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Properties

Label 162.h
Modulus 162162
Conductor 8181
Order 5454
Real no
Primitive no
Minimal yes
Parity odd

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(162, base_ring=CyclotomicField(54)) M = H._module chi = DirichletCharacter(H, M([23])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(5,162)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 162162
Conductor: 8181
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 5454
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 81.h
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: Q(ζ27)\Q(\zeta_{27})
Fixed field: Number field defined by a degree 54 polynomial

Characters in Galois orbit

Character −1-1 11 55 77 1111 1313 1717 1919 2323 2525 2929 3131
χ162(5,⋅)\chi_{162}(5,\cdot) −1-1 11 e(4354)e\left(\frac{43}{54}\right) e(2227)e\left(\frac{22}{27}\right) e(2954)e\left(\frac{29}{54}\right) e(1127)e\left(\frac{11}{27}\right) e(118)e\left(\frac{1}{18}\right) e(49)e\left(\frac{4}{9}\right) e(3754)e\left(\frac{37}{54}\right) e(1627)e\left(\frac{16}{27}\right) e(4154)e\left(\frac{41}{54}\right) e(1427)e\left(\frac{14}{27}\right)
χ162(11,⋅)\chi_{162}(11,\cdot) −1-1 11 e(2954)e\left(\frac{29}{54}\right) e(2327)e\left(\frac{23}{27}\right) e(754)e\left(\frac{7}{54}\right) e(2527)e\left(\frac{25}{27}\right) e(1718)e\left(\frac{17}{18}\right) e(59)e\left(\frac{5}{9}\right) e(3554)e\left(\frac{35}{54}\right) e(227)e\left(\frac{2}{27}\right) e(4954)e\left(\frac{49}{54}\right) e(2227)e\left(\frac{22}{27}\right)
χ162(23,⋅)\chi_{162}(23,\cdot) −1-1 11 e(3754)e\left(\frac{37}{54}\right) e(727)e\left(\frac{7}{27}\right) e(3554)e\left(\frac{35}{54}\right) e(1727)e\left(\frac{17}{27}\right) e(1318)e\left(\frac{13}{18}\right) e(79)e\left(\frac{7}{9}\right) e(1354)e\left(\frac{13}{54}\right) e(1027)e\left(\frac{10}{27}\right) e(2954)e\left(\frac{29}{54}\right) e(227)e\left(\frac{2}{27}\right)
χ162(29,⋅)\chi_{162}(29,\cdot) −1-1 11 e(4154)e\left(\frac{41}{54}\right) e(2627)e\left(\frac{26}{27}\right) e(4954)e\left(\frac{49}{54}\right) e(1327)e\left(\frac{13}{27}\right) e(1118)e\left(\frac{11}{18}\right) e(89)e\left(\frac{8}{9}\right) e(2954)e\left(\frac{29}{54}\right) e(1427)e\left(\frac{14}{27}\right) e(1954)e\left(\frac{19}{54}\right) e(1927)e\left(\frac{19}{27}\right)
χ162(41,⋅)\chi_{162}(41,\cdot) −1-1 11 e(3154)e\left(\frac{31}{54}\right) e(1927)e\left(\frac{19}{27}\right) e(4154)e\left(\frac{41}{54}\right) e(2327)e\left(\frac{23}{27}\right) e(718)e\left(\frac{7}{18}\right) e(19)e\left(\frac{1}{9}\right) e(4354)e\left(\frac{43}{54}\right) e(427)e\left(\frac{4}{27}\right) e(1754)e\left(\frac{17}{54}\right) e(1727)e\left(\frac{17}{27}\right)
χ162(47,⋅)\chi_{162}(47,\cdot) −1-1 11 e(5354)e\left(\frac{53}{54}\right) e(227)e\left(\frac{2}{27}\right) e(3754)e\left(\frac{37}{54}\right) e(127)e\left(\frac{1}{27}\right) e(518)e\left(\frac{5}{18}\right) e(29)e\left(\frac{2}{9}\right) e(2354)e\left(\frac{23}{54}\right) e(2627)e\left(\frac{26}{27}\right) e(4354)e\left(\frac{43}{54}\right) e(1627)e\left(\frac{16}{27}\right)
χ162(59,⋅)\chi_{162}(59,\cdot) −1-1 11 e(2554)e\left(\frac{25}{54}\right) e(427)e\left(\frac{4}{27}\right) e(4754)e\left(\frac{47}{54}\right) e(227)e\left(\frac{2}{27}\right) e(118)e\left(\frac{1}{18}\right) e(49)e\left(\frac{4}{9}\right) e(1954)e\left(\frac{19}{54}\right) e(2527)e\left(\frac{25}{27}\right) e(554)e\left(\frac{5}{54}\right) e(527)e\left(\frac{5}{27}\right)
χ162(65,⋅)\chi_{162}(65,\cdot) −1-1 11 e(1154)e\left(\frac{11}{54}\right) e(527)e\left(\frac{5}{27}\right) e(2554)e\left(\frac{25}{54}\right) e(1627)e\left(\frac{16}{27}\right) e(1718)e\left(\frac{17}{18}\right) e(59)e\left(\frac{5}{9}\right) e(1754)e\left(\frac{17}{54}\right) e(1127)e\left(\frac{11}{27}\right) e(1354)e\left(\frac{13}{54}\right) e(1327)e\left(\frac{13}{27}\right)
