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Properties

Label 3864.ee
Modulus $3864$
Conductor $3864$
Order $66$
Real no
Primitive yes
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([0,33,33,11,30])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(101,3864)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(3864\)
Conductor: \(3864\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(66\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: yes
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 66 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(5\) \(11\) \(13\) \(17\) \(19\) \(25\) \(29\) \(31\) \(37\) \(41\)
\(\chi_{3864}(101,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{5}{11}\right)\)
\(\chi_{3864}(173,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{10}{11}\right)\)
\(\chi_{3864}(269,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{4}{11}\right)\)
\(\chi_{3864}(509,\cdot)\) \(1\) \(1\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{8}{11}\right)\)
\(\chi_{3864}(1181,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{3}{11}\right)\)
\(\chi_{3864}(1277,\cdot)\) \(1\) \(1\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{10}{11}\right)\)
\(\chi_{3864}(1613,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{8}{11}\right)\)
\(\chi_{3864}(1685,\cdot)\) \(1\) \(1\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{9}{11}\right)\)
\(\chi_{3864}(1853,\cdot)\) \(1\) \(1\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{7}{11}\right)\)
\(\chi_{3864}(2189,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{2}{11}\right)\)
\(\chi_{3864}(2285,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{3}{11}\right)\)
\(\chi_{3864}(2525,\cdot)\) \(1\) \(1\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{6}{11}\right)\)
\(\chi_{3864}(2693,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{1}{11}\right)\)
\(\chi_{3864}(2789,\cdot)\) \(1\) \(1\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{9}{11}\right)\)
\(\chi_{3864}(2861,\cdot)\) \(1\) \(1\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{5}{11}\right)\)
\(\chi_{3864}(2957,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{7}{11}\right)\)
\(\chi_{3864}(3029,\cdot)\) \(1\) \(1\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{4}{11}\right)\)
\(\chi_{3864}(3293,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{2}{11}\right)\)
\(\chi_{3864}(3629,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{6}{11}\right)\)
\(\chi_{3864}(3797,\cdot)\) \(1\) \(1\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{1}{11}\right)\)