Properties

Label 2025.br
Modulus $2025$
Conductor $2025$
Order $270$
Real no
Primitive yes
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2025, base_ring=CyclotomicField(270))
 
M = H._module
 
chi = DirichletCharacter(H, M([10,27]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(4,2025))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(2025\)
Conductor: \(2025\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(270\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
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: $\Q(\zeta_{135})$
Fixed field: Number field defined by a degree 270 polynomial (not computed)

First 31 of 72 characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(4\) \(7\) \(8\) \(11\) \(13\) \(14\) \(16\) \(17\) \(19\)
\(\chi_{2025}(4,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{270}\right)\) \(e\left(\frac{37}{135}\right)\) \(e\left(\frac{5}{54}\right)\) \(e\left(\frac{37}{90}\right)\) \(e\left(\frac{11}{135}\right)\) \(e\left(\frac{53}{270}\right)\) \(e\left(\frac{31}{135}\right)\) \(e\left(\frac{74}{135}\right)\) \(e\left(\frac{47}{90}\right)\) \(e\left(\frac{26}{45}\right)\)
\(\chi_{2025}(34,\cdot)\) \(1\) \(1\) \(e\left(\frac{89}{270}\right)\) \(e\left(\frac{89}{135}\right)\) \(e\left(\frac{31}{54}\right)\) \(e\left(\frac{89}{90}\right)\) \(e\left(\frac{52}{135}\right)\) \(e\left(\frac{91}{270}\right)\) \(e\left(\frac{122}{135}\right)\) \(e\left(\frac{43}{135}\right)\) \(e\left(\frac{79}{90}\right)\) \(e\left(\frac{37}{45}\right)\)
\(\chi_{2025}(79,\cdot)\) \(1\) \(1\) \(e\left(\frac{167}{270}\right)\) \(e\left(\frac{32}{135}\right)\) \(e\left(\frac{43}{54}\right)\) \(e\left(\frac{77}{90}\right)\) \(e\left(\frac{46}{135}\right)\) \(e\left(\frac{13}{270}\right)\) \(e\left(\frac{56}{135}\right)\) \(e\left(\frac{64}{135}\right)\) \(e\left(\frac{37}{90}\right)\) \(e\left(\frac{31}{45}\right)\)
\(\chi_{2025}(94,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{270}\right)\) \(e\left(\frac{13}{135}\right)\) \(e\left(\frac{47}{54}\right)\) \(e\left(\frac{13}{90}\right)\) \(e\left(\frac{44}{135}\right)\) \(e\left(\frac{77}{270}\right)\) \(e\left(\frac{124}{135}\right)\) \(e\left(\frac{26}{135}\right)\) \(e\left(\frac{53}{90}\right)\) \(e\left(\frac{14}{45}\right)\)
\(\chi_{2025}(139,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{270}\right)\) \(e\left(\frac{1}{135}\right)\) \(e\left(\frac{41}{54}\right)\) \(e\left(\frac{1}{90}\right)\) \(e\left(\frac{128}{135}\right)\) \(e\left(\frac{89}{270}\right)\) \(e\left(\frac{103}{135}\right)\) \(e\left(\frac{2}{135}\right)\) \(e\left(\frac{11}{90}\right)\) \(e\left(\frac{8}{45}\right)\)
\(\chi_{2025}(169,\cdot)\) \(1\) \(1\) \(e\left(\frac{53}{270}\right)\) \(e\left(\frac{53}{135}\right)\) \(e\left(\frac{13}{54}\right)\) \(e\left(\frac{53}{90}\right)\) \(e\left(\frac{34}{135}\right)\) \(e\left(\frac{127}{270}\right)\) \(e\left(\frac{59}{135}\right)\) \(e\left(\frac{106}{135}\right)\) \(e\left(\frac{43}{90}\right)\) \(e\left(\frac{19}{45}\right)\)
