Properties

Label 4017.co
Modulus $4017$
Conductor $309$
Order $34$
Real no
Primitive no
Minimal yes
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4017, base_ring=CyclotomicField(34))
 
M = H._module
 
chi = DirichletCharacter(H, M([17,0,16]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(14,4017))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(4017\)
Conductor: \(309\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(34\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 309.l
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{17})\)
Fixed field: 34.0.3325466068076643664357827857598159738994734276327509143073421552355865283.1

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(4\) \(5\) \(7\) \(8\) \(10\) \(11\) \(14\) \(16\) \(17\)
\(\chi_{4017}(14,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{15}{34}\right)\)
\(\chi_{4017}(287,\cdot)\) \(-1\) \(1\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{13}{34}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{19}{34}\right)\)
\(\chi_{4017}(755,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{25}{34}\right)\)
\(\chi_{4017}(833,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{1}{34}\right)\)
\(\chi_{4017}(950,\cdot)\) \(-1\) \(1\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{19}{34}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{33}{34}\right)\)
\(\chi_{4017}(1106,\cdot)\) \(-1\) \(1\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{19}{34}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{27}{34}\right)\)
\(\chi_{4017}(1418,\cdot)\) \(-1\) \(1\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{29}{34}\right)\)
\(\chi_{4017}(1535,\cdot)\) \(-1\) \(1\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{13}{34}\right)\)
\(\chi_{4017}(2588,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{34}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{19}{34}\right)\) \(e\left(\frac{13}{34}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{31}{34}\right)\)
\(\chi_{4017}(2744,\cdot)\) \(-1\) \(1\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{11}{34}\right)\)
\(\chi_{4017}(3017,\cdot)\) \(-1\) \(1\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{5}{34}\right)\)
\(\chi_{4017}(3368,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{19}{34}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{21}{34}\right)\)
\(\chi_{4017}(3407,\cdot)\) \(-1\) \(1\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{3}{34}\right)\)
\(\chi_{4017}(3563,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{7}{34}\right)\)
\(\chi_{4017}(3602,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{13}{34}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{9}{34}\right)\)
\(\chi_{4017}(3875,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{34}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{13}{34}\right)\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{23}{34}\right)\)