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Properties

Label 15730.df
Modulus $15730$
Conductor $7865$
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(15730, base_ring=CyclotomicField(44)) M = H._module chi = DirichletCharacter(H, M([11,30,22])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(857,15730)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(15730\)
Conductor: \(7865\)
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 7865.dd
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 \(-1\) \(1\) \(3\) \(7\) \(9\) \(17\) \(19\) \(21\) \(23\) \(27\) \(29\) \(31\)
\(\chi_{15730}(857,\cdot)\) \(1\) \(1\) \(-i\) \(e\left(\frac{23}{44}\right)\) \(-1\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{21}{44}\right)\) \(i\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{3}{22}\right)\)
\(\chi_{15730}(1143,\cdot)\) \(1\) \(1\) \(i\) \(e\left(\frac{5}{44}\right)\) \(-1\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{39}{44}\right)\) \(-i\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{15}{22}\right)\)
\(\chi_{15730}(2287,\cdot)\) \(1\) \(1\) \(-i\) \(e\left(\frac{43}{44}\right)\) \(-1\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{1}{44}\right)\) \(i\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{19}{22}\right)\)
\(\chi_{15730}(2573,\cdot)\) \(1\) \(1\) \(i\) \(e\left(\frac{25}{44}\right)\) \(-1\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{19}{44}\right)\) \(-i\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{9}{22}\right)\)
\(\chi_{15730}(3717,\cdot)\) \(1\) \(1\) \(-i\) \(e\left(\frac{19}{44}\right)\) \(-1\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{25}{44}\right)\) \(i\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{13}{22}\right)\)
\(\chi_{15730}(4003,\cdot)\) \(1\) \(1\) \(i\) \(e\left(\frac{1}{44}\right)\) \(-1\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{43}{44}\right)\) \(-i\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{3}{22}\right)\)
\(\chi_{15730}(5147,\cdot)\) \(1\) \(1\) \(-i\) \(e\left(\frac{39}{44}\right)\) \(-1\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{5}{44}\right)\) \(i\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{7}{22}\right)\)
\(\chi_{15730}(5433,\cdot)\) \(1\) \(1\) \(i\) \(e\left(\frac{21}{44}\right)\) \(-1\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{23}{44}\right)\) \(-i\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{19}{22}\right)\)
\(\chi_{15730}(6577,\cdot)\) \(1\) \(1\) \(-i\) \(e\left(\frac{15}{44}\right)\) \(-1\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{29}{44}\right)\) \(i\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{1}{22}\right)\)
\(\chi_{15730}(6863,\cdot)\) \(1\) \(1\) \(i\) \(e\left(\frac{41}{44}\right)\) \(-1\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{3}{44}\right)\) \(-i\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{13}{22}\right)\)
\(\chi_{15730}(8007,\cdot)\) \(1\) \(1\) \(-i\) \(e\left(\frac{35}{44}\right)\) \(-1\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{9}{44}\right)\) \(i\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{17}{22}\right)\)
\(\chi_{15730}(8293,\cdot)\) \(1\) \(1\) \(i\) \(e\left(\frac{17}{44}\right)\) \(-1\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{27}{44}\right)\) \(-i\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{7}{22}\right)\)
\(\chi_{15730}(9723,\cdot)\) \(1\) \(1\) \(i\) \(e\left(\frac{37}{44}\right)\) \(-1\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{7}{44}\right)\) \(-i\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{1}{22}\right)\)
\(\chi_{15730}(10867,\cdot)\) \(1\) \(1\) \(-i\) \(e\left(\frac{31}{44}\right)\) \(-1\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{13}{44}\right)\) \(i\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{5}{22}\right)\)
\(\chi_{15730}(11153,\cdot)\) \(1\) \(1\) \(i\) \(e\left(\frac{13}{44}\right)\) \(-1\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{31}{44}\right)\) \(-i\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{17}{22}\right)\)
\(\chi_{15730}(12297,\cdot)\) \(1\) \(1\) \(-i\) \(e\left(\frac{7}{44}\right)\) \(-1\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{37}{44}\right)\) \(i\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{21}{22}\right)\)
\(\chi_{15730}(13727,\cdot)\) \(1\) \(1\) \(-i\) \(e\left(\frac{27}{44}\right)\) \(-1\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{17}{44}\right)\) \(i\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{15}{22}\right)\)
\(\chi_{15730}(14013,\cdot)\) \(1\) \(1\) \(i\) \(e\left(\frac{9}{44}\right)\) \(-1\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{35}{44}\right)\) \(-i\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{5}{22}\right)\)
\(\chi_{15730}(15157,\cdot)\) \(1\) \(1\) \(-i\) \(e\left(\frac{3}{44}\right)\) \(-1\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{41}{44}\right)\) \(i\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{9}{22}\right)\)
\(\chi_{15730}(15443,\cdot)\) \(1\) \(1\) \(i\) \(e\left(\frac{29}{44}\right)\) \(-1\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{15}{44}\right)\) \(-i\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{21}{22}\right)\)