Character Table for Point Group C153v

Character table for the C_153v point group

C153v E 2 C153 2 C153^2 2 C51 2 C153^4 2 C153^5 2 C51^2 2 C153^7 2 C153^8 2 C17 2 C153^10 2 C153^11 2 C51^4 2 C153^13 2 C153^14 2 C51^5 2 C153^16 2 C9 2 C17^2 2 C153^19 2 C153^20 2 C51^7 2 C153^22 2 C153^23 2 C51^8 2 C153^25 2 C153^26 2 C17^3 2 C153^28 2 C153^29 2 C51^10 2 C153^31 2 C153^32 2 C51^11 2 C9^2 2 C153^35 2 C17^4 2 C153^37 2 C153^38 2 C51^13 2 C153^40 2 C153^41 2 C51^14 2 C153^43 2 C153^44 2 C17^5 2 C153^46 2 C153^47 2 C51^16 2 C153^49 2 C153^50 2 C3 2 C153^52 2 C153^53 2 C17^6 2 C153^55 2 C153^56 2 C51^19 2 C153^58 2 C153^59 2 C51^20 2 C153^61 2 C153^62 2 C17^7 2 C153^64 2 C153^65 2 C51^22 2 C153^67 2 C9^4 2 C51^23 2 C153^70 2 C153^71 2 C17^8 2 C153^73 2 C153^74 2 C51^25 2 C153^76 153 sv <R> <p> <—d—> <——f——> <———g———> <————h————> <—————i—————> A1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 ... ..T ....T ......T ........T ..........T ............T A2 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 ..T ... ..... ....... ......... ........... ............. E1 2.00000 1.99831 1.99326 1.98484 1.97308 1.95799 1.93959 1.91793 1.89303 1.86494 1.83371 1.79938 1.76202 1.72169 1.67846 1.63239 1.58358 1.53209 1.47802 1.42145 1.36249 1.30124 1.23778 1.17225 1.10473 1.03535 0.96423 0.89148 0.81722 0.74159 0.66471 0.58671 0.50771 0.42787 0.34730 0.26614 0.18454 0.10262 0.02053 -0.06159 -0.14361 -0.22539 -0.30678 -0.38766 -0.46789 -0.54733 -0.62584 -0.70330 -0.77957 -0.85453 -0.92805 -1.00000 -1.07027 -1.13873 -1.20527 -1.26978 -1.33215 -1.39227 -1.45004 -1.50537 -1.55816 -1.60832 -1.65578 -1.70043 -1.74223 -1.78108 -1.81693 -1.84972 -1.87939 -1.90588 -1.92917 -1.94920 -1.96595 -1.97938 -1.98947 -1.99621 -1.99958 0.00000 TT. TT. ..TT. ....TT. ......TT. ........TT. ..........TT. E2 2.00000 1.99326 1.97308 1.93959 1.89303 1.83371 1.76202 1.67846 1.58358 1.47802 1.36249 1.23778 1.10473 0.96423 0.81722 0.66471 0.50771 0.34730 0.18454 0.02053 -0.14361 -0.30678 -0.46789 -0.62584 -0.77957 -0.92805 -1.07027 -1.20527 -1.33215 -1.45004 -1.55816 -1.65578 -1.74223 -1.81693 -1.87939 -1.92917 -1.96595 -1.98947 -1.99958 -1.99621 -1.97938 -1.94920 -1.90588 -1.84972 -1.78108 -1.70043 -1.60832 -1.50537 -1.39227 -1.26978 -1.13873 -1.00000 -0.85453 -0.70330 -0.54733 -0.38766 -0.22539 -0.06159 0.10262 0.26614 0.42787 0.58671 0.74159 0.89148 1.03535 1.17225 1.30124 1.42145 1.53209 1.63239 1.72169 1.79938 1.86494 1.91793 1.95799 1.98484 1.99831 0.00000 ... ... TT... ..TT... ....TT... ......TT... ........TT... E3 2.00000 1.98484 1.93959 1.86494 1.76202 1.63239 1.47802 1.30124 1.10473 0.89148 0.66471 0.42787 0.18454 -0.06159 -0.30678 -0.54733 -0.77957 -1.00000 -1.20527 -1.39227 -1.55816 -1.70043 -1.81693 -1.90588 -1.96595 -1.99621 -1.99621 -1.96595 -1.90588 -1.81693 -1.70043 -1.55816 -1.39227 -1.20527 -1.00000 -0.77957 -0.54733 -0.30678 -0.06159 0.18454 0.42787 0.66471 0.89148 1.10473 1.30124 1.47802 1.63239 1.76202 1.86494 1.93959 1.98484 2.00000 1.98484 1.93959 1.86494 1.76202 1.63239 1.47802 1.30124 1.10473 0.89148 0.66471 0.42787 0.18454 -0.06159 -0.30678 -0.54733 -0.77957 -1.00000 -1.20527 -1.39227 -1.55816 -1.70043 -1.81693 -1.90588 -1.96595 -1.99621 0.00000 ... ... ..... TT..... ..TT..... ....TT..... ......TT..... E4 2.00000 1.97308 1.89303 1.76202 1.58358 1.36249 1.10473 0.81722 0.50771 0.18454 -0.14361 -0.46789 -0.77957 -1.07027 -1.33215 -1.55816 -1.74223 -1.87939 -1.96595 -1.99958 -1.97938 -1.90588 -1.78108 -1.60832 -1.39227 -1.13873 -0.85453 -0.54733 -0.22539 0.10262 0.42787 0.74159 1.03535 1.30124 1.53209 1.72169 1.86494 1.95799 1.99831 1.98484 1.91793 1.79938 1.63239 1.42145 1.17225 0.89148 0.58671 0.26614 -0.06159 -0.38766 -0.70330 -1.00000 -1.26978 -1.50537 -1.70043 -1.84972 -1.94920 -1.99621 -1.98947 -1.92917 -1.81693 -1.65578 -1.45004 -1.20527 -0.92805 -0.62584 -0.30678 0.02053 0.34730 0.66471 0.96423 1.23778 1.47802 1.67846 1.83371 1.93959 1.99326 0.00000 ... ... ..... ....... TT....... ..TT....... ....TT....... E5 2.00000 1.95799 1.83371 1.63239 1.36249 1.03535 0.66471 0.26614 -0.14361 -0.54733 -0.92805 -1.26978 -1.55816 -1.78108 -1.92917 -1.99621 -1.97938 -1.87939 -1.70043 -1.45004 -1.13873 -0.77957 -0.38766 0.02053 0.42787 0.81722 1.17225 1.47802 1.72169 1.89303 1.98484 1.99326 1.91793 1.76202 1.53209 1.23778 0.89148 