Properties

Label 4033.hg
Modulus $4033$
Conductor $4033$
Order $54$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(4033, base_ring=CyclotomicField(54))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([51,23]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(28,4033))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(4033\)
Conductor: \(4033\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(54\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

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

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(11\)
\(\chi_{4033}(28,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{19}{27}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{5}{54}\right)\) \(e\left(\frac{25}{27}\right)\) \(e\left(\frac{7}{27}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{27}\right)\) \(e\left(\frac{17}{54}\right)\) \(e\left(\frac{37}{54}\right)\)
\(\chi_{4033}(363,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{27}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{19}{54}\right)\) \(e\left(\frac{14}{27}\right)\) \(e\left(\frac{5}{27}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{27}\right)\) \(e\left(\frac{43}{54}\right)\) \(e\left(\frac{11}{54}\right)\)
\(\chi_{4033}(411,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{17}{27}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{13}{54}\right)\) \(e\left(\frac{11}{27}\right)\) \(e\left(\frac{2}{27}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{27}\right)\) \(e\left(\frac{1}{54}\right)\) \(e\left(\frac{53}{54}\right)\)
\(\chi_{4033}(465,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{7}{27}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{53}{54}\right)\) \(e\left(\frac{22}{27}\right)\) \(e\left(\frac{4}{27}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{14}{27}\right)\) \(e\left(\frac{29}{54}\right)\) \(e\left(\frac{25}{54}\right)\)
\(\chi_{4033}(632,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{27}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{7}{54}\right)\) \(e\left(\frac{8}{27}\right)\) \(e\left(\frac{26}{27}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{10}{27}\right)\) \(e\left(\frac{13}{54}\right)\) \(e\left(\frac{41}{54}\right)\)
\(\chi_{4033}(1320,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{4}{27}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{11}{54}\right)\) \(e\left(\frac{1}{27}\right)\) \(e\left(\frac{10}{27}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{8}{27}\right)\) \(e\left(\frac{5}{54}\right)\) \(e\left(\frac{49}{54}\right)\)
\(\chi_{4033}(1557,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{14}{27}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{25}{54}\right)\) \(e\left(\frac{17}{27}\right)\) \(e\left(\frac{8}{27}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{27}\right)\) \(e\left(\frac{31}{54}\right)\) \(e\left(\frac{23}{54}\right)\)
\(\chi_{4033}(2282,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{13}{27}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{29}{54}\right)\) \(e\left(\frac{10}{27}\right)\) \(e\left(\frac{19}{27}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{26}{27}\right)\) \(e\left(\frac{23}{54}\right)\) \(e\left(\frac{31}{54}\right)\)
\(\chi_{4033}(2393,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{22}{27}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{47}{54}\right)\) \(e\left(\frac{19}{27}\right)\) \(e\left(\frac{1}{27}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{17}{27}\right)\) \(e\left(\frac{41}{54}\right)\) \(e\left(\frac{13}{54}\right)\)
\(\chi_{4033}(2722,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{25}{27}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{35}{54}\right)\) \(e\left(\frac{13}{27}\right)\) \(e\left(\frac{22}{27}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{23}{27}\right)\) \(e\left(\frac{11}{54}\right)\) \(e\left(\frac{43}{54}\right)\)
\(\chi_{4033}(3112,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{26}{27}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{31}{54}\right)\) \(e\left(\frac{20}{27}\right)\) \(e\left(\frac{11}{27}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{25}{27}\right)\) \(e\left(\frac{19}{54}\right)\) \(e\left(\frac{35}{54}\right)\)
\(\chi_{4033}(3249,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{11}{27}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{37}{54}\right)\) \(e\left(\frac{23}{27}\right)\) \(e\left(\frac{14}{27}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{22}{27}\right)\) \(e\left(\frac{7}{54}\right)\) \(e\left(\frac{47}{54}\right)\)
\(\chi_{4033}(3370,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{23}{27}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{43}{54}\right)\) \(e\left(\frac{26}{27}\right)\) \(e\left(\frac{17}{27}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{19}{27}\right)\) \(e\left(\frac{49}{54}\right)\) \(e\left(\frac{5}{54}\right)\)
\(\chi_{4033}(3462,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{16}{27}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{17}{54}\right)\) \(e\left(\frac{4}{27}\right)\) \(e\left(\frac{13}{27}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{27}\right)\) \(e\left(\frac{47}{54}\right)\) \(e\left(\frac{7}{54}\right)\)
\(\chi_{4033}(3582,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{20}{27}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{54}\right)\) \(e\left(\frac{5}{27}\right)\) \(e\left(\frac{23}{27}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{27}\right)\) \(e\left(\frac{25}{54}\right)\) \(e\left(\frac{29}{54}\right)\)
\(\chi_{4033}(3617,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{27}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{23}{54}\right)\) \(e\left(\frac{7}{27}\right)\) \(e\left(\frac{16}{27}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{27}\right)\) \(e\left(\frac{35}{54}\right)\) \(e\left(\frac{19}{54}\right)\)
\(\chi_{4033}(3876,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{10}{27}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{41}{54}\right)\) \(e\left(\frac{16}{27}\right)\) \(e\left(\frac{25}{27}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{20}{27}\right)\) \(e\left(\frac{53}{54}\right)\) \(e\left(\frac{1}{54}\right)\)
\(\chi_{4033}(3889,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{8}{27}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{49}{54}\right)\) \(e\left(\frac{2}{27}\right)\) \(e\left(\frac{20}{27}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{16}{27}\right)\) \(e\left(\frac{37}{54}\right)\) \(e\left(\frac{17}{54}\right)\)