Properties

Label 173.d
Modulus $173$
Conductor $173$
Order $43$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Learn more

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(173, base_ring=CyclotomicField(86))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([14]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(6,173))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(173\)
Conductor: \(173\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(43\)
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: $\Q(\zeta_{43})$
Fixed field: 43.43.9952594992767664919302480397055915291864099597331865326873171797085952964991380209309055259529.1

First 31 of 42 characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(11\)
\(\chi_{173}(6,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{43}\right)\) \(e\left(\frac{17}{43}\right)\) \(e\left(\frac{14}{43}\right)\) \(e\left(\frac{15}{43}\right)\) \(e\left(\frac{24}{43}\right)\) \(e\left(\frac{20}{43}\right)\) \(e\left(\frac{21}{43}\right)\) \(e\left(\frac{34}{43}\right)\) \(e\left(\frac{22}{43}\right)\) \(e\left(\frac{32}{43}\right)\)
\(\chi_{173}(10,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{43}\right)\) \(e\left(\frac{12}{43}\right)\) \(e\left(\frac{20}{43}\right)\) \(e\left(\frac{3}{43}\right)\) \(e\left(\frac{22}{43}\right)\) \(e\left(\frac{4}{43}\right)\) \(e\left(\frac{30}{43}\right)\) \(e\left(\frac{24}{43}\right)\) \(e\left(\frac{13}{43}\right)\) \(e\left(\frac{15}{43}\right)\)
\(\chi_{173}(14,\cdot)\) \(1\) \(1\) \(e\left(\frac{24}{43}\right)\) \(e\left(\frac{3}{43}\right)\) \(e\left(\frac{5}{43}\right)\) \(e\left(\frac{33}{43}\right)\) \(e\left(\frac{27}{43}\right)\) \(e\left(\frac{1}{43}\right)\) \(e\left(\frac{29}{43}\right)\) \(e\left(\frac{6}{43}\right)\) \(e\left(\frac{14}{43}\right)\) \(e\left(\frac{36}{43}\right)\)
\(\chi_{173}(16,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{43}\right)\) \(e\left(\frac{27}{43}\right)\) \(e\left(\frac{2}{43}\right)\) \(e\left(\frac{39}{43}\right)\) \(e\left(\frac{28}{43}\right)\) \(e\left(\frac{9}{43}\right)\) \(e\left(\frac{3}{43}\right)\) \(e\left(\frac{11}{43}\right)\) \(e\left(\frac{40}{43}\right)\) \(e\left(\frac{23}{43}\right)\)
\(\chi_{173}(22,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{43}\right)\) \(e\left(\frac{33}{43}\right)\) \(e\left(\frac{12}{43}\right)\) \(e\left(\frac{19}{43}\right)\) \(e\left(\frac{39}{43}\right)\) \(e\left(\frac{11}{43}\right)\) \(e\left(\frac{18}{43}\right)\) \(e\left(\frac{23}{43}\right)\) \(e\left(\frac{25}{43}\right)\) \(e\left(\frac{9}{43}\right)\)
\(\chi_{173}(23,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{43}\right)\) \(e\left(\frac{6}{43}\right)\) \(e\left(\frac{10}{43}\right)\) \(e\left(\frac{23}{43}\right)\) \(e\left(\frac{11}{43}\right)\) \(e\left(\frac{2}{43}\right)\) \(e\left(\frac{15}{43}\right)\) \(e\left(\frac{12}{43}\right)\) \(e\left(\frac{28}{43}\right)\) \(e\left(\frac{29}{43}\right)\)
