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Properties

Label 828.z
Modulus $828$
Conductor $207$
Order $66$
Real no
Primitive no
Minimal yes
Parity odd

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(828, base_ring=CyclotomicField(66)) M = H._module chi = DirichletCharacter(H, M([0,44,51])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(61,828)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(828\)
Conductor: \(207\)
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: no, induced from 207.p
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
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 \(-1\) \(1\) \(5\) \(7\) \(11\) \(13\) \(17\) \(19\) \(25\) \(29\) \(31\) \(35\)
\(\chi_{828}(61,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{5}{11}\right)\)
\(\chi_{828}(97,\cdot)\) \(-1\) \(1\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{10}{11}\right)\)
\(\chi_{828}(157,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{7}{11}\right)\)
\(\chi_{828}(205,\cdot)\) \(-1\) \(1\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{9}{11}\right)\)
\(\chi_{828}(241,\cdot)\) \(-1\) \(1\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{2}{11}\right)\)
\(\chi_{828}(313,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{1}{11}\right)\)
\(\chi_{828}(337,\cdot)\) \(-1\) \(1\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{5}{11}\right)\)
\(\chi_{828}(373,\cdot)\) \(-1\) \(1\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{10}{11}\right)\)
\(\chi_{828}(385,\cdot)\) \(-1\) \(1\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{4}{11}\right)\)
\(\chi_{828}(421,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{3}{11}\right)\)
\(\chi_{828}(457,\cdot)\) \(-1\) \(1\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{6}{11}\right)\)
\(\chi_{828}(481,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{9}{11}\right)\)
\(\chi_{828}(493,\cdot)\) \(-1\) \(1\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{8}{11}\right)\)
\(\chi_{828}(517,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{2}{11}\right)\)
\(\chi_{828}(589,\cdot)\) \(-1\) \(1\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{1}{11}\right)\)
\(\chi_{828}(661,\cdot)\) \(-1\) \(1\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{4}{11}\right)\)
\(\chi_{828}(697,\cdot)\) \(-1\) \(1\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{3}{11}\right)\)
\(\chi_{828}(709,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{7}{11}\right)\)
\(\chi_{828}(733,\cdot)\) \(-1\) \(1\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{6}{11}\right)\)
\(\chi_{828}(769,\cdot)\) \(-1\) \(1\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{8}{11}\right)\)