0.50771 0.10262 -0.30678 -0.70330 -1.07027 -1.39227 -1.65578 -1.84972 -1.96595 -1.99958 -1.94920 -1.81693 -1.60832 -1.33215 -1.00000 -0.62584 -0.22539 0.18454 0.58671 0.96423 1.30124 1.58358 1.79938 1.93959 1.99831 1.97308 1.86494 1.67846 1.42145 1.10473 0.74159 0.34730 -0.06159 -0.46789 -0.85453 -1.20527 -1.50537 -1.74223 -1.90588 -1.98947 0.00000 ... ... ..... ....... ......... TT......... ..TT......... E6 2.00000 1.93959 1.76202 1.47802 1.10473 0.66471 0.18454 -0.30678 -0.77957 -1.20527 -1.55816 -1.81693 -1.96595 -1.99621 -1.90588 -1.70043 -1.39227 -1.00000 -0.54733 -0.06159 0.42787 0.89148 1.30124 1.63239 1.86494 1.98484 1.98484 1.86494 1.63239 1.30124 0.89148 0.42787 -0.06159 -0.54733 -1.00000 -1.39227 -1.70043 -1.90588 -1.99621 -1.96595 -1.81693 -1.55816 -1.20527 -0.77957 -0.30678 0.18454 0.66471 1.10473 1.47802 1.76202 1.93959 2.00000 1.93959 1.76202 1.47802 1.10473 0.66471 0.18454 -0.30678 -0.77957 -1.20527 -1.55816 -1.81693 -1.96595 -1.99621 -1.90588 -1.70043 -1.39227 -1.00000 -0.54733 -0.06159 0.42787 0.89148 1.30124 1.63239 1.86494 1.98484 0.00000 ... ... ..... ....... ......... ........... TT........... E7 2.00000 1.91793 1.67846 1.30124 0.81722 0.26614 -0.30678 -0.85453 -1.33215 -1.70043 -1.92917 -1.99958 -1.90588 -1.65578 -1.26978 -0.77957 -0.22539 0.34730 0.89148 1.36249 1.72169 1.93959 1.99831 1.89303 1.63239 1.23778 0.74159 0.18454 -0.38766 -0.92805 -1.39227 -1.74223 -1.94920 -1.99621 -1.87939 -1.60832 -1.20527 -0.70330 -0.14361 0.42787 0.96423 1.42145 1.76202 1.95799 1.99326 1.86494 1.58358 1.17225 0.66471 0.10262 -0.46789 -1.00000 -1.45004 -1.78108 -1.96595 -1.98947 -1.84972 -1.55816 -1.13873 -0.62584 -0.06159 0.50771 1.03535 1.47802 1.79938 1.97308 1.98484 1.83371 1.53209 1.10473 0.58671 0.02053 -0.54733 -1.07027 -1.50537 -1.81693 -1.97938 0.00000 ... ... ..... ....... ......... ........... ............. E8 2.00000 1.89303 1.58358 1.10473 0.50771 -0.14361 -0.77957 -1.33215 -1.74223 -1.96595 -1.97938 -1.78108 -1.39227 -0.85453 -0.22539 0.42787 1.03535 1.53209 1.86494 1.99831 1.91793 1.63239 1.17225 0.58671 -0.06159 -0.70330 -1.26978 -1.70043 -1.94920 -1.98947 -1.81693 -1.45004 -0.92805 -0.30678 0.34730 0.96423 1.47802 1.83371 1.99326 1.93959 1.67846 1.23778 0.66471 0.02053 -0.62584 -1.20527 -1.65578 -1.92917 -1.99621 -1.84972 -1.50537 -1.00000 -0.38766 0.26614 0.89148 1.42145 1.79938 1.98484 1.95799 1.72169 1.30124 0.74159 0.10262 -0.54733 -1.13873 -1.60832 -1.90588 -1.99958 -1.87939 -1.55816 -1.07027 -0.46789 0.18454 0.81722 1.36249 1.76202 1.97308 0.00000 ... ... ..... ....... ......... ........... ............. E9 2.00000 1.86494 1.47802 0.89148 0.18454 -0.54733 -1.20527 -1.70043 -1.96595 -1.96595 -1.70043 -1.20527 -0.54733 0.18454 0.89148 1.47802 1.86494 2.00000 1.86494 1.47802 0.89148 0.18454 -0.54733 -1.20527 -1.70043 -1.96595 -1.96595 -1.70043 -1.20527 -0.54733 0.18454 0.89148 1.47802 1.86494 2.00000 1.86494 1.47802 0.89148 0.18454 -0.54733 -1.20527 -1.70043 -1.96595 -1.96595 -1.70043 -1.20527 -0.54733 0.18454 0.89148 1.47802 1.86494 2.00000 1.86494 1.47802 0.89148 0.18454 -0.54733 -1.20527 -1.70043 -1.96595 -1.96595 -1.70043 -1.20527 -0.54733 0.18454 0.89148 1.47802 1.86494 2.00000 1.86494 1.47802 0.89148 0.18454 -0.54733 -1.20527 -1.70043 -1.96595 0.00000 ... ... ..... ....... ......... ........... ............. E10 2.00000 1.83371 1.36249 0.66471 -0.14361 -0.92805 -1.55816 -1.92917 -1.97938 -1.70043 -1.13873 -0.38766 0.42787 1.17225 1.72169 1.98484 1.91793 1.53209 0.89148 0.10262 -0.70330 -1.39227 -1.84972 -1.99958 -1.81693 -1.33215 -0.62584 0.18454 0.96423 1.58358 1.93959 1.97308 1.67846 1.10473 0.34730 -0.46789 -1.20527 -1.74223 -1.98947 -1.90588 -1.50537 -0.85453 -0.06159 0.74159 1.42145 1.86494 1.99831 1.79938 1.30124 0.58671 -0.22539 -1.00000 -1.60832 -1.94920 -1.96595 -1.65578 -1.07027 -0.30678 0.50771 1.23778 1.76202 1.99326 1.89303 1.47802 0.81722 0.02053 -0.77957 -1.45004 -1.87939 -1.99621 -1.78108 -1.26978 -0.54733 0.26614 1.03535 1.63239 1.95799 0.00000 ... ... ..... ....... ......... ........... ............. E11 2.00000 1.79938 1.23778 0.42787 -0.46789 -1.26978 -1.81693 -1.99958 -1.78108 -1.20527 -0.38766 0.50771 1.30124 1.83371 1.99831 1.76202 1.17225 0.34730 -0.54733 -1.33215 -1.84972 -1.99621 -1.74223 -1.13873 -0.30678 0.58671 1.36249 1.86494 1.99326 1.72169 1.10473 