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Properties

Label 2415.cp
Modulus $2415$
Conductor $2415$
Order $44$
Real no
Primitive yes
Minimal yes
Parity even

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2415, base_ring=CyclotomicField(44)) M = H._module chi = DirichletCharacter(H, M([22,33,22,42])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(83,2415)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(2415\)
Conductor: \(2415\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(44\)
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: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{44})\)
Fixed field: Number field defined by a degree 44 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(4\) \(8\) \(11\) \(13\) \(16\) \(17\) \(19\) \(22\) \(26\)
\(\chi_{2415}(83,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(i\) \(e\left(\frac{3}{11}\right)\)
\(\chi_{2415}(272,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{5}{22}\right)\) \(-i\) \(e\left(\frac{10}{11}\right)\)
\(\chi_{2415}(293,\cdot)\) \(1\) \(1\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(i\) \(e\left(\frac{1}{11}\right)\)
\(\chi_{2415}(398,\cdot)\) \(1\) \(1\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{21}{22}\right)\) \(i\) \(e\left(\frac{9}{11}\right)\)
\(\chi_{2415}(503,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{9}{22}\right)\) \(i\) \(e\left(\frac{7}{11}\right)\)
\(\chi_{2415}(608,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(i\) \(e\left(\frac{2}{11}\right)\)
\(\chi_{2415}(797,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(-i\) \(e\left(\frac{4}{11}\right)\)
\(\chi_{2415}(902,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(-i\) \(e\left(\frac{8}{11}\right)\)
\(\chi_{2415}(1217,\cdot)\) \(1\) \(1\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(-i\) \(e\left(\frac{5}{11}\right)\)
\(\chi_{2415}(1238,\cdot)\) \(1\) \(1\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{5}{22}\right)\) \(i\) \(e\left(\frac{10}{11}\right)\)
\(\chi_{2415}(1322,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(-i\) \(e\left(\frac{6}{11}\right)\)
\(\chi_{2415}(1532,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(-i\) \(e\left(\frac{3}{11}\right)\)
\(\chi_{2415}(1742,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(-i\) \(e\left(\frac{1}{11}\right)\)
\(\chi_{2415}(1763,\cdot)\) \(1\) \(1\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(i\) \(e\left(\frac{4}{11}\right)\)
\(\chi_{2415}(1847,\cdot)\) \(1\) \(1\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{21}{22}\right)\) \(-i\) \(e\left(\frac{9}{11}\right)\)
\(\chi_{2415}(1868,\cdot)\) \(1\) \(1\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(i\) \(e\left(\frac{8}{11}\right)\)
\(\chi_{2415}(1952,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{9}{22}\right)\) \(-i\) \(e\left(\frac{7}{11}\right)\)
\(\chi_{2415}(2057,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(-i\) \(e\left(\frac{2}{11}\right)\)
\(\chi_{2415}(2183,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(i\) \(e\left(\frac{5}{11}\right)\)
\(\chi_{2415}(2288,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(i\) \(e\left(\frac{6}{11}\right)\)