\(\chi_{2025}(184,\cdot)\) \(1\) \(1\) \(e\left(\frac{259}{270}\right)\) \(e\left(\frac{124}{135}\right)\) \(e\left(\frac{35}{54}\right)\) \(e\left(\frac{79}{90}\right)\) \(e\left(\frac{77}{135}\right)\) \(e\left(\frac{101}{270}\right)\) \(e\left(\frac{82}{135}\right)\) \(e\left(\frac{113}{135}\right)\) \(e\left(\frac{59}{90}\right)\) \(e\left(\frac{2}{45}\right)\)
\(\chi_{2025}(214,\cdot)\) \(1\) \(1\) \(e\left(\frac{131}{270}\right)\) \(e\left(\frac{131}{135}\right)\) \(e\left(\frac{25}{54}\right)\) \(e\left(\frac{41}{90}\right)\) \(e\left(\frac{28}{135}\right)\) \(e\left(\frac{49}{270}\right)\) \(e\left(\frac{128}{135}\right)\) \(e\left(\frac{127}{135}\right)\) \(e\left(\frac{1}{90}\right)\) \(e\left(\frac{13}{45}\right)\)
\(\chi_{2025}(229,\cdot)\) \(1\) \(1\) \(e\left(\frac{247}{270}\right)\) \(e\left(\frac{112}{135}\right)\) \(e\left(\frac{29}{54}\right)\) \(e\left(\frac{67}{90}\right)\) \(e\left(\frac{26}{135}\right)\) \(e\left(\frac{113}{270}\right)\) \(e\left(\frac{61}{135}\right)\) \(e\left(\frac{89}{135}\right)\) \(e\left(\frac{17}{90}\right)\) \(e\left(\frac{41}{45}\right)\)
\(\chi_{2025}(259,\cdot)\) \(1\) \(1\) \(e\left(\frac{209}{270}\right)\) \(e\left(\frac{74}{135}\right)\) \(e\left(\frac{37}{54}\right)\) \(e\left(\frac{29}{90}\right)\) \(e\left(\frac{22}{135}\right)\) \(e\left(\frac{241}{270}\right)\) \(e\left(\frac{62}{135}\right)\) \(e\left(\frac{13}{135}\right)\) \(e\left(\frac{49}{90}\right)\) \(e\left(\frac{7}{45}\right)\)
\(\chi_{2025}(304,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{270}\right)\) \(e\left(\frac{17}{135}\right)\) \(e\left(\frac{49}{54}\right)\) \(e\left(\frac{17}{90}\right)\) \(e\left(\frac{16}{135}\right)\) \(e\left(\frac{163}{270}\right)\) \(e\left(\frac{131}{135}\right)\) \(e\left(\frac{34}{135}\right)\) \(e\left(\frac{7}{90}\right)\) \(e\left(\frac{1}{45}\right)\)
\(\chi_{2025}(319,\cdot)\) \(1\) \(1\) \(e\left(\frac{223}{270}\right)\) \(e\left(\frac{88}{135}\right)\) \(e\left(\frac{17}{54}\right)\) \(e\left(\frac{43}{90}\right)\) \(e\left(\frac{59}{135}\right)\) \(e\left(\frac{137}{270}\right)\) \(e\left(\frac{19}{135}\right)\) \(e\left(\frac{41}{135}\right)\) \(e\left(\frac{23}{90}\right)\) \(e\left(\frac{29}{45}\right)\)
\(\chi_{2025}(364,\cdot)\) \(1\) \(1\) \(e\left(\frac{211}{270}\right)\) \(e\left(\frac{76}{135}\right)\) \(e\left(\frac{11}{54}\right)\) \(e\left(\frac{31}{90}\right)\) \(e\left(\frac{8}{135}\right)\) \(e\left(\frac{149}{270}\right)\) \(e\left(\frac{133}{135}\right)\) \(e\left(\frac{17}{135}\right)\) \(e\left(\frac{71}{90}\right)\) \(e\left(\frac{23}{45}\right)\)
\(\chi_{2025}(394,\cdot)\) \(1\) \(1\) \(e\left(\frac{173}{270}\right)\) \(e\left(\frac{38}{135}\right)\) \(e\left(\frac{19}{54}\right)\) \(e\left(\frac{83}{90}\right)\) \(e\left(\frac{4}{135}\right)\) \(e\left(\frac{7}{270}\right)\) \(e\left(\frac{134}{135}\right)\) \(e\left(\frac{76}{135}\right)\) \(e\left(\frac{13}{90}\right)\) \(e\left(\frac{34}{45}\right)\)