0.26614 -0.62584 -1.39227 -1.87939 -1.98947 -1.70043 -1.07027 -0.22539 0.66471 1.42145 1.89303 1.98484 1.67846 1.03535 0.18454 -0.70330 -1.45004 -1.90588 -1.97938 -1.65578 -1.00000 -0.14361 0.74159 1.47802 1.91793 1.97308 1.63239 0.96423 0.10262 -0.77957 -1.50537 -1.92917 -1.96595 -1.60832 -0.92805 -0.06159 0.81722 1.53209 1.93959 1.95799 1.58358 0.89148 0.02053 -0.85453 -1.55816 -1.94920 0.00000 ... ... ..... ....... ......... ........... ............. E12 2.00000 1.76202 1.10473 0.18454 -0.77957 -1.55816 -1.96595 -1.90588 -1.39227 -0.54733 0.42787 1.30124 1.86494 1.98484 1.63239 0.89148 -0.06159 -1.00000 -1.70043 -1.99621 -1.81693 -1.20527 -0.30678 0.66471 1.47802 1.93959 1.93959 1.47802 0.66471 -0.30678 -1.20527 -1.81693 -1.99621 -1.70043 -1.00000 -0.06159 0.89148 1.63239 1.98484 1.86494 1.30124 0.42787 -0.54733 -1.39227 -1.90588 -1.96595 -1.55816 -0.77957 0.18454 1.10473 1.76202 2.00000 1.76202 1.10473 0.18454 -0.77957 -1.55816 -1.96595 -1.90588 -1.39227 -0.54733 0.42787 1.30124 1.86494 1.98484 1.63239 0.89148 -0.06159 -1.00000 -1.70043 -1.99621 -1.81693 -1.20527 -0.30678 0.66471 1.47802 1.93959 0.00000 ... ... ..... ....... ......... ........... ............. E13 2.00000 1.72169 0.96423 -0.06159 -1.07027 -1.78108 -1.99621 -1.65578 -0.85453 0.18454 1.17225 1.83371 1.98484 1.58358 0.74159 -0.30678 -1.26978 -1.87939 -1.96595 -1.50537 -0.62584 0.42787 1.36249 1.91793 1.93959 1.42145 0.50771 -0.54733 -1.45004 -1.94920 -1.90588 -1.33215 -0.38766 0.66471 1.53209 1.97308 1.86494 1.23778 0.26614 -0.77957 -1.60832 -1.98947 -1.81693 -1.13873 -0.14361 0.89148 1.67846 1.99831 1.76202 1.03535 0.02053 -1.00000 -1.74223 -1.99958 -1.70043 -0.92805 0.10262 1.10473 1.79938 1.99326 1.63239 0.81722 -0.22539 -1.20527 -1.84972 -1.97938 -1.55816 -0.70330 0.34730 1.30124 1.89303 1.95799 1.47802 0.58671 -0.46789 -1.39227 -1.92917 0.00000 ... ... ..... ....... ......... ........... ............. E14 2.00000 1.67846 0.81722 -0.30678 -1.33215 -1.92917 -1.90588 -1.26978 -0.22539 0.89148 1.72169 1.99831 1.63239 0.74159 -0.38766 -1.39227 -1.94920 -1.87939 -1.20527 -0.14361 0.96423 1.76202 1.99326 1.58358 0.66471 -0.46789 -1.45004 -1.96595 -1.84972 -1.13873 -0.06159 1.03535 1.79938 1.98484 1.53209 0.58671 -0.54733 -1.50537 -1.97938 -1.81693 -1.07027 0.02053 1.10473 1.83371 1.97308 1.47802 0.50771 -0.62584 -1.55816 -1.98947 -1.78108 -1.00000 0.10262 1.17225 1.86494 1.95799 1.42145 0.42787 -0.70330 -1.60832 -1.99621 -1.74223 -0.92805 0.18454 1.23778 1.89303 1.93959 1.36249 0.34730 -0.77957 -1.65578 -1.99958 -1.70043 -0.85453 0.26614 1.30124 1.91793 0.00000 ... ... ..... ....... ......... ........... ............. E15 2.00000 1.63239 0.66471 -0.54733 -1.55816 -1.99621 -1.70043 -0.77957 0.42787 1.47802 1.98484 1.76202 0.89148 -0.30678 -1.39227 -1.96595 -1.81693 -1.00000 0.18454 1.30124 1.93959 1.86494 1.10473 -0.06159 -1.20527 -1.90588 -1.90588 -1.20527 -0.06159 1.10473 1.86494 1.93959 1.30124 0.18454 -1.00000 -1.81693 -1.96595 -1.39227 -0.30678 0.89148 1.76202 1.98484 1.47802 0.42787 -0.77957 -1.70043 -1.99621 -1.55816 -0.54733 0.66471 1.63239 2.00000 1.63239 0.66471 -0.54733 -1.55816 -1.99621 -1.70043 -0.77957 0.42787 1.47802 1.98484 1.76202 0.89148 -0.30678 -1.39227 -1.96595 -1.81693 -1.00000 0.18454 1.30124 1.93959 1.86494 1.10473 -0.06159 -1.20527 -1.90588 0.00000 ... ... ..... ....... ......... ........... ............. E16 2.00000 1.58358 0.50771 -0.77957 -1.74223 -1.97938 -1.39227 -0.22539 1.03535 1.86494 1.91793 1.17225 -0.06159 -1.26978 -1.94920 -1.81693 -0.92805 0.34730 1.47802 1.99326 1.67846 0.66471 -0.62584 -1.65578 -1.99621 -1.50537 -0.38766 0.89148 1.79938 1.95799 1.30124 0.10262 -1.13873 -1.90588 -1.87939 -1.07027 0.18454 1.36249 1.97308 1.76202 0.81722 -0.46789 -1.55816 -1.99958 -1.60832 -0.54733 0.74159 1.72169 1.98484 1.42145 0.26614 -1.00000 -1.84972 -1.92917 -1.20527 0.02053 1.23778 1.93959 1.83371 0.96423 -0.30678 -1.45004 -1.98947 -1.70043 -0.70330 0.58671 1.63239 1.99831 1.53209 0.42787 -0.85453 -1.78108 -1.96595 -1.33215 -0.14361 1.10473 1.89303 0.00000 ... ... ..... ....... ......... ........... ............. E17 2.00000 1.53209 0.34730 -1.00000 -1.87939 -1.87939 -1.00000 0.34730 1.53209 2.00000 1.53209 0.34730 -1.00000 -1.87939 -1.87939 -1.00000 0.34730 1.53209 2.00000 1.53209 0.34730 -1.00000 -1.87939 -1.87939 -1.00000 0.34730 1.53209 2.00000 1.53209 0.34730 -1.00000 -1.87939 -1.87939 -1.00000 0.34730 1.53209 2.00000 1.53209 0.34730 -1.00000 -1.87939 -1.87939 -1.00000 0.34730 1.53209 2.00000 1.53209 0.34730 -1.00000 -1.87939 -1.87939 -1.00000 0.34730 1.53209 2.00000 1.53209 0.34730 -1.00000 -1.87939 -1.87939 -1.00000 0.34730 1.53209 2.00000 1.53209 0.34730 -1.00000 -1.87939 -1.87939 -1.00000 0.34730 1.53209 2.00000 1.53209 0.34730 -1.00000 -1.87939 0.00000 ... ... ..... ....... ......... ........... ............. E18 2.00000 1.47802 0.18454 -1.20527 -1.96595 -1.70043 -0.54733 0.89148 1.86494 1.86494 0.89148 -0.54733 -1.70043 -1.96595 -1.20527 0.18454 1.47802 2.00000 1.47802 0.18454 -1.20527 -1.96595 -1.70043 -0.54733 0.89148 1.86494 1.86494 0.89148 -0.54733 -1.70043 -1.96595 -1.20527 0.18454 1.47802 2.00000 1.47802 0.18454 -1.20527 -1.96595 -1.70043 -0.54733 0.89148 1.86494 1.86494 0.89148 -0.54733 -1.70043 -1.96595 -1.20527 0.18454 1.47802 2.00000 1.47802 0.18454 -1.20527 -1.96595 -1.70043 -0.54733 0.89148 1.86494 1.86494 0.89148 -0.54733 -1.70043 -1.96595 -1.20527 0.18454 1.47802 2.00000 1.47802 0.18454 -1.20527 -1.96595 -1.70043 -0.54733 0.89148 1.86494 0.00000 ... ... ..... ....... ......... ........... ............. E19 2.00000 1.42145 0.02053 -1.39227 -1.99958 -1.45004 -0.06159 1.36249 1.99831 1.47802 0.10262 -1.33215 -1.99621 -1.50537 -0.14361 1.30124 1.99326 1.53209 0.18454 -1.26978 -1.98947 -1.55816 -0.22539 1.23778 1.98484 1.58358 0.26614 -1.20527 -1.97938 -1.60832 -0.30678 1.17225 1.97308 1.63239 0.34730 -1.13873 -1.96595 -1.65578 -0.38766 1.10473 1.95799 1.67846 0.42787 -1.07027 -1.94920 -1.70043 -0.46789 1.03535 1.93959 1.72169 0.50771 -1.00000 -1.92917 -1.74223 -0.54733 0.96423 1.91793 1.76202 0.58671 -0.92805 -1.90588 -1.78108 -0.62584 0.89148 1.89303 1.79938 0.66471 -0.85453 -1.87939 -1.81693 -0.70330 0.81722 1.86494 1.83371 0.74159 -0.77957 -1.84972 0.00000 ... ... ..... ....... ......... ........... ............. 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E59 2.00000 -1.50537 0.26614 1.10473 -1.92917 1.79938 -0.77957 -0.62584 1.72169 -1.96595 1.23778 0.10262 -1.39227 1.99326 -1.60832 0.42787 0.96423 -1.87939 1.86494 -0.92805 -0.46789 1.63239 -1.98947 1.36249 -0.06159 -1.26978 1.97308 -1.70043 0.58671 0.81722 -1.81693 1.91793 -1.07027 -0.30678 1.53209 -1.99958 1.47802 -0.22539 -1.13873 1.93959 -1.78108 0.74159 0.66471 -1.74223 1.95799 -1.20527 -0.14361 1.42145 -1.99621 1.58358 -0.38766 -1.00000 1.89303 -1.84972 0.89148 0.50771 -1.65578 1.98484 -1.33215 0.02053 1.30124 -1.97938 1.67846 -0.54733 -0.85453 1.83371 -1.90588 1.03535 0.34730 -1.55816 1.99831 -1.45004 0.18454 1.17225 -1.94920 1.76202 -0.70330 0.00000 ... ... ..... ....... ......... ........... ............. E60 2.00000 -1.55816 0.42787 0.89148 -1.81693 1.93959 -1.20527 -0.06159 1.30124 -1.96595 1.76202 -0.77957 -0.54733 1.63239 -1.99621 1.47802 -0.30678 -1.00000 1.86494 -1.90588 1.10473 0.18454 -1.39227 1.98484 -1.70043 0.66471 0.66471 -1.70043 1.98484 -1.39227 0.18454 1.10473 -1.90588 1.86494 -1.00000 -0.30678 1.47802 -1.99621 1.63239 -0.54733 -0.77957 1.76202 -1.96595 1.30124 -0.06159 -1.20527 1.93959 -1.81693 0.89148 0.42787 -1.55816 2.00000 -1.55816 0.42787 0.89148 -1.81693 1.93959 -1.20527 -0.06159 1.30124 -1.96595 1.76202 -0.77957 -0.54733 1.63239 -1.99621 1.47802 -0.30678 -1.00000 1.86494 -1.90588 1.10473 0.18454 -1.39227 1.98484 -1.70043 0.66471 0.00000 ... ... ..... ....... ......... ........... ............. E61 2.00000 -1.60832 0.58671 0.66471 -1.65578 1.99831 -1.55816 0.50771 0.74159 -1.70043 1.99326 -1.50537 0.42787 0.81722 -1.74223 1.98484 -1.45004 0.34730 0.89148 -1.78108 1.97308 -1.39227 0.26614 0.96423 -1.81693 1.95799 -1.33215 0.18454 1.03535 -1.84972 1.93959 -1.26978 0.10262 1.10473 -1.87939 1.91793 -1.20527 0.02053 1.17225 -1.90588 1.89303 -1.13873 -0.06159 1.23778 -1.92917 1.86494 -1.07027 -0.14361 1.30124 -1.94920 1.83371 -1.00000 -0.22539 1.36249 -1.96595 1.79938 -0.92805 -0.30678 1.42145 -1.97938 1.76202 -0.85453 -0.38766 1.47802 -1.98947 1.72169 -0.77957 -0.46789 1.53209 -1.99621 1.67846 -0.70330 -0.54733 1.58358 -1.99958 1.63239 -0.62584 0.00000 ... ... ..... ....... ......... ........... ............. 