History of Cyclotomic polynomials

+Title: Cyclotomic polynomials+Definition: The $n$'th cyclotomic polynomial $\Phi_n(x)$ is the monic polynomial whose+  roots are the primitive $n$'th roots of unity.+Parameters:+  n:+    type: Z+    constraints: $n \geq 1$+Comments: {}+Formulas:+  formula-via-roots: '$\Phi_n(x) = \prod_{1\leq k \leq n: \gcd(n,k)=1} (x-\exp(2\pi+    ik/n)$.'+Programs:+  program-sage:+    language: Sage+    code: 'polynomials = {n: cyclotomic_polynomial(n) for n in [1..100]}'+References: {}+Links:+  Wiki:+    title: 'Wikipedia: Cyclotomic polynomial'+    url: https://en.wikipedia.org/wiki/Cyclotomic_polynomial+Similar tables: ''+Keywords: ''+Tags:+- Polynomial+Data properties:+  type: Z[x]+  complete: 'no'+Display properties:+  number-header: $\Phi_n(x)$+Data:+  '1': x - 1+  '2': x + 1+  '3': x^2 + x + 1+  '4': x^2 + 1+  '5': x^4 + x^3 + x^2 + x + 1+  '6': x^2 - x + 1+  '7': x^6 + x^5 + x^4 + x^3 + x^2 + x + 1+  '8': x^4 + 1+  '9': x^6 + x^3 + 1+  '10': x^4 - x^3 + x^2 - x + 1+  '11': x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1+  '12': x^4 - x^2 + 1+  '13': x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1+  '14': x^6 - x^5 + x^4 - x^3 + x^2 - x + 1+  '15': x^8 - x^7 + x^5 - x^4 + x^3 - x + 1+  '16': x^8 + 1+  '17': x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5+    + x^4 + x^3 + x^2 + x + 1+  '18': x^6 - x^3 + 1+  '19': x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 ++    x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1+  '20': x^8 - x^6 + x^4 - x^2 + 1+  '21': x^12 - x^11 + x^9 - x^8 + x^6 - x^4 + x^3 - x + 1+  '22': x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1+  '23': x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12+    + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1+  '24': x^8 - x^4 + 1+  '25': x^20 + x^15 + x^10 + x^5 + 1+  '26': x^12 - x^11 + x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1+  '27': x^18 + x^9 + 1+  '28': x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1+  '29': x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18+    + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6+    + x^5 + x^4 + x^3 + x^2 + x + 1+  '30': x^8 + x^7 - x^5 - x^4 - x^3 + x + 1+  '31': x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20+    + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 ++    x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1+  '32': x^16 + 1+  '33': x^20 - x^19 + x^17 - x^16 + x^14 - x^13 + x^11 - x^10 + x^9 - x^7 + x^6 -+    x^4 + x^3 - x + 1+  '34': x^16 - x^15 + x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 + x^6 - x^5+    + x^4 - x^3 + x^2 - x + 1+  '35': x^24 - x^23 + x^19 - x^18 + x^17 - x^16 + x^14 - x^13 + x^12 - x^11 + x^10+    - x^8 + x^7 - x^6 + x^5 - x + 1+  '36': x^12 - x^6 + 1+  '37': x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26+    + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 ++    x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2+    + x + 1+  '38': x^18 - x^17 + x^16 - x^15 + x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 -+    x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1+  '39': x^24 - x^23 + x^21 - x^20 + x^18 - x^17 + x^15 - x^14 + x^12 - x^10 + x^9+    - x^7 + x^6 - x^4 + x^3 - x + 1+  '40': x^16 - x^12 + x^8 - x^4 + 1+  '41': x^40 + x^39 + x^38 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30+    + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 ++    x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7+    + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1+  '42': x^12 + x^11 - x^9 - x^8 + x^6 - x^4 - x^3 + x + 1+  '43': x^42 + x^41 + x^40 + x^39 + x^38 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32+    + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 ++    x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9+    + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1+  '44': x^20 - x^18 + x^16 - x^14 + x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1+  '45': x^24 - x^21 + x^15 - x^12 + x^9 - x^3 + 1+  '46': x^22 - x^21 + x^20 - x^19 + x^18 - x^17 + x^16 - x^15 + x^14 - x^13 + x^12+    - x^11 + x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1+  '47': x^46 + x^45 + x^44 + x^43 + x^42 + x^41 + x^40 + x^39 + x^38 + x^37 + x^36+    + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 ++    x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13+    + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1+  '48': x^16 - x^8 + 1+  '49': x^42 + x^35 + x^28 + x^21 + x^14 + x^7 + 1+  '50': x^20 - x^15 + x^10 - x^5 + 1+  '51': x^32 - x^31 + x^29 - x^28 + x^26 - x^25 + x^23 - x^22 + x^20 - x^19 + x^17+    - x^16 + x^15 - x^13 + x^12 - x^10 + x^9 - x^7 + x^6 - x^4 + x^3 - x + 1+  '52': x^24 - x^22 + x^20 - x^18 + x^16 - x^14 + x^12 - x^10 + x^8 - x^6 + x^4 -+    x^2 + 1+  '53': x^52 + x^51 + x^50 + x^49 + x^48 + x^47 + x^46 + x^45 + x^44 + x^43 + x^42+    + x^41 + x^40 + x^39 + x^38 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^31 ++    x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19+    + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7+    + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1+  '54': x^18 - x^9 + 1+  '55': x^40 - x^39 + x^35 - x^34 + x^30 - x^28 + x^25 - x^23 + x^20 - x^17 + x^15+    - x^12 + x^10 - x^6 + x^5 - x + 1+  '56': x^24 - x^20 + x^16 - x^12 + x^8 - x^4 + 1+  '57': x^36 - x^35 + x^33 - x^32 + x^30 - x^29 + x^27 - x^26 + x^24 - x^23 + x^21+    - x^20 + x^18 - x^16 + x^15 - x^13 + x^12 - x^10 + x^9 - x^7 + x^6 - x^4 + x^3+    - x + 1+  '58': x^28 - x^27 + x^26 - x^25 + x^24 - x^23 + x^22 - x^21 + x^20 - x^19 + x^18+    - x^17 + x^16 - x^15 + x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 + x^6+    - x^5 + x^4 - x^3 + x^2 - x + 1+  '59': x^58 + x^57 + x^56 + x^55 + x^54 + x^53 + x^52 + x^51 + x^50 + x^49 + x^48+    + x^47 + x^46 + x^45 + x^44 + x^43 + x^42 + x^41 + x^40 + x^39 + x^38 + x^37 ++    x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25+    + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 ++    x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x+    + 1+  '60': x^16 + x^14 - x^10 - x^8 - x^6 + x^2 + 1+  '61': x^60 + x^59 + x^58 + x^57 + x^56 + x^55 + x^54 + x^53 + x^52 + x^51 + x^50+    + x^49 + x^48 + x^47 + x^46 + x^45 + x^44 + x^43 + x^42 + x^41 + x^40 + x^39 ++    x^38 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27+    + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 ++    x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 ++    x^3 + x^2 + x + 1+  '62': x^30 - x^29 + x^28 - x^27 + x^26 - x^25 + x^24 - x^23 + x^22 - x^21 + x^20+    - x^19 + x^18 - x^17 + x^16 - x^15 + x^14 - x^13 + x^12 - x^11 + x^10 - x^9 ++    x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1+  '63': x^36 - x^33 + x^27 - x^24 + x^18 - x^12 + x^9 - x^3 + 1+  '64': x^32 + 1+  '65': x^48 - x^47 + x^43 - x^42 + x^38 - x^37 + x^35 - x^34 + x^33 - x^32 + x^30+    - x^29 + x^28 - x^27 + x^25 - x^24 + x^23 - x^21 + x^20 - x^19 + x^18 - x^16 ++    x^15 - x^14 + x^13 - x^11 + x^10 - x^6 + x^5 - x + 1+  '66': x^20 + x^19 - x^17 - x^16 + x^14 + x^13 - x^11 - x^10 - x^9 + x^7 + x^6 -+    x^4 - x^3 + x + 1+  '67': x^66 + x^65 + x^64 + x^63 + x^62 + x^61 + x^60 + x^59 + x^58 + x^57 + x^56+    + x^55 + x^54 + x^53 + x^52 + x^51 + x^50 + x^49 + x^48 + x^47 + x^46 + x^45 ++    x^44 + x^43 + x^42 + x^41 + x^40 + x^39 + x^38 + x^37 + x^36 + x^35 + x^34 + x^33+    + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 ++    x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10+    + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1+  '68': x^32 - x^30 + x^28 - x^26 + x^24 - x^22 + x^20 - x^18 + x^16 - x^14 + x^12+    - x^10 + x^8 - x^6 + x^4 - x^2 + 1+  '69': x^44 - x^43 + x^41 - x^40 + x^38 - x^37 + x^35 - x^34 + x^32 - x^31 + x^29+    - x^28 + x^26 - x^25 + x^23 - x^22 + x^21 - x^19 + x^18 - x^16 + x^15 - x^13 ++    x^12 - x^10 + x^9 - x^7 + x^6 - x^4 + x^3 - x + 1+  '70': x^24 + x^23 - x^19 - x^18 - x^17 - x^16 + x^14 + x^13 + x^12 + x^11 + x^10+    - x^8 - x^7 - x^6 - x^5 + x + 1+  '71': x^70 + x^69 + x^68 + x^67 + x^66 + x^65 + x^64 + x^63 + x^62 + x^61 + x^60+    + x^59 + x^58 + x^57 + x^56 + x^55 + x^54 + x^53 + x^52 + x^51 + x^50 + x^49 ++    x^48 + x^47 + x^46 + x^45 + x^44 + x^43 + x^42 + x^41 + x^40 + x^39 + x^38 + x^37+    + x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 ++    x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14+    + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 ++    x + 1+  '72': x^24 - x^12 + 1+  '73': x^72 + x^71 + x^70 + x^69 + x^68 + x^67 + x^66 + x^65 + x^64 + x^63 + x^62+    + x^61 + x^60 + x^59 + x^58 + x^57 + x^56 + x^55 + x^54 + x^53 + x^52 + x^51 ++    x^50 + x^49 + x^48 + x^47 + x^46 + x^45 + x^44 + x^43 + x^42 + x^41 + x^40 + x^39+    + x^38 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 ++    x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16+    + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4+    + x^3 + x^2 + x + 1+  '74': x^36 - x^35 + x^34 - x^33 + x^32 - x^31 + x^30 - x^29 + x^28 - x^27 + x^26+    - x^25 + x^24 - x^23 + x^22 - x^21 + x^20 - x^19 + x^18 - x^17 + x^16 - x^15 ++    x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2+    - x + 1+  '75': x^40 - x^35 + x^25 - x^20 + x^15 - x^5 + 1+  '76': x^36 - x^34 + x^32 - x^30 + x^28 - x^26 + x^24 - x^22 + x^20 - x^18 + x^16+    - x^14 + x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1+  '77': x^60 - x^59 + x^53 - x^52 + x^49 - x^48 + x^46 - x^45 + x^42 - x^41 + x^39+    - x^37 + x^35 - x^34 + x^32 - x^30 + x^28 - x^26 + x^25 - x^23 + x^21 - x^19 ++    x^18 - x^15 + x^14 - x^12 + x^11 - x^8 + x^7 - x + 1+  '78': x^24 + x^23 - x^21 - x^20 + x^18 + x^17 - x^15 - x^14 + x^12 - x^10 - x^9+    + x^7 + x^6 - x^4 - x^3 + x + 1+  '79': x^78 + x^77 + x^76 + x^75 + x^74 + x^73 + x^72 + x^71 + x^70 + x^69 + x^68+    + x^67 + x^66 + x^65 + x^64 + x^63 + x^62 + x^61 + x^60 + x^59 + x^58 + x^57 ++    x^56 + x^55 + x^54 + x^53 + x^52 + x^51 + x^50 + x^49 + x^48 + x^47 + x^46 + x^45+    + x^44 + x^43 + x^42 + x^41 + x^40 + x^39 + x^38 + x^37 + x^36 + x^35 + x^34 ++    x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22+    + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 ++    x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1+  '80': x^32 - x^24 + x^16 - x^8 + 1+  '81': x^54 + x^27 + 1+  '82': x^40 - x^39 + x^38 - x^37 + x^36 - x^35 + x^34 - x^33 + x^32 - x^31 + x^30+    - x^29 + x^28 - x^27 + x^26 - x^25 + x^24 - x^23 + x^22 - x^21 + x^20 - x^19 ++    x^18 - x^17 + x^16 - x^15 + x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7+    + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1+  '83': x^82 + x^81 + x^80 + x^79 + x^78 + x^77 + x^76 + x^75 + x^74 + x^73 + x^72+    + x^71 + x^70 + x^69 + x^68 + x^67 + x^66 + x^65 + x^64 + x^63 + x^62 + x^61 ++    x^60 + x^59 + x^58 + x^57 + x^56 + x^55 + x^54 + x^53 + x^52 + x^51 + x^50 + x^49+    + x^48 + x^47 + x^46 + x^45 + x^44 + x^43 + x^42 + x^41 + x^40 + x^39 + x^38 ++    x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26+    + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 ++    x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2+    + x + 1+  '84': x^24 + x^22 - x^18 - x^16 + x^12 - x^8 - x^6 + x^2 + 1+  '85': x^64 - x^63 + x^59 - x^58 + x^54 - x^53 + x^49 - x^48 + x^47 - x^46 + x^44+    - x^43 + x^42 - x^41 + x^39 - x^38 + x^37 - x^36 + x^34 - x^33 + x^32 - x^31 ++    x^30 - x^28 + x^27 - x^26 + x^25 - x^23 + x^22 - x^21 + x^20 - x^18 + x^17 - x^16+    + x^15 - x^11 + x^10 - x^6 + x^5 - x + 1+  '86': x^42 - x^41 + x^40 - x^39 + x^38 - x^37 + x^36 - x^35 + x^34 - x^33 + x^32+    - x^31 + x^30 - x^29 + x^28 - x^27 + x^26 - x^25 + x^24 - x^23 + x^22 - x^21 ++    x^20 - x^19 + x^18 - x^17 + x^16 - x^15 + x^14 - x^13 + x^12 - x^11 + x^10 - x^9+    + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1+  '87': x^56 - x^55 + x^53 - x^52 + x^50 - x^49 + x^47 - x^46 + x^44 - x^43 + x^41+    - x^40 + x^38 - x^37 + x^35 - x^34 + x^32 - x^31 + x^29 - x^28 + x^27 - x^25 ++    x^24 - x^22 + x^21 - x^19 + x^18 - x^16 + x^15 - x^13 + x^12 - x^10 + x^9 - x^7+    + x^6 - x^4 + x^3 - x + 1+  '88': x^40 - x^36 + x^32 - x^28 + x^24 - x^20 + x^16 - x^12 + x^8 - x^4 + 1+  '89': x^88 + x^87 + x^86 + x^85 + x^84 + x^83 + x^82 + x^81 + x^80 + x^79 + x^78+    + x^77 + x^76 + x^75 + x^74 + x^73 + x^72 + x^71 + x^70 + x^69 + x^68 + x^67 ++    x^66 + x^65 + x^64 + x^63 + x^62 + x^61 + x^60 + x^59 + x^58 + x^57 + x^56 + x^55+    + x^54 + x^53 + x^52 + x^51 + x^50 + x^49 + x^48 + x^47 + x^46 + x^45 + x^44 ++    x^43 + x^42 + x^41 + x^40 + x^39 + x^38 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32+    + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 ++    x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9+    + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1+  '90': x^24 + x^21 - x^15 - x^12 - x^9 + x^3 + 1+  '91': x^72 - x^71 + x^65 - x^64 + x^59 - x^57 + x^52 - x^50 + x^46 - x^43 + x^39+    - x^36 + x^33 - x^29 + x^26 - x^22 + x^20 - x^15 + x^13 - x^8 + x^7 - x + 1+  '92': x^44 - x^42 + x^40 - x^38 + x^36 - x^34 + x^32 - x^30 + x^28 - x^26 + x^24+    - x^22 + x^20 - x^18 + x^16 - x^14 + x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1+  '93': x^60 - x^59 + x^57 - x^56 + x^54 - x^53 + x^51 - x^50 + x^48 - x^47 + x^45+    - x^44 + x^42 - x^41 + x^39 - x^38 + x^36 - x^35 + x^33 - x^32 + x^30 - x^28 ++    x^27 - x^25 + x^24 - x^22 + x^21 - x^19 + x^18 - x^16 + x^15 - x^13 + x^12 - x^10+    + x^9 - x^7 + x^6 - x^4 + x^3 - x + 1+  '94': x^46 - x^45 + x^44 - x^43 + x^42 - x^41 + x^40 - x^39 + x^38 - x^37 + x^36+    - x^35 + x^34 - x^33 + x^32 - x^31 + x^30 - x^29 + x^28 - x^27 + x^26 - x^25 ++    x^24 - x^23 + x^22 - x^21 + x^20 - x^19 + x^18 - x^17 + x^16 - x^15 + x^14 - x^13+    + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1+  '95': x^72 - x^71 + x^67 - x^66 + x^62 - x^61 + x^57 - x^56 + x^53 - x^51 + x^48+    - x^46 + x^43 - x^41 + x^38 - x^36 + x^34 - x^31 + x^29 - x^26 + x^24 - x^21 ++    x^19 - x^16 + x^15 - x^11 + x^10 - x^6 + x^5 - x + 1+  '96': x^32 - x^16 + 1+  '97': x^96 + x^95 + x^94 + x^93 + x^92 + x^91 + x^90 + x^89 + x^88 + x^87 + x^86+    + x^85 + x^84 + x^83 + x^82 + x^81 + x^80 + x^79 + x^78 + x^77 + x^76 + x^75 ++    x^74 + x^73 + x^72 + x^71 + x^70 + x^69 + x^68 + x^67 + x^66 + x^65 + x^64 + x^63+    + x^62 + x^61 + x^60 + x^59 + x^58 + x^57 + x^56 + x^55 + x^54 + x^53 + x^52 ++    x^51 + x^50 + x^49 + x^48 + x^47 + x^46 + x^45 + x^44 + x^43 + x^42 + x^41 + x^40+    + x^39 + x^38 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 ++    x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17+    + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5+    + x^4 + x^3 + x^2 + x + 1+  '98': x^42 - x^35 + x^28 - x^21 + x^14 - x^7 + 1+  '99': x^60 - x^57 + x^51 - x^48 + x^42 - x^39 + x^33 - x^30 + x^27 - x^21 + x^18+    - x^12 + x^9 - x^3 + 1+  '100': x^40 - x^30 + x^20 - x^10 + 1