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Properties

Label 10002.j
Modulus $10002$
Conductor $5001$
Order $34$
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(10002, base_ring=CyclotomicField(34)) M = H._module chi = DirichletCharacter(H, M([17,31])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(263,10002)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(10002\)
Conductor: \(5001\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(34\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 5001.j
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: \(\Q(\zeta_{17})\)
Fixed field: Number field defined by a degree 34 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(5\) \(7\) \(11\) \(13\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\)
\(\chi_{10002}(263,\cdot)\) \(1\) \(1\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{29}{34}\right)\) \(1\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{8}{17}\right)\)
\(\chi_{10002}(479,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{21}{34}\right)\) \(1\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{14}{17}\right)\)
\(\chi_{10002}(605,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{25}{34}\right)\) \(1\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{11}{17}\right)\)
\(\chi_{10002}(845,\cdot)\) \(1\) \(1\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{19}{34}\right)\) \(e\left(\frac{7}{34}\right)\) \(1\) \(e\left(\frac{19}{34}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{16}{17}\right)\)
\(\chi_{10002}(917,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{13}{34}\right)\) \(e\left(\frac{3}{34}\right)\) \(1\) \(e\left(\frac{13}{34}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{2}{17}\right)\)
\(\chi_{10002}(1025,\cdot)\) \(1\) \(1\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{9}{34}\right)\) \(1\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{6}{17}\right)\)
\(\chi_{10002}(4049,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{33}{34}\right)\) \(1\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{5}{17}\right)\)
\(\chi_{10002}(5291,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{27}{34}\right)\) \(1\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{1}{17}\right)\)
\(\chi_{10002}(5327,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{11}{34}\right)\) \(1\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{13}{17}\right)\)
\(\chi_{10002}(6119,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{31}{34}\right)\) \(1\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{15}{17}\right)\)
\(\chi_{10002}(7811,\cdot)\) \(1\) \(1\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{19}{34}\right)\) \(1\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{19}{34}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{7}{17}\right)\)
\(\chi_{10002}(8747,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{5}{34}\right)\) \(1\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{9}{17}\right)\)
\(\chi_{10002}(8879,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{15}{34}\right)\) \(1\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{10}{17}\right)\)
\(\chi_{10002}(9125,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{13}{34}\right)\) \(1\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{13}{34}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{3}{17}\right)\)
\(\chi_{10002}(9281,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{23}{34}\right)\) \(1\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{4}{17}\right)\)
\(\chi_{10002}(9587,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{1}{34}\right)\) \(1\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{12}{17}\right)\)