```
The following is a list of all the Pisot numbers in the sample
interval (1.86,1.9), together with their beta-expansions and
related information about the complementary factor.

To explain the format, here is one entry:

------------------------------------------------------------

15, 6, 31, 1.87475497612152, NC, 22,

[ 1, 0, -1, -2, -2, -3, -3, -3, -2, -1, 0, 1, 1, 1, 1, 1 ]

111001:0100010101000110001000100111000

Quotient,

22    21    17    16    15    14    12    11    10    8    7    6    5
x   - x   + x   - x   + x   - x   + x   - x   + x   - x  + x  - x  + x  - x + 1

------------------------------------------------------------

The first line gives n,m,p,beta,type,q,
where n is the degree of beta, m and p are the prepreiod and period of
the beta expansion of 1, the type is C,NC or NR  meaning that the ``Quotient''
is cyclotomic, reciprocal but non-cyclotomic or non-reciprocal. q is
the degree of the quotient  R(x)/P(x)  of the characteristic polynomial
and the minimal polynomial, i.e. q = n - m - p.   The second line gives
the coefficients of the minimal polynomial, the third line is the beta
expansion and the last few lines are self-explanatory  (and missing if
the quotient is uninteresting).

1.8700000, 1.9000000

187   19
---, ----
100   10

maximum height, 100

initialized

10, 3, 9, 1.87007107568587, Cyc, 2, [ 1, -2, 0, 1, -1, 0, 0, 0, 0, -1, 1 ]

111:001000110

------------------------------------------------------------

8, 3, 5, 1.88166942008708, Cyc, 0, [ 1, -1, -1, -1, 0, -1, 0, 0, 1 ]

111:00110

------------------------------------------------------------

13, 6, 9, 1.87056996121905, Cyc, 2,

[ 1, -2, 0, 1, -1, 0, 0, 0, 0, -1, 1, 0, -1, 1 ]

111001:000111000

------------------------------------------------------------

16, 6, 19, 1.87056375138754, Cyc, 9,

[ 1, -2, 1, -2, 1, 0, 0, 1, -1, 1, -1, 0, 0, -1, 1, -1, 1 ]

111001:0001110000000111000

------------------------------------------------------------

22, 6, 22, 1.87083548713333, Cyc, 6,

[

1, -2, 1, -1, -1, 1, -2, 2, -1, 0, 2, -2, 2, -1, -1, 1, -2, 1, -1, 0, 1, -1, 1

]

111001:0010000100001000111000

------------------------------------------------------------

12, 6, 8, 1.87381019542557, Cyc, 2,

[ 1, -2, 0, 1, -1, 0, 0, 0, -1, 1, 0, -1, 1 ]

111001:00111000

------------------------------------------------------------

15, 6, 31, 1.87475497612152, NC, 22,

[ 1, 0, -1, -2, -2, -3, -3, -3, -2, -1, 0, 1, 1, 1, 1, 1 ]

111001:0100010101000110001000100111000

Quotient,

22    21    17    16    15    14    12    11    10    8    7    6    5
x   - x   + x   - x   + x   - x   + x   - x   + x   - x  + x  - x  + x  - x + 1

------------------------------------------------------------

14, 6, 13, 1.87426999402814, Cyc, 5,

[ 1, -2, 1, -2, 1, 0, 0, 1, -1, 0, 0, -1, 1, -1, 1 ]

111001:0100000111000

------------------------------------------------------------

11, 6, 7, 1.87975376563615, Cyc, 2, [ 1, -2, 0, 1, -1, 0, 0, -1, 1, 0, -1, 1 ]

111001:0111000

------------------------------------------------------------

12, 6, 18, 1.88138423716174, Cyc, 12,

[ 1, 0, -1, -2, -3, -3, -2, -1, 0, 1, 1, 1, 1 ]

111001:100010100010111000

------------------------------------------------------------

10, 7, 4, 1.87025043967004, Cyc, 1, [ 1, -2, 1, -2, 1, 0, 0, 1, -1, 1, -1 ]

1110010:0011

------------------------------------------------------------

12, 13, 4, 1.88565249635501, Cyc, 5,

[ 1, -1, -1, -1, -1, 0, 1, 1, 1, 0, 0, 0, -1 ]

1110011011000:1001

------------------------------------------------------------

10, 5, 15, 1.89059777258556, Cyc, 10, [ 1, -2, 0, 1, -1, 0, -1, 1, 0, -1, 1 ]

11101:000010001011100

------------------------------------------------------------

11, 5, 10, 1.89375038237605, Cyc, 4,

[ 1, -1, 0, -2, -1, -2, -1, 0, 0, 1, 0, 1 ]

11101:0001011100

------------------------------------------------------------

14, 9, 7, 1.88000047865555, Cyc, 2,

[ 1, -2, 0, 1, -1, 0, 0, -1, 1, 0, -1, 1, 0, -1, 1 ]

111001011:1001010

------------------------------------------------------------

