Properties

Label 7098.cq
Modulus $7098$
Conductor $169$
Order $39$
Real no
Primitive no
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7098, base_ring=CyclotomicField(78))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,0,38]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(211,7098))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(7098\)
Conductor: \(169\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(39\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 169.i
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 39 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(5\) \(11\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\) \(37\) \(41\)
\(\chi_{7098}(211,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{7}{39}\right)\) \(e\left(\frac{5}{39}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{19}{39}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{22}{39}\right)\) \(e\left(\frac{16}{39}\right)\)
\(\chi_{7098}(295,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{2}{39}\right)\) \(e\left(\frac{7}{39}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{11}{39}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{23}{39}\right)\) \(e\left(\frac{38}{39}\right)\)
\(\chi_{7098}(757,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{19}{39}\right)\) \(e\left(\frac{8}{39}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{7}{39}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{4}{39}\right)\) \(e\left(\frac{10}{39}\right)\)
\(\chi_{7098}(841,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{32}{39}\right)\) \(e\left(\frac{34}{39}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{20}{39}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{17}{39}\right)\) \(e\left(\frac{23}{39}\right)\)
\(\chi_{7098}(1303,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{31}{39}\right)\) \(e\left(\frac{11}{39}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{34}{39}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{25}{39}\right)\) \(e\left(\frac{4}{39}\right)\)
\(\chi_{7098}(1387,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{23}{39}\right)\) \(e\left(\frac{22}{39}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{29}{39}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{11}{39}\right)\) \(e\left(\frac{8}{39}\right)\)
\(\chi_{7098}(1849,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{4}{39}\right)\) \(e\left(\frac{14}{39}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{22}{39}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{7}{39}\right)\) \(e\left(\frac{37}{39}\right)\)
\(\chi_{7098}(1933,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{14}{39}\right)\) \(e\left(\frac{10}{39}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{38}{39}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{5}{39}\right)\) \(e\left(\frac{32}{39}\right)\)
\(\chi_{7098}(2395,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{16}{39}\right)\) \(e\left(\frac{17}{39}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{10}{39}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{28}{39}\right)\) \(e\left(\frac{31}{39}\right)\)
\(\chi_{7098}(2479,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{5}{39}\right)\) \(e\left(\frac{37}{39}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{8}{39}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{38}{39}\right)\) \(e\left(\frac{17}{39}\right)\)
\(\chi_{7098}(2941,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{28}{39}\right)\) \(e\left(\frac{20}{39}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{37}{39}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{10}{39}\right)\) \(e\left(\frac{25}{39}\right)\)
\(\chi_{7098}(3025,\cdot)\) \(1\) \(1\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{35}{39}\right)\) \(e\left(\frac{25}{39}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{17}{39}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{32}{39}\right)\) \(e\left(\frac{2}{39}\right)\)
\(\chi_{7098}(3487,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{1}{39}\right)\) \(e\left(\frac{23}{39}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{25}{39}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{31}{39}\right)\) \(e\left(\frac{19}{39}\right)\)
\(\chi_{7098}(4117,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{17}{39}\right)\) \(e\left(\frac{1}{39}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{35}{39}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{20}{39}\right)\) \(e\left(\frac{11}{39}\right)\)
\(\chi_{7098}(4579,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{25}{39}\right)\) \(e\left(\frac{29}{39}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{1}{39}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{34}{39}\right)\) \(e\left(\frac{7}{39}\right)\)
\(\chi_{7098}(4663,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{8}{39}\right)\) \(e\left(\frac{28}{39}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{5}{39}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{14}{39}\right)\) \(e\left(\frac{35}{39}\right)\)
\(\chi_{7098}(5125,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{37}{39}\right)\) \(e\left(\frac{32}{39}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{28}{39}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{16}{39}\right)\) \(e\left(\frac{1}{39}\right)\)
\(\chi_{7098}(5209,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{38}{39}\right)\) \(e\left(\frac{16}{39}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{14}{39}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{8}{39}\right)\) \(e\left(\frac{20}{39}\right)\)
\(\chi_{7098}(5671,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{10}{39}\right)\) \(e\left(\frac{35}{39}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{16}{39}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{37}{39}\right)\) \(e\left(\frac{34}{39}\right)\)
\(\chi_{7098}(5755,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{29}{39}\right)\) \(e\left(\frac{4}{39}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{23}{39}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{2}{39}\right)\) \(e\left(\frac{5}{39}\right)\)
\(\chi_{7098}(6217,\cdot)\) \(1\) \(1\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{22}{39}\right)\) \(e\left(\frac{38}{39}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{4}{39}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{19}{39}\right)\) \(e\left(\frac{28}{39}\right)\)
\(\chi_{7098}(6301,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{20}{39}\right)\) \(e\left(\frac{31}{39}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{32}{39}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{35}{39}\right)\) \(e\left(\frac{29}{39}\right)\)
\(\chi_{7098}(6763,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{34}{39}\right)\) \(e\left(\frac{2}{39}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{31}{39}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{1}{39}\right)\) \(e\left(\frac{22}{39}\right)\)
\(\chi_{7098}(6847,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{11}{39}\right)\) \(e\left(\frac{19}{39}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{2}{39}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{29}{39}\right)\) \(e\left(\frac{14}{39}\right)\)