\(\chi_{173}(29,\cdot)\) \(1\) \(1\) \(e\left(\frac{36}{43}\right)\) \(e\left(\frac{26}{43}\right)\) \(e\left(\frac{29}{43}\right)\) \(e\left(\frac{28}{43}\right)\) \(e\left(\frac{19}{43}\right)\) \(e\left(\frac{23}{43}\right)\) \(e\left(\frac{22}{43}\right)\) \(e\left(\frac{9}{43}\right)\) \(e\left(\frac{21}{43}\right)\) \(e\left(\frac{11}{43}\right)\)
\(\chi_{173}(36,\cdot)\) \(1\) \(1\) \(e\left(\frac{14}{43}\right)\) \(e\left(\frac{34}{43}\right)\) \(e\left(\frac{28}{43}\right)\) \(e\left(\frac{30}{43}\right)\) \(e\left(\frac{5}{43}\right)\) \(e\left(\frac{40}{43}\right)\) \(e\left(\frac{42}{43}\right)\) \(e\left(\frac{25}{43}\right)\) \(e\left(\frac{1}{43}\right)\) \(e\left(\frac{21}{43}\right)\)
\(\chi_{173}(43,\cdot)\) \(1\) \(1\) \(e\left(\frac{21}{43}\right)\) \(e\left(\frac{8}{43}\right)\) \(e\left(\frac{42}{43}\right)\) \(e\left(\frac{2}{43}\right)\) \(e\left(\frac{29}{43}\right)\) \(e\left(\frac{17}{43}\right)\) \(e\left(\frac{20}{43}\right)\) \(e\left(\frac{16}{43}\right)\) \(e\left(\frac{23}{43}\right)\) \(e\left(\frac{10}{43}\right)\)
\(\chi_{173}(47,\cdot)\) \(1\) \(1\) \(e\left(\frac{16}{43}\right)\) \(e\left(\frac{2}{43}\right)\) \(e\left(\frac{32}{43}\right)\) \(e\left(\frac{22}{43}\right)\) \(e\left(\frac{18}{43}\right)\) \(e\left(\frac{15}{43}\right)\) \(e\left(\frac{5}{43}\right)\) \(e\left(\frac{4}{43}\right)\) \(e\left(\frac{38}{43}\right)\) \(e\left(\frac{24}{43}\right)\)
\(\chi_{173}(51,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{43}\right)\) \(e\left(\frac{30}{43}\right)\) \(e\left(\frac{7}{43}\right)\) \(e\left(\frac{29}{43}\right)\) \(e\left(\frac{12}{43}\right)\) \(e\left(\frac{10}{43}\right)\) \(e\left(\frac{32}{43}\right)\) \(e\left(\frac{17}{43}\right)\) \(e\left(\frac{11}{43}\right)\) \(e\left(\frac{16}{43}\right)\)
\(\chi_{173}(52,\cdot)\) \(1\) \(1\) \(e\left(\frac{33}{43}\right)\) \(e\left(\frac{31}{43}\right)\) \(e\left(\frac{23}{43}\right)\) \(e\left(\frac{40}{43}\right)\) \(e\left(\frac{21}{43}\right)\) \(e\left(\frac{39}{43}\right)\) \(e\left(\frac{13}{43}\right)\) \(e\left(\frac{19}{43}\right)\) \(e\left(\frac{30}{43}\right)\) \(e\left(\frac{28}{43}\right)\)
\(\chi_{173}(57,\cdot)\) \(1\) \(1\) \(e\left(\frac{15}{43}\right)\) \(e\left(\frac{18}{43}\right)\) \(e\left(\frac{30}{43}\right)\) \(e\left(\frac{26}{43}\right)\) \(e\left(\frac{33}{43}\right)\) \(e\left(\frac{6}{43}\right)\) \(e\left(\frac{2}{43}\right)\) \(e\left(\frac{36}{43}\right)\) \(e\left(\frac{41}{43}\right)\) \(e\left(\frac{1}{43}\right)\)
\(\chi_{173}(60,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{43}\right)\) \(e\left(\frac{29}{43}\right)\) \(e\left(\frac{34}{43}\right)\) \(e\left(\frac{18}{43}\right)\) \(e\left(\frac{3}{43}\right)\) \(e\left(\frac{24}{43}\right)\) \(e\left(\frac{8}{43}\right)\) \(e\left(\frac{15}{43}\right)\) \(e\left(\frac{35}{43}\right)\) \(e\left(\frac{4}{43}\right)\)
