Properties

Label 7098.dv
Modulus $7098$
Conductor $3549$
Order $78$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Learn more

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(7098, base_ring=CyclotomicField(78))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([39,13,2]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(185,7098))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(7098\)
Conductor: \(3549\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(78\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 3549.dk
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: $\Q(\zeta_{39})$
Fixed field: Number field defined by a degree 78 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(5\) \(11\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\) \(37\) \(41\)
\(\chi_{7098}(185,\cdot)\) \(1\) \(1\) \(e\left(\frac{22}{39}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{16}{39}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{39}\right)\) \(e\left(\frac{41}{78}\right)\) \(e\left(\frac{55}{78}\right)\) \(e\left(\frac{8}{39}\right)\) \(e\left(\frac{7}{39}\right)\)
\(\chi_{7098}(425,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{39}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{32}{39}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{10}{39}\right)\) \(e\left(\frac{43}{78}\right)\) \(e\left(\frac{71}{78}\right)\) \(e\left(\frac{16}{39}\right)\) \(e\left(\frac{14}{39}\right)\)
\(\chi_{7098}(731,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{39}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{19}{39}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{23}{39}\right)\) \(e\left(\frac{17}{78}\right)\) \(e\left(\frac{19}{78}\right)\) \(e\left(\frac{29}{39}\right)\) \(e\left(\frac{1}{39}\right)\)
\(\chi_{7098}(971,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{39}\right)\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{20}{39}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{16}{39}\right)\) \(e\left(\frac{61}{78}\right)\) \(e\left(\frac{59}{78}\right)\) \(e\left(\frac{10}{39}\right)\) \(e\left(\frac{38}{39}\right)\)
\(\chi_{7098}(1277,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{39}\right)\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{22}{39}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{39}\right)\) \(e\left(\frac{71}{78}\right)\) \(e\left(\frac{61}{78}\right)\) \(e\left(\frac{11}{39}\right)\) \(e\left(\frac{34}{39}\right)\)
\(\chi_{7098}(1517,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{39}\right)\) \(e\left(\frac{17}{26}\right)\) \(e\left(\frac{8}{39}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{22}{39}\right)\) \(e\left(\frac{1}{78}\right)\) \(e\left(\frac{47}{78}\right)\) \(e\left(\frac{4}{39}\right)\) \(e\left(\frac{23}{39}\right)\)
\(\chi_{7098}(1823,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{39}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{25}{39}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{20}{39}\right)\) \(e\left(\frac{47}{78}\right)\) \(e\left(\frac{25}{78}\right)\) \(e\left(\frac{32}{39}\right)\) \(e\left(\frac{28}{39}\right)\)
\(\chi_{7098}(2063,\cdot)\) \(1\) \(1\) \(e\left(\frac{14}{39}\right)\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{35}{39}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{28}{39}\right)\) \(e\left(\frac{19}{78}\right)\) \(e\left(\frac{35}{78}\right)\) \(e\left(\frac{37}{39}\right)\) \(e\left(\frac{8}{39}\right)\)
\(\chi_{7098}(2369,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{39}\right)\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{28}{39}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{38}{39}\right)\) \(e\left(\frac{23}{78}\right)\) \(e\left(\frac{67}{78}\right)\) \(e\left(\frac{14}{39}\right)\) \(e\left(\frac{22}{39}\right)\)
\(\chi_{7098}(2609,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{39}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{23}{39}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{34}{39}\right)\) \(e\left(\frac{37}{78}\right)\) \(e\left(\frac{23}{78}\right)\) \(e\left(\frac{31}{39}\right)\) \(e\left(\frac{32}{39}\right)\)
\(\chi_{7098}(2915,\cdot)\) \(1\) \(1\) \(e\left(\frac{28}{39}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{31}{39}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{17}{39}\right)\) \(e\left(\frac{77}{78}\right)\) \(e\left(\frac{31}{78}\right)\) \(e\left(\frac{35}{39}\right)\) \(e\left(\frac{16}{39}\right)\)