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E63 2.00000 -1.70043 0.89148 0.18454 -1.20527 1.86494 -1.96595 1.47802 -0.54733 -0.54733 1.47802 -1.96595 1.86494 -1.20527 0.18454 0.89148 -1.70043 2.00000 -1.70043 0.89148 0.18454 -1.20527 1.86494 -1.96595 1.47802 -0.54733 -0.54733 1.47802 -1.96595 1.86494 -1.20527 0.18454 0.89148 -1.70043 2.00000 -1.70043 0.89148 0.18454 -1.20527 1.86494 -1.96595 1.47802 -0.54733 -0.54733 1.47802 -1.96595 1.86494 -1.20527 0.18454 0.89148 -1.70043 2.00000 -1.70043 0.89148 0.18454 -1.20527 1.86494 -1.96595 1.47802 -0.54733 -0.54733 1.47802 -1.96595 1.86494 -1.20527 0.18454 0.89148 -1.70043 2.00000 -1.70043 0.89148 0.18454 -1.20527 1.86494 -1.96595 1.47802 -0.54733 0.00000 ... ... ..... ....... ......... ........... ............. E64 2.00000 -1.74223 1.03535 -0.06159 -0.92805 1.67846 -1.99621 1.79938 -1.13873 0.18454 0.81722 -1.60832 1.98484 -1.84972 1.23778 -0.30678 -0.70330 1.53209 -1.96595 1.89303 -1.33215 0.42787 0.58671 -1.45004 1.93959 -1.92917 1.42145 -0.54733 -0.46789 1.36249 -1.90588 1.95799 -1.50537 0.66471 0.34730 -1.26978 1.86494 -1.97938 1.58358 -0.77957 -0.22539 1.17225 -1.81693 1.99326 -1.65578 0.89148 0.10262 -1.07027 1.76202 -1.99958 1.72169 -1.00000 0.02053 0.96423 -1.70043 1.99831 -1.78108 1.10473 -0.14361 -0.85453 1.63239 -1.98947 1.83371 -1.20527 0.26614 0.74159 -1.55816 1.97308 -1.87939 1.30124 -0.38766 -0.62584 1.47802 -1.94920 1.91793 -1.39227 0.50771 0.00000 ... ... ..... ....... ......... ........... ............. E65 2.00000 -1.78108 1.17225 -0.30678 -0.62584 1.42145 -1.90588 1.97308 -1.60832 0.89148 0.02053 -0.92805 1.63239 -1.97938 1.89303 -1.39227 0.58671 0.34730 -1.20527 1.79938 -1.99958 1.76202 -1.13873 0.26614 0.66471 -1.45004 1.91793 -1.96595 1.58358 -0.85453 -0.06159 0.96423 -1.65578 1.98484 -1.87939 1.36249 -0.54733 -0.38766 1.23778 -1.81693 1.99831 -1.74223 1.10473 -0.22539 -0.70330 1.47802 -1.92917 1.95799 -1.55816 0.81722 0.10262 -1.00000 1.67846 -1.98947 1.86494 -1.33215 0.50771 0.42787 -1.26978 1.83371 -1.99621 1.72169 -1.07027 0.18454 0.74159 -1.50537 1.93959 -1.94920 1.53209 -0.77957 -0.14361 1.03535 -1.70043 1.99326 -1.84972 1.30124 -0.46789 0.00000 ... ... ..... ....... ......... ........... ............. E66 2.00000 -1.81693 1.30124 -0.54733 -0.30678 1.10473 -1.70043 1.98484 -1.90588 1.47802 -0.77957 -0.06159 0.89148 -1.55816 1.93959 -1.96595 1.63239 -1.00000 0.18454 0.66471 -1.39227 1.86494 -1.99621 1.76202 -1.20527 0.42787 0.42787 -1.20527 1.76202 -1.99621 1.86494 -1.39227 0.66471 0.18454 -1.00000 1.63239 -1.96595 1.93959 -1.55816 0.89148 -0.06159 -0.77957 1.47802 -1.90588 1.98484 -1.70043 1.10473 -0.30678 -0.54733 1.30124 -1.81693 2.00000 -1.81693 1.30124 -0.54733 -0.30678 1.10473 -1.70043 1.98484 -1.90588 1.47802 -0.77957 -0.06159 0.89148 -1.55816 1.93959 -1.96595 1.63239 -1.00000 0.18454 0.66471 -1.39227 1.86494 -1.99621 1.76202 -1.20527 0.42787 0.00000 ... ... ..... ....... ......... ........... ............. E67 2.00000 -1.84972 1.42145 -0.77957 0.02053 0.74159 -1.39227 1.83371 -1.99958 1.86494 -1.45004 0.81722 -0.06159 -0.70330 1.36249 -1.81693 1.99831 -1.87939 1.47802 -0.85453 0.10262 0.66471 -1.33215 1.79938 -1.99621 1.89303 -1.50537 0.89148 -0.14361 -0.62584 1.30124 -1.78108 1.99326 -1.90588 1.53209 -0.92805 0.18454 0.58671 -1.26978 1.76202 -1.98947 1.91793 -1.55816 0.96423 -0.22539 -0.54733 1.23778 -1.74223 1.98484 -1.92917 1.58358 -1.00000 0.26614 0.50771 -1.20527 1.72169 -1.97938 1.93959 -1.60832 1.03535 -0.30678 -0.46789 1.17225 -1.70043 1.97308 -1.94920 1.63239 -1.07027 0.34730 0.42787 -1.13873 1.67846 -1.96595 1.95799 -1.65578 1.10473 -0.38766 0.00000 ... ... ..... ....... ......... ........... ............. E68 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.34730 -1.00000 1.53209 -1.87939 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.34730 -1.00000 1.53209 -1.87939 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.34730 -1.00000 1.53209 -1.87939 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.34730 -1.00000 1.53209 -1.87939 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.34730 -1.00000 1.53209 -1.87939 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.34730 -1.00000 1.53209 -1.87939 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.34730 -1.00000 1.53209 -1.87939 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.34730 -1.00000 1.53209 -1.87939 