↑

Properties

Label 695.n
Modulus $695$
Conductor $695$
Order $46$
Real no
Primitive yes
Minimal yes
Parity odd

Related objects

Downloads

Learn more

Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(695, base_ring=CyclotomicField(46)) M = H._module chi = DirichletCharacter(H, M([23,17])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(14,695)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(695\)
Conductor: \(695\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(46\)
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: odd
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{23})\)
Fixed field: 46.0.32506941609913674715356871213478525555718840947168228744163199689015235118467271106844101910141694545745849609375.1

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(6\) \(7\) \(8\) \(9\) \(11\) \(12\) \(13\)
\(\chi_{695}(14,\cdot)\) \(-1\) \(1\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{45}{46}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{7}{46}\right)\)
\(\chi_{695}(39,\cdot)\) \(-1\) \(1\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{25}{46}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{9}{46}\right)\)
\(\chi_{695}(59,\cdot)\) \(-1\) \(1\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{5}{46}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{11}{46}\right)\)
\(\chi_{695}(74,\cdot)\) \(-1\) \(1\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{39}{46}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{3}{46}\right)\)
\(\chi_{695}(84,\cdot)\) \(-1\) \(1\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{9}{46}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{29}{46}\right)\)
\(\chi_{695}(94,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{17}{46}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{19}{46}\right)\)
\(\chi_{695}(149,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{1}{46}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{39}{46}\right)\)
\(\chi_{695}(199,\cdot)\) \(-1\) \(1\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{11}{46}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{15}{46}\right)\)
\(\chi_{695}(214,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{31}{46}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{13}{46}\right)\)
\(\chi_{695}(234,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{35}{46}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{31}{46}\right)\)
\(\chi_{695}(244,\cdot)\) \(-1\) \(1\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{29}{46}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{27}{46}\right)\)
\(\chi_{695}(354,\cdot)\) \(-1\) \(1\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{15}{46}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{33}{46}\right)\)
\(\chi_{695}(444,\cdot)\) \(-1\) \(1\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{3}{46}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{25}{46}\right)\)
\(\chi_{695}(479,\cdot)\) \(-1\) \(1\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{7}{46}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{43}{46}\right)\)
\(\chi_{695}(499,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{21}{46}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{37}{46}\right)\)
\(\chi_{695}(504,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{19}{46}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{5}{46}\right)\)
\(\chi_{695}(564,\cdot)\) \(-1\) \(1\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{27}{46}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{41}{46}\right)\)
\(\chi_{695}(579,\cdot)\) \(-1\) \(1\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{13}{46}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{1}{46}\right)\)
\(\chi_{695}(589,\cdot)\) \(-1\) \(1\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{41}{46}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{35}{46}\right)\)
\(\chi_{695}(604,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{37}{46}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{17}{46}\right)\)
\(\chi_{695}(659,\cdot)\) \(-1\) \(1\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{43}{46}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{21}{46}\right)\)
\(\chi_{695}(689,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{33}{46}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{45}{46}\right)\)