\(\chi_{7098}(3155,\cdot)\) \(1\) \(1\) \(e\left(\frac{20}{39}\right)\) \(e\left(\frac{25}{26}\right)\) \(e\left(\frac{11}{39}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{39}\right)\) \(e\left(\frac{55}{78}\right)\) \(e\left(\frac{11}{78}\right)\) \(e\left(\frac{25}{39}\right)\) \(e\left(\frac{17}{39}\right)\)
\(\chi_{7098}(3461,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{39}\right)\) \(e\left(\frac{17}{26}\right)\) \(e\left(\frac{34}{39}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{35}{39}\right)\) \(e\left(\frac{53}{78}\right)\) \(e\left(\frac{73}{78}\right)\) \(e\left(\frac{17}{39}\right)\) \(e\left(\frac{10}{39}\right)\)
\(\chi_{7098}(3701,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{39}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{38}{39}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{39}\right)\) \(e\left(\frac{73}{78}\right)\) \(e\left(\frac{77}{78}\right)\) \(e\left(\frac{19}{39}\right)\) \(e\left(\frac{2}{39}\right)\)
\(\chi_{7098}(4007,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{39}\right)\) \(e\left(\frac{25}{26}\right)\) \(e\left(\frac{37}{39}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{14}{39}\right)\) \(e\left(\frac{29}{78}\right)\) \(e\left(\frac{37}{78}\right)\) \(e\left(\frac{38}{39}\right)\) \(e\left(\frac{4}{39}\right)\)
\(\chi_{7098}(4553,\cdot)\) \(1\) \(1\) \(e\left(\frac{16}{39}\right)\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{1}{39}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{32}{39}\right)\) \(e\left(\frac{5}{78}\right)\) \(e\left(\frac{1}{78}\right)\) \(e\left(\frac{20}{39}\right)\) \(e\left(\frac{37}{39}\right)\)
\(\chi_{7098}(4793,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{39}\right)\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{14}{39}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{19}{39}\right)\) \(e\left(\frac{31}{78}\right)\) \(e\left(\frac{53}{78}\right)\) \(e\left(\frac{7}{39}\right)\) \(e\left(\frac{11}{39}\right)\)
\(\chi_{7098}(5099,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{39}\right)\) \(e\left(\frac{15}{26}\right)\) \(e\left(\frac{4}{39}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{39}\right)\) \(e\left(\frac{59}{78}\right)\) \(e\left(\frac{43}{78}\right)\) \(e\left(\frac{2}{39}\right)\) \(e\left(\frac{31}{39}\right)\)
\(\chi_{7098}(5339,\cdot)\) \(1\) \(1\) \(e\left(\frac{32}{39}\right)\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{2}{39}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{25}{39}\right)\) \(e\left(\frac{49}{78}\right)\) \(e\left(\frac{41}{78}\right)\) \(e\left(\frac{1}{39}\right)\) \(e\left(\frac{35}{39}\right)\)
\(\chi_{7098}(5645,\cdot)\) \(1\) \(1\) \(e\left(\frac{34}{39}\right)\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{7}{39}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{29}{39}\right)\) \(e\left(\frac{35}{78}\right)\) \(e\left(\frac{7}{78}\right)\) \(e\left(\frac{23}{39}\right)\) \(e\left(\frac{25}{39}\right)\)
\(\chi_{7098}(5885,\cdot)\) \(1\) \(1\) \(e\left(\frac{35}{39}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{29}{39}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{31}{39}\right)\) \(e\left(\frac{67}{78}\right)\) \(e\left(\frac{29}{78}\right)\) \(e\left(\frac{34}{39}\right)\) \(e\left(\frac{20}{39}\right)\)
\(\chi_{7098}(6191,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{39}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{10}{39}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{8}{39}\right)\) \(e\left(\frac{11}{78}\right)\) \(e\left(\frac{49}{78}\right)\) \(e\left(\frac{5}{39}\right)\) \(e\left(\frac{19}{39}\right)\)
\(\chi_{7098}(6431,\cdot)\) \(1\) \(1\) \(e\left(\frac{38}{39}\right)\) \(e\left(\frac{15}{26}\right)\) \(e\left(\frac{17}{39}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{37}{39}\right)\) \(e\left(\frac{7}{78}\right)\) \(e\left(\frac{17}{78}\right)\) \(e\left(\frac{28}{39}\right)\) \(e\left(\frac{5}{39}\right)\)
\(\chi_{7098}(6977,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{39}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{5}{39}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{4}{39}\right)\) \(e\left(\frac{25}{78}\right)\) \(e\left(\frac{5}{78}\right)\) \(e\left(\frac{22}{39}\right)\) \(e\left(\frac{29}{39}\right)\)