Properties

Label 2025.bl
Modulus $2025$
Conductor $675$
Order $90$
Real no
Primitive no
Minimal no
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2025, base_ring=CyclotomicField(90))
 
M = H._module
 
chi = DirichletCharacter(H, M([25,81]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(44,2025))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(2025\)
Conductor: \(675\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(90\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 675.bh
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: $\Q(\zeta_{45})$
Fixed field: Number field defined by a degree 90 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(4\) \(7\) \(8\) \(11\) \(13\) \(14\) \(16\) \(17\) \(19\)
\(\chi_{2025}(44,\cdot)\) \(-1\) \(1\) \(e\left(\frac{8}{45}\right)\) \(e\left(\frac{16}{45}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{90}\right)\) \(e\left(\frac{29}{90}\right)\) \(e\left(\frac{11}{90}\right)\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{8}{15}\right)\)
\(\chi_{2025}(89,\cdot)\) \(-1\) \(1\) \(e\left(\frac{16}{45}\right)\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{47}{90}\right)\) \(e\left(\frac{13}{90}\right)\) \(e\left(\frac{67}{90}\right)\) \(e\left(\frac{19}{45}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{1}{15}\right)\)
\(\chi_{2025}(179,\cdot)\) \(-1\) \(1\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{19}{45}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{49}{90}\right)\) \(e\left(\frac{71}{90}\right)\) \(e\left(\frac{89}{90}\right)\) \(e\left(\frac{38}{45}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{2}{15}\right)\)
\(\chi_{2025}(314,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{45}\right)\) \(e\left(\frac{22}{45}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{7}{90}\right)\) \(e\left(\frac{23}{90}\right)\) \(e\left(\frac{77}{90}\right)\) \(e\left(\frac{44}{45}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{11}{15}\right)\)
\(\chi_{2025}(359,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{45}\right)\) \(e\left(\frac{38}{45}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{53}{90}\right)\) \(e\left(\frac{7}{90}\right)\) \(e\left(\frac{43}{90}\right)\) \(e\left(\frac{31}{45}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{4}{15}\right)\)
\(\chi_{2025}(494,\cdot)\) \(-1\) \(1\) \(e\left(\frac{43}{45}\right)\) \(e\left(\frac{41}{45}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{11}{90}\right)\) \(e\left(\frac{49}{90}\right)\) \(e\left(\frac{31}{90}\right)\) \(e\left(\frac{37}{45}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{13}{15}\right)\)
\(\chi_{2025}(584,\cdot)\) \(-1\) \(1\) \(e\left(\frac{14}{45}\right)\) \(e\left(\frac{28}{45}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{13}{90}\right)\) \(e\left(\frac{17}{90}\right)\) \(e\left(\frac{53}{90}\right)\) \(e\left(\frac{11}{45}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{14}{15}\right)\)
\(\chi_{2025}(629,\cdot)\) \(-1\) \(1\) \(e\left(\frac{22}{45}\right)\) \(e\left(\frac{44}{45}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{59}{90}\right)\) \(e\left(\frac{1}{90}\right)\) \(e\left(\frac{19}{90}\right)\) \(e\left(\frac{43}{45}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{7}{15}\right)\)
\(\chi_{2025}(719,\cdot)\) \(-1\) \(1\) \(e\left(\frac{38}{45}\right)\) \(e\left(\frac{31}{45}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{61}{90}\right)\) \(e\left(\frac{59}{90}\right)\) \(e\left(\frac{41}{90}\right)\) \(e\left(\frac{17}{45}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{8}{15}\right)\)
\(\chi_{2025}(764,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{45}\right)\) \(e\left(\frac{2}{45}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{17}{90}\right)\) \(e\left(\frac{43}{90}\right)\) \(e\left(\frac{7}{90}\right)\) \(e\left(\frac{4}{45}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{1}{15}\right)\)
\(\chi_{2025}(854,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{45}\right)\) \(e\left(\frac{34}{45}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{19}{90}\right)\) \(e\left(\frac{11}{90}\right)\) \(e\left(\frac{29}{90}\right)\) \(e\left(\frac{23}{45}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{2}{15}\right)\)
