Properties

Label 1849.i
Modulus $1849$
Conductor $1849$
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(1849, base_ring=CyclotomicField(86))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([44]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(44,1849))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1849\)
Conductor: \(1849\)
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: 43.43.162686032778208990102858628859785420567496242104134005559503199497609643882923419981647276367075859293620549051195773051892887390454194801.1

First 31 of 42 characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(11\)
\(\chi_{1849}(44,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{43}\right)\) \(e\left(\frac{22}{43}\right)\) \(e\left(\frac{34}{43}\right)\) \(e\left(\frac{32}{43}\right)\) \(e\left(\frac{39}{43}\right)\) \(e\left(\frac{15}{43}\right)\) \(e\left(\frac{8}{43}\right)\) \(e\left(\frac{1}{43}\right)\) \(e\left(\frac{6}{43}\right)\) \(e\left(\frac{41}{43}\right)\)
\(\chi_{1849}(87,\cdot)\) \(1\) \(1\) \(e\left(\frac{34}{43}\right)\) \(e\left(\frac{1}{43}\right)\) \(e\left(\frac{25}{43}\right)\) \(e\left(\frac{21}{43}\right)\) \(e\left(\frac{35}{43}\right)\) \(e\left(\frac{30}{43}\right)\) \(e\left(\frac{16}{43}\right)\) \(e\left(\frac{2}{43}\right)\) \(e\left(\frac{12}{43}\right)\) \(e\left(\frac{39}{43}\right)\)
\(\chi_{1849}(130,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{43}\right)\) \(e\left(\frac{23}{43}\right)\) \(e\left(\frac{16}{43}\right)\) \(e\left(\frac{10}{43}\right)\) \(e\left(\frac{31}{43}\right)\) \(e\left(\frac{2}{43}\right)\) \(e\left(\frac{24}{43}\right)\) \(e\left(\frac{3}{43}\right)\) \(e\left(\frac{18}{43}\right)\) \(e\left(\frac{37}{43}\right)\)
\(\chi_{1849}(173,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{43}\right)\) \(e\left(\frac{2}{43}\right)\) \(e\left(\frac{7}{43}\right)\) \(e\left(\frac{42}{43}\right)\) \(e\left(\frac{27}{43}\right)\) \(e\left(\frac{17}{43}\right)\) \(e\left(\frac{32}{43}\right)\) \(e\left(\frac{4}{43}\right)\) \(e\left(\frac{24}{43}\right)\) \(e\left(\frac{35}{43}\right)\)
\(\chi_{1849}(216,\cdot)\) \(1\) \(1\) \(e\left(\frac{42}{43}\right)\) \(e\left(\frac{24}{43}\right)\) \(e\left(\frac{41}{43}\right)\) \(e\left(\frac{31}{43}\right)\) \(e\left(\frac{23}{43}\right)\) \(e\left(\frac{32}{43}\right)\) \(e\left(\frac{40}{43}\right)\) \(e\left(\frac{5}{43}\right)\) \(e\left(\frac{30}{43}\right)\) \(e\left(\frac{33}{43}\right)\)
\(\chi_{1849}(259,\cdot)\) \(1\) \(1\) \(e\left(\frac{16}{43}\right)\) \(e\left(\frac{3}{43}\right)\) \(e\left(\frac{32}{43}\right)\) \(e\left(\frac{20}{43}\right)\) \(e\left(\frac{19}{43}\right)\) \(e\left(\frac{4}{43}\right)\) \(e\left(\frac{5}{43}\right)\) \(e\left(\frac{6}{43}\right)\) \(e\left(\frac{36}{43}\right)\) \(e\left(\frac{31}{43}\right)\)
