Properties

Label 1045.ce
Modulus $1045$
Conductor $209$
Order $45$
Real no
Primitive no
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1045, base_ring=CyclotomicField(90))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,36,20]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(16,1045))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1045\)
Conductor: \(209\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(45\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 209.u
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: $\Q(\zeta_{45})$
Fixed field: 45.45.43679806300610465846484971330073185012597520004657724600953543350870941304329239684756561.1

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(6\) \(7\) \(8\) \(9\) \(12\) \(13\) \(14\)
\(\chi_{1045}(16,\cdot)\) \(1\) \(1\) \(e\left(\frac{28}{45}\right)\) \(e\left(\frac{4}{45}\right)\) \(e\left(\frac{11}{45}\right)\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{8}{45}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{23}{45}\right)\) \(e\left(\frac{34}{45}\right)\)
\(\chi_{1045}(36,\cdot)\) \(1\) \(1\) \(e\left(\frac{16}{45}\right)\) \(e\left(\frac{28}{45}\right)\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{44}{45}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{11}{45}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{26}{45}\right)\) \(e\left(\frac{13}{45}\right)\)
\(\chi_{1045}(81,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{45}\right)\) \(e\left(\frac{7}{45}\right)\) \(e\left(\frac{8}{45}\right)\) \(e\left(\frac{11}{45}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{14}{45}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{29}{45}\right)\) \(e\left(\frac{37}{45}\right)\)
\(\chi_{1045}(196,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{45}\right)\) \(e\left(\frac{41}{45}\right)\) \(e\left(\frac{34}{45}\right)\) \(e\left(\frac{13}{45}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{37}{45}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{22}{45}\right)\) \(e\left(\frac{11}{45}\right)\)
\(\chi_{1045}(251,\cdot)\) \(1\) \(1\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{11}{45}\right)\) \(e\left(\frac{19}{45}\right)\) \(e\left(\frac{43}{45}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{22}{45}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{45}\right)\) \(e\left(\frac{26}{45}\right)\)
\(\chi_{1045}(256,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{45}\right)\) \(e\left(\frac{8}{45}\right)\) \(e\left(\frac{22}{45}\right)\) \(e\left(\frac{19}{45}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{16}{45}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{45}\right)\) \(e\left(\frac{23}{45}\right)\)
\(\chi_{1045}(291,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{45}\right)\) \(e\left(\frac{14}{45}\right)\) \(e\left(\frac{16}{45}\right)\) \(e\left(\frac{22}{45}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{28}{45}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{13}{45}\right)\) \(e\left(\frac{29}{45}\right)\)
\(\chi_{1045}(301,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{45}\right)\) \(e\left(\frac{22}{45}\right)\) \(e\left(\frac{38}{45}\right)\) \(e\left(\frac{41}{45}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{44}{45}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{14}{45}\right)\) \(e\left(\frac{7}{45}\right)\)
\(\chi_{1045}(346,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{45}\right)\) \(e\left(\frac{29}{45}\right)\) \(e\left(\frac{1}{45}\right)\) \(e\left(\frac{7}{45}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{13}{45}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{43}{45}\right)\) \(e\left(\frac{44}{45}\right)\)
\(\chi_{1045}(366,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{45}\right)\) \(e\left(\frac{43}{45}\right)\) \(e\left(\frac{17}{45}\right)\) \(e\left(\frac{29}{45}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{41}{45}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{45}\right)\) \(e\left(\frac{28}{45}\right)\)
\(\chi_{1045}(416,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{45}\right)\) \(e\left(\frac{1}{45}\right)\) \(e\left(\frac{14}{45}\right)\) \(e\left(\frac{8}{45}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{2}{45}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{17}{45}\right)\) \(e\left(\frac{31}{45}\right)\)
