Properties

Label 571.k
Modulus $571$
Conductor $571$
Order $57$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(571, base_ring=CyclotomicField(114))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([104]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(4,571))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(571\)
Conductor: \(571\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(57\)
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: $\Q(\zeta_{57})$
Fixed field: Number field defined by a degree 57 polynomial

First 31 of 36 characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(11\)
\(\chi_{571}(4,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{57}\right)\) \(e\left(\frac{52}{57}\right)\) \(e\left(\frac{22}{57}\right)\) \(e\left(\frac{56}{57}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{47}{57}\right)\) \(e\left(\frac{10}{57}\right)\) \(e\left(\frac{28}{57}\right)\)
\(\chi_{571}(16,\cdot)\) \(1\) \(1\) \(e\left(\frac{22}{57}\right)\) \(e\left(\frac{47}{57}\right)\) \(e\left(\frac{44}{57}\right)\) \(e\left(\frac{55}{57}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{37}{57}\right)\) \(e\left(\frac{20}{57}\right)\) \(e\left(\frac{56}{57}\right)\)
\(\chi_{571}(29,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{57}\right)\) \(e\left(\frac{20}{57}\right)\) \(e\left(\frac{26}{57}\right)\) \(e\left(\frac{4}{57}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{40}{57}\right)\) \(e\left(\frac{17}{57}\right)\) \(e\left(\frac{2}{57}\right)\)
\(\chi_{571}(82,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{57}\right)\) \(e\left(\frac{34}{57}\right)\) \(e\left(\frac{10}{57}\right)\) \(e\left(\frac{41}{57}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{11}{57}\right)\) \(e\left(\frac{46}{57}\right)\) \(e\left(\frac{49}{57}\right)\)
\(\chi_{571}(124,\cdot)\) \(1\) \(1\) \(e\left(\frac{14}{57}\right)\) \(e\left(\frac{4}{57}\right)\) \(e\left(\frac{28}{57}\right)\) \(e\left(\frac{35}{57}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{8}{57}\right)\) \(e\left(\frac{49}{57}\right)\) \(e\left(\frac{46}{57}\right)\)
\(\chi_{571}(143,\cdot)\) \(1\) \(1\) \(e\left(\frac{46}{57}\right)\) \(e\left(\frac{5}{57}\right)\) \(e\left(\frac{35}{57}\right)\) \(e\left(\frac{1}{57}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{10}{57}\right)\) \(e\left(\frac{47}{57}\right)\) \(e\left(\frac{29}{57}\right)\)
\(\chi_{571}(150,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{57}\right)\) \(e\left(\frac{25}{57}\right)\) \(e\left(\frac{4}{57}\right)\) \(e\left(\frac{5}{57}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{50}{57}\right)\) \(e\left(\frac{7}{57}\right)\) \(e\left(\frac{31}{57}\right)\)
\(\chi_{571}(220,\cdot)\) \(1\) \(1\) \(e\left(\frac{53}{57}\right)\) \(e\left(\frac{7}{57}\right)\) \(e\left(\frac{49}{57}\right)\) \(e\left(\frac{47}{57}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{14}{57}\right)\) \(e\left(\frac{43}{57}\right)\) \(e\left(\frac{52}{57}\right)\)
\(\chi_{571}(231,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{57}\right)\) \(e\left(\frac{50}{57}\right)\) \(e\left(\frac{8}{57}\right)\) \(e\left(\frac{10}{57}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{43}{57}\right)\) \(e\left(\frac{14}{57}\right)\) \(e\left(\frac{5}{57}\right)\)
\(\chi_{571}(236,\cdot)\) \(1\) \(1\) \(e\left(\frac{32}{57}\right)\) \(e\left(\frac{1}{57}\right)\) \(e\left(\frac{7}{57}\right)\) \(e\left(\frac{23}{57}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{2}{57}\right)\) \(e\left(\frac{55}{57}\right)\) \(e\left(\frac{40}{57}\right)\)
\(\chi_{571}(256,\cdot)\) \(1\) \(1\) \(e\left(\frac{44}{57}\right)\) \(e\left(\frac{37}{57}\right)\) \(e\left(\frac{31}{57}\right)\) \(e\left(\frac{53}{57}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{17}{57}\right)\) \(e\left(\frac{40}{57}\right)\) \(e\left(\frac{55}{57}\right)\)
\(\chi_{571}(258,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{57}\right)\) \(e\left(\frac{43}{57}\right)\) \(e\left(\frac{16}{57}\right)\) \(e\left(\frac{20}{57}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{29}{57}\right)\) \(e\left(\frac{28}{57}\right)\) \(e\left(\frac{10}{57}\right)\)
\(\chi_{571}(270,\cdot)\) \(1\) \(1\) \(e\left(\frac{26}{57}\right)\) \(e\left(\frac{40}{57}\right)\) \(e\left(\frac{52}{57}\right)\) \(e\left(\frac{8}{57}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{23}{57}\right)\) \(e\left(\frac{34}{57}\right)\) \(e\left(\frac{4}{57}\right)\)
\(\chi_{571}(285,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{57}\right)\) \(e\left(\frac{31}{57}\right)\) \(e\left(\frac{46}{57}\right)\) \(e\left(\frac{29}{57}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{5}{57}\right)\) \(e\left(\frac{52}{57}\right)\) \(e\left(\frac{43}{57}\right)\)
