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Properties

Label 25410.eb
Modulus $25410$
Conductor $605$
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(25410, base_ring=CyclotomicField(44)) M = H._module chi = DirichletCharacter(H, M([0,33,0,10])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(43,25410)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(25410\)
Conductor: \(605\)
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 605.r
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: 44.44.2885428559557085084648615903962269104974580506944665166312236845353556846511909399754484184086322784423828125.1

Characters in Galois orbit

Character \(-1\) \(1\) \(13\) \(17\) \(19\) \(23\) \(29\) \(31\) \(37\) \(41\) \(43\) \(47\)
\(\chi_{25410}(43,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{1}{44}\right)\)
\(\chi_{25410}(2353,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{37}{44}\right)\)
\(\chi_{25410}(3277,\cdot)\) \(1\) \(1\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{3}{44}\right)\)
\(\chi_{25410}(4663,\cdot)\) \(1\) \(1\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{29}{44}\right)\)
\(\chi_{25410}(5587,\cdot)\) \(1\) \(1\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{39}{44}\right)\)
\(\chi_{25410}(6973,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{21}{44}\right)\)
\(\chi_{25410}(7897,\cdot)\) \(1\) \(1\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{31}{44}\right)\)
\(\chi_{25410}(9283,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{13}{44}\right)\)
\(\chi_{25410}(10207,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{23}{44}\right)\)
\(\chi_{25410}(11593,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{5}{44}\right)\)
\(\chi_{25410}(12517,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{15}{44}\right)\)
\(\chi_{25410}(13903,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{41}{44}\right)\)
\(\chi_{25410}(14827,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{7}{44}\right)\)
\(\chi_{25410}(17137,\cdot)\) \(1\) \(1\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{43}{44}\right)\)
\(\chi_{25410}(18523,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{25}{44}\right)\)
\(\chi_{25410}(19447,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{35}{44}\right)\)
\(\chi_{25410}(20833,\cdot)\) \(1\) \(1\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{17}{44}\right)\)
\(\chi_{25410}(21757,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{27}{44}\right)\)
\(\chi_{25410}(23143,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{9}{44}\right)\)
\(\chi_{25410}(24067,\cdot)\) \(1\) \(1\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{19}{44}\right)\)