\(\chi_{1849}(302,\cdot)\) \(1\) \(1\) \(e\left(\frac{33}{43}\right)\) \(e\left(\frac{25}{43}\right)\) \(e\left(\frac{23}{43}\right)\) \(e\left(\frac{9}{43}\right)\) \(e\left(\frac{15}{43}\right)\) \(e\left(\frac{19}{43}\right)\) \(e\left(\frac{13}{43}\right)\) \(e\left(\frac{7}{43}\right)\) \(e\left(\frac{42}{43}\right)\) \(e\left(\frac{29}{43}\right)\)
\(\chi_{1849}(345,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{43}\right)\) \(e\left(\frac{4}{43}\right)\) \(e\left(\frac{14}{43}\right)\) \(e\left(\frac{41}{43}\right)\) \(e\left(\frac{11}{43}\right)\) \(e\left(\frac{34}{43}\right)\) \(e\left(\frac{21}{43}\right)\) \(e\left(\frac{8}{43}\right)\) \(e\left(\frac{5}{43}\right)\) \(e\left(\frac{27}{43}\right)\)
\(\chi_{1849}(388,\cdot)\) \(1\) \(1\) \(e\left(\frac{24}{43}\right)\) \(e\left(\frac{26}{43}\right)\) \(e\left(\frac{5}{43}\right)\) \(e\left(\frac{30}{43}\right)\) \(e\left(\frac{7}{43}\right)\) \(e\left(\frac{6}{43}\right)\) \(e\left(\frac{29}{43}\right)\) \(e\left(\frac{9}{43}\right)\) \(e\left(\frac{11}{43}\right)\) \(e\left(\frac{25}{43}\right)\)
\(\chi_{1849}(431,\cdot)\) \(1\) \(1\) \(e\left(\frac{41}{43}\right)\) \(e\left(\frac{5}{43}\right)\) \(e\left(\frac{39}{43}\right)\) \(e\left(\frac{19}{43}\right)\) \(e\left(\frac{3}{43}\right)\) \(e\left(\frac{21}{43}\right)\) \(e\left(\frac{37}{43}\right)\) \(e\left(\frac{10}{43}\right)\) \(e\left(\frac{17}{43}\right)\) \(e\left(\frac{23}{43}\right)\)
\(\chi_{1849}(474,\cdot)\) \(1\) \(1\) \(e\left(\frac{15}{43}\right)\) \(e\left(\frac{27}{43}\right)\) \(e\left(\frac{30}{43}\right)\) \(e\left(\frac{8}{43}\right)\) \(e\left(\frac{42}{43}\right)\) \(e\left(\frac{36}{43}\right)\) \(e\left(\frac{2}{43}\right)\) \(e\left(\frac{11}{43}\right)\) \(e\left(\frac{23}{43}\right)\) \(e\left(\frac{21}{43}\right)\)
\(\chi_{1849}(517,\cdot)\) \(1\) \(1\) \(e\left(\frac{32}{43}\right)\) \(e\left(\frac{6}{43}\right)\) \(e\left(\frac{21}{43}\right)\) \(e\left(\frac{40}{43}\right)\) \(e\left(\frac{38}{43}\right)\) \(e\left(\frac{8}{43}\right)\) \(e\left(\frac{10}{43}\right)\) \(e\left(\frac{12}{43}\right)\) \(e\left(\frac{29}{43}\right)\) \(e\left(\frac{19}{43}\right)\)
\(\chi_{1849}(560,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{43}\right)\) \(e\left(\frac{28}{43}\right)\) \(e\left(\frac{12}{43}\right)\) \(e\left(\frac{29}{43}\right)\) \(e\left(\frac{34}{43}\right)\) \(e\left(\frac{23}{43}\right)\) \(e\left(\frac{18}{43}\right)\) \(e\left(\frac{13}{43}\right)\) \(e\left(\frac{35}{43}\right)\) \(e\left(\frac{17}{43}\right)\)
\(\chi_{1849}(603,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{43}\right)\) \(e\left(\frac{7}{43}\right)\) \(e\left(\frac{3}{43}\right)\) \(e\left(\frac{18}{43}\right)\) \(e\left(\frac{30}{43}\right)\) \(e\left(\frac{38}{43}\right)\) \(e\left(\frac{26}{43}\right)\) \(e\left(\frac{14}{43}\right)\) \(e\left(\frac{41}{43}\right)\) \(e\left(\frac{15}{43}\right)\)
\(\chi_{1849}(646,\cdot)\) \(1\) \(1\) \(e\left(\frac{40}{43}\right)\) \(e\left(\frac{29}{43}\right)\) \(e\left(\frac{37}{43}\right)\) \(e\left(\frac{7}{43}\right)\) \(e\left(\frac{26}{43}\right)\) \(e\left(\frac{10}{43}\right)\) \(e\left(\frac{34}{43}\right)\) \(e\left(\frac{15}{43}\right)\) \(e\left(\frac{4}{43}\right)\) \(e\left(\frac{13}{43}\right)\)