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.00000 ... ... ..... ....... ......... ........... ............. E69 2.00000 -1.90588 1.63239 -1.20527 0.66471 -0.06159 -0.54733 1.10473 -1.55816 1.86494 -1.99621 1.93959 -1.70043 1.30124 -0.77957 0.18454 0.42787 -1.00000 1.47802 -1.81693 1.98484 -1.96595 1.76202 -1.39227 0.89148 -0.30678 -0.30678 0.89148 -1.39227 1.76202 -1.96595 1.98484 -1.81693 1.47802 -1.00000 0.42787 0.18454 -0.77957 1.30124 -1.70043 1.93959 -1.99621 1.86494 -1.55816 1.10473 -0.54733 -0.06159 0.66471 -1.20527 1.63239 -1.90588 2.00000 -1.90588 1.63239 -1.20527 0.66471 -0.06159 -0.54733 1.10473 -1.55816 1.86494 -1.99621 1.93959 -1.70043 1.30124 -0.77957 0.18454 0.42787 -1.00000 1.47802 -1.81693 1.98484 -1.96595 1.76202 -1.39227 0.89148 -0.30678 0.00000 ... ... ..... ....... ......... ........... ............. 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E72 2.00000 -1.96595 1.86494 -1.70043 1.47802 -1.20527 0.89148 -0.54733 0.18454 0.18454 -0.54733 0.89148 -1.20527 1.47802 -1.70043 1.86494 -1.96595 2.00000 -1.96595 1.86494 -1.70043 1.47802 -1.20527 0.89148 -0.54733 0.18454 0.18454 -0.54733 0.89148 -1.20527 1.47802 -1.70043 1.86494 -1.96595 2.00000 -1.96595 1.86494 -1.70043 1.47802 -1.20527 0.89148 -0.54733 0.18454 0.18454 -0.54733 0.89148 -1.20527 1.47802 -1.70043 1.86494 -1.96595 2.00000 -1.96595 1.86494 -1.70043 1.47802 -1.20527 0.89148 -0.54733 0.18454 0.18454 -0.54733 0.89148 -1.20527 1.47802 -1.70043 1.86494 -1.96595 2.00000 -1.96595 1.86494 -1.70043 1.47802 -1.20527 0.89148 -0.54733 0.18454 0.00000 ... ... ..... ....... ......... ........... ............. E73 2.00000 -1.97938 1.91793 -1.81693 1.67846 -1.50537 1.30124 -1.07027 0.81722 -0.54733 0.26614 0.02053 -0.30678 0.58671 -0.85453 1.10473 -1.33215 1.53209 -1.70043 1.83371 -1.92917 1.98484 -1.99958 1.97308 -1.90588 1.79938 -1.65578 1.47802 -1.26978 1.03535 -0.77957 0.50771 -0.22539 -0.06159 0.34730 -0.62584 0.89148 -1.13873 1.36249 -1.55816 1.72169 -1.84972 1.93959 -1.98947 1.99831 -1.96595 1.89303 -1.78108 1.63239 -1.45004 1.23778 -1.00000 0.74159 -0.46789 0.18454 0.10262 -0.38766 0.66471 -0.92805 1.17225 -1.39227 1.58358 -1.74223 1.86494 -1.94920 1.99326 -1.99621 1.95799 -1.87939 1.76202 -1.60832 1.42145 -1.20527 0.96423 -0.70330 0.42787 -0.14361 0.00000 ... ... ..... ....... ......... ........... ............. E74 2.00000 -1.98947 1.95799 -1.90588 1.83371 -1.74223 1.63239 -1.50537 1.36249 -1.20527 1.03535 -0.85453 0.66471 -0.46789 0.26614 -0.06159 -0.14361 0.34730 -0.54733 0.74159 -0.92805 1.10473 -1.26978 1.42145 -1.55816 1.67846 -1.78108 1.86494 -1.92917 1.97308 -1.99621 1.99831 -1.97938 1.93959 -1.87939 1.79938 -1.70043 1.58358 -1.45004 1.30124 -1.13873 0.96423 -0.77957 0.58671 -0.38766 0.18454 0.02053 -0.22539 0.42787 -0.62584 0.81722 -1.00000 1.17225 -1.33215 1.47802 -1.60832 1.72169 -1.81693 1.89303 -1.94920 1.98484 -1.99958 1.99326 -1.96595 1.91793 -1.84972 1.76202 -1.65578 1.53209 -1.39227 1.23778 -1.07027 0.89148 -0.70330 0.50771 -0.30678 0.10262 0.00000 ... ... ..... ....... ......... ........... ............. E75 2.00000 -1.99621 1.98484 -1.96595 1.93959 -1.90588 1.86494 -1.81693 1.76202 -1.70043 1.63239 -1.55816 1.47802 -1.39227 1.30124 -1.20527 1.10473 -1.00000 0.89148 -0.77957 0.66471 -0.54733 0.42787 -0.30678 0.18454 -0.06159 -0.06159 0.18454 -0.30678 0.42787 -0.54733 0.66471 -0.77957 0.89148 -1.00000 1.10473 -1.20527 1.30124 -1.39227 1.47802 -1.55816 1.63239 -1.70043 1.76202 -1.81693 1.86494 -1.90588 1.93959 -1.96595 1.98484 -1.99621 2.00000 -1.99621 1.98484 -1.96595 1.93959 -1.90588 1.86494 -1.81693 1.76202 -1.70043 1.63239 -1.55816 1.47802 -1.39227 1.30124 -1.20527 1.10473 -1.00000 0.89148 -0.77957 0.66471 -0.54733 0.42787 -0.30678 0.18454 -0.06159 0.00000 ... ... ..... ....... ......... ........... ............. E76 2.00000 -1.99958 1.99831 -1.99621 1.99326 -1.98947 1.98484 -1.97938 1.97308 -1.96595 1.95799 -1.94920 1.93959 -1.92917 1.91793 -1.90588 1.89303 -1.87939 1.86494 -1.84972 1.83371 -1.81693 1.79938 -1.78108 1.76202 -1.74223 1.72169 -1.70043 1.67846 -1.65578 1.63239 -1.60832 1.58358 -1.55816 1.53209 -1.50537 1.47802 -1.45004 1.42145 -1.39227 1.36249 -1.33215 1.30124 -1.26978 1.23778 -1.20527 1.17225 -1.13873 1.10473 -1.07027 1.03535 -1.00000 0.96423 -0.92805 0.89148 -0.85453 0.81722 -0.77957 0.74159 -0.70330 0.66471 -0.62584 