Properties

Label 8470.cb
Modulus $8470$
Conductor $605$
Order $44$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(8470, base_ring=CyclotomicField(44))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([33,0,10]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(43,8470))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(8470\)
Conductor: \(605\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(44\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 605.r
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{44})\)
Fixed field: 44.44.2885428559557085084648615903962269104974580506944665166312236845353556846511909399754484184086322784423828125.1

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(9\) \(13\) \(17\) \(19\) \(23\) \(27\) \(29\) \(31\) \(37\)
\(\chi_{8470}(43,\cdot)\) \(1\) \(1\) \(i\) \(-1\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{7}{44}\right)\) \(-i\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{13}{44}\right)\)
\(\chi_{8470}(197,\cdot)\) \(1\) \(1\) \(-i\) \(-1\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{37}{44}\right)\) \(i\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{31}{44}\right)\)
\(\chi_{8470}(813,\cdot)\) \(1\) \(1\) \(i\) \(-1\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{3}{44}\right)\) \(-i\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{37}{44}\right)\)
\(\chi_{8470}(1583,\cdot)\) \(1\) \(1\) \(i\) \(-1\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{43}{44}\right)\) \(-i\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{17}{44}\right)\)
\(\chi_{8470}(1737,\cdot)\) \(1\) \(1\) \(-i\) \(-1\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{29}{44}\right)\) \(i\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{35}{44}\right)\)
\(\chi_{8470}(2353,\cdot)\) \(1\) \(1\) \(i\) \(-1\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{39}{44}\right)\) \(-i\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{41}{44}\right)\)
\(\chi_{8470}(2507,\cdot)\) \(1\) \(1\) \(-i\) \(-1\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{25}{44}\right)\) \(i\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{15}{44}\right)\)
\(\chi_{8470}(3123,\cdot)\) \(1\) \(1\) \(i\) \(-1\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{35}{44}\right)\) \(-i\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{21}{44}\right)\)
\(\chi_{8470}(3277,\cdot)\) \(1\) \(1\) \(-i\) \(-1\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{21}{44}\right)\) \(i\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{39}{44}\right)\)
\(\chi_{8470}(3893,\cdot)\) \(1\) \(1\) \(i\) \(-1\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{31}{44}\right)\) \(-i\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{1}{44}\right)\)
\(\chi_{8470}(4047,\cdot)\) \(1\) \(1\) \(-i\) \(-1\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{17}{44}\right)\) \(i\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{19}{44}\right)\)
\(\chi_{8470}(4663,\cdot)\) \(1\) \(1\) \(i\) \(-1\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{27}{44}\right)\) \(-i\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{25}{44}\right)\)
\(\chi_{8470}(4817,\cdot)\) \(1\) \(1\) \(-i\) \(-1\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{13}{44}\right)\) \(i\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{43}{44}\right)\)
\(\chi_{8470}(5433,\cdot)\) \(1\) \(1\) \(i\) \(-1\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{23}{44}\right)\) \(-i\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{5}{44}\right)\)
\(\chi_{8470}(5587,\cdot)\) \(1\) \(1\) \(-i\) \(-1\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{9}{44}\right)\) \(i\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{23}{44}\right)\)
\(\chi_{8470}(6203,\cdot)\) \(1\) \(1\) \(i\) \(-1\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{19}{44}\right)\) \(-i\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{29}{44}\right)\)
\(\chi_{8470}(6357,\cdot)\) \(1\) \(1\) \(-i\) \(-1\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{5}{44}\right)\) \(i\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{3}{44}\right)\)
\(\chi_{8470}(6973,\cdot)\) \(1\) \(1\) \(i\) \(-1\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{15}{44}\right)\) \(-i\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{9}{44}\right)\)
\(\chi_{8470}(7127,\cdot)\) \(1\) \(1\) \(-i\) \(-1\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{1}{44}\right)\) \(i\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{27}{44}\right)\)
\(\chi_{8470}(7897,\cdot)\) \(1\) \(1\) \(-i\) \(-1\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{41}{44}\right)\) \(i\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{44}\right)\)