χ162(77,⋅)\chi_{162}(77,\cdot) −1-1 11 e(1954)e\left(\frac{19}{54}\right) e(1627)e\left(\frac{16}{27}\right) e(5354)e\left(\frac{53}{54}\right) e(827)e\left(\frac{8}{27}\right) e(1318)e\left(\frac{13}{18}\right) e(79)e\left(\frac{7}{9}\right) e(4954)e\left(\frac{49}{54}\right) e(1927)e\left(\frac{19}{27}\right) e(4754)e\left(\frac{47}{54}\right) e(2027)e\left(\frac{20}{27}\right)
χ162(83,⋅)\chi_{162}(83,\cdot) −1-1 11 e(2354)e\left(\frac{23}{54}\right) e(827)e\left(\frac{8}{27}\right) e(1354)e\left(\frac{13}{54}\right) e(427)e\left(\frac{4}{27}\right) e(1118)e\left(\frac{11}{18}\right) e(89)e\left(\frac{8}{9}\right) e(1154)e\left(\frac{11}{54}\right) e(2327)e\left(\frac{23}{27}\right) e(3754)e\left(\frac{37}{54}\right) e(1027)e\left(\frac{10}{27}\right)
χ162(95,⋅)\chi_{162}(95,\cdot) −1-1 11 e(1354)e\left(\frac{13}{54}\right) e(127)e\left(\frac{1}{27}\right) e(554)e\left(\frac{5}{54}\right) e(1427)e\left(\frac{14}{27}\right) e(718)e\left(\frac{7}{18}\right) e(19)e\left(\frac{1}{9}\right) e(2554)e\left(\frac{25}{54}\right) e(1327)e\left(\frac{13}{27}\right) e(3554)e\left(\frac{35}{54}\right) e(827)e\left(\frac{8}{27}\right)
χ162(101,⋅)\chi_{162}(101,\cdot) −1-1 11 e(3554)e\left(\frac{35}{54}\right) e(1127)e\left(\frac{11}{27}\right) e(154)e\left(\frac{1}{54}\right) e(1927)e\left(\frac{19}{27}\right) e(518)e\left(\frac{5}{18}\right) e(29)e\left(\frac{2}{9}\right) e(554)e\left(\frac{5}{54}\right) e(827)e\left(\frac{8}{27}\right) e(754)e\left(\frac{7}{54}\right) e(727)e\left(\frac{7}{27}\right)
χ162(113,⋅)\chi_{162}(113,\cdot) −1-1 11 e(754)e\left(\frac{7}{54}\right) e(1327)e\left(\frac{13}{27}\right) e(1154)e\left(\frac{11}{54}\right) e(2027)e\left(\frac{20}{27}\right) e(118)e\left(\frac{1}{18}\right) e(49)e\left(\frac{4}{9}\right) e(154)e\left(\frac{1}{54}\right) e(727)e\left(\frac{7}{27}\right) e(2354)e\left(\frac{23}{54}\right) e(2327)e\left(\frac{23}{27}\right)
χ162(119,⋅)\chi_{162}(119,\cdot) −1-1 11 e(4754)e\left(\frac{47}{54}\right) e(1427)e\left(\frac{14}{27}\right) e(4354)e\left(\frac{43}{54}\right) e(727)e\left(\frac{7}{27}\right) e(1718)e\left(\frac{17}{18}\right) e(59)e\left(\frac{5}{9}\right) e(5354)e\left(\frac{53}{54}\right) e(2027)e\left(\frac{20}{27}\right) e(3154)e\left(\frac{31}{54}\right) e(427)e\left(\frac{4}{27}\right)
χ162(131,⋅)\chi_{162}(131,\cdot) −1-1 11 e(154)e\left(\frac{1}{54}\right) e(2527)e\left(\frac{25}{27}\right) e(1754)e\left(\frac{17}{54}\right) e(2627)e\left(\frac{26}{27}\right) e(1318)e\left(\frac{13}{18}\right) e(79)e\left(\frac{7}{9}\right) e(3154)e\left(\frac{31}{54}\right) e(127)e\left(\frac{1}{27}\right) e(1154)e\left(\frac{11}{54}\right) e(1127)e\left(\frac{11}{27}\right)
χ162(137,⋅)\chi_{162}(137,\cdot) −1-1 11 e(554)e\left(\frac{5}{54}\right) e(1727)e\left(\frac{17}{27}\right) e(3154)e\left(\frac{31}{54}\right) e(2227)e\left(\frac{22}{27}\right) e(1118)e\left(\frac{11}{18}\right) e(89)e\left(\frac{8}{9}\right) e(4754)e\left(\frac{47}{54}\right) e(527)e\left(\frac{5}{27}\right) e(154)e\left(\frac{1}{54}\right) e(127)e\left(\frac{1}{27}\right)
χ162(149,⋅)\chi_{162}(149,\cdot) −1-1 11 e(4954)e\left(\frac{49}{54}\right) e(1027)e\left(\frac{10}{27}\right) e(2354)e\left(\frac{23}{54}\right) e(527)e\left(\frac{5}{27}\right) e(718)e\left(\frac{7}{18}\right) e(19)e\left(\frac{1}{9}\right) e(754)e\left(\frac{7}{54}\right) e(2227)e\left(\frac{22}{27}\right) e(5354)e\left(\frac{53}{54}\right) e(2627)e\left(\frac{26}{27}\right)
χ162(155,⋅)\chi_{162}(155,\cdot) −1-1 11 e(1754)e\left(\frac{17}{54}\right) e(2027)e\left(\frac{20}{27}\right) e(1954)e\left(\frac{19}{54}\right) e(1027)e\left(\frac{10}{27}\right) e(518)e\left(\frac{5}{18}\right) e(29)e\left(\frac{2}{9}\right) e(4154)e\left(\frac{41}{54}\right) e(1727)e\left(\frac{17}{27}\right) e(2554)e\left(\frac{25}{54}\right) e(2527)e\left(\frac{25}{27}\right)