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TT. ..... ....TT. ......... ........TT. ............. E2 2.00000 1.99985 1.99940 1.99864 1.99759 1.99624 1.99458 1.99263 1.99037 1.98781 1.98496 1.98181 1.97835 1.97460 1.97056 1.96621 1.96157 1.95663 1.95140 1.94588 1.94006 1.93395 1.92755 1.92086 1.91388 1.90661 1.89906 1.89121 1.88309 1.87468 1.86599 1.85701 1.84776 1.83823 1.82842 1.81834 1.80798 1.79735 1.78645 1.77528 1.76384 1.75214 1.74017 1.72795 1.71546 1.70271 1.68971 1.67645 1.66294 1.64918 1.63517 1.62091 1.60642 1.59167 1.57669 1.56147 1.54602 1.53033 1.51442 1.49827 1.48190 1.46531 1.44849 1.43146 1.41421 1.39675 1.37908 1.36120 1.34312 1.32483 1.30635 1.28766 1.26879 1.24972 1.23046 1.21102 1.19140 1.17160 1.15162 1.13146 1.11114 1.09065 1.07000 1.04918 1.02821 1.00708 0.98580 0.96437 0.94279 0.92108 0.89922 0.87723 0.85511 0.83286 0.81048 0.78798 0.76537 0.74263 0.71979 0.69684 0.67378 0.65062 0.62736 0.60401 0.58057 0.55704 0.53343 0.50973 0.48596 0.46212 0.43820 0.41422 0.39018 0.36608 0.34192 0.31772 0.29346 0.26916 0.24482 0.22044 0.19603 0.17159 0.14713 0.12264 0.09814 0.07361 0.04908 0.02454 0.00000 -0.02454 -0.04908 -0.07361 -0.09814 -0.12264 -0.14713 -0.17159 -0.19603 -0.22044 -0.24482 -0.26916 -0.29346 -0.31772 -0.34192 -0.36608 -0.39018 -0.41422 -0.43820 -0.46212 -0.48596 -0.50973 -0.53343 -0.55704 -0.58057 -0.60401 -0.62736 -0.65062 -0.67378 -0.69684 -0.71979 -0.74263 -0.76537 -0.78798 -0.81048 -0.83286 -0.85511 -0.87723 -0.89922 -0.92108 -0.94279 -0.96437 -0.98580 -1.00708 -1.02821 -1.04918 -1.07000 -1.09065 -1.11114 -1.13146 -1.15162 -1.17160 -1.19140 -1.21102 -1.23046 -1.24972 -1.26879 -1.28766 -1.30635 -1.32483 -1.34312 -1.36120 -1.37908 -1.39675 -1.41421 -1.43146 -1.44849 -1.46531 -1.48190 -1.49827 -1.51442 -1.53033 -1.54602 -1.56147 -1.57669 -1.59167 -1.60642 -1.62091 -1.63517 -1.64918 -1.66294 -1.67645 -1.68971 -1.70271 -1.71546 -1.72795 -1.74017 -1.75214 -1.76384 -1.77528 -1.78645 -1.79735 -1.80798 -1.81834 -1.82842 -1.83823 -1.84776 -1.85701 -1.86599 -1.87468 -1.88309 -1.89121 -1.89906 -1.90661 -1.91388 -1.92086 -1.92755 -1.93395 -1.94006 -1.94588 -1.95140 -1.95663 -1.96157 -1.96621 -1.97056 -1.97460 -1.97835 -1.98181 -1.98496 -1.98781 -1.99037 -1.99263 -1.99458 -1.99624 -1.99759 -1.99864 -1.99940 -1.99985 -2.00000 -1.99985 -1.99940 -1.99864 -1.99759 -1.99624 -1.99458 -1.99263 -1.99037 -1.98781 -1.98496 -1.98181 -1.97835 -1.97460 -1.97056 -1.96621 -1.96157 -1.95663 -1.95140 -1.94588 -1.94006 -1.93395 -1.92755 -1.92086 -1.91388 -1.90661 -1.89906 -1.89121 -1.88309 -1.87468 -1.86599 -1.85701 -1.84776 -1.83823 -1.82842 -1.81834 -1.80798 -1.79735 -1.78645 -1.77528 -1.76384 -1.75214 -1.74017 -1.72795 -1.71546 -1.70271 -1.68971 -1.67645 -1.66294 -1.64918 -1.63517 -1.62091 -1.60642 -1.59167 -1.57669 -1.56147 -1.54602 -1.53033 -1.51442 -1.49827 -1.48190 -1.46531 -1.44849 -1.43146 -1.41421 -1.39675 -1.37908 -1.36120 -1.34312 -1.32483 -1.30635 -1.28766 -1.26879 -1.24972 -1.23046 -1.21102 -1.19140 -1.17160 -1.15162 -1.13146 -1.11114 -1.09065 -1.07000 -1.04918 -1.02821 -1.00708 -0.98580 -0.96437 -0.94279 -0.92108 -0.89922 -0.87723 -0.85511 -0.83286 -0.81048 -0.78798 -0.76537 -0.74263 -0.71979 -0.69684 -0.67378 -0.65062 -0.62736 -0.60401 -0.58057 -0.55704 -0.53343 -0.50973 -0.48596 -0.46212 -0.43820 -0.41422 -0.39018 -0.36608 -0.34192 -0.31772 -0.29346 -0.26916 -0.24482 -0.22044 -0.19603 -0.17159 -0.14713 -0.12264 -0.09814 -0.07361 -0.04908 -0.02454 0.00000 0.02454 0.04908 0.07361 0.09814 0.12264 0.14713 0.17159 0.19603 0.22044 0.24482 0.26916 0.29346 0.31772 0.34192 0.36608 0.39018 0.41422 0.43820 0.46212 0.48596 0.50973 0.53343 0.55704 0.58057 0.60401 0.62736 0.65062 0.67378 0.69684 0.71979 0.74263 0.76537 0.78798 0.81048 0.83286 0.85511 0.87723 0.89922 0.92108 0.94279 0.96437 0.98580 1.00708 1.02821 1.04918 1.07000 1.09065 1.11114 1.13146 1.15162 1.17160 1.19140 1.21102 1.23046 1.24972 1.26879 1.28766 1.30635 1.32483 1.34312 1.36120 1.37908 1.39675 1.41421 1.43146 1.44849 1.46531 1.48190 1.49827 1.51442 1.53033 1.54602 1.56147 1.57669 1.59167 1.60642 1.62091 1.63517 1.64918 1.66294 1.67645 1.68971 1.70271 1.71546 1.72795 1.74017 1.75214 1.76384 1.77528 1.78645 1.79735 1.80798 1.81834 1.82842 1.83823 1.84776 1.85701 1.86599 1.87468 1.88309 1.89121 1.89906 1.90661 1.91388 1.92086 1.92755 1.93395 1.94006 1.94588 1.95140 1.95663 1.96157 1.96621 1.97056 1.97460 1.97835 1.98181 1.98496 1.98781 1.99037 1.99263 1.99458 1.99624 1.99759 1.99864 1.99940 1.99985 2.00000 0.00000 0.00000 ... ... TT... ....... ....TT... ........... ........TT... 