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Properties

Label 3864.ds
Modulus $3864$
Conductor $161$
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(3864, base_ring=CyclotomicField(66)) M = H._module chi = DirichletCharacter(H, M([0,0,0,44,6])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(25,3864)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(3864\)
Conductor: \(161\)
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 161.m
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: 33.33.277966181338944111003326058293667039541136678070715028736001.1

Characters in Galois orbit

Character \(-1\) \(1\) \(5\) \(11\) \(13\) \(17\) \(19\) \(25\) \(29\) \(31\) \(37\) \(41\)
\(\chi_{3864}(25,\cdot)\) \(1\) \(1\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{1}{11}\right)\)
\(\chi_{3864}(121,\cdot)\) \(1\) \(1\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{9}{11}\right)\)
\(\chi_{3864}(193,\cdot)\) \(1\) \(1\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{5}{11}\right)\)
\(\chi_{3864}(289,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{7}{11}\right)\)
\(\chi_{3864}(361,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{4}{11}\right)\)
\(\chi_{3864}(625,\cdot)\) \(1\) \(1\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{2}{11}\right)\)
\(\chi_{3864}(961,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{6}{11}\right)\)
\(\chi_{3864}(1129,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{1}{11}\right)\)
\(\chi_{3864}(1297,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{5}{11}\right)\)
\(\chi_{3864}(1369,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{10}{11}\right)\)
\(\chi_{3864}(1465,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{4}{11}\right)\)
\(\chi_{3864}(1705,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{8}{11}\right)\)
\(\chi_{3864}(2377,\cdot)\) \(1\) \(1\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{3}{11}\right)\)
\(\chi_{3864}(2473,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{10}{11}\right)\)
\(\chi_{3864}(2809,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{8}{11}\right)\)
\(\chi_{3864}(2881,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{9}{11}\right)\)
\(\chi_{3864}(3049,\cdot)\) \(1\) \(1\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{7}{11}\right)\)
\(\chi_{3864}(3385,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{2}{11}\right)\)
\(\chi_{3864}(3481,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{3}{11}\right)\)
\(\chi_{3864}(3721,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{6}{11}\right)\)