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Properties

Label 2415.cr
Modulus $2415$
Conductor $2415$
Order $44$
Real no
Primitive yes
Minimal yes
Parity odd

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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([22,11,22,16])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(62,2415)) 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: odd
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 \(-1\) \(1\) \(2\) \(4\) \(8\) \(11\) \(13\) \(16\) \(17\) \(19\) \(22\) \(26\)
\(\chi_{2415}(62,\cdot)\) \(-1\) \(1\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(i\) \(e\left(\frac{9}{11}\right)\)
\(\chi_{2415}(167,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(i\) \(e\left(\frac{1}{11}\right)\)
\(\chi_{2415}(188,\cdot)\) \(-1\) \(1\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(-i\) \(e\left(\frac{10}{11}\right)\)
\(\chi_{2415}(377,\cdot)\) \(-1\) \(1\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(i\) \(e\left(\frac{3}{11}\right)\)
\(\chi_{2415}(587,\cdot)\) \(-1\) \(1\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(i\) \(e\left(\frac{6}{11}\right)\)
\(\chi_{2415}(692,\cdot)\) \(-1\) \(1\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(i\) \(e\left(\frac{5}{11}\right)\)
\(\chi_{2415}(818,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{6}{11}\right)\) \(-i\) \(e\left(\frac{2}{11}\right)\)
\(\chi_{2415}(923,\cdot)\) \(-1\) \(1\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(-i\) \(e\left(\frac{7}{11}\right)\)
\(\chi_{2415}(1007,\cdot)\) \(-1\) \(1\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{2}{11}\right)\) \(i\) \(e\left(\frac{8}{11}\right)\)
\(\chi_{2415}(1028,\cdot)\) \(-1\) \(1\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(-i\) \(e\left(\frac{9}{11}\right)\)
\(\chi_{2415}(1112,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{1}{11}\right)\) \(i\) \(e\left(\frac{4}{11}\right)\)
\(\chi_{2415}(1133,\cdot)\) \(-1\) \(1\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(-i\) \(e\left(\frac{1}{11}\right)\)
\(\chi_{2415}(1343,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(-i\) \(e\left(\frac{3}{11}\right)\)
\(\chi_{2415}(1553,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(-i\) \(e\left(\frac{6}{11}\right)\)
\(\chi_{2415}(1637,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(i\) \(e\left(\frac{10}{11}\right)\)
\(\chi_{2415}(1658,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(-i\) \(e\left(\frac{5}{11}\right)\)
\(\chi_{2415}(1973,\cdot)\) \(-1\) \(1\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{2}{11}\right)\) \(-i\) \(e\left(\frac{8}{11}\right)\)
\(\chi_{2415}(2078,\cdot)\) \(-1\) \(1\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{1}{11}\right)\) \(-i\) \(e\left(\frac{4}{11}\right)\)
\(\chi_{2415}(2267,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{6}{11}\right)\) \(i\) \(e\left(\frac{2}{11}\right)\)
\(\chi_{2415}(2372,\cdot)\) \(-1\) \(1\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(i\) \(e\left(\frac{7}{11}\right)\)