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Properties

Label 25410.ea
Modulus $25410$
Conductor $847$
Order $33$
Real no
Primitive no
Minimal yes
Parity even

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(25410, base_ring=CyclotomicField(66)) M = H._module chi = DirichletCharacter(H, M([0,0,22,36])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(331,25410)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(25410\)
Conductor: \(847\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(33\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 847.u
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{33})\)
Fixed field: Number field defined by a degree 33 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(13\) \(17\) \(19\) \(23\) \(29\) \(31\) \(37\) \(41\) \(43\) \(47\)
\(\chi_{25410}(331,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{4}{33}\right)\)
\(\chi_{25410}(991,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{23}{33}\right)\)
\(\chi_{25410}(2641,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{10}{33}\right)\)
\(\chi_{25410}(3301,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{29}{33}\right)\)
\(\chi_{25410}(4951,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{16}{33}\right)\)
\(\chi_{25410}(5611,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{2}{33}\right)\)
\(\chi_{25410}(7921,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{8}{33}\right)\)
\(\chi_{25410}(9571,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{28}{33}\right)\)
\(\chi_{25410}(10231,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{14}{33}\right)\)
\(\chi_{25410}(11881,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{1}{33}\right)\)
\(\chi_{25410}(12541,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{20}{33}\right)\)
\(\chi_{25410}(14191,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{7}{33}\right)\)
\(\chi_{25410}(14851,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{26}{33}\right)\)
\(\chi_{25410}(16501,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{13}{33}\right)\)
\(\chi_{25410}(17161,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{32}{33}\right)\)
\(\chi_{25410}(18811,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{19}{33}\right)\)
\(\chi_{25410}(19471,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{5}{33}\right)\)
\(\chi_{25410}(21121,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{25}{33}\right)\)
\(\chi_{25410}(23431,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{31}{33}\right)\)
\(\chi_{25410}(24091,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{17}{33}\right)\)