13, 34, 40, 1.87918177588894, NR, 61,

[ 1, -1, -1, 0, -2, -1, 1, -1, 1, 1, -1, 0, 0, -1 ]

1110010110101100101001101101000101:1100011010100100001010110100100001010100

------------------------------------------------------------

12, 9, 4, 1.88668143754934, Cyc, 1,

[ 1, -2, 1, -2, 1, 0, 0, 0, 0, -1, 1, -1, 1 ]

111001101:1100

------------------------------------------------------------

15, 10, 15, 1.88901845650351, Cyc, 10,

[ 1, -1, -1, 0, -2, -1, 0, 0, 1, 0, 1, 1, -1, 0, 0, -1 ]

1110100000:001101110000001

------------------------------------------------------------

17, 10, 9, 1.89003800603578, Cyc, 2,

[ 1, -2, 0, 1, -1, -1, 2, -1, -1, 1, 1, -2, 1, 1, -1, 0, 1, -1 ]

1110100000:110000001

------------------------------------------------------------

22, 15, 9, 1.89011465553901, Cyc, 2,

[

1, -2, 0, 1, -1, -1, 2, -1, -1, 1, 1, -2, 1, 1, -1, -1, 2, -1, -1, 1, 0, -1, 1

]

111010000011001:000111000

------------------------------------------------------------

12, 5, 9, 1.89187283990744, Cyc, 2,

[ 1, -2, 0, 1, -1, -1, 2, -1, -1, 1, 0, -1, 1 ]

11101:000011100

------------------------------------------------------------

16, 63, 4, 1.89172540277736, NR, 51,

[ 1, -2, 1, -1, -1, 0, 0, 0, 0, 1, 0, 0, 1, 0, -1, 1, -1 ]

111010000110101010100100110000000011100101110010100001110011010:1001

------------------------------------------------------------

12, 5, 50, 1.89566925905467, NC, 43,

[ 1, 0, -2, -2, -1, -1, -1, -1, 0, 0, 0, 1, 1 ]

11101:00100010010110100110100101100101001000001100011100

Quotient,

11      12      10      9    8    6    5    4    3    2    23    20
1 - x + 2 x   - 2 x   - 2 x   + 2 x  - x  + x  - x  + x  - x  + x  + x   + x

19      18      17      16    14      13    43    42    41    40
- 2 x   + 3 x   - 3 x   + 2 x   - x   + 2 x   + x   - x   + x   - x

39    38    37    35      34      33      32      31      30    29
+ x   - x   + x   - x   + 2 x   - 2 x   + 2 x   - 2 x   + 2 x   - x

27      26      25      24
+ 2 x   - 3 x   + 3 x   - 2 x

2        4    3    2            2            6    3        28    26
(x + 1) (x  + 1) (x  - x  + x  - x + 1) (x  - x + 1) (x  - x  + 1) (x   - x

24    23    22      21      19    18      17      16    15      14
+ x   - x   - x   + 2 x   - 2 x   + x   + 2 x   - 2 x   - x   + 3 x

13      12      11    10      9      7    6    5    4    2
- x   - 2 x   + 2 x   + x   - 2 x  + 2 x  - x  - x  + x  - x  + 1)

------------------------------------------------------------

9, 7, 2, 1.89334302884660, Cyc, 0, [ 1, -1, -2, 0, 1, 0, 0, 1, 0, -1 ]

1110100:01

------------------------------------------------------------

16, 7, 15, 1.89845651809020, Cyc, 6,

[ 1, -2, 0, 1, -2, 1, 2, -2, 0, 1, -2, 0, 2, -1, 0, 1, -1 ]

1110100:110000001010101

------------------------------------------------------------

9, 0, 13, 1.88697502928005, Cyc, 4, [ 1, -1, -1, -1, -1, 1, 0, 0, 0, -1 ]

:1110011100001

------------------------------------------------------------

13, 0, 15, 1.87005942163016, Cyc, 2,

[ 1, -2, 0, 1, -1, 0, 0, 0, 0, 0, -1, 0, 1, -1 ]

:111001000110001

------------------------------------------------------------

11, 0, 14, 1.87285790586745, Cyc, 3,

[ 1, -3, 3, -2, 1, -1, 1, -1, 1, -2, 2, -1 ]

:11100100110001

------------------------------------------------------------

20, 7, 17, 1.88060018829068, Cyc, 4,

[ 1, -1, -2, 0, 1, 1, 0, -2, -1, 1, 1, 1, -1, -2, 0, 1, 1, 0, -1, 0, 1 ]

1110011:00001000001000010

------------------------------------------------------------

18, 7, 11, 1.88061097948205, Cyc, 0,

[ 1, -1, -1, -1, 0, 0, -1, -1, 0, 0, 0, -1, 0, 1, 1, 0, 0, 0, 1 ]

1110011:00001000010

------------------------------------------------------------

12, 7, 5, 1.88110840522068, Cyc, 0,

[ 1, -1, -1, -1, 0, -1, 0, 0, 1, 0, 0, 0, 1 ]

1110011:00010

------------------------------------------------------------

13, 0, 20, 1.87441309286692, Cyc, 7,

[ 1, -2, 0, 0, 1, 0, -1, 1, 0, -1, 0, 0, 1, -1 ]

:11100101000010110001

------------------------------------------------------------