\(\chi_{1045}(511,\cdot)\) \(1\) \(1\) \(e\left(\frac{43}{45}\right)\) \(e\left(\frac{19}{45}\right)\) \(e\left(\frac{41}{45}\right)\) \(e\left(\frac{17}{45}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{38}{45}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{8}{45}\right)\) \(e\left(\frac{4}{45}\right)\)
\(\chi_{1045}(576,\cdot)\) \(1\) \(1\) \(e\left(\frac{44}{45}\right)\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{43}{45}\right)\) \(e\left(\frac{31}{45}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{19}{45}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{4}{45}\right)\) \(e\left(\frac{2}{45}\right)\)
\(\chi_{1045}(586,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{45}\right)\) \(e\left(\frac{13}{45}\right)\) \(e\left(\frac{2}{45}\right)\) \(e\left(\frac{14}{45}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{26}{45}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{41}{45}\right)\) \(e\left(\frac{43}{45}\right)\)
\(\chi_{1045}(631,\cdot)\) \(1\) \(1\) \(e\left(\frac{14}{45}\right)\) \(e\left(\frac{2}{45}\right)\) \(e\left(\frac{28}{45}\right)\) \(e\left(\frac{16}{45}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{4}{45}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{34}{45}\right)\) \(e\left(\frac{17}{45}\right)\)
\(\chi_{1045}(636,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{45}\right)\) \(e\left(\frac{26}{45}\right)\) \(e\left(\frac{4}{45}\right)\) \(e\left(\frac{28}{45}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{7}{45}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{37}{45}\right)\) \(e\left(\frac{41}{45}\right)\)
\(\chi_{1045}(731,\cdot)\) \(1\) \(1\) \(e\left(\frac{38}{45}\right)\) \(e\left(\frac{44}{45}\right)\) \(e\left(\frac{31}{45}\right)\) \(e\left(\frac{37}{45}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{43}{45}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{28}{45}\right)\) \(e\left(\frac{14}{45}\right)\)
\(\chi_{1045}(746,\cdot)\) \(1\) \(1\) \(e\left(\frac{22}{45}\right)\) \(e\left(\frac{16}{45}\right)\) \(e\left(\frac{44}{45}\right)\) \(e\left(\frac{38}{45}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{45}\right)\) \(e\left(\frac{1}{45}\right)\)
\(\chi_{1045}(796,\cdot)\) \(1\) \(1\) \(e\left(\frac{34}{45}\right)\) \(e\left(\frac{37}{45}\right)\) \(e\left(\frac{23}{45}\right)\) \(e\left(\frac{26}{45}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{29}{45}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{44}{45}\right)\) \(e\left(\frac{22}{45}\right)\)
\(\chi_{1045}(841,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{45}\right)\) \(e\left(\frac{34}{45}\right)\) \(e\left(\frac{26}{45}\right)\) \(e\left(\frac{2}{45}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{23}{45}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{38}{45}\right)\) \(e\left(\frac{19}{45}\right)\)
\(\chi_{1045}(861,\cdot)\) \(1\) \(1\) \(e\left(\frac{26}{45}\right)\) \(e\left(\frac{23}{45}\right)\) \(e\left(\frac{7}{45}\right)\) \(e\left(\frac{4}{45}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{1}{45}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{31}{45}\right)\) \(e\left(\frac{38}{45}\right)\)
\(\chi_{1045}(916,\cdot)\) \(1\) \(1\) \(e\left(\frac{41}{45}\right)\) \(e\left(\frac{38}{45}\right)\) \(e\left(\frac{37}{45}\right)\) \(e\left(\frac{34}{45}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{31}{45}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{16}{45}\right)\) \(e\left(\frac{8}{45}\right)\)
\(\chi_{1045}(966,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{45}\right)\) \(e\left(\frac{31}{45}\right)\) \(e\left(\frac{29}{45}\right)\) \(e\left(\frac{23}{45}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{17}{45}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{16}{45}\right)\)
\(\chi_{1045}(1016,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{45}\right)\) \(e\left(\frac{17}{45}\right)\) \(e\left(\frac{13}{45}\right)\) \(e\left(\frac{1}{45}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{34}{45}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{19}{45}\right)\) \(e\left(\frac{32}{45}\right)\)