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Properties

Label 4830.ct
Modulus $4830$
Conductor $345$
Order $44$
Real no
Primitive no
Minimal yes
Parity even

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4830, base_ring=CyclotomicField(44)) M = H._module chi = DirichletCharacter(H, M([22,11,0,28])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(197,4830)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(4830\)
Conductor: \(345\)
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: no, induced from 345.x
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 \(-1\) \(1\) \(11\) \(13\) \(17\) \(19\) \(29\) \(31\) \(37\) \(41\) \(43\) \(47\)
\(\chi_{4830}(197,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{41}{44}\right)\) \(-i\)
\(\chi_{4830}(407,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{25}{44}\right)\) \(-i\)
\(\chi_{4830}(533,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{7}{44}\right)\) \(i\)
\(\chi_{4830}(1037,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{9}{44}\right)\) \(-i\)
\(\chi_{4830}(1163,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{19}{44}\right)\) \(i\)
\(\chi_{4830}(1373,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{3}{44}\right)\) \(i\)
\(\chi_{4830}(1457,\cdot)\) \(1\) \(1\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{5}{44}\right)\) \(-i\)
\(\chi_{4830}(2003,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{31}{44}\right)\) \(i\)
\(\chi_{4830}(2423,\cdot)\) \(1\) \(1\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{27}{44}\right)\) \(i\)
\(\chi_{4830}(2717,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{17}{44}\right)\) \(-i\)
\(\chi_{4830}(2927,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{37}{44}\right)\) \(-i\)
\(\chi_{4830}(3137,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{1}{44}\right)\) \(-i\)
\(\chi_{4830}(3347,\cdot)\) \(1\) \(1\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{13}{44}\right)\) \(-i\)
\(\chi_{4830}(3683,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{39}{44}\right)\) \(i\)
\(\chi_{4830}(3767,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{21}{44}\right)\) \(-i\)
\(\chi_{4830}(3893,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{15}{44}\right)\) \(i\)
\(\chi_{4830}(4103,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{23}{44}\right)\) \(i\)
\(\chi_{4830}(4313,\cdot)\) \(1\) \(1\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{35}{44}\right)\) \(i\)
\(\chi_{4830}(4397,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{29}{44}\right)\) \(-i\)
\(\chi_{4830}(4733,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{43}{44}\right)\) \(i\)