Properties

Label 571.m
Modulus $571$
Conductor $571$
Order $114$
Real no
Primitive yes
Minimal yes
Parity odd

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([109]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(2,571))
 
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: \(114\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
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 114 polynomial (not computed)

First 31 of 36 characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(11\)
\(\chi_{571}(2,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{114}\right)\) \(e\left(\frac{109}{114}\right)\) \(e\left(\frac{11}{57}\right)\) \(e\left(\frac{28}{57}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{33}{38}\right)\) \(e\left(\frac{11}{38}\right)\) \(e\left(\frac{52}{57}\right)\) \(e\left(\frac{67}{114}\right)\) \(e\left(\frac{14}{57}\right)\)
\(\chi_{571}(32,\cdot)\) \(-1\) \(1\) \(e\left(\frac{55}{114}\right)\) \(e\left(\frac{89}{114}\right)\) \(e\left(\frac{55}{57}\right)\) \(e\left(\frac{26}{57}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{13}{38}\right)\) \(e\left(\frac{17}{38}\right)\) \(e\left(\frac{32}{57}\right)\) \(e\left(\frac{107}{114}\right)\) \(e\left(\frac{13}{57}\right)\)
\(\chi_{571}(41,\cdot)\) \(-1\) \(1\) \(e\left(\frac{113}{114}\right)\) \(e\left(\frac{73}{114}\right)\) \(e\left(\frac{56}{57}\right)\) \(e\left(\frac{13}{57}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{35}{38}\right)\) \(e\left(\frac{37}{38}\right)\) \(e\left(\frac{16}{57}\right)\) \(e\left(\frac{25}{114}\right)\) \(e\left(\frac{35}{57}\right)\)
\(\chi_{571}(47,\cdot)\) \(-1\) \(1\) \(e\left(\frac{25}{114}\right)\) \(e\left(\frac{113}{114}\right)\) \(e\left(\frac{25}{57}\right)\) \(e\left(\frac{17}{57}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{37}{38}\right)\) \(e\left(\frac{25}{38}\right)\) \(e\left(\frac{56}{57}\right)\) \(e\left(\frac{59}{114}\right)\) \(e\left(\frac{37}{57}\right)\)
\(\chi_{571}(58,\cdot)\) \(-1\) \(1\) \(e\left(\frac{37}{114}\right)\) \(e\left(\frac{35}{114}\right)\) \(e\left(\frac{37}{57}\right)\) \(e\left(\frac{32}{57}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{35}{38}\right)\) \(e\left(\frac{37}{38}\right)\) \(e\left(\frac{35}{57}\right)\) \(e\left(\frac{101}{114}\right)\) \(e\left(\frac{16}{57}\right)\)
\(\chi_{571}(62,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{114}\right)\) \(e\left(\frac{13}{114}\right)\) \(e\left(\frac{17}{57}\right)\) \(e\left(\frac{7}{57}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{13}{38}\right)\) \(e\left(\frac{17}{38}\right)\) \(e\left(\frac{13}{57}\right)\) \(e\left(\frac{31}{114}\right)\) \(e\left(\frac{32}{57}\right)\)
\(\chi_{571}(75,\cdot)\) \(-1\) \(1\) \(e\left(\frac{107}{114}\right)\) \(e\left(\frac{55}{114}\right)\) \(e\left(\frac{50}{57}\right)\) \(e\left(\frac{34}{57}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{17}{38}\right)\) \(e\left(\frac{31}{38}\right)\) \(e\left(\frac{55}{57}\right)\) \(e\left(\frac{61}{114}\right)\) \(e\left(\frac{17}{57}\right)\)
\(\chi_{571}(85,\cdot)\) \(-1\) \(1\) \(e\left(\frac{43}{114}\right)\) \(e\left(\frac{53}{114}\right)\) \(e\left(\frac{43}{57}\right)\) \(e\left(\frac{11}{57}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{15}{38}\right)\) \(e\left(\frac{5}{38}\right)\) \(e\left(\frac{53}{57}\right)\) \(e\left(\frac{65}{114}\right)\) \(e\left(\frac{34}{57}\right)\)
\(\chi_{571}(107,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{114}\right)\) \(e\left(\frac{77}{114}\right)\) \(e\left(\frac{13}{57}\right)\) \(e\left(\frac{2}{57}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{1}{38}\right)\) \(e\left(\frac{13}{38}\right)\) \(e\left(\frac{20}{57}\right)\) \(e\left(\frac{17}{114}\right)\) \(e\left(\frac{1}{57}\right)\)