15, 0, 24, 1.87607972751053, Cyc, 9,

[ 1, -2, 0, 0, 1, 0, -1, 1, -1, 1, 0, -1, 0, 0, 1, -1 ]

:111001010100001010110001

------------------------------------------------------------

18, 0, 37, 1.87651316411586, Cyc, 19,

[ 1, -2, 1, -1, 0, -1, 0, -1, -1, -1, 0, -1, -1, 0, -1, 0, -1, 1, -1 ]

:1110010101001110001110001101010110001

------------------------------------------------------------

17, 0, 28, 1.87655171683667, Cyc, 11,

[ 1, -2, 0, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, -1, 0, 0, 1, -1 ]

:1110010101010000101010110001

------------------------------------------------------------

16, 0, 17, 1.87683801095422, Cyc, 1,

[ 1, -2, 1, -2, 2, -2, 1, -1, 0, 0, -1, 1, -2, 1, -1, 1, -1 ]

:11100101010110001

------------------------------------------------------------

15, 0, 15, 1.87708857460957, Cyc, 0,

[ 1, -1, -1, -1, 0, 0, -1, 0, -1, 0, -1, -1, 0, 0, 0, -1 ]

:111001010110001

------------------------------------------------------------

19, 86, 44, 1.87771837844686, NR, 111,

[ 1, -1, -1, 0, -1, -2, 0, -1, -1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1 ]

------------------------------------------------------------

17, 53, 78, 1.87918192686796, NR, 114,

[ 1, -1, -1, -1, 0, 0, -1, -1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1 ]

------------------------------------------------------------

11      10    8    7    3                                              -48
x   - 2 x   + x  - x  - x  + x - 1, error after 25 iterations, .11378*10

11, 0, 13, 1.87796937623904, Cyc, 2, [ 1, -2, 0, 1, -1, 0, 0, 0, -1, 0, 1, -1 ]

:1110010110001

------------------------------------------------------------

16, 11, 17, 1.88108552254611, Cyc, 12,

[ 1, 0, -1, -2, -3, -3, -2, -1, 0, 1, 1, 1, 1, 1, 1, 1, 1 ]

11100110001:00000011100000000

------------------------------------------------------------

14, 8, 75, 1.88709602671733, NR, 69,

[ 1, -2, 1, -1, -1, 1, -2, 1, -1, 1, 0, 0, 1, -1, 1 ]

11100111:000010110001010100101000010011100010100001110001000010010101000010100\
000010

------------------------------------------------------------

11, 0, 11, 1.88106344570501, Cyc, 0,

[ 1, -1, -1, -1, 0, 0, -1, -1, 0, 0, 0, -1 ]

:11100110001

------------------------------------------------------------

21, 0, 26, 1.88199159208899, Cyc, 5,

[ 1, -1, -1, -1, 0, -1, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1 ]

:11100110010000001100110001

------------------------------------------------------------

16, 11, 9, 1.88296193051436, Cyc, 4,

[ 1, 0, -2, -2, -1, -1, -1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1 ]

11100110011:000000010

------------------------------------------------------------

14, 0, 22, 1.88379896146344, Cyc, 8,

[ 1, -2, 0, 0, 1, 0, -1, 0, 1, 0, -1, 0, 0, 1, -1 ]

:1110011010000100110001

------------------------------------------------------------

17, 0, 19, 1.88483453988385, Cyc, 2,

[ 1, -2, 0, 1, -1, 0, 0, -1, 1, -1, 0, 0, 0, 0, -1, 0, 1, -1 ]

:1110011010100110001

------------------------------------------------------------

20, 177, 68, 1.88490086744867, NR, 225,

[ 1, 0, -2, -2, -1, -1, -1, 0, 1, 0, -1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1 ]

------------------------------------------------------------

14, 11, 8, 1.88647555974093, Cyc, 5,

[ 1, -1, -1, -1, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 1 ]

11100110111:00000110

------------------------------------------------------------

17, 0, 17, 1.88750747832684, Cyc, 0,

[ 1, -1, -1, -1, 0, 0, -1, -1, -1, 0, 0, 0, -1, -1, 0, 0, 0, -1 ]

:11100111000110001

------------------------------------------------------------

26, 0, 41, 1.88752647198916, Cyc, 15,

[ 1, -2, 0, 0, 1, 0, -1, 0, 0, 1, 0, 0, -1, 0, 1, 0, 0, -1, 0, 0, 1, 0, -1, 0,

0, 1, -1 ]

:11100111000110010000000001100111000110001

------------------------------------------------------------

32, 0, 42, 1.88766848027915, Cyc, 10,

[ 1, -2, 0, 0, 1, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, 0, -1,

