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Properties

Label 11025.fo
Modulus $11025$
Conductor $2205$
Order $42$
Real no
Primitive no
Minimal no
Parity even

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(11025, base_ring=CyclotomicField(42)) M = H._module chi = DirichletCharacter(H, M([7,21,29])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(299,11025)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(11025\)
Conductor: \(2205\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(42\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 2205.dv
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{21})\)
Fixed field: 42.42.64499777946714835177141019992254259402911208109553981749879955329445342864388015575823925406164646148681640625.2

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(4\) \(8\) \(11\) \(13\) \(16\) \(17\) \(19\) \(22\) \(23\)
\(\chi_{11025}(299,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{4}{7}\right)\)
\(\chi_{11025}(1874,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{2}{7}\right)\)
\(\chi_{11025}(1949,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{6}{7}\right)\)
\(\chi_{11025}(3524,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{5}{7}\right)\)
\(\chi_{11025}(5024,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{5}{7}\right)\)
\(\chi_{11025}(5099,\cdot)\) \(1\) \(1\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{4}{7}\right)\)
\(\chi_{11025}(6599,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{3}{7}\right)\)
\(\chi_{11025}(6674,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{3}{7}\right)\)
\(\chi_{11025}(8174,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{1}{7}\right)\)
\(\chi_{11025}(8249,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{2}{7}\right)\)
\(\chi_{11025}(9749,\cdot)\) \(1\) \(1\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{6}{7}\right)\)
\(\chi_{11025}(9824,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{1}{7}\right)\)