11 8 4 3) (1 7 10 9 6 2))
Alpha: ((0 1) (2 3) (4 5) (6 7) (8 9) (10 11))
Phi:   ((0 2 4) (1 3 6) (5 8 10) (7 9 11))

     Order number:    2
     Passport:        6(2)
     Modulus:         1.73205080756887729352744634150587236694280525381038062805580697945193301690880004 I
        root of  z^2 + 3
     Klein invariant: 54000
        root of  z + -54000
     g2 coefficient:  130.46423093384007167195319462449019609921131587816068010593707184693511930929576078
        root of 7511757053 z^7 + -983544567736 z^6 + 458667956287 z^5 + 227658246905 z^4 + -163140446267 z^3 + -435683252379 z^2 + 737739739648 z + 834516858498
     g3 coefficient:  282.15840024609745190231652198469525293042747982373495527860643477967583404939423882
        root of 2502993620 z^7 + -710799561526 z^6 + 1281704190215 z^5 + 1308216325313 z^4 + -1011590134000 z^3 + 53659402050 z^2 + -59818562583 z + -345993297988

Sigma: ((0 7 8 5 2 1 9 10 4) (3 11 6))
Alpha: ((0 1) (2 3) (4 5) (6 7) (8 9) (10 11))
Phi:   ((0 2 6) (1 4 8) (3 5 10) (7 11 9))

     Order number:    3
     Passport:        9(1) 3(1)
     Modulus:         (0.50000000000000000000000000000000000000000000000000000000000000000000000000000000 + 0.86602540378443864676372317075293618347140262690519031402790348972596650845440002 I)
        root of  z^2 + -1 z + 1
     Klein invariant: 0
        root of  z
     g2 coefficient:  0
        root of  z
     g3 coefficient:  820.82443707955622371582988213729528125215266857813805171958235572269333541641960385
        root of 39762433522 z^6 + -32517252516083 z^5 + -99156309618280 z^4 + 51432061473788 z^3 + -32604443787213 z^2 + -1418955005544 z + -6166823948287