↑

Properties

Label 15730.di
Modulus $15730$
Conductor $7865$
Order $44$
Real no
Primitive no
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(15730, base_ring=CyclotomicField(44)) M = H._module chi = DirichletCharacter(H, M([33,16,11])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(463,15730)) 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.da
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 \(-1\) \(1\) \(3\) \(7\) \(9\) \(17\) \(19\) \(21\) \(23\) \(27\) \(29\) \(31\)
\(\chi_{15730}(463,\cdot)\) \(1\) \(1\) \(i\) \(e\left(\frac{1}{22}\right)\) \(-1\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{9}{44}\right)\) \(-i\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{23}{44}\right)\)
\(\chi_{15730}(837,\cdot)\) \(1\) \(1\) \(-i\) \(e\left(\frac{17}{22}\right)\) \(-1\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{43}{44}\right)\) \(i\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{17}{44}\right)\)
\(\chi_{15730}(1893,\cdot)\) \(1\) \(1\) \(i\) \(e\left(\frac{13}{22}\right)\) \(-1\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{29}{44}\right)\) \(-i\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{35}{44}\right)\)
\(\chi_{15730}(2267,\cdot)\) \(1\) \(1\) \(-i\) \(e\left(\frac{7}{22}\right)\) \(-1\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{19}{44}\right)\) \(i\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{29}{44}\right)\)
\(\chi_{15730}(3323,\cdot)\) \(1\) \(1\) \(i\) \(e\left(\frac{3}{22}\right)\) \(-1\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{5}{44}\right)\) \(-i\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{3}{44}\right)\)
\(\chi_{15730}(3697,\cdot)\) \(1\) \(1\) \(-i\) \(e\left(\frac{19}{22}\right)\) \(-1\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{39}{44}\right)\) \(i\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{41}{44}\right)\)
\(\chi_{15730}(4753,\cdot)\) \(1\) \(1\) \(i\) \(e\left(\frac{15}{22}\right)\) \(-1\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{25}{44}\right)\) \(-i\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{15}{44}\right)\)
\(\chi_{15730}(5127,\cdot)\) \(1\) \(1\) \(-i\) \(e\left(\frac{9}{22}\right)\) \(-1\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{15}{44}\right)\) \(i\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{9}{44}\right)\)
\(\chi_{15730}(6183,\cdot)\) \(1\) \(1\) \(i\) \(e\left(\frac{5}{22}\right)\) \(-1\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{1}{44}\right)\) \(-i\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{27}{44}\right)\)
\(\chi_{15730}(6557,\cdot)\) \(1\) \(1\) \(-i\) \(e\left(\frac{21}{22}\right)\) \(-1\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{35}{44}\right)\) \(i\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{21}{44}\right)\)
\(\chi_{15730}(7613,\cdot)\) \(1\) \(1\) \(i\) \(e\left(\frac{17}{22}\right)\) \(-1\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{21}{44}\right)\) \(-i\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{39}{44}\right)\)
\(\chi_{15730}(9043,\cdot)\) \(1\) \(1\) \(i\) \(e\left(\frac{7}{22}\right)\) \(-1\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{41}{44}\right)\) \(-i\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{7}{44}\right)\)
\(\chi_{15730}(9417,\cdot)\) \(1\) \(1\) \(-i\) \(e\left(\frac{1}{22}\right)\) \(-1\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{31}{44}\right)\) \(i\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{1}{44}\right)\)
\(\chi_{15730}(10473,\cdot)\) \(1\) \(1\) \(i\) \(e\left(\frac{19}{22}\right)\) \(-1\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{17}{44}\right)\) \(-i\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{19}{44}\right)\)
\(\chi_{15730}(10847,\cdot)\) \(1\) \(1\) \(-i\) \(e\left(\frac{13}{22}\right)\) \(-1\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{7}{44}\right)\) \(i\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{13}{44}\right)\)
\(\chi_{15730}(11903,\cdot)\) \(1\) \(1\) \(i\) \(e\left(\frac{9}{22}\right)\) \(-1\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{37}{44}\right)\) \(-i\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{31}{44}\right)\)
\(\chi_{15730}(12277,\cdot)\) \(1\) \(1\) \(-i\) \(e\left(\frac{3}{22}\right)\) \(-1\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{27}{44}\right)\) \(i\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{25}{44}\right)\)
\(\chi_{15730}(13333,\cdot)\) \(1\) \(1\) \(i\) \(e\left(\frac{21}{22}\right)\) \(-1\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{13}{44}\right)\) \(-i\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{43}{44}\right)\)
\(\chi_{15730}(13707,\cdot)\) \(1\) \(1\) \(-i\) \(e\left(\frac{15}{22}\right)\) \(-1\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{3}{44}\right)\) \(i\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{37}{44}\right)\)
\(\chi_{15730}(15137,\cdot)\) \(1\) \(1\) \(-i\) \(e\left(\frac{5}{22}\right)\) \(-1\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{23}{44}\right)\) \(i\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{5}{44}\right)\)