0, 0, 1, 0, -1, 0, 0, 1, -1 ]

:111001110010000000000000000000011000110001

------------------------------------------------------------

21, 0, 31, 1.88767114657863, Cyc, 10,

[ 1, -2, 0, 0, 1, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, -1 ]

:1110011100100000000011000110001

------------------------------------------------------------

17, 12, 5, 1.88821774567746, Cyc, 0,

[ 1, -1, -1, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1 ]

111001110011:00010

------------------------------------------------------------

19, 0, 25, 1.88805796277468, Cyc, 6,

[ 1, -1, -2, 0, 1, 1, -1, -1, 1, 0, -1, -1, 1, 1, -1, -1, 0, 1, 0, -1 ]

:1110011100101011000110001

------------------------------------------------------------

19, 0, 21, 1.88823875342193, Cyc, 2,

[ 1, -1, -2, 0, 2, 0, -3, -1, 2, 1, -2, -2, 1, 2, -1, -2, 0, 1, 0, -1 ]

:111001110011000110001

------------------------------------------------------------

27, 0, 27, 1.88847744191720, Cyc, 0,

[ 1, -1, -1, -1, 0, 0, -1, -1, -1, 0, 0, -1, -1, -1, 0, 0, 0, -1, -1, 0, 0, 0,

-1, -1, 0, 0, 0, -1 ]

:111001110011100011000110001

------------------------------------------------------------

31, 0, 46, 1.88848361275634, Cyc, 15,

[ 1, -2, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, -1, 0,

0, 1, 0, -1, 0, 0, 1, -1 ]

:1110011100111001000000000000001100011000110001

------------------------------------------------------------

22, 17, 5, 1.88850633293177, Cyc, 0,

[ 1, -1, -1, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1 ]

11100111001110011:00010

------------------------------------------------------------

35, 0, 37, 1.88851712328244, Cyc, 2,

[ 1, -1, -2, 0, 2, 0, -3, -1, 2, 1, -2, -2, 1, 1, -1, -1, 0, 0, -1, 0, 1, 0,

-2, -1, 2, 1, -2, -2, 1, 2, -1, -2, 0, 1, 0, -1 ]

:1110011100111001110001100011000110001

------------------------------------------------------------

27, 22, 5, 1.88851832465678, Cyc, 0,

[ 1, -1, -1, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,

0, 0, 0, 1 ]

1110011100111001110011:00010

------------------------------------------------------------

35, 0, 39, 1.88851884573748, Cyc, 4,

[ 1, -2, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0,

1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, -1 ]

:111010000000000000000000000000000010001

------------------------------------------------------------

30, 0, 34, 1.88851885156355, Cyc, 4,

[ 1, -2, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0,

1, 0, -1, 0, 0, 1, -1 ]

:1110100000000000000000000000010001

------------------------------------------------------------

25, 0, 29, 1.88851899151640, Cyc, 4,

[ 1, -2, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0,

1, -1 ]

:11101000000000000000000010001

------------------------------------------------------------

20, 0, 24, 1.88852235332918, Cyc, 4,

[ 1, -2, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, -1 ]

:111010000000000000010001

------------------------------------------------------------

21, 0, 21, 1.88854246845039, Cyc, 0,

[ 1, -1, -1, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1 ]

:111010000000000010001

------------------------------------------------------------

15, 0, 19, 1.88860306212665, Cyc, 4,

[ 1, -2, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, -1 ]

:1110100000000010001

------------------------------------------------------------

16, 0, 16, 1.88908461856766, Cyc, 0,

[ 1, -1, -1, -1, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1 ]

:1110100000010001

------------------------------------------------------------

19, 67, 34, 1.89005025363079, NR, 82,

[ 1, -2, 0, 1, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 1 ]

1110100000110000100010000000001101100100110100110110000010001101101:1010010101\
101101101011010100100100

------------------------------------------------------------

19, 0, 33, 1.89011295110734, Cyc, 14,

[ 1, -2, 0, 0, 1, 0, -1, 0, 0, 1, -1, 0, 0, 1, 0, -1, 0, 0, 1, -1 ]

:111010000011001000110000000010001

------------------------------------------------------------