\(\chi_{571}(309,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{57}\right)\) \(e\left(\frac{2}{57}\right)\) \(e\left(\frac{14}{57}\right)\) \(e\left(\frac{46}{57}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{4}{57}\right)\) \(e\left(\frac{53}{57}\right)\) \(e\left(\frac{23}{57}\right)\)
\(\chi_{571}(328,\cdot)\) \(1\) \(1\) \(e\left(\frac{16}{57}\right)\) \(e\left(\frac{29}{57}\right)\) \(e\left(\frac{32}{57}\right)\) \(e\left(\frac{40}{57}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{1}{57}\right)\) \(e\left(\frac{56}{57}\right)\) \(e\left(\frac{20}{57}\right)\)
\(\chi_{571}(339,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{57}\right)\) \(e\left(\frac{41}{57}\right)\) \(e\left(\frac{2}{57}\right)\) \(e\left(\frac{31}{57}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{25}{57}\right)\) \(e\left(\frac{32}{57}\right)\) \(e\left(\frac{44}{57}\right)\)
\(\chi_{571}(362,\cdot)\) \(1\) \(1\) \(e\left(\frac{40}{57}\right)\) \(e\left(\frac{44}{57}\right)\) \(e\left(\frac{23}{57}\right)\) \(e\left(\frac{43}{57}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{31}{57}\right)\) \(e\left(\frac{26}{57}\right)\) \(e\left(\frac{50}{57}\right)\)
\(\chi_{571}(373,\cdot)\) \(1\) \(1\) \(e\left(\frac{43}{57}\right)\) \(e\left(\frac{53}{57}\right)\) \(e\left(\frac{29}{57}\right)\) \(e\left(\frac{22}{57}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{49}{57}\right)\) \(e\left(\frac{8}{57}\right)\) \(e\left(\frac{11}{57}\right)\)
\(\chi_{571}(376,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{57}\right)\) \(e\left(\frac{49}{57}\right)\) \(e\left(\frac{1}{57}\right)\) \(e\left(\frac{44}{57}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{41}{57}\right)\) \(e\left(\frac{16}{57}\right)\) \(e\left(\frac{22}{57}\right)\)
\(\chi_{571}(383,\cdot)\) \(1\) \(1\) \(e\left(\frac{52}{57}\right)\) \(e\left(\frac{23}{57}\right)\) \(e\left(\frac{47}{57}\right)\) \(e\left(\frac{16}{57}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{46}{57}\right)\) \(e\left(\frac{11}{57}\right)\) \(e\left(\frac{8}{57}\right)\)
\(\chi_{571}(396,\cdot)\) \(1\) \(1\) \(e\left(\frac{20}{57}\right)\) \(e\left(\frac{22}{57}\right)\) \(e\left(\frac{40}{57}\right)\) \(e\left(\frac{50}{57}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{44}{57}\right)\) \(e\left(\frac{13}{57}\right)\) \(e\left(\frac{25}{57}\right)\)
\(\chi_{571}(418,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{57}\right)\) \(e\left(\frac{13}{57}\right)\) \(e\left(\frac{34}{57}\right)\) \(e\left(\frac{14}{57}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{26}{57}\right)\) \(e\left(\frac{31}{57}\right)\) \(e\left(\frac{7}{57}\right)\)
\(\chi_{571}(436,\cdot)\) \(1\) \(1\) \(e\left(\frac{49}{57}\right)\) \(e\left(\frac{14}{57}\right)\) \(e\left(\frac{41}{57}\right)\) \(e\left(\frac{37}{57}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{28}{57}\right)\) \(e\left(\frac{29}{57}\right)\) \(e\left(\frac{47}{57}\right)\)
\(\chi_{571}(442,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{57}\right)\) \(e\left(\frac{17}{57}\right)\) \(e\left(\frac{5}{57}\right)\) \(e\left(\frac{49}{57}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{34}{57}\right)\) \(e\left(\frac{23}{57}\right)\) \(e\left(\frac{53}{57}\right)\)
\(\chi_{571}(443,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{57}\right)\) \(e\left(\frac{11}{57}\right)\) \(e\left(\frac{20}{57}\right)\) \(e\left(\frac{25}{57}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{22}{57}\right)\) \(e\left(\frac{35}{57}\right)\) \(e\left(\frac{41}{57}\right)\)
\(\chi_{571}(453,\cdot)\) \(1\) \(1\) \(e\left(\frac{55}{57}\right)\) \(e\left(\frac{32}{57}\right)\) \(e\left(\frac{53}{57}\right)\) \(e\left(\frac{52}{57}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{7}{57}\right)\) \(e\left(\frac{50}{57}\right)\) \(e\left(\frac{26}{57}\right)\)
\(\chi_{571}(464,\cdot)\) \(1\) \(1\) \(e\left(\frac{35}{57}\right)\) \(e\left(\frac{10}{57}\right)\) \(e\left(\frac{13}{57}\right)\) \(e\left(\frac{2}{57}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{20}{57}\right)\) \(e\left(\frac{37}{57}\right)\) \(e\left(\frac{1}{57}\right)\)
\(\chi_{571}(486,\cdot)\) \(1\) \(1\) \(e\left(\frac{50}{57}\right)\) \(e\left(\frac{55}{57}\right)\) \(e\left(\frac{43}{57}\right)\) \(e\left(\frac{11}{57}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{53}{57}\right)\) \(e\left(\frac{4}{57}\right)\) \(e\left(\frac{34}{57}\right)\)
\(\chi_{571}(496,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{57}\right)\) \(e\left(\frac{56}{57}\right)\) \(e\left(\frac{50}{57}\right)\) \(e\left(\frac{34}{57}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{55}{57}\right)\) \(e\left(\frac{2}{57}\right)\) \(e\left(\frac{17}{57}\right)\)
\(\chi_{571}(509,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{57}\right)\) \(e\left(\frac{35}{57}\right)\) \(e\left(\frac{17}{57}\right)\) \(e\left(\frac{7}{57}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{13}{57}\right)\) \(e\left(\frac{44}{57}\right)\) \(e\left(\frac{32}{57}\right)\)