Properties

Label 3525.bh
Modulus $3525$
Conductor $235$
Order $92$
Real no
Primitive no
Minimal no
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3525, base_ring=CyclotomicField(92))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,23,64]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(7,3525))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(3525\)
Conductor: \(235\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(92\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 235.k
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: $\Q(\zeta_{92})$
Fixed field: Number field defined by a degree 92 polynomial

First 31 of 44 characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(4\) \(7\) \(8\) \(11\) \(13\) \(14\) \(16\) \(17\) \(19\)
\(\chi_{3525}(7,\cdot)\) \(-1\) \(1\) \(e\left(\frac{71}{92}\right)\) \(e\left(\frac{25}{46}\right)\) \(e\left(\frac{47}{92}\right)\) \(e\left(\frac{29}{92}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{37}{92}\right)\) \(e\left(\frac{13}{46}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{35}{92}\right)\) \(e\left(\frac{37}{46}\right)\)
\(\chi_{3525}(118,\cdot)\) \(-1\) \(1\) \(e\left(\frac{65}{92}\right)\) \(e\left(\frac{19}{46}\right)\) \(e\left(\frac{21}{92}\right)\) \(e\left(\frac{11}{92}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{87}{92}\right)\) \(e\left(\frac{43}{46}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{45}{92}\right)\) \(e\left(\frac{41}{46}\right)\)
\(\chi_{3525}(157,\cdot)\) \(-1\) \(1\) \(e\left(\frac{39}{92}\right)\) \(e\left(\frac{39}{46}\right)\) \(e\left(\frac{31}{92}\right)\) \(e\left(\frac{25}{92}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{89}{92}\right)\) \(e\left(\frac{35}{46}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{27}{92}\right)\) \(e\left(\frac{43}{46}\right)\)
\(\chi_{3525}(307,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{92}\right)\) \(e\left(\frac{3}{46}\right)\) \(e\left(\frac{59}{92}\right)\) \(e\left(\frac{9}{92}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{21}{92}\right)\) \(e\left(\frac{31}{46}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{87}{92}\right)\) \(e\left(\frac{21}{46}\right)\)
\(\chi_{3525}(343,\cdot)\) \(-1\) \(1\) \(e\left(\frac{29}{92}\right)\) \(e\left(\frac{29}{46}\right)\) \(e\left(\frac{49}{92}\right)\) \(e\left(\frac{87}{92}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{19}{92}\right)\) \(e\left(\frac{39}{46}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{13}{92}\right)\) \(e\left(\frac{19}{46}\right)\)
\(\chi_{3525}(382,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{92}\right)\) \(e\left(\frac{11}{46}\right)\) \(e\left(\frac{63}{92}\right)\) \(e\left(\frac{33}{92}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{77}{92}\right)\) \(e\left(\frac{37}{46}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{43}{92}\right)\) \(e\left(\frac{31}{46}\right)\)
\(\chi_{3525}(418,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{92}\right)\) \(e\left(\frac{13}{46}\right)\) \(e\left(\frac{41}{92}\right)\) \(e\left(\frac{39}{92}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{91}{92}\right)\) \(e\left(\frac{27}{46}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{9}{92}\right)\) \(e\left(\frac{45}{46}\right)\)
\(\chi_{3525}(457,\cdot)\) \(-1\) \(1\) \(e\left(\frac{51}{92}\right)\) \(e\left(\frac{5}{46}\right)\) \(e\left(\frac{83}{92}\right)\) \(e\left(\frac{61}{92}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{81}{92}\right)\) \(e\left(\frac{21}{46}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{7}{92}\right)\) \(e\left(\frac{35}{46}\right)\)
\(\chi_{3525}(568,\cdot)\) \(-1\) \(1\) \(e\left(\frac{77}{92}\right)\) \(e\left(\frac{31}{46}\right)\) \(e\left(\frac{73}{92}\right)\) \(e\left(\frac{47}{92}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{79}{92}\right)\) \(e\left(\frac{29}{46}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{25}{92}\right)\) \(e\left(\frac{33}{46}\right)\)