23, 0, 53, 1.89037975013258, Cyc, 30,

[ 1, -2, 0, 1, -1, 0, -1, 1, 0, -1, 1, 0, 0, 0, 1, 0, -1, 1, 0, 0, -1, 0, 1, -1

]

:11101000001110100000110010001100000000100000000010001

------------------------------------------------------------

18, 21, 36, 1.89052123458116, Cyc, 39,

[ 1, -1, -1, 0, -1, -2, -1, 0, -1, -1, 0, 1, 0, 0, 1, 1, 0, 0, 1 ]

111010000100001110001:101000110000010110010000110001100000

------------------------------------------------------------

16, 0, 29, 1.89109037483467, Cyc, 13,

[ 1, -2, 0, 0, 1, 0, -1, 0, 0, 0, 1, 0, -1, 0, 0, 1, -1 ]

:11101000010101010100000010001

------------------------------------------------------------

21, 0, 30, 1.89152731428321, Cyc, 9,

[ 1, -1, -1, -1, 0, -1, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, -1 ]

:111010000110010011000000010001

------------------------------------------------------------

23, 41, 16, 1.89156947992814, NR, 34,

[ 1, -2, 0, 0, 1, 0, -1, 0, 0, 0, 1, -1, 1, -1, 0, 0, 0, 1, 0, -1, 0, 0, 1, -1

]

11101000011001011100101100011100010110001:1100100110010000

------------------------------------------------------------

20, 93, 15, 1.89181782110395, NR, 88,

[ 1, -1, -2, 0, 1, 1, -1, -1, 0, 0, 1, 0, 0, -1, -1, 1, 1, 0, -1, 0, 1 ]

111010000110110101001011100010010101100000111000000100011100100000100011000100\
010100111000010:000100110010001

------------------------------------------------------------

18, 15, 12, 1.89186171183916, Cyc, 9,

[ 1, -1, -1, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 1 ]

111010000110111:010000100110

------------------------------------------------------------

31, 0, 58, 1.89201518641894, NR, 27,

[ 1, -2, 0, 0, 1, 0, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0,

0, 1, 0, -1, 0, 0, 1, -1 ]

:1110100001110100001110011011001100000001000000000000110001

Quotient,

27    26    25    24    23    18    17    16    15    14    9    8    7    6
x   + x   + x   + x   + x   + x   + x   + x   + x   + x   + x  + x  + x  + x

5    4    3    2
+ x  + x  + x  + x  + x + 1

4    3    2
(x + 1) (x  + x  + x  + x + 1)

20    19    16    15    12    10    8    6    4            2
(x   - x   + x   - x   + x   - x   + x  - x  + x  - x + 1) (x  + 1)

------------------------------------------------------------

28, 9, 25, 1.89201537326921, Cyc, 6,

[ 1, 0, -2, -2, -1, -1, -1, -1, 0, 1, 1, 1, 1, 1, 1, 0, -1, -1, -1, -1, -1,

-1, 0, 1, 1, 0, 0, 1, 1 ]

111010001:0000000000000000111000000

------------------------------------------------------------

20, 9, 27, 1.89205811860941, Cyc, 16,

[ 1, -2, 0, 1, -1, 0, -1, 1, 0, -1, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1 ]

111010001:000000100010000000111000000

------------------------------------------------------------

22, 9, 15, 1.89208707168182, Cyc, 2,

[ 1, -2, 0, 1, -1, -1, 2, -1, -1, 1, 0, -1, 1, 0, -1, 0, 1, -1, 0, 1, 0, -1, 1

]

111010001:000000111000000

------------------------------------------------------------

14, 9, 11, 1.89293201975951, Cyc, 6,

[ 1, 0, -2, -2, -1, -1, -1, -1, 0, 1, 1, 0, 0, 1, 1 ]

111010001:00111000000

------------------------------------------------------------

13, 11, 2, 1.89238790953178, Cyc, 0,

[ 1, -1, -2, 0, 1, 0, 0, 1, 0, -1, 0, 1, 0, -1 ]

11101000100:01

------------------------------------------------------------

12, 8, 20, 1.89527173289623, NR, 16,

[ 1, -2, 1, -1, -1, 0, 0, 0, 0, 0, 1, -1, 1 ]

11101001:00000101101011000000

16    15    13    11    10    8    6    5
Quotient, x   + x   - x   + x   + x   - x  + x  + x  + x + 1

4    3    2            11    10    8
(x + 1) (x  - x  + x  - x + 1) (x   + x   - x  + x + 1)

------------------------------------------------------------

10, 0, 14, 1.89052464271654, Cyc, 4, [ 1, -2, 0, 0, 1, 0, -1, 0, 0, 1, -1 ]

:11101000010001

------------------------------------------------------------

18, 59, 45, 1.89606049654463, NR, 86,

[ 1, -2, 1, -2, 1, 0, -1, 2, -2, 2, -2, 1, -1, 0, 1, -1, 1, -1, 1 ]

11101001001000010110101101101110010000011100100111001010101:100011000110100110\