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TT..... ......... ....TT..... ............. E4 2.00000 1.99940 1.99759 1.99458 1.99037 1.98496 1.97835 1.97056 1.96157 1.95140 1.94006 1.92755 1.91388 1.89906 1.88309 1.86599 1.84776 1.82842 1.80798 1.78645 1.76384 1.74017 1.71546 1.68971 1.66294 1.63517 1.60642 1.57669 1.54602 1.51442 1.48190 1.44849 1.41421 1.37908 1.34312 1.30635 1.26879 1.23046 1.19140 1.15162 1.11114 1.07000 1.02821 0.98580 0.94279 0.89922 0.85511 0.81048 0.76537 0.71979 0.67378 0.62736 0.58057 0.53343 0.48596 0.43820 0.39018 0.34192 0.29346 0.24482 0.19603 0.14713 0.09814 0.04908 0.00000 -0.04908 -0.09814 -0.14713 -0.19603 -0.24482 -0.29346 -0.34192 -0.39018 -0.43820 -0.48596 -0.53343 -0.58057 -0.62736 -0.67378 -0.71979 -0.76537 -0.81048 -0.85511 -0.89922 -0.94279 -0.98580 -1.02821 -1.07000 -1.11114 -1.15162 -1.19140 -1.23046 -1.26879 -1.30635 -1.34312 -1.37908 -1.41421 -1.44849 -1.48190 -1.51442 -1.54602 -1.57669 -1.60642 -1.63517 -1.66294 -1.68971 -1.71546 -1.74017 -1.76384 -1.78645 -1.80798 -1.82842 -1.84776 -1.86599 -1.88309 -1.89906 -1.91388 -1.92755 -1.94006 -1.95140 -1.96157 -1.97056 -1.97835 -1.98496 -1.99037 -1.99458 -1.99759 -1.99940 -2.00000 -1.99940 -1.99759 -1.99458 -1.99037 -1.98496 -1.97835 -1.97056 -1.96157 -1.95140 -1.94006 -1.92755 -1.91388 -1.89906 -1.88309 -1.86599 -1.84776 -1.82842 -1.80798 -1.78645 -1.76384 -1.74017 -1.71546 -1.68971 -1.66294 -1.63517 -1.60642 -1.57669 -1.54602 -1.51442 -1.48190 -1.44849 -1.41421 -1.37908 -1.34312 -1.30635 -1.26879 -1.23046 -1.19140 -1.15162 -1.11114 -1.07000 -1.02821 -0.98580 -0.94279 -0.89922 -0.85511 -0.81048 -0.76537 -0.71979 -0.67378 -0.62736 -0.58057 -0.53343 -0.48596 -0.43820 -0.39018 -0.34192 -0.29346 -0.24482 -0.19603 -0.14713 -0.09814 -0.04908 0.00000 0.04908 0.09814 0.14713 0.19603 0.24482 0.29346 0.34192 0.39018 0.43820 0.48596 0.53343 0.58057 0.62736 0.67378 0.71979 0.76537 0.81048 0.85511 0.89922 0.94279 0.98580 1.02821 1.07000 1.11114 1.15162 1.19140 1.23046 1.26879 1.30635 1.34312 1.37908 1.41421 1.44849 1.48190 1.51442 1.54602 1.57669 1.60642 1.63517 1.66294 1.68971 1.71546 1.74017 1.76384 1.78645 1.80798 1.82842 1.84776 1.86599 1.88309 1.89906 1.91388 1.92755 1.94006 1.95140 1.96157 1.97056 1.97835 1.98496 1.99037 1.99458 1.99759 1.99940 2.00000 1.99940 1.99759 1.99458 1.99037 1.98496 1.97835 1.97056 1.96157 1.95140 1.94006 1.92755 1.91388 1.89906 1.88309 1.86599 1.84776 1.82842 1.80798 1.78645 1.76384 1.74017 1.71546 1.68971 1.66294 1.63517 1.60642 1.57669 1.54602 1.51442 1.48190 1.44849 1.41421 1.37908 1.34312 1.30635 1.26879 1.23046 1.19140 1.15162 1.11114 1.07000 1.02821 0.98580 0.94279 0.89922 0.85511 0.81048 0.76537 0.71979 0.67378 0.62736 0.58057 0.53343 0.48596 0.43820 0.39018 0.34192 0.29346 0.24482 0.19603 0.14713 0.09814 0.04908 0.00000 -0.04908 -0.09814 -0.14713 -0.19603 -0.24482 -0.29346 -0.34192 -0.39018 -0.43820 -0.48596 -0.53343 -0.58057 -0.62736 -0.67378 -0.71979 -0.76537 -0.81048 -0.85511 -0.89922 -0.94279 -0.98580 -1.02821 -1.07000 -1.11114 -1.15162 -1.19140 -1.23046 -1.26879 -1.30635 -1.34312 -1.37908 -1.41421 -1.44849 -1.48190 -1.51442 -1.54602 -1.57669 -1.60642 -1.63517 -1.66294 -1.68971 -1.71546 -1.74017 -1.76384 -1.78645 -1.80798 -1.82842 -1.84776 -1.86599 -1.88309 -1.89906 -1.91388 -1.92755 -1.94006 -1.95140 -1.96157 -1.97056 -1.97835 -1.98496 -1.99037 -1.99458 -1.99759 -1.99940 -2.00000 -1.99940 -1.99759 -1.99458 -1.99037 -1.98496 -1.97835 -1.97056 -1.96157 -1.95140 -1.94006 -1.92755 -1.91388 -1.89906 -1.88309 -1.86599 -1.84776 -1.82842 -1.80798 -1.78645 -1.76384 -1.74017 -1.71546 -1.68971 -1.66294 -1.63517 -1.60642 -1.57669 -1.54602 -1.51442 -1.48190 -1.44849 -1.41421 -1.37908 -1.34312 -1.30635 -1.26879 -1.23046 -1.19140 -1.15162 -1.11114 -1.07000 -1.02821 -0.98580 -0.94279 -0.89922 -0.85511 -0.81048 -0.76537 -0.71979 -0.67378 -0.62736 -0.58057 -0.53343 -0.48596 -0.43820 -0.39018 -0.34192 -0.29346 -0.24482 -0.19603 -0.14713 -0.09814 -0.04908 0.00000 0.04908 0.09814 0.14713 0.19603 0.24482 0.29346 0.34192 0.39018 0.43820 0.48596 0.53343 0.58057 0.62736 0.67378 0.71979 0.76537 0.81048 0.85511 0.89922 0.94279 0.98580 1.02821 1.07000 1.11114 1.15162 1.19140 1.23046 1.26879 1.30635 1.34312 1.37908 1.41421 1.44849 1.48190 1.51442 1.54602 1.57669 1.60642 1.63517 1.66294 1.68971 1.71546 1.74017 1.76384 1.78645 1.80798 1.82842 1.84776 1.86599 1.88309 1.89906 1.91388 1.92755 1.94006 1.95140 1.96157 1.97056 1.97835 1.98496 1.99037 1.99458 1.99759 1.99940 2.00000 0.00000 0.00000 ... ... ..... ....... TT....... ........... ....TT....... E5 2.00000 1.99906 1.99624 1.99153 1.98496 1.97652 1.96621 1.95406 1.94006 1.92424 1.90661 1.88719 1.86599 1.84303 1.81834 1.79193 1.76384 1.73409 1.70271 1.66973 1.63517 1.59907 1.56147 1.52240 1.48190 1.44001 1.39675 1.35219 1.30635 1.25928 1.21102 1.16163 1.11114 1.05961 1.00708 0.95360 0.89922 0.84400 0.78798 0.73123 0.67378 0.61570 0.55704 0.49786 0.43820 0.37814 0.31772 0.25700 0.19603 0.13489 0.07361 0.01227 -0.04908 -0.11039 -0.17159 -0.23264 -0.29346 -0.35401 -0.41422 -0.47405 -0.53343 -0.59230 -0.65062 -0.70833 -0.76537 -0.82169 -0.87723 -0.93195 -0.98580 -1.03871 -1.09065 -1.14156 -1.19140 -1.24011 -1.28766 -1.33400 -1.37908 -1.42286 -1.46531 -1.50637 -1.54602 -1.58421 -1.62091 -1.65609 -1.68971 -1.72173 -1.75214 -1.78090 -1.80798 -1.83336 -1.85701 -1.87892 -1.89906 -1.91741 -1.93395 -1.94868 -1.96157 -1.97262 -1.98181 -1.98913 -1.99458 -1.99816 -1.99985 -1.99966 -1.99759 -1.99364 -1.98781 -1.98012 -1.97056 -1.95914 -1.94588 -1.93079 -1.91388 -1.89517 -1.87468 -1.85242 -1.82842 -1.80270 -1.77528 -1.74619 -1.71546 -1.68311 -1.64918 -1.61370 -1.57669 -1.53821 -1.49827 -1.45693 -1.41421 -1.37017 -1.32483 -1.27825 -1.23046 -1.18152 -1.13146 -1.08034 -1.02821 -0.97510 -0.92108 -0.86619 -0.81048 -0.75401 -0.69684 -0.63900 -0.58057 -0.52159 -0.46212 -0.40221 -0.34192 -0.28132 -0.22044 -0.15936 -0.09814 -0.03681 0.02454 0.08588 0.14713 0.20824 0.26916 0.32983 0.39018 0.45017 0.50973 0.56882 0.62736 0.68532 0.74263 0.79925 0.85511 0.91017 0.96437 1.01766 1.07000 1.12132 1.17160 1.22077 1.26879 1.31561 1.36120 1.40551 1.44849 1.49012 1.53033 1.56911 1.60642 1.64221 1.67645 1.70912 1.74017 1.76959 1.79735 1.82341 1.84776 1.87037 1.89121 1.91028 1.92755 1.94301 1.95663 1.96842 1.97835 1.98642 1.99263 1.99695 1.99940 1.99996 1.99864 1.99545 1.99037 1.98342 1.97460 1.96393 1.95140 1.93704 1.92086 1.90287 1.88309 1.86153 1.83823 1.81319 1.78645 1.75802 1.72795 1.69624 1.66294 1.62807 1.59167 1.55378 1.51442 1.47363 1.43146 1.38794 1.34312 1.29703 1.24972 1.20123 1.15162 1.10092 1.04918 0.99646 0.94279 0.88824 0.83286 0.77669 0.71979 0.66221 0.60401 0.54524 0.48596 0.42622 0.36608 0.30559 0.24482 0.18382 0.12264 0.06135 0.00000 -0.06135 -0.12264 -0.18382 -0.24482 -0.30559 -0.36608 -0.42622 -0.48596 -0.54524 -0.60401 -0.66221 -0.71979 -0.77669 -0.83286 -0.88824 -0.94279 -0.99646 -1.04918 -1.10092 -1.15162 -1.20123 -1.24972 -1.29703 -1.34312 -1.38794 -1.43146 -1.47363 -1.51442 -1.55378 -1.59167 -1.62807 -1.66294 -1.69624 -1.72795 -1.75802 -1.78645 -1.81319 -1.83823 -1.86153 -1.88309 -1.90287 -1.92086 -1.93704 -1.95140 -1.96393 -1.97460 -1.98342 -1.99037 -1.99545 -1.99864 -1.99996 -1.99940 -1.99695 -1.99263 -1.98642 -1.97835 -1.96842 -1.95663 -1.94301 -1.92755 -1.91028 -1.89121 -1.87037 -1.84776 -1.82341 -1.79735 -1.76959 -1.74017 -1.70912 -1.67645 -1.64221 -1.60642 -1.56911 -1.53033 -1.49012 -1.44849 -1.40551 -1.36120 -1.31561 -1.26879 -1.22077 -1.17160 -1.12132 -1.07000 -1.01766 -0.96437 -0.91017 -0.85511 -0.79925 -0.74263 -0.68532 -0.62736 -0.56882 -0.50973 -0.45017 -0.39018 -0.32983 -0.26916 -0.20824 -0.14713 -0.08588 -0.02454 0.03681 0.09814 0.15936 0.22044 0.28132 0.34192 0.40221 0.46212 0.52159 0.58057 0.63900 0.69684 0.75401 0.81048 0.86619 0.92108 0.97510 1.02821 1.08034 1.13146 1.18152 1.23046 1.27825 1.32483 1.37017 1.41421 1.45693 1.49827 1.53821 1.57669 1.61370 1.64918 1.68311 1.71546 1.74619 1.77528 1.80270 1.82842 1.85242 1.87468 1.89517 1.91388 1.93079 1.94588 1.95914 1.97056 1.98012 1.98781 1.99364 1.99759 1.99966 1.99985 1.99816 1.99458 1.98913 1.98181 1.97262 1.96157 1.94868 1.93395 1.91741 1.89906 1.87892 1.85701 1.83336 1.80798 1.78090 1.75214 1.72173 1.68971 1.65609 1.62091 1.58421 1.54602 1.50637 1.46531 1.42286 1.37908 1.33400 1.28766 1.24011 1.19140 1.14156 1.09065 1.03871 0.98580 0.93195 0.87723 0.82169 0.76537 0.70833 0.65062 0.59230 0.53343 0.47405 0.41422 0.35401 0.29346 0.23264 0.17159 0.11039 0.04908 -0.01227 -0.07361 -0.13489 -0.19603 -0.25700 -0.31772 -0.37814 -0.43820 -0.49786 -0.55704 -0.61570 -0.67378 -0.73123 -0.78798 -0.84400 -0.89922 -0.95360 -1.00708 -1.05961 -1.11114 -1.16163 -1.21102 -1.25928 -1.30635 -1.35219 -1.39675 -1.44001 -1.48190 -1.52240 -1.56147 -1.59907 -1.63517 -1.66973 -1.70271 -1.73409 -1.76384 -1.79193 -1.81834 -1.84303 -1.86599 -1.88719 -1.90661 -1.92424 -1.94006 -1.95406 -1.96621 -1.97652 -1.98496 -1.99153 -1.99624 -1.99906 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... TT......... ............. E6 2.00000 1.99864 1.99458 1.98781 1.97835 1.96621 1.95140 1.93395 1.91388 1.89121 1.86599 1.83823 1.80798 1.77528 1.74017 1.70271 1.66294 1.62091 1.57669 1.53033 1.48190 1.43146 1.37908 1.32483 1.26879 1.21102 1.15162 1.09065 1.02821 0.96437 0.89922 0.83286 0.76537 0.69684 0.62736 0.55704 0.48596 0.41422 0.34192 0.26916 0.19603 0.12264 0.04908 -0.02454 -0.09814 -0.17159 -0.24482 -0.31772 -0.39018 -0.46212 -0.53343 -0.60401 -0.67378 -0.74263 -0.81048 -0.87723 -0.94279 -1.00708 -1.07000 -1.13146 -1.19140 -1.24972 -1.30635 -1.36120 -1.41421 -1.46531 -1.51442 -1.56147 -1.60642 -1.64918 -1.68971 -1.72795 -1.76384 -1.79735 -1.82842 -1.85701 -1.88309 -1.90661 -1.92755 -1.94588 -1.96157 -1.97460 -1.98496 -1.99263 -1.99759 -1.99985 -1.99940 -1.99624 -1.99037 -1.98181 -1.97056 -1.95663 -1.94006 -1.92086 -1.89906 -1.87468 -1.84776 -1.81834 -1.78645 -1.75214 -1.71546 -1.67645 -1.63517 -1.59167 -1.54602 -1.49827 -1.44849 -1.39675 -1.34312 -1.28766 -1.23046 -1.17160 -1.11114 -1.04918 -0.98580 -0.92108 -0.85511 -0.78798 -0.71979 -0.65062 -0.58057 -0.50973 -0.43820 -0.36608 -0.29346 -0.22044 -0.14713 -0.07361 0.00000 0.07361 0.14713 0.22044 0.29346 0.36608 0.43820 0.50973 0.58057 0.65062 0.71979 0.78798 0.85511 0.92108 0.98580 1.04918 1.11114 1.17160 1.23046 1.28766 1.34312 1.39675 1.44849 1.49827 1.54602 1.59167 1.63517 1.67645 1.71546 1.75214 1.78645 1.81834 1.84776 1.87468 1.89906 1.92086 1.94006 1.95663 1.97056 1.98181 1.99037 1.99624 1.99940 1.99985 1.99759 1.99263 1.98496 1.97460 1.96157 1.94588 1.92755 1.90661 1.88309 1.85701 1.82842 1.79735 1.76384 1.72795 1.68971 1.64918 1.60642 1.56147 1.51442 1.46531 1.41421 1.36120 1.30635 1.24972 1.19140 1.13146 1.07000 1.00708 0.94279 0.87723 0.81048 0.74263 0.67378 0.60401 0.53343 0.46212 0.39018 0.31772 0.24482 0.17159 0.09814 0.02454 -0.04908 -0.12264 -0.19603 -0.26916 -0.34192 -0.41422 -0.48596 -0.55704 -0.62736 -0.69684 -0.76537 -0.83286 -0.89922 -0.96437 -1.02821 -1.09065 -1.15162 -1.21102 -1.26879 -1.32483 -1.37908 -1.43146 -1.48190 -1.53033 -1.57669 -1.62091 -1.66294 -1.70271 -1.74017 -1.77528 -1.80798 -1.83823 -1.86599 -1.89121 -1.91388 -1.93395 -1.95140 -1.96621 -1.97835 -1.98781 -1.99458 -1.99864 -2.00000 -1.99864 -1.99458 -1.98781 -1.97835 -1.96621 -1.95140 -1.93395 -1.91388 -1.89121 -1.86599 -1.83823 -1.80798 -1.77528 -1.74017 -1.70271 -1.66294 -1.62091 -1.57669 -1.53033 -1.48190 -1.43146 -1.37908 -1.32483 -1.26879 -1.21102 -1.15162 -1.09065 -1.02821 -0.96437 -0.89922 -0.83286 -0.76537 -0.69684 -0.62736 -0.55704 -0.48596 -0.41422 -0.34192 -0.26916 -0.19603 -0.12264 -0.04908 0.02454 0.09814 0.17159 0.24482 0.31772 0.39018 0.46212 0.53343 0.60401 0.67378 0.74263 0.81048 0.87723 0.94279 1.00708 1.07000 1.13146 1.19140 1.24972 1.30635 1.36120 1.41421 1.46531 1.51442 1.56147 1.60642 1.64918 1.68971 1.72795 1.76384 1.79735 1.82842 1.85701 1.88309 1.90661 1.92755 1.94588 1.96157 1.97460 1.98496 1.99263 1.99759 1.99985 1.99940 1.99624 1.99037 1.98181 1.97056 1.95663 1.94006 1.92086 1.89906 1.87468 1.84776 1.81834 1.78645 1.75214 1.71546 1.67645 1.63517 1.59167 1.54602 1.49827 1.44849 1.39675 1.34312 1.28766 1.23046 1.17160 1.11114 1.04918 0.98580 0.92108 0.85511 0.78798 0.71979 0.65062 0.58057 0.50973 0.43820 0.36608 0.29346 0.22044 0.14713 0.07361 0.00000 -0.07361 -0.14713 -0.22044 -0.29346 -0.36608 -0.43820 -0.50973 -0.58057 -0.65062 -0.71979 -0.78798 -0.85511 -0.92108 -0.98580 -1.04918 -1.11114 -1.17160 -1.23046 -1.28766 -1.34312 -1.39675 -1.44849 -1.49827 -1.54602 -1.59167 -1.63517 -1.67645 -1.71546 -1.75214 -1.78645 -1.81834 -1.84776 -1.87468 -1.89906 -1.92086 -1.94006 -1.95663 -1.97056 -1.98181 -1.99037 -1.99624 -1.99940 -1.99985 -1.99759 -1.99263 -1.98496 -1.97460 -1.96157 -1.94588 -1.92755 -1.90661 -1.88309 -1.85701 -1.82842 -1.79735 -1.76384 -1.72795 -1.68971 -1.64918 -1.60642 -1.56147 -1.51442 -1.46531 -1.41421 -1.36120 -1.30635 -1.24972 -1.19140 -1.13146 -1.07000 -1.00708 -0.94279 -0.87723 -0.81048 -0.74263 -0.67378 -0.60401 -0.53343 -0.46212 -0.39018 -0.31772 -0.24482 -0.17159 -0.09814 -0.02454 0.04908 0.12264 0.19603 0.26916 0.34192 0.41422 0.48596 0.55704 0.62736 0.69684 0.76537 0.83286 0.89922 0.96437 1.02821 1.09065 1.15162 1.21102 1.26879 1.32483 1.37908 1.43146 1.48190 1.53033 1.57669 1.62091 1.66294 1.70271 1.74017 1.77528 1.80798 1.83823 1.86599 1.89121 1.91388 1.93395 1.95140 1.96621 1.97835 1.98781 1.99458 1.99864 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... TT........... 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E511 2.00000 -1.99996 1.99985 -1.99966 1.99940 -1.99906 1.99864 -1.99816 1.99759 -1.99695 1.99624 -1.99545 1.99458 -1.99364 1.99263 -1.99153 1.99037 -1.98913 1.98781 -1.98642 1.98496 -1.98342 1.98181 -1.98012 1.97835 -1.97652 1.97460 -1.97262 1.97056 -1.96842 1.96621 -1.96393 1.96157 -1.95914 1.95663 -1.95406 1.95140 -1.94868 1.94588 -1.94301 1.94006 -1.93704 1.93395 -1.93079 1.92755 -1.92424 1.92086 -1.91741 1.91388 -1.91028 1.90661 -1.90287 1.89906 -1.89517 1.89121 -1.88719 1.88309 -1.87892 1.87468 -1.87037 1.86599 -1.86153 1.85701 -1.85242 1.84776 -1.84303 1.83823 -1.83336 1.82842 -1.82341 1.81834 -1.81319 1.80798 -1.80270 1.79735 -1.79193 1.78645 -1.78090 1.77528 -1.76959 1.76384 -1.75802 1.75214 -1.74619 1.74017 -1.73409 1.72795 -1.72173 1.71546 -1.70912 1.70271 -1.69624 1.68971 -1.68311 1.67645 -1.66973 1.66294 -1.65609 1.64918 -1.64221 1.63517 -1.62807 1.62091 -1.61370 1.60642 -1.59907 1.59167 -1.58421 1.57669 -1.56911 1.56147 -1.55378 1.54602 -1.53821 1.53033 -1.52240 1.51442 -1.50637 1.49827 -1.49012 1.48190 -1.47363 1.46531 -1.45693 1.44849 -1.44001 1.43146 -1.42286 1.41421 -1.40551 1.39675 -1.38794 1.37908 -1.37017 1.36120 -1.35219 1.34312 -1.33400 1.32483 -1.31561 1.30635 -1.29703 1.28766 -1.27825 1.26879 -1.25928 1.24972 -1.24011 1.23046 -1.22077 1.21102 -1.20123 1.19140 -1.18152 1.17160 -1.16163 1.15162 -1.14156 1.13146 -1.12132 1.11114 -1.10092 1.09065 -1.08034 1.07000 -1.05961 1.04918 -1.03871 1.02821 -1.01766 1.00708 -0.99646 0.98580 -0.97510 0.96437 -0.95360 0.94279 -0.93195 0.92108 -0.91017 0.89922 -0.88824 0.87723 -0.86619 0.85511 -0.84400 0.83286 -0.82169 0.81048 -0.79925 0.78798 -0.77669 0.76537 -0.75401 0.74263 -0.73123 0.71979 -0.70833 0.69684 -0.68532 0.67378 -0.66221 0.65062 -0.63900 0.62736 -0.61570 0.60401 -0.59230 0.58057 -0.56882 0.55704 -0.54524 0.53343 -0.52159 0.50973 -0.49786 0.48596 -0.47405 0.46212 -0.45017 0.43820 -0.42622 0.41422 -0.40221 0.39018 -0.37814 0.36608 -0.35401 0.34192 -0.32983 0.31772 -0.30559 0.29346 -0.28132 0.26916 -0.25700 0.24482 -0.23264 0.22044 -0.20824 0.19603 -0.18382 0.17159 -0.15936 0.14713 -0.13489 0.12264 -0.11039 0.09814 -0.08588 0.07361 -0.06135 0.04908 -0.03681 0.02454 -0.01227 0.00000 0.01227 -0.02454 0.03681 -0.04908 0.06135 -0.07361 0.08588 -0.09814 0.11039 -0.12264 0.13489 -0.14713 0.15936 -0.17159 0.18382 -0.19603 0.20824 -0.22044 0.23264 -0.24482 0.25700 -0.26916 0.28132 -0.29346 0.30559 -0.31772 0.32983 -0.34192 0.35401 -0.36608 0.37814 -0.39018 0.40221 -0.41422 