Properties

Label 647.c
Modulus $647$
Conductor $647$
Order $17$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Learn more

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(647, base_ring=CyclotomicField(34))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([6]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(43,647))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(647\)
Conductor: \(647\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(17\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{17})\)
Fixed field: 17.17.942906198449660107953222334097149309547713921.1

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(11\)
\(\chi_{647}(43,\cdot)\) \(1\) \(1\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{14}{17}\right)\)
\(\chi_{647}(53,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{5}{17}\right)\)
\(\chi_{647}(67,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{15}{17}\right)\)
\(\chi_{647}(218,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{6}{17}\right)\)
\(\chi_{647}(221,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{10}{17}\right)\)
\(\chi_{647}(293,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{12}{17}\right)\)
\(\chi_{647}(300,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{16}{17}\right)\)
\(\chi_{647}(306,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{9}{17}\right)\)
\(\chi_{647}(316,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{3}{17}\right)\)
\(\chi_{647}(338,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{2}{17}\right)\)
\(\chi_{647}(372,\cdot)\) \(1\) \(1\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{4}{17}\right)\)
\(\chi_{647}(445,\cdot)\) \(1\) \(1\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{7}{17}\right)\)
\(\chi_{647}(468,\cdot)\) \(1\) \(1\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{1}{17}\right)\)
\(\chi_{647}(555,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{11}{17}\right)\)
\(\chi_{647}(573,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{8}{17}\right)\)
\(\chi_{647}(607,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{13}{17}\right)\)