010100110010110001101010110

------------------------------------------------------------

12, 9, 12, 1.89886445620998, Cyc, 9,

[ 1, -1, -2, 0, 2, -1, -2, 0, 2, 0, -1, 0, 1 ]

111010011:000111000010

------------------------------------------------------------

9, 8, 16, 1.87950972959281, NR, 15, [ 1, 0, -2, -2, -1, -1, 0, 0, -1, -1 ]

11100101:1011011010000100

Quotient,

15    14    13    12    11    9      8      7      6    5    3    2
x   - x   + x   - x   + x   - x  + 2 x  - 2 x  + 2 x  - x  + x  - x  + x - 1

------------------------------------------------------------

9, 0, 12, 1.88721569211643, Cyc, 3, [ 1, -3, 3, -2, 1, -1, 1, -2, 2, -1 ]

:111001110001

------------------------------------------------------------

9, 0, 9, 1.89201525102806, Cyc, 0, [ 1, -1, -1, -1, 0, -1, 0, 0, 0, -1 ]

:111010001

------------------------------------------------------------

17, 0, 17, 1.89504868790152, Cyc, 0,

[ 1, -1, -1, -1, 0, -1, 0, 0, 0, -1, -1, -1, 0, -1, 0, 0, 0, -1 ]

:11101000111010001

------------------------------------------------------------

20, 43, 9, 1.89512982684574, NC, 32,

[ 1, 0, -1, -2, -3, -3, -2, -2, -1, -1, 0, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1 ]

1110100100000001100101011100000000111010001:100000000

Quotient,

32    31    28    27    25    24    21    20    18    16    14    12    11
x   - x   + x   - x   + x   - x   + x   - x   + x   - x   + x   - x   + x

8    7    5    4
- x  + x  - x  + x  - x + 1

------------------------------------------------------------

17, 0, 21, 1.89529964148990, Cyc, 4,

[ 1, -1, -1, -1, -1, 0, 1, 1, 0, 0, -1, -1, 0, 0, 0, 0, 0, -1 ]

:111010010000011010001

------------------------------------------------------------

25, 21, 20, 1.89531917890217, NR, 16,

[ 1, -1, -1, -1, 0, -1, 0, 0, -1, 0, 0, 0, -1, 1, 0, 0, 0, 0, -1, -1, 0, -1,

0, 0, 0, -1 ]

111010010000011100001:11010001110100100000

16    4
Quotient, x   + x  - 1

------------------------------------------------------------

22, 0, 41, 1.89532069341269, Cyc, 19,

[ 1, -2, 0, 0, 1, -1, 1, 0, 0, -1, 0, 0, 0, 1, 0, 0, -1, 1, -1, 0, 0, 1, -1 ]

:11101001000001110001011100010000011010001

------------------------------------------------------------

20, 9, 15, 1.89844236826911, Cyc, 4,

[ 1, -1, -1, -1, -1, 0, 1, 1, 0, -1, -1, -1, 0, 1, 1, 0, 0, 0, 0, 0, 1 ]

111010011:000000100000010

------------------------------------------------------------

16, 9, 7, 1.89847604678109, Cyc, 0,

[ 1, -1, -1, -1, 0, -1, 0, -1, 0, 0, 1, 0, 1, 0, 0, 0, 1 ]

111010011:0000010

------------------------------------------------------------

17, 0, 19, 1.89921247100705, Cyc, 2,

[ 1, -2, 0, 1, -1, -1, 2, -1, -2, 2, 0, -2, 1, 0, -1, 0, 1, -1 ]

:1110100110011010001

------------------------------------------------------------

20, 23, 7, 1.89926966790868, Cyc, 10,

[ 1, 0, -2, -2, -1, -1, -1, -1, -1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1 ]

11101001100110111010011:0000010

------------------------------------------------------------

11, 10, 20, 1.89836798718501, NR, 19,

[ 1, 0, -2, -2, -1, -1, -1, -1, 0, 0, -1, -1 ]

1110100101:11001101110010000100

Quotient,

19    18    17    16    15    14    13    11      10      9      8      7
x   - x   + x   - x   + x   - x   + x   - x   + 2 x   - 2 x  + 2 x  - 2 x

6    5    3    2
+ 2 x  - x  + x  - x  + x - 1

------------------------------------------------------------

5, 0, 5, 1.88851884548441, Cyc, 0, [ 1, -1, -1, -1, 0, -1 ]

:11101

------------------------------------------------------------

12, 0, 38, 1.87232418029148, Cyc, 26,

[ 1, -1, -1, -1, -1, 0, 1, 2, 1, 0, 0, -1, -1 ]

:11100100101011100011000010100100000011

------------------------------------------------------------

20, 0, 38, 1.87055453081114, Cyc, 18,

[

1, -1, -1, 0, -1, -1, -1, -1, -1, -2, -1, -1, -2, -1, -1, -1, -1, -1, 0, -1, -1

]

:11100100011011100011100011011100100011

------------------------------------------------------------

23, 0, 23, 1.87055629864562, Cyc, 0,