0.42622 -0.43820 0.45017 -0.46212 0.47405 -0.48596 0.49786 -0.50973 0.52159 -0.53343 0.54524 -0.55704 0.56882 -0.58057 0.59230 -0.60401 0.61570 -0.62736 0.63900 -0.65062 0.66221 -0.67378 0.68532 -0.69684 0.70833 -0.71979 0.73123 -0.74263 0.75401 -0.76537 0.77669 -0.78798 0.79925 -0.81048 0.82169 -0.83286 0.84400 -0.85511 0.86619 -0.87723 0.88824 -0.89922 0.91017 -0.92108 0.93195 -0.94279 0.95360 -0.96437 0.97510 -0.98580 0.99646 -1.00708 1.01766 -1.02821 1.03871 -1.04918 1.05961 -1.07000 1.08034 -1.09065 1.10092 -1.11114 1.12132 -1.13146 1.14156 -1.15162 1.16163 -1.17160 1.18152 -1.19140 1.20123 -1.21102 1.22077 -1.23046 1.24011 -1.24972 1.25928 -1.26879 1.27825 -1.28766 1.29703 -1.30635 1.31561 -1.32483 1.33400 -1.34312 1.35219 -1.36120 1.37017 -1.37908 1.38794 -1.39675 1.40551 -1.41421 1.42286 -1.43146 1.44001 -1.44849 1.45693 -1.46531 1.47363 -1.48190 1.49012 -1.49827 1.50637 -1.51442 1.52240 -1.53033 1.53821 -1.54602 1.55378 -1.56147 1.56911 -1.57669 1.58421 -1.59167 1.59907 -1.60642 1.61370 -1.62091 1.62807 -1.63517 1.64221 -1.64918 1.65609 -1.66294 1.66973 -1.67645 1.68311 -1.68971 1.69624 -1.70271 1.70912 -1.71546 1.72173 -1.72795 1.73409 -1.74017 1.74619 -1.75214 1.75802 -1.76384 1.76959 -1.77528 1.78090 -1.78645 1.79193 -1.79735 1.80270 -1.80798 1.81319 -1.81834 1.82341 -1.82842 1.83336 -1.83823 1.84303 -1.84776 1.85242 -1.85701 1.86153 -1.86599 1.87037 -1.87468 1.87892 -1.88309 1.88719 -1.89121 1.89517 -1.89906 1.90287 -1.90661 1.91028 -1.91388 1.91741 -1.92086 1.92424 -1.92755 1.93079 -1.93395 1.93704 -1.94006 1.94301 -1.94588 1.94868 -1.95140 1.95406 -1.95663 1.95914 -1.96157 1.96393 -1.96621 1.96842 -1.97056 1.97262 -1.97460 1.97652 -1.97835 1.98012 -1.98181 1.98342 -1.98496 1.98642 -1.98781 1.98913 -1.99037 1.99153 -1.99263 1.99364 -1.99458 1.99545 -1.99624 1.99695 -1.99759 1.99816 -1.99864 1.99906 -1.99940 1.99966 -1.99985 1.99996 -2.00000 0.00000 0.00000 TT. ... ..TT. ....... ......TT. ........... ..........TT. Irrational character values: 1.999962350565 = 2*cos(2*π/1024) = 2*cos(π/512) 1.999849403678 = 2*cos(4*π/1024) = 2*cos(π/256) = √2+√2+√2+√2+√2+√2+√2 1.999661163592 = 2*cos(6*π/1024) = 2*cos(3*π/512) 1.999397637392 = 2*cos(8*π/1024) = 2*cos(π/128) = √2+√2+√2+√2+√2+√2 1.999058835002 = 2*cos(10*π/1024) = 2*cos(5*π/512) 1.998644769177 = 2*cos(12*π/1024) = 2*cos(3*π/256) = √2+√2+√2+√2+√2+√2−√2 1.998155455505 = 2*cos(14*π/1024) = 2*cos(7*π/512) 1.997590912410 = 2*cos(16*π/1024) = 2*cos(π/64) = √2+√2+√2+√2+√2 1.996951161147 = 2*cos(18*π/1024) = 2*cos(9*π/512) 1.996236225800 = 2*cos(20*π/1024) = 2*cos(5*π/256) = √2+√2+√2+√2+√2−√2−√2 1.995446133288 = 2*cos(22*π/1024) = 2*cos(11*π/512) 1.994580913357 = 2*cos(24*π/1024) = 2*cos(3*π/128) = √2+√2+√2+√2+√2−√2 1.993640598582 = 2*cos(26*π/1024) = 2*cos(13*π/512) 1.992625224366 = 2*cos(28*π/1024) = 2*cos(7*π/256) = √2+√2+√2+√2+√2−√2+√2 1.991534828935 = 2*cos(30*π/1024) = 2*cos(15*π/512) 1.990369453344 = 2*cos(32*π/1024) = 2*cos(π/32) = √2+√2+√2+√2 1.989129141469 = 2*cos(34*π/1024) = 2*cos(17*π/512) 1.987813940005 = 2*cos(36*π/1024) = 2*cos(9*π/256) = √2+√2+√2+√2−√2−√2+√2 1.986423898470 = 2*cos(38*π/1024) = 2*cos(19*π/512) 1.984959069197 = 2*cos(40*π/1024) = 2*cos(5*π/128) = √2+√2+√2+√2−√2−√2 1.983419507338 = 2*cos(42*π/1024) = 2*cos(21*π/512) 1.981805270856 = 2*cos(44*π/1024) = 2*cos(11*π/256) = √2+√2+√2+√2−√2−√2−√2 1.980116420525 = 2*cos(46*π/1024) = 2*cos(23*π/512) 1.978353019930 = 2*cos(48*π/1024) = 2*cos(3*π/64) = √2+√2+√2+√2−√2 1.976515135461 = 2*cos(50*π/1024) = 2*cos(25*π/512) 1.974602836316 = 2*cos(52*π/1024) = 2*cos(13*π/256) = √2+√2+√2+√2−√2+√2−√2 1.972616194489 = 2*cos(54*π/1024) = 2*cos(27*π/512) 1.970555284778 = 2*cos(56*π/1024) = 2*cos(7*π/128) = √2+√2+√2+√2−√2+√2 1.968420184774 = 2*cos(58*π/1024) = 2*cos(29*π/512) 1.966210974862 = 2*cos(60*π/1024) = 2*cos(15*π/256) = √2+√2+√2+√2−√2+√2+√2 1.963927738219 = 2*cos(62*π/1024) = 2*cos(31*π/512) 1.961570560806 = 2*cos(64*π/1024) = 2*cos(π/16) = √2+√2+√2 1.959139531371 = 2*cos(66*π/1024) = 2*cos(33*π/512) 1.956634741439 = 2*cos(68*π/1024) = 2*cos(17*π/256) = √2+√2+√2−√2−√2+√2+√2 1.954056285316 = 2*cos(70*π/1024) = 2*cos(35*π/512) 1.951404260077 = 2*cos(72*π/1024) = 2*cos(9*π/128) = √2+√2+√2−√2−√2+√2 1.948678765571 = 2*cos(74*π/1024) = 2*cos(37*π/512) 1.945879904411 = 2*cos(76*π/1024) = 2*cos(19*π/256) = √2+√2+√2−√2−√2+√2−√2 1.943007781973 = 2*cos(78*π/1024) = 2*cos(39*π/512) 1.940062506389 = 2*cos(80*π/1024) = 2*cos(5*π/64) = √2+√2+√2−√2−√2 1.937044188549 = 2*cos(82*π/1024) = 2*cos(41*π/512) 1.933952942090 = 2*cos(84*π/1024) = 2*cos(21*π/256) = √2+√2+√2−√2−√2−√2−√2 1.930788883395 = 2*cos(86*π/1024) = 2*cos(43*π/512) 1.927552131591 = 2*cos(88*π/1024) = 2*cos(11*π/128) = √2+√2+√2−√2−√2−√2 1.924242808538 = 2*cos(90*π/1024) = 2*cos(45*π/512) 1.920861038831 = 2*cos(92*π/1024) = 2*cos(23*π/256) = √2+√2+√2−√2−√2−√2+√2 1.917406949792 = 2*cos(94*π/1024) = 2*cos(47*π/512) 1.913880671464 = 2*cos(96*π/1024) = 2*cos(3*π/32) = √2+√2+√2−√2 1.910282336612 = 2*cos(98*π/1024) = 2*cos(49*π/512) 1.906612080708 = 2*cos(100*π/1024) = 2*cos(25*π/256) = √2+√2+√2−√2+√2−√2+√2 1.902870041938 = 2*cos(102*π/1024) = 2*cos(51*π/512) 