\(\chi_{2025}(409,\cdot)\) \(1\) \(1\) \(e\left(\frac{199}{270}\right)\) \(e\left(\frac{64}{135}\right)\) \(e\left(\frac{5}{54}\right)\) \(e\left(\frac{19}{90}\right)\) \(e\left(\frac{92}{135}\right)\) \(e\left(\frac{161}{270}\right)\) \(e\left(\frac{112}{135}\right)\) \(e\left(\frac{128}{135}\right)\) \(e\left(\frac{29}{90}\right)\) \(e\left(\frac{17}{45}\right)\)
\(\chi_{2025}(439,\cdot)\) \(1\) \(1\) \(e\left(\frac{251}{270}\right)\) \(e\left(\frac{116}{135}\right)\) \(e\left(\frac{31}{54}\right)\) \(e\left(\frac{71}{90}\right)\) \(e\left(\frac{133}{135}\right)\) \(e\left(\frac{199}{270}\right)\) \(e\left(\frac{68}{135}\right)\) \(e\left(\frac{97}{135}\right)\) \(e\left(\frac{61}{90}\right)\) \(e\left(\frac{28}{45}\right)\)
\(\chi_{2025}(454,\cdot)\) \(1\) \(1\) \(e\left(\frac{187}{270}\right)\) \(e\left(\frac{52}{135}\right)\) \(e\left(\frac{53}{54}\right)\) \(e\left(\frac{7}{90}\right)\) \(e\left(\frac{41}{135}\right)\) \(e\left(\frac{173}{270}\right)\) \(e\left(\frac{91}{135}\right)\) \(e\left(\frac{104}{135}\right)\) \(e\left(\frac{77}{90}\right)\) \(e\left(\frac{11}{45}\right)\)
\(\chi_{2025}(484,\cdot)\) \(1\) \(1\) \(e\left(\frac{59}{270}\right)\) \(e\left(\frac{59}{135}\right)\) \(e\left(\frac{43}{54}\right)\) \(e\left(\frac{59}{90}\right)\) \(e\left(\frac{127}{135}\right)\) \(e\left(\frac{121}{270}\right)\) \(e\left(\frac{2}{135}\right)\) \(e\left(\frac{118}{135}\right)\) \(e\left(\frac{19}{90}\right)\) \(e\left(\frac{22}{45}\right)\)
\(\chi_{2025}(529,\cdot)\) \(1\) \(1\) \(e\left(\frac{137}{270}\right)\) \(e\left(\frac{2}{135}\right)\) \(e\left(\frac{1}{54}\right)\) \(e\left(\frac{47}{90}\right)\) \(e\left(\frac{121}{135}\right)\) \(e\left(\frac{43}{270}\right)\) \(e\left(\frac{71}{135}\right)\) \(e\left(\frac{4}{135}\right)\) \(e\left(\frac{67}{90}\right)\) \(e\left(\frac{16}{45}\right)\)
\(\chi_{2025}(544,\cdot)\) \(1\) \(1\) \(e\left(\frac{163}{270}\right)\) \(e\left(\frac{28}{135}\right)\) \(e\left(\frac{41}{54}\right)\) \(e\left(\frac{73}{90}\right)\) \(e\left(\frac{74}{135}\right)\) \(e\left(\frac{197}{270}\right)\) \(e\left(\frac{49}{135}\right)\) \(e\left(\frac{56}{135}\right)\) \(e\left(\frac{83}{90}\right)\) \(e\left(\frac{44}{45}\right)\)
\(\chi_{2025}(589,\cdot)\) \(1\) \(1\) \(e\left(\frac{151}{270}\right)\) \(e\left(\frac{16}{135}\right)\) \(e\left(\frac{35}{54}\right)\) \(e\left(\frac{61}{90}\right)\) \(e\left(\frac{23}{135}\right)\) \(e\left(\frac{209}{270}\right)\) \(e\left(\frac{28}{135}\right)\) \(e\left(\frac{32}{135}\right)\) \(e\left(\frac{41}{90}\right)\) \(e\left(\frac{38}{45}\right)\)
\(\chi_{2025}(619,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{270}\right)\) \(e\left(\frac{23}{135}\right)\) \(e\left(\frac{25}{54}\right)\) \(e\left(\frac{23}{90}\right)\) \(e\left(\frac{109}{135}\right)\) \(e\left(\frac{157}{270}\right)\) \(e\left(\frac{74}{135}\right)\) \(e\left(\frac{46}{135}\right)\) \(e\left(\frac{73}{90}\right)\) \(e\left(\frac{4}{45}\right)\)
\(\chi_{2025}(634,\cdot)\) \(1\) \(1\) \(e\left(\frac{139}{270}\right)\) \(e\left(\frac{4}{135}\right)\) \(e\left(\frac{29}{54}\right)\) \(e\left(\frac{49}{90}\right)\) \(e\left(\frac{107}{135}\right)\) \(e\left(\frac{221}{270}\right)\) \(e\left(\frac{7}{135}\right)\) \(e\left(\frac{8}{135}\right)\) \(e\left(\frac{89}{90}\right)\) \(e\left(\frac{32}{45}\right)\)