[ 1, -1, -1, -1, 0, 0, -1, 0, 0, 0, -1, -1, 0, -1, -1, -1, 0, 0, -1, 0, 0, 0,

-1, -1 ]

:11100100011011100100011

------------------------------------------------------------

24, 0, 41, 1.87055662489394, Cyc, 17,

[ 1, -2, 0, 1, -1, 0, -1, 2, 0, -2, 2, 0, 0, -1, 0, 2, -2, 0, 1, 0, 0, -1, 1,

0, -1 ]

:11100100011100000000000000000011100100011

------------------------------------------------------------

18, 0, 29, 1.87057027249168, Cyc, 11,

[ 1, -2, 0, 0, 1, 0, -1, 1, 0, 0, -1, 0, 1, -1, 0, 0, 1, 0, -1 ]

:11100100011100000011100100011

------------------------------------------------------------

23, 0, 47, 1.87064359130361, Cyc, 24,

[ 1, -1, -1, 0, -1, -1, -1, -1, -1, -2, -1, -1, -2, -1, -1, -2, -1, -1, -1,

-1, -1, 0, -1, -1 ]

:11100100011100011011100100011011100011100100011

------------------------------------------------------------

24, 0, 41, 1.87064390972666, Cyc, 17,

[

1, -2, 0, 0, 1, 0, -1, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 1, -1, 0, 0, 1, 0, -1

]

:11100100011100011100000011100011100100011

------------------------------------------------------------

21, 0, 26, 1.87064593801613, Cyc, 5,

[ 1, -2, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, -1 ]

:11100100011100011100100011

------------------------------------------------------------

18, 0, 20, 1.87065718652437, Cyc, 2,

[ 1, -2, 0, 1, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 1, 0, -1 ]

:11100100011100100011

------------------------------------------------------------

12, 0, 14, 1.87113945950622, Cyc, 2,

[ 1, -2, 0, 1, -1, 0, 0, 0, 0, -1, 1, 0, -1 ]

:11100100100011

------------------------------------------------------------

16, 0, 22, 1.87288590690027, Cyc, 6,

[ 1, -2, 1, -1, -1, 1, -2, 2, -1, 0, 1, -1, 1, -1, 0, 0, -1 ]

:1110010011000100100011

------------------------------------------------------------

17, 0, 28, 1.87299619341656, Cyc, 11,

[ 1, -3, 3, -2, 1, -1, 1, -1, 0, 1, -1, 1, -1, 1, -1, 0, 1, -1 ]

:1110010011000111000100100011

------------------------------------------------------------

18, 0, 27, 1.87394821161362, Cyc, 9,

[ 1, -2, 0, 1, -1, 0, 0, -1, 2, -1, -1, 1, 0, 0, 0, -1, 1, 0, -1 ]

:111001001110010001100100011

------------------------------------------------------------

17, 0, 24, 1.87501255746791, Cyc, 7,

[ 1, -1, -1, -1, 0, 0, -1, -1, 0, 1, 1, 0, -1, 0, 0, 0, -1, -1 ]

:111001010001110000100011

------------------------------------------------------------

20, 46, 46, 1.87530706874314, NR, 72,

[ 1, -1, -2, 0, 1, 1, -1, -1, 2, 1, -1, -2, 0, 2, 0, -1, 0, 1, 1, -1, -1 ]

1110010100100110011100100011100010110010010011:1000111000000100100100100000001\
110010000010000

------------------------------------------------------------

14, 13, 18, 1.87590934903956, Cyc, 17,

[ 1, -1, -1, -1, 0, 0, -1, -1, 0, 1, 0, 0, 0, 1, 1 ]

1110010100111:000001100010000100

------------------------------------------------------------

10, 0, 13, 1.87484410361487, Cyc, 3, [ 1, -3, 3, -2, 1, -1, 1, -1, 0, 1, -1 ]

:1110010100011

------------------------------------------------------------

18, 0, 25, 1.87993069324496, Cyc, 7,

[ 1, -2, 0, 1, -1, -1, 2, 0, -2, 1, 1, -2, 0, 1, 0, -1, 1, 0, -1 ]

:1110010111001000110100011

------------------------------------------------------------

13, 0, 19, 1.88021697817134, Cyc, 6,

[ 1, -2, 0, 0, 1, 0, -1, 1, -1, 0, 0, 1, 0, -1 ]

:1110011000000100011

------------------------------------------------------------

14, 0, 19, 1.88212330763723, Cyc, 5,

[ 1, -1, -1, -1, 0, -1, 0, 0, 1, 0, 0, 0, 0, -1, -1 ]

:1110011001000100011

------------------------------------------------------------

18, 22, 63, 1.88257019810747, NR, 67,

[ 1, 0, -2, -3, -1, 1, 2, 1, 0, -1, -1, -1, 0, 1, 2, 1, -1, -2, -1 ]

1110011001010010000011:0110111000000001101101000000011011100001001000110011100\
10010000

------------------------------------------------------------

17, 248, 55, 1.88264884026259, NR, 286,

[ 1, -1, -1, -1, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 1, 1 ]