0.58671 -0.54733 0.50771 -0.46789 0.42787 -0.38766 0.34730 -0.30678 0.26614 -0.22539 0.18454 -0.14361 0.10262 -0.06159 0.02053 0.00000 ... ... ..... ....... ......... ........... ............. Irrational character values: 1.998313773776 = 2*cos(2*π/153) 1.993257938463 = 2*cos(4*π/153) 1.984841019344 = 2*cos(6*π/153) = 2*cos(2*π/51) = (1+√17+√34+2*√17−2*√17−3*√17+√34+2*√17−2*√34−2*√17)/16 + √6*√17+√17−√34+2*√17+2*√17−3*√17−√34+2*√17+2*√34−2*√17/8 1.973077209247 = 2*cos(8*π/153) 1.957986344619 = 2*cos(10*π/153) 1.939593872070 = 2*cos(12*π/153) = 2*cos(4*π/51) = (1+√17−√34+2*√17+2*√17−3*√17−√34+2*√17+2*√34−2*√17)/16 + √6*√17+√17+√34+2*√17+2*√17−3*√17+√34+2*√17−2*√34−2*√17/8 1.917930805470 = 2*cos(14*π/153) 1.893033673651 = 2*cos(16*π/153) 1.864944458809 = 2*cos(18*π/153) = 2*cos(2*π/17) = (−1+√17+√34−2*√17+2*√17+3*√17−√34−2*√17−2*√34+2*√17)/8 1.833710525714 = 2*cos(20*π/153) 1.799384541843 = 2*cos(22*π/153) 1.762024388572 = 2*cos(24*π/153) = 2*cos(8*π/51) = (1+√17+√34+2*√17+2*√17−3*√17+√34+2*√17−2*√34−2*√17)/16 + √6*√17+√17−√34+2*√17−2*√17−3*√17−√34+2*√17+2*√34−2*√17/8 1.721693063569 = 2*cos(26*π/153) 1.678458574573 = 2*cos(28*π/153) 1.632393824712 = 2*cos(30*π/153) = 2*cos(10*π/51) = (1−√17−√34−2*√17+2*√17+3*√17−√34−2*√17−2*√34+2*√17)/16 + √6*√17−√17+√34−2*√17+2*√17+3*√17+√34−2*√17+2*√34+2*√17/8 1.583576489577 = 2*cos(32*π/153) 1.532088886238 = 2*cos(34*π/153) = 2*cos(2*π/9) 1.478017834441 = 2*cos(36*π/153) = 2*cos(4*π/17) = (−1+√17−√34−2*√17+2*√17+3*√17+√34−2*√17+2*√34+2*√17)/8 1.421454510213 = 2*cos(38*π/153) 1.362494292113 = 2*cos(40*π/153) 1.301236600408 = 2*cos(42*π/153) = 2*cos(14*π/51) = (1−√17+√34−2*√17+2*√17+3*√17+√34−2*√17+2*√34+2*√17)/16 + √6*√17−√17−√34−2*√17−2*√17+3*√17−√34−2*√17−2*√34+2*√17/8 1.237784729425 = 2*cos(44*π/153) 1.172245673370 = 2*cos(46*π/153) 1.104729945921 = 2*cos(48*π/153) = 2*cos(16*π/51) = (1+√17−√34+2*√17−2*√17−3*√17−√34+2*√17+2*√34−2*√17)/16 + √6*√17+√17+√34+2*√17−2*√17−3*√17+√34+2*√17−2*√34−2*√17/8 1.035351393866 = 2*cos(50*π/153) 0.964227005141 = 2*cos(52*π/153) 0.891476711553 = 2*cos(54*π/153) = 2*cos(6*π/17) = (−1−√17+√34+2*√17+2*√17−3*√17−√34+2*√17+2*√34−2*√17)/8 0.817223186556 = 2*cos(56*π/153) 0.741591638392 = 2*cos(58*π/153) 0.664709598959 = 2*cos(60*π/153) = 2*cos(20*π/51) = (1−√17+√34−2*√17+2*√17+3*√17+√34−2*√17+2*√34+2*√17)/16 − √6*√17−√17−√34−2*√17−2*√17+3*√17−√34−2*√17−2*√34+2*√17/8 0.586706708770 = 2*cos(62*π/153) 0.507714498342 = 2*cos(64*π/153) 0.427866166413 = 2*cos(66*π/153) = 2*cos(22*π/51) = (1−√17+√34−2*√17−2*√17+3*√17+√34−2*√17+2*√34+2*√17)/16 + √6*√17−√17−√34−2*√17+2*√17+3*√17−√34−2*√17−2*√34+2*√17/8 0.347296355334 = 2*cos(68*π/153) = 2*cos(4*π/9) 0.266140924033 = 2*cos(70*π/153) 0.184536718927 = 2*cos(72*π/153) = 2*cos(8*π/17) = (−1+√17+√34−2*√17−2*√17+3*√17−√34−2*√17−2*√34+2*√17)/8 0.102621343166 = 2*cos(74*π/153) 0.020532924605 = 2*cos(76*π/153) -0.061590117112 = 2*cos(78*π/153) = 2*cos(26*π/51) = −((−1−√17−√34+2*√17−2*√17−3*√17+√34+2*√17−2*√34−2*√17)/16 + √6*√17+√17−√34+2*√17−2*√17−3*√17−√34+2*√17+2*√34−2*√17/8) -0.143609303959 = 2*cos(80*π/153) -0.225386333031 = 2*cos(82*π/153) -0.306783309757 = 2*cos(84*π/153) = 2*cos(28*π/51) = −((−1+√17+√34−2*√17+2*√17+3*√17−√34−2*√17−2*√34+2*√17)/16 − √6*√17−√17+√34−2*√17−2*√17+3*√17+√34−2*√17+2*√34+2*√17/8) -0.387662980422 = 2*cos(86*π/153) -0.467888963603 = 2*cos(88*π/153) -0.547325980144 = 2*cos(90*π/153) = 2*cos(10*π/17) = −(1+√17−√34+2*√17+2*√17−3*√17−√34+2*√17+2*√34−2*√17)/8 -0.625840081264 = 2*cos(92*π/153) -0.703298874427 = 2*cos(94*π/153) -0.779571746585 = 2*cos(96*π/153) = 2*cos(32*π/51) = −((−1−√17−√34+2*√17+2*√17−3*√17+√34+2*√17−2*√34−2*√17)/16 + √6*√17+√17−√34+2*√17+2*√17−3*√17−√34+2*√17+2*√34−2*√17/8) -0.854530084421 = 2*cos(98*π/153) -0.928047491219 = 2*cos(100*π/153) -1.070266282557 = 2*cos(104*π/153) -1.138727854043 = 2*cos(106*π/153) -1.205269272759 = 2*cos(108*π/153) = 2*cos(12*π/17) = −(1+√17+√34+2*√17−2*√17−3*√17+√34+2*√17−2*√34−2*√17)/8 -1.269778334820 = 2*cos(110*π/153) -1.332146263355 = 2*cos(112*π/153) -1.392267891926 = 2*cos(114*π/153) = 2*cos(38*π/51) = −((−1−√17+√34+2*√17−2*√17−3*√17−√34+2*√17+2*√34−2*√17)/16 + √6*√17+√17+√34+2*√17+2*√17−3*√17+√34+2*√17−2*√34−2*√17/8) -1.450041841867 = 2*cos(116*π/153) -1.505370693229 = 2*cos(118*π/153) -1.558161149051 = 2*cos(120*π/153) = 