\(\chi_{2025}(664,\cdot)\) \(1\) \(1\) \(e\left(\frac{101}{270}\right)\) \(e\left(\frac{101}{135}\right)\) \(e\left(\frac{37}{54}\right)\) \(e\left(\frac{11}{90}\right)\) \(e\left(\frac{103}{135}\right)\) \(e\left(\frac{79}{270}\right)\) \(e\left(\frac{8}{135}\right)\) \(e\left(\frac{67}{135}\right)\) \(e\left(\frac{31}{90}\right)\) \(e\left(\frac{43}{45}\right)\)
\(\chi_{2025}(679,\cdot)\) \(1\) \(1\) \(e\left(\frac{127}{270}\right)\) \(e\left(\frac{127}{135}\right)\) \(e\left(\frac{23}{54}\right)\) \(e\left(\frac{37}{90}\right)\) \(e\left(\frac{56}{135}\right)\) \(e\left(\frac{233}{270}\right)\) \(e\left(\frac{121}{135}\right)\) \(e\left(\frac{119}{135}\right)\) \(e\left(\frac{47}{90}\right)\) \(e\left(\frac{26}{45}\right)\)
\(\chi_{2025}(709,\cdot)\) \(1\) \(1\) \(e\left(\frac{179}{270}\right)\) \(e\left(\frac{44}{135}\right)\) \(e\left(\frac{49}{54}\right)\) \(e\left(\frac{89}{90}\right)\) \(e\left(\frac{97}{135}\right)\) \(e\left(\frac{1}{270}\right)\) \(e\left(\frac{77}{135}\right)\) \(e\left(\frac{88}{135}\right)\) \(e\left(\frac{79}{90}\right)\) \(e\left(\frac{37}{45}\right)\)
\(\chi_{2025}(754,\cdot)\) \(1\) \(1\) \(e\left(\frac{257}{270}\right)\) \(e\left(\frac{122}{135}\right)\) \(e\left(\frac{7}{54}\right)\) \(e\left(\frac{77}{90}\right)\) \(e\left(\frac{91}{135}\right)\) \(e\left(\frac{193}{270}\right)\) \(e\left(\frac{11}{135}\right)\) \(e\left(\frac{109}{135}\right)\) \(e\left(\frac{37}{90}\right)\) \(e\left(\frac{31}{45}\right)\)
\(\chi_{2025}(769,\cdot)\) \(1\) \(1\) \(e\left(\frac{103}{270}\right)\) \(e\left(\frac{103}{135}\right)\) \(e\left(\frac{11}{54}\right)\) \(e\left(\frac{13}{90}\right)\) \(e\left(\frac{89}{135}\right)\) \(e\left(\frac{257}{270}\right)\) \(e\left(\frac{79}{135}\right)\) \(e\left(\frac{71}{135}\right)\) \(e\left(\frac{53}{90}\right)\) \(e\left(\frac{14}{45}\right)\)
\(\chi_{2025}(814,\cdot)\) \(1\) \(1\) \(e\left(\frac{91}{270}\right)\) \(e\left(\frac{91}{135}\right)\) \(e\left(\frac{5}{54}\right)\) \(e\left(\frac{1}{90}\right)\) \(e\left(\frac{38}{135}\right)\) \(e\left(\frac{269}{270}\right)\) \(e\left(\frac{58}{135}\right)\) \(e\left(\frac{47}{135}\right)\) \(e\left(\frac{11}{90}\right)\) \(e\left(\frac{8}{45}\right)\)
\(\chi_{2025}(844,\cdot)\) \(1\) \(1\) \(e\left(\frac{143}{270}\right)\) \(e\left(\frac{8}{135}\right)\) \(e\left(\frac{31}{54}\right)\) \(e\left(\frac{53}{90}\right)\) \(e\left(\frac{79}{135}\right)\) \(e\left(\frac{37}{270}\right)\) \(e\left(\frac{14}{135}\right)\) \(e\left(\frac{16}{135}\right)\) \(e\left(\frac{43}{90}\right)\) \(e\left(\frac{19}{45}\right)\)
\(\chi_{2025}(859,\cdot)\) \(1\) \(1\) \(e\left(\frac{79}{270}\right)\) \(e\left(\frac{79}{135}\right)\) \(e\left(\frac{53}{54}\right)\) \(e\left(\frac{79}{90}\right)\) \(e\left(\frac{122}{135}\right)\) \(e\left(\frac{11}{270}\right)\) \(e\left(\frac{37}{135}\right)\) \(e\left(\frac{23}{135}\right)\) \(e\left(\frac{59}{90}\right)\) \(e\left(\frac{2}{45}\right)\)