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Properties

Label 834.l
Modulus $834$
Conductor $417$
Order $46$
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(834, base_ring=CyclotomicField(46)) M = H._module chi = DirichletCharacter(H, M([23,4])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(65,834)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(834\)
Conductor: \(417\)
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: no, induced from 417.l
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: 46.0.1846885917150184816801956108608187290274879518836200811774628627713584413482455417169884083661381807955707.1

Characters in Galois orbit

Character \(-1\) \(1\) \(5\) \(7\) \(11\) \(13\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\)
\(\chi_{834}(65,\cdot)\) \(-1\) \(1\) \(e\left(\frac{45}{46}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{5}{46}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{37}{46}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{39}{46}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{31}{46}\right)\) \(e\left(\frac{20}{23}\right)\)
\(\chi_{834}(77,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{46}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{41}{46}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{9}{46}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{7}{46}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{15}{46}\right)\) \(e\left(\frac{3}{23}\right)\)
\(\chi_{834}(125,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{46}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{27}{46}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{25}{46}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{45}{46}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{11}{46}\right)\) \(e\left(\frac{16}{23}\right)\)
\(\chi_{834}(131,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{46}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{7}{46}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{15}{46}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{27}{46}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{25}{46}\right)\) \(e\left(\frac{5}{23}\right)\)
\(\chi_{834}(173,\cdot)\) \(-1\) \(1\) \(e\left(\frac{37}{46}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{45}{46}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{11}{46}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{29}{46}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{3}{46}\right)\) \(e\left(\frac{19}{23}\right)\)
\(\chi_{834}(191,\cdot)\) \(-1\) \(1\) \(e\left(\frac{29}{46}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{39}{46}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{31}{46}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{19}{46}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{21}{46}\right)\) \(e\left(\frac{18}{23}\right)\)
\(\chi_{834}(203,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{46}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{37}{46}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{7}{46}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{31}{46}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{27}{46}\right)\) \(e\left(\frac{10}{23}\right)\)
\(\chi_{834}(239,\cdot)\) \(-1\) \(1\) \(e\left(\frac{43}{46}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{15}{46}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{19}{46}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{25}{46}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{1}{46}\right)\) \(e\left(\frac{14}{23}\right)\)
\(\chi_{834}(245,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{46}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{43}{46}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{33}{46}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{41}{46}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{9}{46}\right)\) \(e\left(\frac{11}{23}\right)\)
\(\chi_{834}(251,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{46}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{11}{46}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{17}{46}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{3}{46}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{13}{46}\right)\) \(e\left(\frac{21}{23}\right)\)
\(\chi_{834}(323,\cdot)\) \(-1\) \(1\) \(e\left(\frac{9}{46}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{1}{46}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{35}{46}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{17}{46}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{43}{46}\right)\) \(e\left(\frac{4}{23}\right)\)
\(\chi_{834}(335,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{46}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{31}{46}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{27}{46}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{21}{46}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{45}{46}\right)\) \(e\left(\frac{9}{23}\right)\)
\(\chi_{834}(341,\cdot)\) \(-1\) \(1\) \(e\left(\frac{35}{46}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{9}{46}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{39}{46}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{15}{46}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{19}{46}\right)\) \(e\left(\frac{13}{23}\right)\)
\(\chi_{834}(407,\cdot)\) \(-1\) \(1\) \(e\left(\frac{33}{46}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{19}{46}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{21}{46}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{1}{46}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{35}{46}\right)\) \(e\left(\frac{7}{23}\right)\)
\(\chi_{834}(461,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{46}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{21}{46}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{45}{46}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{35}{46}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{29}{46}\right)\) \(e\left(\frac{15}{23}\right)\)
\(\chi_{834}(497,\cdot)\) \(-1\) \(1\) \(e\left(\frac{27}{46}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{3}{46}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{13}{46}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{5}{46}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{37}{46}\right)\) \(e\left(\frac{12}{23}\right)\)
\(\chi_{834}(533,\cdot)\) \(-1\) \(1\) \(e\left(\frac{15}{46}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{17}{46}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{43}{46}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{13}{46}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{41}{46}\right)\) \(e\left(\frac{22}{23}\right)\)
\(\chi_{834}(611,\cdot)\) \(-1\) \(1\) \(e\left(\frac{21}{46}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{33}{46}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{5}{46}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{9}{46}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{39}{46}\right)\) \(e\left(\frac{17}{23}\right)\)
\(\chi_{834}(635,\cdot)\) \(-1\) \(1\) \(e\left(\frac{41}{46}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{25}{46}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{1}{46}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{11}{46}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{17}{46}\right)\) \(e\left(\frac{8}{23}\right)\)
\(\chi_{834}(647,\cdot)\) \(-1\) \(1\) \(e\left(\frac{25}{46}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{13}{46}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{41}{46}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{37}{46}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{7}{46}\right)\) \(e\left(\frac{6}{23}\right)\)
\(\chi_{834}(701,\cdot)\) \(-1\) \(1\) \(e\left(\frac{31}{46}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{29}{46}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{3}{46}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{33}{46}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{5}{46}\right)\) \(e\left(\frac{1}{23}\right)\)
\(\chi_{834}(731,\cdot)\) \(-1\) \(1\) \(e\left(\frac{39}{46}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{35}{46}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{29}{46}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{43}{46}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{33}{46}\right)\) \(e\left(\frac{2}{23}\right)\)