\(\chi_{571}(118,\cdot)\) \(-1\) \(1\) \(e\left(\frac{53}{114}\right)\) \(e\left(\frac{7}{114}\right)\) \(e\left(\frac{53}{57}\right)\) \(e\left(\frac{52}{57}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{7}{38}\right)\) \(e\left(\frac{15}{38}\right)\) \(e\left(\frac{7}{57}\right)\) \(e\left(\frac{43}{114}\right)\) \(e\left(\frac{26}{57}\right)\)
\(\chi_{571}(128,\cdot)\) \(-1\) \(1\) \(e\left(\frac{77}{114}\right)\) \(e\left(\frac{79}{114}\right)\) \(e\left(\frac{20}{57}\right)\) \(e\left(\frac{25}{57}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{3}{38}\right)\) \(e\left(\frac{1}{38}\right)\) \(e\left(\frac{22}{57}\right)\) \(e\left(\frac{13}{114}\right)\) \(e\left(\frac{41}{57}\right)\)
\(\chi_{571}(129,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{114}\right)\) \(e\left(\frac{91}{114}\right)\) \(e\left(\frac{5}{57}\right)\) \(e\left(\frac{49}{57}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{15}{38}\right)\) \(e\left(\frac{5}{38}\right)\) \(e\left(\frac{34}{57}\right)\) \(e\left(\frac{103}{114}\right)\) \(e\left(\frac{53}{57}\right)\)
\(\chi_{571}(135,\cdot)\) \(-1\) \(1\) \(e\left(\frac{41}{114}\right)\) \(e\left(\frac{85}{114}\right)\) \(e\left(\frac{41}{57}\right)\) \(e\left(\frac{37}{57}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{9}{38}\right)\) \(e\left(\frac{3}{38}\right)\) \(e\left(\frac{28}{57}\right)\) \(e\left(\frac{1}{114}\right)\) \(e\left(\frac{47}{57}\right)\)
\(\chi_{571}(153,\cdot)\) \(-1\) \(1\) \(e\left(\frac{91}{114}\right)\) \(e\left(\frac{83}{114}\right)\) \(e\left(\frac{34}{57}\right)\) \(e\left(\frac{14}{57}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{7}{38}\right)\) \(e\left(\frac{15}{38}\right)\) \(e\left(\frac{26}{57}\right)\) \(e\left(\frac{5}{114}\right)\) \(e\left(\frac{7}{57}\right)\)
\(\chi_{571}(175,\cdot)\) \(-1\) \(1\) \(e\left(\frac{97}{114}\right)\) \(e\left(\frac{101}{114}\right)\) \(e\left(\frac{40}{57}\right)\) \(e\left(\frac{50}{57}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{25}{38}\right)\) \(e\left(\frac{21}{38}\right)\) \(e\left(\frac{44}{57}\right)\) \(e\left(\frac{83}{114}\right)\) \(e\left(\frac{25}{57}\right)\)
\(\chi_{571}(188,\cdot)\) \(-1\) \(1\) \(e\left(\frac{47}{114}\right)\) \(e\left(\frac{103}{114}\right)\) \(e\left(\frac{47}{57}\right)\) \(e\left(\frac{16}{57}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{27}{38}\right)\) \(e\left(\frac{9}{38}\right)\) \(e\left(\frac{46}{57}\right)\) \(e\left(\frac{79}{114}\right)\) \(e\left(\frac{8}{57}\right)\)
\(\chi_{571}(195,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{114}\right)\) \(e\left(\frac{41}{114}\right)\) \(e\left(\frac{1}{57}\right)\) \(e\left(\frac{44}{57}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{3}{38}\right)\) \(e\left(\frac{1}{38}\right)\) \(e\left(\frac{41}{57}\right)\) \(e\left(\frac{89}{114}\right)\) \(e\left(\frac{22}{57}\right)\)
\(\chi_{571}(198,\cdot)\) \(-1\) \(1\) \(e\left(\frac{29}{114}\right)\) \(e\left(\frac{49}{114}\right)\) \(e\left(\frac{29}{57}\right)\) \(e\left(\frac{22}{57}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{11}{38}\right)\) \(e\left(\frac{29}{38}\right)\) \(e\left(\frac{49}{57}\right)\) \(e\left(\frac{73}{114}\right)\) \(e\left(\frac{11}{57}\right)\)
\(\chi_{571}(209,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{114}\right)\) \(e\left(\frac{31}{114}\right)\) \(e\left(\frac{23}{57}\right)\) \(e\left(\frac{43}{57}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{31}{38}\right)\) \(e\left(\frac{23}{38}\right)\) \(e\left(\frac{31}{57}\right)\) \(e\left(\frac{109}{114}\right)\) \(e\left(\frac{50}{57}\right)\)
\(\chi_{571}(232,\cdot)\) \(-1\) \(1\) \(e\left(\frac{59}{114}\right)\) \(e\left(\frac{25}{114}\right)\) \(e\left(\frac{2}{57}\right)\) \(e\left(\frac{31}{57}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{25}{38}\right)\) \(e\left(\frac{21}{38}\right)\) \(e\left(\frac{25}{57}\right)\) \(e\left(\frac{7}{114}\right)\) \(e\left(\frac{44}{57}\right)\)
