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Properties

Label 1875.o
Modulus $1875$
Conductor $125$
Order $50$
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(1875, base_ring=CyclotomicField(50)) M = H._module chi = DirichletCharacter(H, M([0,47])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(49,1875)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1875\)
Conductor: \(125\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(50\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 125.h
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: \(\Q(\zeta_{25})\)
Fixed field: Number field defined by a degree 50 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(4\) \(7\) \(8\) \(11\) \(13\) \(14\) \(16\) \(17\) \(19\)
\(\chi_{1875}(49,\cdot)\) \(1\) \(1\) \(e\left(\frac{47}{50}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{41}{50}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{33}{50}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{31}{50}\right)\) \(e\left(\frac{23}{25}\right)\)
\(\chi_{1875}(199,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{50}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{39}{50}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{7}{50}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{49}{50}\right)\) \(e\left(\frac{17}{25}\right)\)
\(\chi_{1875}(274,\cdot)\) \(1\) \(1\) \(e\left(\frac{21}{50}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{13}{50}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{19}{50}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{33}{50}\right)\) \(e\left(\frac{14}{25}\right)\)
\(\chi_{1875}(349,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{50}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{37}{50}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{31}{50}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{17}{50}\right)\) \(e\left(\frac{11}{25}\right)\)
\(\chi_{1875}(424,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{50}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{11}{50}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{43}{50}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{1}{50}\right)\) \(e\left(\frac{8}{25}\right)\)
\(\chi_{1875}(574,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{50}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{50}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{17}{50}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{19}{50}\right)\) \(e\left(\frac{2}{25}\right)\)
\(\chi_{1875}(649,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{50}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{33}{50}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{29}{50}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{3}{50}\right)\) \(e\left(\frac{24}{25}\right)\)
\(\chi_{1875}(724,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{50}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{50}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{41}{50}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{37}{50}\right)\) \(e\left(\frac{21}{25}\right)\)
\(\chi_{1875}(799,\cdot)\) \(1\) \(1\) \(e\left(\frac{27}{50}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{31}{50}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{3}{50}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{21}{50}\right)\) \(e\left(\frac{18}{25}\right)\)
\(\chi_{1875}(949,\cdot)\) \(1\) \(1\) \(e\left(\frac{43}{50}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{29}{50}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{27}{50}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{39}{50}\right)\) \(e\left(\frac{12}{25}\right)\)
\(\chi_{1875}(1024,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{50}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{50}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{39}{50}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{23}{50}\right)\) \(e\left(\frac{9}{25}\right)\)
\(\chi_{1875}(1099,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{50}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{27}{50}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{1}{50}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{7}{50}\right)\) \(e\left(\frac{6}{25}\right)\)
\(\chi_{1875}(1174,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{50}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{50}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{13}{50}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{41}{50}\right)\) \(e\left(\frac{3}{25}\right)\)
\(\chi_{1875}(1324,\cdot)\) \(1\) \(1\) \(e\left(\frac{33}{50}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{49}{50}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{37}{50}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{9}{50}\right)\) \(e\left(\frac{22}{25}\right)\)
\(\chi_{1875}(1399,\cdot)\) \(1\) \(1\) \(e\left(\frac{41}{50}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{23}{50}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{49}{50}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{43}{50}\right)\) \(e\left(\frac{19}{25}\right)\)
\(\chi_{1875}(1474,\cdot)\) \(1\) \(1\) \(e\left(\frac{49}{50}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{47}{50}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{11}{50}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{27}{50}\right)\) \(e\left(\frac{16}{25}\right)\)
\(\chi_{1875}(1549,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{50}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{21}{50}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{23}{50}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{11}{50}\right)\) \(e\left(\frac{13}{25}\right)\)
\(\chi_{1875}(1699,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{50}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{19}{50}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{47}{50}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{29}{50}\right)\) \(e\left(\frac{7}{25}\right)\)
\(\chi_{1875}(1774,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{50}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{43}{50}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{9}{50}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{13}{50}\right)\) \(e\left(\frac{4}{25}\right)\)
\(\chi_{1875}(1849,\cdot)\) \(1\) \(1\) \(e\left(\frac{39}{50}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{17}{50}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{21}{50}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{47}{50}\right)\) \(e\left(\frac{1}{25}\right)\)