↑

Properties

Label 368.x
Modulus $368$
Conductor $368$
Order $44$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Downloads

Learn more

Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(368, base_ring=CyclotomicField(44)) M = H._module chi = DirichletCharacter(H, M([22,11,18])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(11,368)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(368\)
Conductor: \(368\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(44\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: yes
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{44})\)
Fixed field: 44.44.4141890260646712580912980965306954513336276372715662057543551492310346739946349214617837764608.1

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(5\) \(7\) \(9\) \(11\) \(13\) \(15\) \(17\) \(19\) \(21\)
\(\chi_{368}(11,\cdot)\) \(1\) \(1\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{25}{44}\right)\)
\(\chi_{368}(19,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{27}{44}\right)\)
\(\chi_{368}(43,\cdot)\) \(1\) \(1\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{9}{44}\right)\)
\(\chi_{368}(51,\cdot)\) \(1\) \(1\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{15}{44}\right)\)
\(\chi_{368}(67,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{19}{44}\right)\)
\(\chi_{368}(83,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{7}{44}\right)\)
\(\chi_{368}(99,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{43}{44}\right)\)
\(\chi_{368}(107,\cdot)\) \(1\) \(1\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{13}{44}\right)\)
\(\chi_{368}(155,\cdot)\) \(1\) \(1\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{17}{44}\right)\)
\(\chi_{368}(171,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{1}{44}\right)\)
\(\chi_{368}(195,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{3}{44}\right)\)
\(\chi_{368}(203,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{5}{44}\right)\)
\(\chi_{368}(227,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{31}{44}\right)\)
\(\chi_{368}(235,\cdot)\) \(1\) \(1\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{37}{44}\right)\)
\(\chi_{368}(251,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{41}{44}\right)\)
\(\chi_{368}(267,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{29}{44}\right)\)
\(\chi_{368}(283,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{21}{44}\right)\)
\(\chi_{368}(291,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{35}{44}\right)\)
\(\chi_{368}(339,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{39}{44}\right)\)
\(\chi_{368}(355,\cdot)\) \(1\) \(1\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{23}{44}\right)\)