\(\chi_{571}(243,\cdot)\) \(-1\) \(1\) \(e\left(\frac{89}{114}\right)\) \(e\left(\frac{1}{114}\right)\) \(e\left(\frac{32}{57}\right)\) \(e\left(\frac{40}{57}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{1}{38}\right)\) \(e\left(\frac{13}{38}\right)\) \(e\left(\frac{1}{57}\right)\) \(e\left(\frac{55}{114}\right)\) \(e\left(\frac{20}{57}\right)\)
\(\chi_{571}(262,\cdot)\) \(-1\) \(1\) \(e\left(\frac{71}{114}\right)\) \(e\left(\frac{61}{114}\right)\) \(e\left(\frac{14}{57}\right)\) \(e\left(\frac{46}{57}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{23}{38}\right)\) \(e\left(\frac{33}{38}\right)\) \(e\left(\frac{4}{57}\right)\) \(e\left(\frac{49}{114}\right)\) \(e\left(\frac{23}{57}\right)\)
\(\chi_{571}(286,\cdot)\) \(-1\) \(1\) \(e\left(\frac{103}{114}\right)\) \(e\left(\frac{5}{114}\right)\) \(e\left(\frac{46}{57}\right)\) \(e\left(\frac{29}{57}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{5}{38}\right)\) \(e\left(\frac{27}{38}\right)\) \(e\left(\frac{5}{57}\right)\) \(e\left(\frac{47}{114}\right)\) \(e\left(\frac{43}{57}\right)\)
\(\chi_{571}(301,\cdot)\) \(-1\) \(1\) \(e\left(\frac{109}{114}\right)\) \(e\left(\frac{23}{114}\right)\) \(e\left(\frac{52}{57}\right)\) \(e\left(\frac{8}{57}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{23}{38}\right)\) \(e\left(\frac{33}{38}\right)\) \(e\left(\frac{23}{57}\right)\) \(e\left(\frac{11}{114}\right)\) \(e\left(\frac{4}{57}\right)\)
\(\chi_{571}(313,\cdot)\) \(-1\) \(1\) \(e\left(\frac{73}{114}\right)\) \(e\left(\frac{29}{114}\right)\) \(e\left(\frac{16}{57}\right)\) \(e\left(\frac{20}{57}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{29}{38}\right)\) \(e\left(\frac{35}{38}\right)\) \(e\left(\frac{29}{57}\right)\) \(e\left(\frac{113}{114}\right)\) \(e\left(\frac{10}{57}\right)\)
\(\chi_{571}(315,\cdot)\) \(-1\) \(1\) \(e\left(\frac{31}{114}\right)\) \(e\left(\frac{17}{114}\right)\) \(e\left(\frac{31}{57}\right)\) \(e\left(\frac{53}{57}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{17}{38}\right)\) \(e\left(\frac{31}{38}\right)\) \(e\left(\frac{17}{57}\right)\) \(e\left(\frac{23}{114}\right)\) \(e\left(\frac{55}{57}\right)\)
\(\chi_{571}(335,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{114}\right)\) \(e\left(\frac{59}{114}\right)\) \(e\left(\frac{7}{57}\right)\) \(e\left(\frac{23}{57}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{21}{38}\right)\) \(e\left(\frac{7}{38}\right)\) \(e\left(\frac{2}{57}\right)\) \(e\left(\frac{53}{114}\right)\) \(e\left(\frac{40}{57}\right)\)
\(\chi_{571}(340,\cdot)\) \(-1\) \(1\) \(e\left(\frac{65}{114}\right)\) \(e\left(\frac{43}{114}\right)\) \(e\left(\frac{8}{57}\right)\) \(e\left(\frac{10}{57}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{5}{38}\right)\) \(e\left(\frac{27}{38}\right)\) \(e\left(\frac{43}{57}\right)\) \(e\left(\frac{85}{114}\right)\) \(e\left(\frac{5}{57}\right)\)
\(\chi_{571}(351,\cdot)\) \(-1\) \(1\) \(e\left(\frac{49}{114}\right)\) \(e\left(\frac{71}{114}\right)\) \(e\left(\frac{49}{57}\right)\) \(e\left(\frac{47}{57}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{33}{38}\right)\) \(e\left(\frac{11}{38}\right)\) \(e\left(\frac{14}{57}\right)\) \(e\left(\frac{29}{114}\right)\) \(e\left(\frac{52}{57}\right)\)
\(\chi_{571}(421,\cdot)\) \(-1\) \(1\) \(e\left(\frac{61}{114}\right)\) \(e\left(\frac{107}{114}\right)\) \(e\left(\frac{4}{57}\right)\) \(e\left(\frac{5}{57}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{31}{38}\right)\) \(e\left(\frac{23}{38}\right)\) \(e\left(\frac{50}{57}\right)\) \(e\left(\frac{71}{114}\right)\) \(e\left(\frac{31}{57}\right)\)
\(\chi_{571}(428,\cdot)\) \(-1\) \(1\) \(e\left(\frac{35}{114}\right)\) \(e\left(\frac{67}{114}\right)\) \(e\left(\frac{35}{57}\right)\) \(e\left(\frac{1}{57}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{29}{38}\right)\) \(e\left(\frac{35}{38}\right)\) \(e\left(\frac{10}{57}\right)\) \(e\left(\frac{37}{114}\right)\) \(e\left(\frac{29}{57}\right)\)