Properties

Label 2850.ce
Modulus $2850$
Conductor $475$
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(2850, base_ring=CyclotomicField(90))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,72,10]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(61,2850))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(2850\)
Conductor: \(475\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(45\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 475.bc
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: Number field defined by a degree 45 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(7\) \(11\) \(13\) \(17\) \(23\) \(29\) \(31\) \(37\) \(41\) \(43\)
\(\chi_{2850}(61,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{34}{45}\right)\) \(e\left(\frac{23}{45}\right)\) \(e\left(\frac{1}{45}\right)\) \(e\left(\frac{22}{45}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{29}{45}\right)\) \(e\left(\frac{7}{9}\right)\)
\(\chi_{2850}(271,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{38}{45}\right)\) \(e\left(\frac{31}{45}\right)\) \(e\left(\frac{17}{45}\right)\) \(e\left(\frac{14}{45}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{43}{45}\right)\) \(e\left(\frac{2}{9}\right)\)
\(\chi_{2850}(481,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{22}{45}\right)\) \(e\left(\frac{44}{45}\right)\) \(e\left(\frac{43}{45}\right)\) \(e\left(\frac{1}{45}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{4}{9}\right)\)
\(\chi_{2850}(511,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{44}{45}\right)\) \(e\left(\frac{43}{45}\right)\) \(e\left(\frac{41}{45}\right)\) \(e\left(\frac{2}{45}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{19}{45}\right)\) \(e\left(\frac{8}{9}\right)\)
\(\chi_{2850}(541,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{45}\right)\) \(e\left(\frac{2}{45}\right)\) \(e\left(\frac{4}{45}\right)\) \(e\left(\frac{43}{45}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{26}{45}\right)\) \(e\left(\frac{1}{9}\right)\)
\(\chi_{2850}(631,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{7}{45}\right)\) \(e\left(\frac{14}{45}\right)\) \(e\left(\frac{28}{45}\right)\) \(e\left(\frac{31}{45}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{45}\right)\) \(e\left(\frac{7}{9}\right)\)
\(\chi_{2850}(841,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{11}{45}\right)\) \(e\left(\frac{22}{45}\right)\) \(e\left(\frac{44}{45}\right)\) \(e\left(\frac{23}{45}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{16}{45}\right)\) \(e\left(\frac{2}{9}\right)\)
\(\chi_{2850}(871,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{23}{45}\right)\) \(e\left(\frac{1}{45}\right)\) \(e\left(\frac{2}{45}\right)\) \(e\left(\frac{44}{45}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{13}{45}\right)\) \(e\left(\frac{5}{9}\right)\)
\(\chi_{2850}(1081,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{17}{45}\right)\) \(e\left(\frac{34}{45}\right)\) \(e\left(\frac{23}{45}\right)\) \(e\left(\frac{11}{45}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{37}{45}\right)\) \(e\left(\frac{8}{9}\right)\)
\(\chi_{2850}(1111,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{19}{45}\right)\) \(e\left(\frac{38}{45}\right)\) \(e\left(\frac{31}{45}\right)\) \(e\left(\frac{7}{45}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{44}{45}\right)\) \(e\left(\frac{1}{9}\right)\)
\(\chi_{2850}(1411,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{29}{45}\right)\) \(e\left(\frac{13}{45}\right)\) \(e\left(\frac{26}{45}\right)\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{34}{45}\right)\) \(e\left(\frac{2}{9}\right)\)
\(\chi_{2850}(1441,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{41}{45}\right)\) \(e\left(\frac{37}{45}\right)\) \(e\left(\frac{29}{45}\right)\) \(e\left(\frac{8}{45}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{31}{45}\right)\) \(e\left(\frac{5}{9}\right)\)
\(\chi_{2850}(1621,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{13}{45}\right)\) \(e\left(\frac{26}{45}\right)\) \(e\left(\frac{7}{45}\right)\) \(e\left(\frac{19}{45}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{23}{45}\right)\) \(e\left(\frac{4}{9}\right)\)
\(\chi_{2850}(1681,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{37}{45}\right)\) \(e\left(\frac{29}{45}\right)\) \(e\left(\frac{13}{45}\right)\) \(e\left(\frac{16}{45}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{17}{45}\right)\) \(e\left(\frac{1}{9}\right)\)
\(\chi_{2850}(1771,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{43}{45}\right)\) \(e\left(\frac{41}{45}\right)\) \(e\left(\frac{37}{45}\right)\) \(e\left(\frac{4}{45}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{38}{45}\right)\) \(e\left(\frac{7}{9}\right)\)
\(\chi_{2850}(1981,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{2}{45}\right)\) \(e\left(\frac{4}{45}\right)\) \(e\left(\frac{8}{45}\right)\) \(e\left(\frac{41}{45}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{45}\right)\) \(e\left(\frac{2}{9}\right)\)
\(\chi_{2850}(2011,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{14}{45}\right)\) \(e\left(\frac{28}{45}\right)\) \(e\left(\frac{11}{45}\right)\) \(e\left(\frac{17}{45}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{45}\right)\) \(e\left(\frac{5}{9}\right)\)
\(\chi_{2850}(2191,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{31}{45}\right)\) \(e\left(\frac{17}{45}\right)\) \(e\left(\frac{34}{45}\right)\) \(e\left(\frac{28}{45}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{41}{45}\right)\) \(e\left(\frac{4}{9}\right)\)
\(\chi_{2850}(2221,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{8}{45}\right)\) \(e\left(\frac{16}{45}\right)\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{29}{45}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{28}{45}\right)\) \(e\left(\frac{8}{9}\right)\)
\(\chi_{2850}(2341,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{16}{45}\right)\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{19}{45}\right)\) \(e\left(\frac{13}{45}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{11}{45}\right)\) \(e\left(\frac{7}{9}\right)\)
\(\chi_{2850}(2581,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{19}{45}\right)\) \(e\left(\frac{38}{45}\right)\) \(e\left(\frac{26}{45}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{22}{45}\right)\) \(e\left(\frac{5}{9}\right)\)
\(\chi_{2850}(2761,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{4}{45}\right)\) \(e\left(\frac{8}{45}\right)\) \(e\left(\frac{16}{45}\right)\) \(e\left(\frac{37}{45}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{14}{45}\right)\) \(e\left(\frac{4}{9}\right)\)
\(\chi_{2850}(2791,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{26}{45}\right)\) \(e\left(\frac{7}{45}\right)\) \(e\left(\frac{14}{45}\right)\) \(e\left(\frac{38}{45}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{45}\right)\) \(e\left(\frac{8}{9}\right)\)
\(\chi_{2850}(2821,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{28}{45}\right)\) \(e\left(\frac{11}{45}\right)\) \(e\left(\frac{22}{45}\right)\) \(e\left(\frac{34}{45}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{8}{45}\right)\) \(e\left(\frac{1}{9}\right)\)