\(\chi_{3525}(643,\cdot)\) \(-1\) \(1\) \(e\left(\frac{89}{92}\right)\) \(e\left(\frac{43}{46}\right)\) \(e\left(\frac{33}{92}\right)\) \(e\left(\frac{83}{92}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{71}{92}\right)\) \(e\left(\frac{15}{46}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{5}{92}\right)\) \(e\left(\frac{25}{46}\right)\)
\(\chi_{3525}(682,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{92}\right)\) \(e\left(\frac{19}{46}\right)\) \(e\left(\frac{67}{92}\right)\) \(e\left(\frac{57}{92}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{41}{92}\right)\) \(e\left(\frac{43}{46}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{91}{92}\right)\) \(e\left(\frac{41}{46}\right)\)
\(\chi_{3525}(907,\cdot)\) \(-1\) \(1\) \(e\left(\frac{75}{92}\right)\) \(e\left(\frac{29}{46}\right)\) \(e\left(\frac{3}{92}\right)\) \(e\left(\frac{41}{92}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{65}{92}\right)\) \(e\left(\frac{39}{46}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{59}{92}\right)\) \(e\left(\frac{19}{46}\right)\)
\(\chi_{3525}(943,\cdot)\) \(-1\) \(1\) \(e\left(\frac{53}{92}\right)\) \(e\left(\frac{7}{46}\right)\) \(e\left(\frac{61}{92}\right)\) \(e\left(\frac{67}{92}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{3}{92}\right)\) \(e\left(\frac{11}{46}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{65}{92}\right)\) \(e\left(\frac{3}{46}\right)\)
\(\chi_{3525}(982,\cdot)\) \(-1\) \(1\) \(e\left(\frac{59}{92}\right)\) \(e\left(\frac{13}{46}\right)\) \(e\left(\frac{87}{92}\right)\) \(e\left(\frac{85}{92}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{45}{92}\right)\) \(e\left(\frac{27}{46}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{55}{92}\right)\) \(e\left(\frac{45}{46}\right)\)
\(\chi_{3525}(1093,\cdot)\) \(-1\) \(1\) \(e\left(\frac{61}{92}\right)\) \(e\left(\frac{15}{46}\right)\) \(e\left(\frac{65}{92}\right)\) \(e\left(\frac{91}{92}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{59}{92}\right)\) \(e\left(\frac{17}{46}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{21}{92}\right)\) \(e\left(\frac{13}{46}\right)\)
\(\chi_{3525}(1132,\cdot)\) \(-1\) \(1\) \(e\left(\frac{31}{92}\right)\) \(e\left(\frac{31}{46}\right)\) \(e\left(\frac{27}{92}\right)\) \(e\left(\frac{1}{92}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{33}{92}\right)\) \(e\left(\frac{29}{46}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{71}{92}\right)\) \(e\left(\frac{33}{46}\right)\)
\(\chi_{3525}(1207,\cdot)\) \(-1\) \(1\) \(e\left(\frac{43}{92}\right)\) \(e\left(\frac{43}{46}\right)\) \(e\left(\frac{79}{92}\right)\) \(e\left(\frac{37}{92}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{25}{92}\right)\) \(e\left(\frac{15}{46}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{51}{92}\right)\) \(e\left(\frac{25}{46}\right)\)
\(\chi_{3525}(1243,\cdot)\) \(-1\) \(1\) \(e\left(\frac{9}{92}\right)\) \(e\left(\frac{9}{46}\right)\) \(e\left(\frac{85}{92}\right)\) \(e\left(\frac{27}{92}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{63}{92}\right)\) \(e\left(\frac{1}{46}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{77}{92}\right)\) \(e\left(\frac{17}{46}\right)\)
\(\chi_{3525}(1318,\cdot)\) \(-1\) \(1\) \(e\left(\frac{73}{92}\right)\) \(e\left(\frac{27}{46}\right)\) \(e\left(\frac{25}{92}\right)\) \(e\left(\frac{35}{92}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{51}{92}\right)\) \(e\left(\frac{3}{46}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{1}{92}\right)\) \(e\left(\frac{5}{46}\right)\)
\(\chi_{3525}(1507,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{92}\right)\) \(e\left(\frac{7}{46}\right)\) \(e\left(\frac{15}{92}\right)\) \(e\left(\frac{21}{92}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{49}{92}\right)\) \(e\left(\frac{11}{46}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{19}{92}\right)\) \(e\left(\frac{3}{46}\right)\)