\(\chi_{173}(81,\cdot)\) \(1\) \(1\) \(e\left(\frac{27}{43}\right)\) \(e\left(\frac{41}{43}\right)\) \(e\left(\frac{11}{43}\right)\) \(e\left(\frac{21}{43}\right)\) \(e\left(\frac{25}{43}\right)\) \(e\left(\frac{28}{43}\right)\) \(e\left(\frac{38}{43}\right)\) \(e\left(\frac{39}{43}\right)\) \(e\left(\frac{5}{43}\right)\) \(e\left(\frac{19}{43}\right)\)
\(\chi_{173}(83,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{43}\right)\) \(e\left(\frac{11}{43}\right)\) \(e\left(\frac{4}{43}\right)\) \(e\left(\frac{35}{43}\right)\) \(e\left(\frac{13}{43}\right)\) \(e\left(\frac{18}{43}\right)\) \(e\left(\frac{6}{43}\right)\) \(e\left(\frac{22}{43}\right)\) \(e\left(\frac{37}{43}\right)\) \(e\left(\frac{3}{43}\right)\)
\(\chi_{173}(84,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{43}\right)\) \(e\left(\frac{20}{43}\right)\) \(e\left(\frac{19}{43}\right)\) \(e\left(\frac{5}{43}\right)\) \(e\left(\frac{8}{43}\right)\) \(e\left(\frac{21}{43}\right)\) \(e\left(\frac{7}{43}\right)\) \(e\left(\frac{40}{43}\right)\) \(e\left(\frac{36}{43}\right)\) \(e\left(\frac{25}{43}\right)\)
\(\chi_{173}(85,\cdot)\) \(1\) \(1\) \(e\left(\frac{28}{43}\right)\) \(e\left(\frac{25}{43}\right)\) \(e\left(\frac{13}{43}\right)\) \(e\left(\frac{17}{43}\right)\) \(e\left(\frac{10}{43}\right)\) \(e\left(\frac{37}{43}\right)\) \(e\left(\frac{41}{43}\right)\) \(e\left(\frac{7}{43}\right)\) \(e\left(\frac{2}{43}\right)\) \(e\left(\frac{42}{43}\right)\)
\(\chi_{173}(95,\cdot)\) \(1\) \(1\) \(e\left(\frac{18}{43}\right)\) \(e\left(\frac{13}{43}\right)\) \(e\left(\frac{36}{43}\right)\) \(e\left(\frac{14}{43}\right)\) \(e\left(\frac{31}{43}\right)\) \(e\left(\frac{33}{43}\right)\) \(e\left(\frac{11}{43}\right)\) \(e\left(\frac{26}{43}\right)\) \(e\left(\frac{32}{43}\right)\) \(e\left(\frac{27}{43}\right)\)
\(\chi_{173}(96,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{43}\right)\) \(e\left(\frac{1}{43}\right)\) \(e\left(\frac{16}{43}\right)\) \(e\left(\frac{11}{43}\right)\) \(e\left(\frac{9}{43}\right)\) \(e\left(\frac{29}{43}\right)\) \(e\left(\frac{24}{43}\right)\) \(e\left(\frac{2}{43}\right)\) \(e\left(\frac{19}{43}\right)\) \(e\left(\frac{12}{43}\right)\)
\(\chi_{173}(100,\cdot)\) \(1\) \(1\) \(e\left(\frac{20}{43}\right)\) \(e\left(\frac{24}{43}\right)\) \(e\left(\frac{40}{43}\right)\) \(e\left(\frac{6}{43}\right)\) \(e\left(\frac{1}{43}\right)\) \(e\left(\frac{8}{43}\right)\) \(e\left(\frac{17}{43}\right)\) \(e\left(\frac{5}{43}\right)\) \(e\left(\frac{26}{43}\right)\) \(e\left(\frac{30}{43}\right)\)
\(\chi_{173}(106,\cdot)\) \(1\) \(1\) \(e\left(\frac{39}{43}\right)\) \(e\left(\frac{21}{43}\right)\) \(e\left(\frac{35}{43}\right)\) \(e\left(\frac{16}{43}\right)\) \(e\left(\frac{17}{43}\right)\) \(e\left(\frac{7}{43}\right)\) \(e\left(\frac{31}{43}\right)\) \(e\left(\frac{42}{43}\right)\) \(e\left(\frac{12}{43}\right)\) \(e\left(\frac{37}{43}\right)\)
\(\chi_{173}(109,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{43}\right)\) \(e\left(\frac{19}{43}\right)\) \(e\left(\frac{3}{43}\right)\) \(e\left(\frac{37}{43}\right)\) \(e\left(\frac{42}{43}\right)\) \(e\left(\frac{35}{43}\right)\) \(e\left(\frac{26}{43}\right)\) \(e\left(\frac{38}{43}\right)\) \(e\left(\frac{17}{43}\right)\) \(e\left(\frac{13}{43}\right)\)