\(\chi_{2025}(989,\cdot)\) \(-1\) \(1\) \(e\left(\frac{41}{45}\right)\) \(e\left(\frac{37}{45}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{67}{90}\right)\) \(e\left(\frac{53}{90}\right)\) \(e\left(\frac{17}{90}\right)\) \(e\left(\frac{29}{45}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{11}{15}\right)\)
\(\chi_{2025}(1034,\cdot)\) \(-1\) \(1\) \(e\left(\frac{4}{45}\right)\) \(e\left(\frac{8}{45}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{23}{90}\right)\) \(e\left(\frac{37}{90}\right)\) \(e\left(\frac{73}{90}\right)\) \(e\left(\frac{16}{45}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{4}{15}\right)\)
\(\chi_{2025}(1169,\cdot)\) \(-1\) \(1\) \(e\left(\frac{28}{45}\right)\) \(e\left(\frac{11}{45}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{71}{90}\right)\) \(e\left(\frac{79}{90}\right)\) \(e\left(\frac{61}{90}\right)\) \(e\left(\frac{22}{45}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{13}{15}\right)\)
\(\chi_{2025}(1259,\cdot)\) \(-1\) \(1\) \(e\left(\frac{44}{45}\right)\) \(e\left(\frac{43}{45}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{73}{90}\right)\) \(e\left(\frac{47}{90}\right)\) \(e\left(\frac{83}{90}\right)\) \(e\left(\frac{41}{45}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{14}{15}\right)\)
\(\chi_{2025}(1304,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{45}\right)\) \(e\left(\frac{14}{45}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{29}{90}\right)\) \(e\left(\frac{31}{90}\right)\) \(e\left(\frac{49}{90}\right)\) \(e\left(\frac{28}{45}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{7}{15}\right)\)
\(\chi_{2025}(1394,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{45}\right)\) \(e\left(\frac{1}{45}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{31}{90}\right)\) \(e\left(\frac{89}{90}\right)\) \(e\left(\frac{71}{90}\right)\) \(e\left(\frac{2}{45}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{8}{15}\right)\)
\(\chi_{2025}(1439,\cdot)\) \(-1\) \(1\) \(e\left(\frac{31}{45}\right)\) \(e\left(\frac{17}{45}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{77}{90}\right)\) \(e\left(\frac{73}{90}\right)\) \(e\left(\frac{37}{90}\right)\) \(e\left(\frac{34}{45}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{1}{15}\right)\)
\(\chi_{2025}(1529,\cdot)\) \(-1\) \(1\) \(e\left(\frac{2}{45}\right)\) \(e\left(\frac{4}{45}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{79}{90}\right)\) \(e\left(\frac{41}{90}\right)\) \(e\left(\frac{59}{90}\right)\) \(e\left(\frac{8}{45}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{2}{15}\right)\)
\(\chi_{2025}(1664,\cdot)\) \(-1\) \(1\) \(e\left(\frac{26}{45}\right)\) \(e\left(\frac{7}{45}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{37}{90}\right)\) \(e\left(\frac{83}{90}\right)\) \(e\left(\frac{47}{90}\right)\) \(e\left(\frac{14}{45}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{11}{15}\right)\)
\(\chi_{2025}(1709,\cdot)\) \(-1\) \(1\) \(e\left(\frac{34}{45}\right)\) \(e\left(\frac{23}{45}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{83}{90}\right)\) \(e\left(\frac{67}{90}\right)\) \(e\left(\frac{13}{90}\right)\) \(e\left(\frac{1}{45}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{4}{15}\right)\)
\(\chi_{2025}(1844,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{45}\right)\) \(e\left(\frac{26}{45}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{41}{90}\right)\) \(e\left(\frac{19}{90}\right)\) \(e\left(\frac{1}{90}\right)\) \(e\left(\frac{7}{45}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{13}{15}\right)\)
\(\chi_{2025}(1934,\cdot)\) \(-1\) \(1\) \(e\left(\frac{29}{45}\right)\) \(e\left(\frac{13}{45}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{43}{90}\right)\) \(e\left(\frac{77}{90}\right)\) \(e\left(\frac{23}{90}\right)\) \(e\left(\frac{26}{45}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{14}{15}\right)\)
\(\chi_{2025}(1979,\cdot)\) \(-1\) \(1\) \(e\left(\frac{37}{45}\right)\) \(e\left(\frac{29}{45}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{89}{90}\right)\) \(e\left(\frac{61}{90}\right)\) \(e\left(\frac{79}{90}\right)\) \(e\left(\frac{13}{45}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{7}{15}\right)\)