\(\chi_{1849}(689,\cdot)\) \(1\) \(1\) \(e\left(\frac{14}{43}\right)\) \(e\left(\frac{8}{43}\right)\) \(e\left(\frac{28}{43}\right)\) \(e\left(\frac{39}{43}\right)\) \(e\left(\frac{22}{43}\right)\) \(e\left(\frac{25}{43}\right)\) \(e\left(\frac{42}{43}\right)\) \(e\left(\frac{16}{43}\right)\) \(e\left(\frac{10}{43}\right)\) \(e\left(\frac{11}{43}\right)\)
\(\chi_{1849}(732,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{43}\right)\) \(e\left(\frac{30}{43}\right)\) \(e\left(\frac{19}{43}\right)\) \(e\left(\frac{28}{43}\right)\) \(e\left(\frac{18}{43}\right)\) \(e\left(\frac{40}{43}\right)\) \(e\left(\frac{7}{43}\right)\) \(e\left(\frac{17}{43}\right)\) \(e\left(\frac{16}{43}\right)\) \(e\left(\frac{9}{43}\right)\)
\(\chi_{1849}(775,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{43}\right)\) \(e\left(\frac{9}{43}\right)\) \(e\left(\frac{10}{43}\right)\) \(e\left(\frac{17}{43}\right)\) \(e\left(\frac{14}{43}\right)\) \(e\left(\frac{12}{43}\right)\) \(e\left(\frac{15}{43}\right)\) \(e\left(\frac{18}{43}\right)\) \(e\left(\frac{22}{43}\right)\) \(e\left(\frac{7}{43}\right)\)
\(\chi_{1849}(818,\cdot)\) \(1\) \(1\) \(e\left(\frac{22}{43}\right)\) \(e\left(\frac{31}{43}\right)\) \(e\left(\frac{1}{43}\right)\) \(e\left(\frac{6}{43}\right)\) \(e\left(\frac{10}{43}\right)\) \(e\left(\frac{27}{43}\right)\) \(e\left(\frac{23}{43}\right)\) \(e\left(\frac{19}{43}\right)\) \(e\left(\frac{28}{43}\right)\) \(e\left(\frac{5}{43}\right)\)
\(\chi_{1849}(861,\cdot)\) \(1\) \(1\) \(e\left(\frac{39}{43}\right)\) \(e\left(\frac{10}{43}\right)\) \(e\left(\frac{35}{43}\right)\) \(e\left(\frac{38}{43}\right)\) \(e\left(\frac{6}{43}\right)\) \(e\left(\frac{42}{43}\right)\) \(e\left(\frac{31}{43}\right)\) \(e\left(\frac{20}{43}\right)\) \(e\left(\frac{34}{43}\right)\) \(e\left(\frac{3}{43}\right)\)
\(\chi_{1849}(904,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{43}\right)\) \(e\left(\frac{32}{43}\right)\) \(e\left(\frac{26}{43}\right)\) \(e\left(\frac{27}{43}\right)\) \(e\left(\frac{2}{43}\right)\) \(e\left(\frac{14}{43}\right)\) \(e\left(\frac{39}{43}\right)\) \(e\left(\frac{21}{43}\right)\) \(e\left(\frac{40}{43}\right)\) \(e\left(\frac{1}{43}\right)\)
\(\chi_{1849}(947,\cdot)\) \(1\) \(1\) \(e\left(\frac{30}{43}\right)\) \(e\left(\frac{11}{43}\right)\) \(e\left(\frac{17}{43}\right)\) \(e\left(\frac{16}{43}\right)\) \(e\left(\frac{41}{43}\right)\) \(e\left(\frac{29}{43}\right)\) \(e\left(\frac{4}{43}\right)\) \(e\left(\frac{22}{43}\right)\) \(e\left(\frac{3}{43}\right)\) \(e\left(\frac{42}{43}\right)\)
\(\chi_{1849}(990,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{43}\right)\) \(e\left(\frac{33}{43}\right)\) \(e\left(\frac{8}{43}\right)\) \(e\left(\frac{5}{43}\right)\) \(e\left(\frac{37}{43}\right)\) \(e\left(\frac{1}{43}\right)\) \(e\left(\frac{12}{43}\right)\) \(e\left(\frac{23}{43}\right)\) \(e\left(\frac{9}{43}\right)\) \(e\left(\frac{40}{43}\right)\)