\(\chi_{173}(117,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{43}\right)\) \(e\left(\frac{38}{43}\right)\) \(e\left(\frac{6}{43}\right)\) \(e\left(\frac{31}{43}\right)\) \(e\left(\frac{41}{43}\right)\) \(e\left(\frac{27}{43}\right)\) \(e\left(\frac{9}{43}\right)\) \(e\left(\frac{33}{43}\right)\) \(e\left(\frac{34}{43}\right)\) \(e\left(\frac{26}{43}\right)\)
\(\chi_{173}(118,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{43}\right)\) \(e\left(\frac{10}{43}\right)\) \(e\left(\frac{31}{43}\right)\) \(e\left(\frac{24}{43}\right)\) \(e\left(\frac{4}{43}\right)\) \(e\left(\frac{32}{43}\right)\) \(e\left(\frac{25}{43}\right)\) \(e\left(\frac{20}{43}\right)\) \(e\left(\frac{18}{43}\right)\) \(e\left(\frac{34}{43}\right)\)
\(\chi_{173}(119,\cdot)\) \(1\) \(1\) \(e\left(\frac{42}{43}\right)\) \(e\left(\frac{16}{43}\right)\) \(e\left(\frac{41}{43}\right)\) \(e\left(\frac{4}{43}\right)\) \(e\left(\frac{15}{43}\right)\) \(e\left(\frac{34}{43}\right)\) \(e\left(\frac{40}{43}\right)\) \(e\left(\frac{32}{43}\right)\) \(e\left(\frac{3}{43}\right)\) \(e\left(\frac{20}{43}\right)\)
\(\chi_{173}(124,\cdot)\) \(1\) \(1\) \(e\left(\frac{26}{43}\right)\) \(e\left(\frac{14}{43}\right)\) \(e\left(\frac{9}{43}\right)\) \(e\left(\frac{25}{43}\right)\) \(e\left(\frac{40}{43}\right)\) \(e\left(\frac{19}{43}\right)\) \(e\left(\frac{35}{43}\right)\) \(e\left(\frac{28}{43}\right)\) \(e\left(\frac{8}{43}\right)\) \(e\left(\frac{39}{43}\right)\)
\(\chi_{173}(132,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{43}\right)\) \(e\left(\frac{7}{43}\right)\) \(e\left(\frac{26}{43}\right)\) \(e\left(\frac{34}{43}\right)\) \(e\left(\frac{20}{43}\right)\) \(e\left(\frac{31}{43}\right)\) \(e\left(\frac{39}{43}\right)\) \(e\left(\frac{14}{43}\right)\) \(e\left(\frac{4}{43}\right)\) \(e\left(\frac{41}{43}\right)\)
\(\chi_{173}(133,\cdot)\) \(1\) \(1\) \(e\left(\frac{32}{43}\right)\) \(e\left(\frac{4}{43}\right)\) \(e\left(\frac{21}{43}\right)\) \(e\left(\frac{1}{43}\right)\) \(e\left(\frac{36}{43}\right)\) \(e\left(\frac{30}{43}\right)\) \(e\left(\frac{10}{43}\right)\) \(e\left(\frac{8}{43}\right)\) \(e\left(\frac{33}{43}\right)\) \(e\left(\frac{5}{43}\right)\)
\(\chi_{173}(135,\cdot)\) \(1\) \(1\) \(e\left(\frac{30}{43}\right)\) \(e\left(\frac{36}{43}\right)\) \(e\left(\frac{17}{43}\right)\) \(e\left(\frac{9}{43}\right)\) \(e\left(\frac{23}{43}\right)\) \(e\left(\frac{12}{43}\right)\) \(e\left(\frac{4}{43}\right)\) \(e\left(\frac{29}{43}\right)\) \(e\left(\frac{39}{43}\right)\) \(e\left(\frac{2}{43}\right)\)
\(\chi_{173}(136,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{43}\right)\) \(e\left(\frac{40}{43}\right)\) \(e\left(\frac{38}{43}\right)\) \(e\left(\frac{10}{43}\right)\) \(e\left(\frac{16}{43}\right)\) \(e\left(\frac{42}{43}\right)\) \(e\left(\frac{14}{43}\right)\) \(e\left(\frac{37}{43}\right)\) \(e\left(\frac{29}{43}\right)\) \(e\left(\frac{7}{43}\right)\)