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Properties

Label 5175.ce
Modulus $5175$
Conductor $345$
Order $44$
Real no
Primitive no
Minimal yes
Parity even

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5175, base_ring=CyclotomicField(44)) M = H._module chi = DirichletCharacter(H, M([22,33,24])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(593,5175)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(5175\)
Conductor: \(345\)
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: no, induced from 345.x
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: Number field defined by a degree 44 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(4\) \(7\) \(8\) \(11\) \(13\) \(14\) \(16\) \(17\) \(19\)
\(\chi_{5175}(593,\cdot)\) \(1\) \(1\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{15}{22}\right)\)
\(\chi_{5175}(818,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{1}{22}\right)\)
\(\chi_{5175}(1007,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{15}{22}\right)\)
\(\chi_{5175}(1043,\cdot)\) \(1\) \(1\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{13}{22}\right)\)
\(\chi_{5175}(1232,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{1}{22}\right)\)
\(\chi_{5175}(1268,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{9}{22}\right)\)
\(\chi_{5175}(1457,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{13}{22}\right)\)
\(\chi_{5175}(1682,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{9}{22}\right)\)
\(\chi_{5175}(1718,\cdot)\) \(1\) \(1\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{21}{22}\right)\)
\(\chi_{5175}(2132,\cdot)\) \(1\) \(1\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{21}{22}\right)\)
\(\chi_{5175}(2168,\cdot)\) \(1\) \(1\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{17}{22}\right)\)
\(\chi_{5175}(2582,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{17}{22}\right)\)
\(\chi_{5175}(3068,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{7}{22}\right)\)
\(\chi_{5175}(3293,\cdot)\) \(1\) \(1\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{5}{22}\right)\)
\(\chi_{5175}(3482,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{7}{22}\right)\)
\(\chi_{5175}(3707,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{5}{22}\right)\)
\(\chi_{5175}(3968,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{3}{22}\right)\)
\(\chi_{5175}(4382,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{3}{22}\right)\)
\(\chi_{5175}(4418,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{19}{22}\right)\)
\(\chi_{5175}(4832,\cdot)\) \(1\) \(1\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{19}{22}\right)\)