1.899056361186 = 2*cos(104*π/1024) = 2*cos(13*π/128) = √2+√2+√2−√2+√2−√2 1.895171182035 = 2*cos(106*π/1024) = 2*cos(53*π/512) 1.891214650761 = 2*cos(108*π/1024) = 2*cos(27*π/256) = √2+√2+√2−√2+√2−√2−√2 1.887186916324 = 2*cos(110*π/1024) = 2*cos(55*π/512) 1.883088130366 = 2*cos(112*π/1024) = 2*cos(7*π/64) = √2+√2+√2−√2+√2 1.878918447204 = 2*cos(114*π/1024) = 2*cos(57*π/512) 1.874678023825 = 2*cos(116*π/1024) = 2*cos(29*π/256) = √2+√2+√2−√2+√2+√2−√2 1.870367019878 = 2*cos(118*π/1024) = 2*cos(59*π/512) 1.865985597669 = 2*cos(120*π/1024) = 2*cos(15*π/128) = √2+√2+√2−√2+√2+√2 1.861533922158 = 2*cos(122*π/1024) = 2*cos(61*π/512) 1.857012160946 = 2*cos(124*π/1024) = 2*cos(31*π/256) = √2+√2+√2−√2+√2+√2+√2 1.852420484277 = 2*cos(126*π/1024) = 2*cos(63*π/512) 1.847759065023 = 2*cos(128*π/1024) = 2*cos(π/8) = √2+√2 1.843028078684 = 2*cos(130*π/1024) = 2*cos(65*π/512) 1.838227703380 = 2*cos(132*π/1024) = 2*cos(33*π/256) = √2+√2−√2−√2+√2+√2+√2 1.833358119842 = 2*cos(134*π/1024) = 2*cos(67*π/512) 1.828419511407 = 2*cos(136*π/1024) = 2*cos(17*π/128) = √2+√2−√2−√2+√2+√2 1.823412064011 = 2*cos(138*π/1024) = 2*cos(69*π/512) 1.818335966181 = 2*cos(140*π/1024) = 2*cos(35*π/256) = √2+√2−√2−√2+√2+√2−√2 1.813191409030 = 2*cos(142*π/1024) = 2*cos(71*π/512) 1.807978586247 = 2*cos(144*π/1024) = 2*cos(9*π/64) = √2+√2−√2−√2+√2 1.802697694092 = 2*cos(146*π/1024) = 2*cos(73*π/512) 1.797348931388 = 2*cos(148*π/1024) = 2*cos(37*π/256) = √2+√2−√2−√2+√2−√2−√2 1.791932499512 = 2*cos(150*π/1024) = 2*cos(75*π/512) 1.786448602391 = 2*cos(152*π/1024) = 2*cos(19*π/128) = √2+√2−√2−√2+√2−√2 1.780897446490 = 2*cos(154*π/1024) = 2*cos(77*π/512) 1.775279240806 = 2*cos(156*π/1024) = 2*cos(39*π/256) = √2+√2−√2−√2+√2−√2+√2 1.769594196862 = 2*cos(158*π/1024) = 2*cos(79*π/512) 1.763842528697 = 2*cos(160*π/1024) = 2*cos(5*π/32) = √2+√2−√2−√2 1.758024452857 = 2*cos(162*π/1024) = 2*cos(81*π/512) 1.752140188391 = 2*cos(164*π/1024) = 2*cos(41*π/256) = √2+√2−√2−√2−√2−√2+√2 1.746189956837 = 2*cos(166*π/1024) = 2*cos(83*π/512) 1.740173982217 = 2*cos(168*π/1024) = 2*cos(21*π/128) = √2+√2−√2−√2−√2−√2 1.734092491031 = 2*cos(170*π/1024) = 2*cos(85*π/512) 1.727945712243 = 2*cos(172*π/1024) = 2*cos(43*π/256) = √2+√2−√2−√2−√2−√2−√2 1.721733877276 = 2*cos(174*π/1024) = 2*cos(87*π/512) 1.715457220001 = 2*cos(176*π/1024) = 2*cos(11*π/64) = √2+√2−√2−√2−√2 1.709115976731 = 2*cos(178*π/1024) = 2*cos(89*π/512) 1.702710386211 = 2*cos(180*π/1024) = 2*cos(45*π/256) = √2+√2−√2−√2−√2+√2−√2 1.696240689607 = 2*cos(182*π/1024) = 2*cos(91*π/512) 1.689707130499 = 2*cos(184*π/1024) = 2*cos(23*π/128) = √2+√2−√2−√2−√2+√2 1.683109954874 = 2*cos(186*π/1024) = 2*cos(93*π/512) 1.676449411110 = 2*cos(188*π/1024) = 2*cos(47*π/256) = √2+√2−√2−√2−√2+√2+√2 1.669725749973 = 2*cos(190*π/1024) = 2*cos(95*π/512) 1.662939224605 = 2*cos(192*π/1024) = 2*cos(3*π/16) = √2+√2−√2 1.656090090516 = 2*cos(194*π/1024) = 2*cos(97*π/512) 1.649178605570 = 2*cos(196*π/1024) = 2*cos(49*π/256) = √2+√2−√2+√2−√2+√2+√2 1.642205029982 = 2*cos(198*π/1024) = 2*cos(99*π/512) 1.635169626303 = 2*cos(200*π/1024) = 2*cos(25*π/128) = √2+√2−√2+√2−√2+√2 1.628072659412 = 2*cos(202*π/1024) = 2*cos(101*π/512) 1.620914396505 = 2*cos(204*π/1024) = 2*cos(51*π/256) = √2+√2−√2+√2−√2+√2−√2 1.613695107088 = 2*cos(206*π/1024) = 2*cos(103*π/512) 1.606415062961 = 2*cos(208*π/1024) = 2*cos(13*π/64) = √2+√2−√2+√2−√2 1.599074538216 = 2*cos(210*π/1024) = 2*cos(105*π/512) 1.591673809218 = 2*cos(212*π/1024) = 2*cos(53*π/256) = √2+√2−√2+√2−√2−√2−√2 1.584213154600 = 2*cos(214*π/1024) = 2*cos(107*π/512) 1.576692855253 = 2*cos(216*π/1024) = 2*cos(27*π/128) = √2+√2−√2+√2−√2−√2 1.569113194311 = 2*cos(218*π/1024) = 2*cos(109*π/512) 1.561474457144 = 2*cos(220*π/1024) = 2*cos(55*π/256) = √2+√2−√2+√2−√2−√2+√2 1.553776931346 = 2*cos(222*π/1024) = 2*cos(111*π/512) 1.546020906725 = 2*cos(224*π/1024) = 2*cos(7*π/32) = √2+√2−√2+√2 1.538206675291 = 2*cos(226*π/1024) = 2*cos(113*π/512) 1.530334531245 = 2*cos(228*π/1024) = 2*cos(57*π/256) = √2+√2−√2+√2+√2−√2+√2 1.522404770969 = 2*cos(230*π/1024) = 2*cos(115*π/512) 1.514417693013 = 2*cos(232*π/1024) = 2*cos(29*π/128) = √2+√2−√2+√2+√2−√2 1.506373598087 = 2*cos(234*π/1024) = 2*cos(117*π/512) 1.498272789047 = 2*cos(236*π/1024) = 2*cos(59*π/256) = √2+√2−√2+√2+√2−√2−√2 1.490115570883 = 2*cos(238*π/1024) = 2*cos(119*π/512) 1.481902250710 = 2*cos(240*π/1024) = 2*cos(15*π/64) = √2+√2−√2+√2+√2 1.473633137755 = 2*cos(242*π/1024) = 2*cos(121*π/512) 1.465308543345 = 2*cos(244*π/1024) = 2*cos(61*π/256) = √2+√2−√2+√2+√2+√2−√2 1.456928780896 = 2*cos(246*π/1024) = 2*cos(123*π/512) 1.448494165903 = 2*cos(248*π/1024) = 2*cos(31*π/128) = √2+√2−√2+√2+√2+√2 1.440005015923 = 2*cos(250*π/1024) = 2*cos(125*π/512) 1.431461650568 = 2*cos(252*π/1024) = 2*cos(63*π/256) = √2+√2−√2+√2+√2+√2+√2 1.422864391490 = 2*cos(254*π/1024) = 2*cos(127*π/512) 1.414213562373 = 2*cos(256*π/1024) = 2*cos(π/4) = √2 1.405509488914 = 2*cos(258*π/1024) = 2*cos(129*π/512) 1.396752498818 = 2*cos(260*π/1024) = 2*cos(65*π/256) = √2−√2−√2+√2+√2+√2+√2 1.387942921779 = 2*cos(262*π/1024) = 2*cos(131*π/512) 1.379081089474 = 2*cos(264*π/1024) = 2*cos(33*π/128) = √2−√2−√2+√2+√2+√2 1.370167335545 = 