\(\chi_{3525}(1657,\cdot)\) \(-1\) \(1\) \(e\left(\frac{15}{92}\right)\) \(e\left(\frac{15}{46}\right)\) \(e\left(\frac{19}{92}\right)\) \(e\left(\frac{45}{92}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{13}{92}\right)\) \(e\left(\frac{17}{46}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{67}{92}\right)\) \(e\left(\frac{13}{46}\right)\)
\(\chi_{3525}(1807,\cdot)\) \(-1\) \(1\) \(e\left(\frac{55}{92}\right)\) \(e\left(\frac{9}{46}\right)\) \(e\left(\frac{39}{92}\right)\) \(e\left(\frac{73}{92}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{17}{92}\right)\) \(e\left(\frac{1}{46}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{31}{92}\right)\) \(e\left(\frac{17}{46}\right)\)
\(\chi_{3525}(1882,\cdot)\) \(-1\) \(1\) \(e\left(\frac{27}{92}\right)\) \(e\left(\frac{27}{46}\right)\) \(e\left(\frac{71}{92}\right)\) \(e\left(\frac{81}{92}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{5}{92}\right)\) \(e\left(\frac{3}{46}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{47}{92}\right)\) \(e\left(\frac{5}{46}\right)\)
\(\chi_{3525}(2143,\cdot)\) \(-1\) \(1\) \(e\left(\frac{33}{92}\right)\) \(e\left(\frac{33}{46}\right)\) \(e\left(\frac{5}{92}\right)\) \(e\left(\frac{7}{92}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{47}{92}\right)\) \(e\left(\frac{19}{46}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{37}{92}\right)\) \(e\left(\frac{1}{46}\right)\)
\(\chi_{3525}(2218,\cdot)\) \(-1\) \(1\) \(e\left(\frac{37}{92}\right)\) \(e\left(\frac{37}{46}\right)\) \(e\left(\frac{53}{92}\right)\) \(e\left(\frac{19}{92}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{75}{92}\right)\) \(e\left(\frac{45}{46}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{61}{92}\right)\) \(e\left(\frac{29}{46}\right)\)
\(\chi_{3525}(2293,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{92}\right)\) \(e\left(\frac{17}{46}\right)\) \(e\left(\frac{89}{92}\right)\) \(e\left(\frac{51}{92}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{27}{92}\right)\) \(e\left(\frac{7}{46}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{33}{92}\right)\) \(e\left(\frac{27}{46}\right)\)
\(\chi_{3525}(2368,\cdot)\) \(-1\) \(1\) \(e\left(\frac{41}{92}\right)\) \(e\left(\frac{41}{46}\right)\) \(e\left(\frac{9}{92}\right)\) \(e\left(\frac{31}{92}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{11}{92}\right)\) \(e\left(\frac{25}{46}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{85}{92}\right)\) \(e\left(\frac{11}{46}\right)\)
\(\chi_{3525}(2518,\cdot)\) \(-1\) \(1\) \(e\left(\frac{21}{92}\right)\) \(e\left(\frac{21}{46}\right)\) \(e\left(\frac{45}{92}\right)\) \(e\left(\frac{63}{92}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{55}{92}\right)\) \(e\left(\frac{33}{46}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{57}{92}\right)\) \(e\left(\frac{9}{46}\right)\)
\(\chi_{3525}(2593,\cdot)\) \(-1\) \(1\) \(e\left(\frac{81}{92}\right)\) \(e\left(\frac{35}{46}\right)\) \(e\left(\frac{29}{92}\right)\) \(e\left(\frac{59}{92}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{15}{92}\right)\) \(e\left(\frac{9}{46}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{49}{92}\right)\) \(e\left(\frac{15}{46}\right)\)
\(\chi_{3525}(2668,\cdot)\) \(-1\) \(1\) \(e\left(\frac{45}{92}\right)\) \(e\left(\frac{45}{46}\right)\) \(e\left(\frac{57}{92}\right)\) \(e\left(\frac{43}{92}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{39}{92}\right)\) \(e\left(\frac{5}{46}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{17}{92}\right)\) \(e\left(\frac{39}{46}\right)\)
\(\chi_{3525}(2707,\cdot)\) \(-1\) \(1\) \(e\left(\frac{79}{92}\right)\) \(e\left(\frac{33}{46}\right)\) \(e\left(\frac{51}{92}\right)\) \(e\left(\frac{53}{92}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{1}{92}\right)\) \(e\left(\frac{19}{46}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{83}{92}\right)\) \(e\left(\frac{1}{46}\right)\)