\(\chi_{1849}(1033,\cdot)\) \(1\) \(1\) \(e\left(\frac{21}{43}\right)\) \(e\left(\frac{12}{43}\right)\) \(e\left(\frac{42}{43}\right)\) \(e\left(\frac{37}{43}\right)\) \(e\left(\frac{33}{43}\right)\) \(e\left(\frac{16}{43}\right)\) \(e\left(\frac{20}{43}\right)\) \(e\left(\frac{24}{43}\right)\) \(e\left(\frac{15}{43}\right)\) \(e\left(\frac{38}{43}\right)\)
\(\chi_{1849}(1076,\cdot)\) \(1\) \(1\) \(e\left(\frac{38}{43}\right)\) \(e\left(\frac{34}{43}\right)\) \(e\left(\frac{33}{43}\right)\) \(e\left(\frac{26}{43}\right)\) \(e\left(\frac{29}{43}\right)\) \(e\left(\frac{31}{43}\right)\) \(e\left(\frac{28}{43}\right)\) \(e\left(\frac{25}{43}\right)\) \(e\left(\frac{21}{43}\right)\) \(e\left(\frac{36}{43}\right)\)
\(\chi_{1849}(1119,\cdot)\) \(1\) \(1\) \(e\left(\frac{12}{43}\right)\) \(e\left(\frac{13}{43}\right)\) \(e\left(\frac{24}{43}\right)\) \(e\left(\frac{15}{43}\right)\) \(e\left(\frac{25}{43}\right)\) \(e\left(\frac{3}{43}\right)\) \(e\left(\frac{36}{43}\right)\) \(e\left(\frac{26}{43}\right)\) \(e\left(\frac{27}{43}\right)\) \(e\left(\frac{34}{43}\right)\)
\(\chi_{1849}(1162,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{43}\right)\) \(e\left(\frac{35}{43}\right)\) \(e\left(\frac{15}{43}\right)\) \(e\left(\frac{4}{43}\right)\) \(e\left(\frac{21}{43}\right)\) \(e\left(\frac{18}{43}\right)\) \(e\left(\frac{1}{43}\right)\) \(e\left(\frac{27}{43}\right)\) \(e\left(\frac{33}{43}\right)\) \(e\left(\frac{32}{43}\right)\)
\(\chi_{1849}(1205,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{43}\right)\) \(e\left(\frac{14}{43}\right)\) \(e\left(\frac{6}{43}\right)\) \(e\left(\frac{36}{43}\right)\) \(e\left(\frac{17}{43}\right)\) \(e\left(\frac{33}{43}\right)\) \(e\left(\frac{9}{43}\right)\) \(e\left(\frac{28}{43}\right)\) \(e\left(\frac{39}{43}\right)\) \(e\left(\frac{30}{43}\right)\)
\(\chi_{1849}(1248,\cdot)\) \(1\) \(1\) \(e\left(\frac{20}{43}\right)\) \(e\left(\frac{36}{43}\right)\) \(e\left(\frac{40}{43}\right)\) \(e\left(\frac{25}{43}\right)\) \(e\left(\frac{13}{43}\right)\) \(e\left(\frac{5}{43}\right)\) \(e\left(\frac{17}{43}\right)\) \(e\left(\frac{29}{43}\right)\) \(e\left(\frac{2}{43}\right)\) \(e\left(\frac{28}{43}\right)\)
\(\chi_{1849}(1291,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{43}\right)\) \(e\left(\frac{15}{43}\right)\) \(e\left(\frac{31}{43}\right)\) \(e\left(\frac{14}{43}\right)\) \(e\left(\frac{9}{43}\right)\) \(e\left(\frac{20}{43}\right)\) \(e\left(\frac{25}{43}\right)\) \(e\left(\frac{30}{43}\right)\) \(e\left(\frac{8}{43}\right)\) \(e\left(\frac{26}{43}\right)\)
\(\chi_{1849}(1334,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{43}\right)\) \(e\left(\frac{37}{43}\right)\) \(e\left(\frac{22}{43}\right)\) \(e\left(\frac{3}{43}\right)\) \(e\left(\frac{5}{43}\right)\) \(e\left(\frac{35}{43}\right)\) \(e\left(\frac{33}{43}\right)\) \(e\left(\frac{31}{43}\right)\) \(e\left(\frac{14}{43}\right)\) \(e\left(\frac{24}{43}\right)\)