2*cos(266*π/1024) = 2*cos(133*π/512) 1.361201995591 = 2*cos(268*π/1024) = 2*cos(67*π/256) = √2−√2−√2+√2+√2+√2−√2 1.352185407151 = 2*cos(270*π/1024) = 2*cos(135*π/512) 1.343117909694 = 2*cos(272*π/1024) = 2*cos(17*π/64) = √2−√2−√2+√2+√2 1.333999844607 = 2*cos(274*π/1024) = 2*cos(137*π/512) 1.324831555180 = 2*cos(276*π/1024) = 2*cos(69*π/256) = √2−√2−√2+√2+√2−√2−√2 1.315613386594 = 2*cos(278*π/1024) = 2*cos(139*π/512) 1.306345685908 = 2*cos(280*π/1024) = 2*cos(35*π/128) = √2−√2−√2+√2+√2−√2 1.297028802044 = 2*cos(282*π/1024) = 2*cos(141*π/512) 1.287663085780 = 2*cos(284*π/1024) = 2*cos(71*π/256) = √2−√2−√2+√2+√2−√2+√2 1.278248889728 = 2*cos(286*π/1024) = 2*cos(143*π/512) 1.268786568327 = 2*cos(288*π/1024) = 2*cos(9*π/32) = √2−√2−√2+√2 1.259276477830 = 2*cos(290*π/1024) = 2*cos(145*π/512) 1.249718976285 = 2*cos(292*π/1024) = 2*cos(73*π/256) = √2−√2−√2+√2−√2−√2+√2 1.240114423527 = 2*cos(294*π/1024) = 2*cos(147*π/512) 1.230463181161 = 2*cos(296*π/1024) = 2*cos(37*π/128) = √2−√2−√2+√2−√2−√2 1.220765612553 = 2*cos(298*π/1024) = 2*cos(149*π/512) 1.211022082809 = 2*cos(300*π/1024) = 2*cos(75*π/256) = √2−√2−√2+√2−√2−√2−√2 1.201232958768 = 2*cos(302*π/1024) = 2*cos(151*π/512) 1.191398608985 = 2*cos(304*π/1024) = 2*cos(19*π/64) = √2−√2−√2+√2−√2 1.181519403718 = 2*cos(306*π/1024) = 2*cos(153*π/512) 1.171595714913 = 2*cos(308*π/1024) = 2*cos(77*π/256) = √2−√2−√2+√2−√2+√2−√2 1.161627916192 = 2*cos(310*π/1024) = 2*cos(155*π/512) 1.151616382836 = 2*cos(312*π/1024) = 2*cos(39*π/128) = √2−√2−√2+√2−√2+√2 1.141561491774 = 2*cos(314*π/1024) = 2*cos(157*π/512) 1.131463621567 = 2*cos(316*π/1024) = 2*cos(79*π/256) = √2−√2−√2+√2−√2+√2+√2 1.121323152395 = 2*cos(318*π/1024) = 2*cos(159*π/512) 1.111140466039 = 2*cos(320*π/1024) = 2*cos(5*π/16) = √2−√2−√2 1.100915945873 = 2*cos(322*π/1024) = 2*cos(161*π/512) 1.090649976844 = 2*cos(324*π/1024) = 2*cos(81*π/256) = √2−√2−√2−√2−√2+√2+√2 1.080342945460 = 2*cos(326*π/1024) = 2*cos(163*π/512) 1.069995239774 = 2*cos(328*π/1024) = 2*cos(41*π/128) = √2−√2−√2−√2−√2+√2 1.059607249373 = 2*cos(330*π/1024) = 2*cos(165*π/512) 1.049179365357 = 2*cos(332*π/1024) = 2*cos(83*π/256) = √2−√2−√2−√2−√2+√2−√2 1.038711980331 = 2*cos(334*π/1024) = 2*cos(167*π/512) 1.028205488386 = 2*cos(336*π/1024) = 2*cos(21*π/64) = √2−√2−√2−√2−√2 1.017660285086 = 2*cos(338*π/1024) = 2*cos(169*π/512) 1.007076767451 = 2*cos(340*π/1024) = 2*cos(85*π/256) = √2−√2−√2−√2−√2−√2−√2 0.996455333946 = 2*cos(342*π/1024) = 2*cos(171*π/512) 0.985796384460 = 2*cos(344*π/1024) = 2*cos(43*π/128) = √2−√2−√2−√2−√2−√2 0.975100320297 = 2*cos(346*π/1024) = 2*cos(173*π/512) 0.964367544158 = 2*cos(348*π/1024) = 2*cos(87*π/256) = √2−√2−√2−√2−√2−√2+√2 0.953598460127 = 2*cos(350*π/1024) = 2*cos(175*π/512) 0.942793473652 = 2*cos(352*π/1024) = 2*cos(11*π/32) = √2−√2−√2−√2 0.931952991536 = 2*cos(354*π/1024) = 2*cos(177*π/512) 0.921077421916 = 2*cos(356*π/1024) = 2*cos(89*π/256) = √2−√2−√2−√2+√2−√2+√2 0.910167174253 = 2*cos(358*π/1024) = 2*cos(179*π/512) 0.899222659309 = 2*cos(360*π/1024) = 2*cos(45*π/128) = √2−√2−√2−√2+√2−√2 0.888244289141 = 2*cos(362*π/1024) = 2*cos(181*π/512) 0.877232477077 = 2*cos(364*π/1024) = 2*cos(91*π/256) = √2−√2−√2−√2+√2−√2−√2 0.866187637706 = 2*cos(366*π/1024) = 2*cos(183*π/512) 0.855110186861 = 2*cos(368*π/1024) = 2*cos(23*π/64) = √2−√2−√2−√2+√2 0.844000541600 = 2*cos(370*π/1024) = 2*cos(185*π/512) 0.832859120195 = 2*cos(372*π/1024) = 2*cos(93*π/256) = √2−√2−√2−√2+√2+√2−√2 0.821686342116 = 2*cos(374*π/1024) = 2*cos(187*π/512) 0.810482628010 = 2*cos(376*π/1024) = 2*cos(47*π/128) = √2−√2−√2−√2+√2+√2 0.799248399691 = 2*cos(378*π/1024) = 2*cos(189*π/512) 0.787984080122 = 2*cos(380*π/1024) = 2*cos(95*π/256) = √2−√2−√2−√2+√2+√2+√2 0.776690093398 = 2*cos(382*π/1024) = 2*cos(191*π/512) 0.765366864730 = 2*cos(384*π/1024) = 2*cos(3*π/8) = √2−√2 0.754014820433 = 2*cos(386*π/1024) = 2*cos(193*π/512) 0.742634387904 = 2*cos(388*π/1024) = 2*cos(97*π/256) = √2−√2+√2−√2+√2+√2+√2 0.731225995610 = 2*cos(390*π/1024) = 2*cos(195*π/512) 0.719790073070 = 2*cos(392*π/1024) = 2*cos(49*π/128) = √2−√2+√2−√2+√2+√2 0.708327050841 = 2*cos(394*π/1024) = 2*cos(197*π/512) 0.696837360499 = 2*cos(396*π/1024) = 2*cos(99*π/256) = √2−√2+√2−√2+√2+√2−√2 0.685321434624 = 2*cos(398*π/1024) = 2*cos(199*π/512) 0.673779706784 = 2*cos(400*π/1024) = 2*cos(25*π/64) = √2−√2+√2−√2+√2 0.662212611520 = 2*cos(402*π/1024) = 2*cos(201*π/512) 0.650620584325 = 2*cos(404*π/1024) = 2*cos(101*π/256) = √2−√2+√2−√2+√2−√2−√2 0.639004061632 = 2*cos(406*π/1024) = 2*cos(203*π/512) 0.627363480798 = 2*cos(408*π/1024) = 2*cos(51*π/128) = √2−√2+√2−√2+√2−√2 0.615699280083 = 2*cos(410*π/1024) = 2*cos(205*π/512) 0.604011898638 = 2*cos(412*π/1024) = 2*cos(103*π/256) = √2−√2+√2−√2+√2−√2+√2 0.592301776487 = 2*cos(414*π/1024) = 2*cos(207*π/512) 0.580569354509 = 2*cos(416*π/1024) = 2*cos(13*π/32) = √2−√2+√2−√2 0.568815074423 = 2*cos(418*π/1024) = 2*cos(209*π/512) 0.557039378770 = 2*cos(420*π/1024) = 2*cos(105*π/256) = √2−√2+√2−√2−√2−√2+√2 0.545242710900 = 2*cos(422*π/1024) = 2*cos(211*π/512) 0.533425514950 = 2*cos(424*π/1024) = 2*cos(53*π/128) = √2−√2+√2−√2−√2−√2 0.521588235831 = 2*cos(426*π/1024) = 2*cos(213*π/512) 