------------------------------------------------------------

11, 10, 52, 1.88560964173114, NR, 51,

[ 1, -1, -1, -1, 0, -1, 0, 0, 0, 0, 1, 1 ]

1110011011:0000110110110101000010000001001001101011001100000000

------------------------------------------------------------

10, 0, 21, 1.88674840984824, Cyc, 11, [ 1, -1, -2, 0, 1, 0, 0, 1, 1, -1, -1 ]

:111001110000000100011

------------------------------------------------------------

16, 19, 32, 1.88865687246862, Cyc, 35,

[ 1, -1, -1, -1, -1, 0, 1, 1, 1, 0, -1, -1, -1, 0, 0, 1, 1 ]

1110100000000011011:00100000100001110000000001011000

------------------------------------------------------------

10, 0, 12, 1.88160106282372, Cyc, 2, [ 1, -2, 0, 1, -1, 0, 0, -1, 1, 0, -1 ]

:111001100011

------------------------------------------------------------

14, 14, 15, 1.88718158271536, NR, 15,

[ 1, -2, 1, -1, -1, 1, -2, 1, 0, -1, 1, -1, 0, 0, -1 ]

11100111000011:011000010010000

15    14    12    10    9    7    6    4    3
Quotient, x   + x   - x   + x   + x  - x  - x  + x  + x  - x - 1

------------------------------------------------------------

16, 0, 18, 1.88751874708316, Cyc, 2,

[ 1, -2, 0, 1, -1, 0, 0, -1, 0, 1, -1, 0, 0, -1, 1, 0, -1 ]

:111001110001100011

------------------------------------------------------------

17, 0, 24, 1.88764708474790, Cyc, 7,

[ 1, -3, 3, -2, 0, 2, -2, 0, 2, -3, 2, 0, -2, 2, -1, 0, 1, -1 ]

:111001110001110001100011

------------------------------------------------------------

17, 0, 21, 1.88778898752038, Cyc, 4,

[ 1, -1, -1, -1, -1, 1, 0, 0, 0, -1, 0, -1, 0, 1, 0, 0, -1, -1 ]

:111001110010001100011

------------------------------------------------------------

23, 433, 19, 1.88791392772609, NR, 429,

[ 1, -1, -1, -1, -1, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1, 0, -1, 0, 0, 1, 1

]

------------------------------------------------------------

11, 0, 15, 1.88874417210160, Cyc, 4, [ 1, -2, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1 ]

:111010000000011

------------------------------------------------------------

15, 31, 32, 1.89049173545937, NR, 48,

[ 1, -2, 1, -1, -1, 1, -2, 1, -1, 0, 1, -1, 1, 0, 0, 1 ]

1110100001000010110010110001011:01010000010101011000110110001000

------------------------------------------------------------

11, 14, 15, 1.89341534773790, Cyc, 18,

[ 1, -1, -1, -1, -1, 1, 0, -1, 0, 0, 1, 1 ]

11101000101011:001101000101000

------------------------------------------------------------

11, 0, 24, 1.89570030883221, Cyc, 13,

[ 1, -1, -2, 0, 1, 0, 0, 0, 1, 1, -1, -1 ]

:111010010001010000000011

------------------------------------------------------------

10, 0, 12, 1.89002709754561, Cyc, 2, [ 1, 0, -2, -3, -1, 1, 2, 1, -1, -2, -1 ]

:111010000011

------------------------------------------------------------

11, 0, 15, 1.89527781156751, Cyc, 4,

[ 1, -1, -1, -1, -1, 0, 1, 1, 0, 0, -1, -1 ]

:111010010000011

------------------------------------------------------------

18, 0, 25, 1.89902869931337, Cyc, 7,

[ 1, -1, -1, -1, 0, -1, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, -1 ]

:1110100110010100010000011

------------------------------------------------------------

17, 16, 19, 1.89924892435554, Cyc, 18,

[ 1, -1, -1, -1, -1, 0, 1, 0, 1, 0, 0, 0, -1, -1, 0, 0, 1, 1 ]

1110100110011011:0001110000100011000

------------------------------------------------------------

6, 0, 10, 1.89382408771630, Cyc, 4, [ 1, -2, 0, 0, 1, 0, -1 ]

:1110100011

------------------------------------------------------------

7, 0, 7, 1.88004410996717, Cyc, 0, [ 1, -1, -1, -1, 0, 0, -1, -1 ]

:1110011

------------------------------------------------------------

7, 0, 19, 1.88506607809056, Cyc, 12, [ 1, 0, -1, -2, -3, -3, -2, -1 ]

:1110011010101100111

------------------------------------------------------------

8, 0, 8, 1.88670294847150, Cyc, 0, [ 1, -1, -1, -1, 0, 0, -1, -1, -1 ]

:11100111

------------------------------------------------------------

finished

total output, 144

cyclotomic, 119, nonreciprocal, 22, noncyclotomic, 3

```