2*cos(40*π/51) = −((−1+√17+√34−2*√17+2*√17+3*√17−√34−2*√17−2*√34+2*√17)/16 + √6*√17−√17+√34−2*√17−2*√17+3*√17+√34−2*√17+2*√34+2*√17/8) -1.608324192683 = 2*cos(122*π/153) -1.655775237885 = 2*cos(124*π/153) -1.700434271459 = 2*cos(126*π/153) = 2*cos(14*π/17) = −(1+√17+√34+2*√17+2*√17−3*√17+√34+2*√17−2*√34−2*√17)/8 -1.742225988173 = 2*cos(128*π/153) -1.781079917738 = 2*cos(130*π/153) -1.816930543639 = 2*cos(132*π/153) = 2*cos(44*π/51) = −((−1+√17+√34−2*√17−2*√17+3*√17−√34−2*√17−2*√34+2*√17)/16 + √6*√17−√17+√34−2*√17+2*√17+3*√17+√34−2*√17+2*√34+2*√17/8) -1.849717413610 = 2*cos(134*π/153) -1.879385241572 = 2*cos(136*π/153) = 2*cos(8*π/9) -1.905884000854 = 2*cos(138*π/153) = 2*cos(46*π/51) = −((−1+√17−√34−2*√17+2*√17+3*√17+√34−2*√17+2*√34+2*√17)/16 + √6*√17−√17−√34−2*√17+2*√17+3*√17−√34−2*√17−2*√34+2*√17/8) -1.929169008555 = 2*cos(140*π/153) -1.949201000883 = 2*cos(142*π/153) -1.965946199368 = 2*cos(144*π/153) = 2*cos(16*π/17) = −(1−√17+√34−2*√17+2*√17+3*√17+√34−2*√17+2*√34+2*√17)/8 -1.979376367817 = 2*cos(146*π/153) -1.989468859927 = 2*cos(148*π/153) -1.996206657474 = 2*cos(150*π/153) = 2*cos(50*π/51) = −((−1−√17+√34+2*√17+2*√17−3*√17−√34+2*√17+2*√34−2*√17)/16 + √6*√17+√17+√34+2*√17−2*√17−3*√17+√34+2*√17−2*√34−2*√17/8) -1.999578399007 = 2*cos(152*π/153) Symmetry of Rotations and Cartesian products A1 p+d+f+g+h+i+j+k+l+m z, z², z³, z⁴, z⁵, z⁶ A2 R R_z E1 R+p+d+f+g+h+i+j+k+l+m {R_x, R_y}, {x, y}, {xz, yz}, {xz², yz²}, {xz³, yz³}, {xz⁴, yz⁴}, {xz⁵, yz⁵} E2 d+f+g+h+i+j+k+l+m {x²−y², xy}, {z(x²−y²), xyz}, {z²(x²−y²), xyz²}, {z³(x²−y²), xyz³}, {z⁴(x²−y²), xyz⁴} E3 f+g+h+i+j+k+l+m {x(x²−3y²), y(3x²−y²)}, {xz(x²−3y²), yz(3x²−y²)}, {xz²(x²−3y²), yz²(3x²−y²)}, {xz³(x²−3y²), yz³(3x²−y²)} E4 g+h+i+j+k+l+m {(x²−y²)²−4x²y², xy(x²−y²)}, {z((x²−y²)²−4x²y²), xyz(x²−y²)}, {z²((x²−y²)²−4x²y²), xyz²(x²−y²)} E5 h+i+j+k+l+m {x(x²−(5+2√5)y²)(x²−(5−2√5)y²), y((5+2√5)x²−y²)((5−2√5)x²−y²)}, {xz(x²−(5+2√5)y²)(x²−(5−2√5)y²), yz((5+2√5)x²−y²)((5−2√5)x²−y²)} E6 i+j+k+l+m {x²(x²−3y²)²−y²(3x²−y²)², xy(x²−3y²)(3x²−y²)} E7 j+k+l+m E8 k+l+m E9 l+m E10 m Notes: α The order of the C_153v point group is 306, and the order of the principal axis (C₁₅₃) is 153. The group has 78 irreducible representations. β The C_153v point group is isomorphic to D₁₅₃. γ The C_153v point group is generated by two symmetry elements, C₁₅₃ and any σ_v. Also, the group may be generated from two σ_v planes (some pairs will yield smaller groups, though; choosing a minimum angle is safe). δ The group contains one set of symmetry planes σ_v intersecting in the principal (z) axis. The xz plane (but not the yz plane) is a member of that set. ε The lowest nonvanishing multipole moment in C_153v is 2 (dipole moment). ζ This point group is non-Abelian (some symmetry operations are not commutative). Therefore, the character table contains multi-membered classes and degenerate irreducible representations. η Some of the characters in the table are irrational because the order of the principal axis is neither 1,2,3,4 nor 6. These irrational values can be expressed as cosine values, or as solutions of algebraic equations with a leading coefficient of 1. All characters are algebraic integers of a degree much less than half the order of the principal axis. θ The point group corresponds to a polygon inconstructible by the classical means of ruler and compass. Yet it becomes constructible if angle trisection is allowed, e.g., with neusis construction or origami. This is because the order of the principal axis is given by a product of any number of different Pierpont primes (...,5,7,13,17,19,37,73,97,109,163,...) times arbitrary powers of two and three. While some characters of this group can be expressed using real integers and square roots alone, others need complex numbers and third roots. ι That a regular 17-gon can be constructed with compass and ruler was unknown to mathematicians until Gauss proved it in 1796. The first actual construction was performed thirty years later by Johannes Erchinger in 1825.

This Character Table for the C_153v point group was created by Gernot Katzer.

For other groups and some explanations, see the Main Page.

	C_136v
	C_144v
C₁₅₃	C_153v	C_153h D₁₅₃ D_153h D_153d
	C_160v
	C_170v

Character table for the C153v point group

Character table for the C_153v point group