0.509731319209 = 2*cos(428*π/1024) = 2*cos(107*π/256) = √2−√2+√2−√2−√2−√2−√2 0.497855211491 = 2*cos(430*π/1024) = 2*cos(215*π/512) 0.485960359807 = 2*cos(432*π/1024) = 2*cos(27*π/64) = √2−√2+√2−√2−√2 0.474047211989 = 2*cos(434*π/1024) = 2*cos(217*π/512) 0.462116216561 = 2*cos(436*π/1024) = 2*cos(109*π/256) = √2−√2+√2−√2−√2+√2−√2 0.450167822720 = 2*cos(438*π/1024) = 2*cos(219*π/512) 0.438202480314 = 2*cos(440*π/1024) = 2*cos(55*π/128) = √2−√2+√2−√2−√2+√2 0.426220639832 = 2*cos(442*π/1024) = 2*cos(221*π/512) 0.414222752384 = 2*cos(444*π/1024) = 2*cos(111*π/256) = √2−√2+√2−√2−√2+√2+√2 0.402209269684 = 2*cos(446*π/1024) = 2*cos(223*π/512) 0.390180644032 = 2*cos(448*π/1024) = 2*cos(7*π/16) = √2−√2+√2 0.378137328300 = 2*cos(450*π/1024) = 2*cos(225*π/512) 0.366079775910 = 2*cos(452*π/1024) = 2*cos(113*π/256) = √2−√2+√2+√2−√2+√2+√2 0.354008440824 = 2*cos(454*π/1024) = 2*cos(227*π/512) 0.341923777521 = 2*cos(456*π/1024) = 2*cos(57*π/128) = √2−√2+√2+√2−√2+√2 0.329826240980 = 2*cos(458*π/1024) = 2*cos(229*π/512) 0.317716286668 = 2*cos(460*π/1024) = 2*cos(115*π/256) = √2−√2+√2+√2−√2+√2−√2 0.305594370517 = 2*cos(462*π/1024) = 2*cos(231*π/512) 0.293460948911 = 2*cos(464*π/1024) = 2*cos(29*π/64) = √2−√2+√2+√2−√2 0.281316478666 = 2*cos(466*π/1024) = 2*cos(233*π/512) 0.269161417014 = 2*cos(468*π/1024) = 2*cos(117*π/256) = √2−√2+√2+√2−√2−√2−√2 0.256996221588 = 2*cos(470*π/1024) = 2*cos(235*π/512) 0.244821350398 = 2*cos(472*π/1024) = 2*cos(59*π/128) = √2−√2+√2+√2−√2−√2 0.232637261824 = 2*cos(474*π/1024) = 2*cos(237*π/512) 0.220444414588 = 2*cos(476*π/1024) = 2*cos(119*π/256) = √2−√2+√2+√2−√2−√2+√2 0.208243267744 = 2*cos(478*π/1024) = 2*cos(239*π/512) 0.196034280659 = 2*cos(480*π/1024) = 2*cos(15*π/32) = √2−√2+√2+√2 0.183817912994 = 2*cos(482*π/1024) = 2*cos(241*π/512) 0.171594624689 = 2*cos(484*π/1024) = 2*cos(121*π/256) = √2−√2+√2+√2+√2−√2+√2 0.159364875943 = 2*cos(486*π/1024) = 2*cos(243*π/512) 0.147129127199 = 2*cos(488*π/1024) = 2*cos(61*π/128) = √2−√2+√2+√2+√2−√2 0.134887839127 = 2*cos(490*π/1024) = 2*cos(245*π/512) 0.122641472604 = 2*cos(492*π/1024) = 2*cos(123*π/256) = √2−√2+√2+√2+√2−√2−√2 0.110390488699 = 2*cos(494*π/1024) = 2*cos(247*π/512) 0.098135348655 = 2*cos(496*π/1024) = 2*cos(31*π/64) = √2−√2+√2+√2+√2 0.085876513870 = 2*cos(498*π/1024) = 2*cos(249*π/512) 0.073614445883 = 2*cos(500*π/1024) = 2*cos(125*π/256) = √2−√2+√2+√2+√2+√2−√2 0.061349606353 = 2*cos(502*π/1024) = 2*cos(251*π/512) 0.049082457046 = 2*cos(504*π/1024) = 2*cos(63*π/128) = √2−√2+√2+√2+√2+√2 0.036813459812 = 2*cos(506*π/1024) = 2*cos(253*π/512) 0.024543076571 = 2*cos(508*π/1024) = 2*cos(127*π/256) = √2−√2+√2+√2+√2+√2+√2 0.012271769298 = 2*cos(510*π/1024) = 2*cos(255*π/512) Symmetry of Rotations and Cartesian products A1 d+g+i+k+m z2, z4, z6 A2 R Rz B2 p+f+h+j+l z, z3, z5 E1 p+f+h+j+l {x, y}, {xz2, yz2}, {xz4, yz4} E2 d+g+i+k+m {x2−y2, xy}, {z2(x2−y2), xyz2}, {z4(x2−y2), xyz4} E3 f+h+j+l {x(x2−3y2), y(3x2−y2)}, {xz2(x2−3y2), yz2(3x2−y2)} E4 g+i+k+m {(x2−y2)2−4x2y2, xy(x2−y2)}, {z2((x2−y2)2−4x2y2), xyz2(x2−y2)} E5 h+j+l {x(x2−(5+2√5)y2)(x2−(5−2√5)y2), y((5+2√5)x2−y2)((5−2√5)x2−y2)} E6 i+k+m {x2(x2−3y2)2−y2(3x2−y2)2, xy(x2−3y2)(3x2−y2)} E7 j+l E8 k+m E9 l E10 m E503 m E504 l E505 k+m E506 j+l E507 i+k+m {xz(x2−(5+2√5)y2)(x2−(5−2√5)y2), yz((5+2√5)x2−y2)((5−2√5)x2−y2)} E508 h+j+l {z((x2−y2)2−4x2y2), xyz(x2−y2)} E509 g+i+k+m {xz(x2−3y2), yz(3x2−y2)}, {xz3(x2−3y2), yz3(3x2−y2)} E510 f+h+j+l {z(x2−y2), xyz}, {z3(x2−y2), xyz3} E511 R+d+g+i+k+m {Rx, Ry}, {xz, yz}, {xz3, yz3}, {xz5, yz5} Notes: α The order of the D512d point group is 2048, and the order of the principal axis (S1024) is 1024. The group has 515 irreducible representations. β The D512d point group is isomorphic to C1024v and D1024. γ The D512d point group is generated by two symmetry elements, S1024 and either a perpendicular C2′ or a vertical σd. Also, the group may be generated from any C2′ plus any σd plane. δ The group contains one set of twofold symmetry axes (C2′) perpendicular to the principal (z) axis. Both x and y axes are members of that set. ε The single σd set of symmetry planes contains neither the xz nor the yz planes. ζ The lowest nonvanishing multipole moment in D512d is 4 (quadrupole moment). η This point group is non-Abelian (some symmetry operations are not commutative). Therefore, the character table contains multi-membered classes and degenerate irreducible representations. θ 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. ι The point group corresponds to a constructible polygon, as the order of the principal axis is a product of any number of different Fermat primes (3,5,17,257,65537) times an arbitrary power of two. Therefore, all characters have an algebraic degree which is a power of two and can be expressed as radicals involving only square roots and integer numbers. Some of these algebraic expressions, however, are too complicated to be included in the list above.
| D257d | ||
| D340d | ||
| C512 C512v C512h D512 D512h | D512d | S512 |
| D666d | ||
This Character Table for the D512d point group was created by Gernot Katzer.
For other groups and some explanations, see the Main Page.