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Properties

Label 875.y
Modulus $875$
Conductor $125$
Order $50$
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(875, base_ring=CyclotomicField(50)) M = H._module chi = DirichletCharacter(H, M([31,0])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(29,875)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(875\)
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: yes
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 \(-1\) \(1\) \(2\) \(3\) \(4\) \(6\) \(8\) \(9\) \(11\) \(12\) \(13\) \(16\)
\(\chi_{875}(29,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{50}\right)\) \(e\left(\frac{17}{50}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{43}{50}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{29}{50}\right)\) \(e\left(\frac{9}{50}\right)\) \(e\left(\frac{12}{25}\right)\)
\(\chi_{875}(64,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{50}\right)\) \(e\left(\frac{21}{50}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{9}{50}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{27}{50}\right)\) \(e\left(\frac{17}{50}\right)\) \(e\left(\frac{6}{25}\right)\)
\(\chi_{875}(134,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{50}\right)\) \(e\left(\frac{49}{50}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{21}{50}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{13}{50}\right)\) \(e\left(\frac{23}{50}\right)\) \(e\left(\frac{14}{25}\right)\)
\(\chi_{875}(169,\cdot)\) \(1\) \(1\) \(e\left(\frac{39}{50}\right)\) \(e\left(\frac{23}{50}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{17}{50}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{1}{50}\right)\) \(e\left(\frac{21}{50}\right)\) \(e\left(\frac{3}{25}\right)\)
\(\chi_{875}(204,\cdot)\) \(1\) \(1\) \(e\left(\frac{41}{50}\right)\) \(e\left(\frac{37}{50}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{23}{50}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{19}{50}\right)\) \(e\left(\frac{49}{50}\right)\) \(e\left(\frac{7}{25}\right)\)
\(\chi_{875}(239,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{50}\right)\) \(e\left(\frac{41}{50}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{39}{50}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{17}{50}\right)\) \(e\left(\frac{7}{50}\right)\) \(e\left(\frac{1}{25}\right)\)
\(\chi_{875}(309,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{50}\right)\) \(e\left(\frac{19}{50}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{1}{50}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{3}{50}\right)\) \(e\left(\frac{13}{50}\right)\) \(e\left(\frac{9}{25}\right)\)
\(\chi_{875}(344,\cdot)\) \(1\) \(1\) \(e\left(\frac{49}{50}\right)\) \(e\left(\frac{43}{50}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{47}{50}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{41}{50}\right)\) \(e\left(\frac{11}{50}\right)\) \(e\left(\frac{23}{25}\right)\)
\(\chi_{875}(379,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{50}\right)\) \(e\left(\frac{7}{50}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{3}{50}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{9}{50}\right)\) \(e\left(\frac{39}{50}\right)\) \(e\left(\frac{2}{25}\right)\)
\(\chi_{875}(414,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{50}\right)\) \(e\left(\frac{11}{50}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{19}{50}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{7}{50}\right)\) \(e\left(\frac{47}{50}\right)\) \(e\left(\frac{21}{25}\right)\)
\(\chi_{875}(484,\cdot)\) \(1\) \(1\) \(e\left(\frac{27}{50}\right)\) \(e\left(\frac{39}{50}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{31}{50}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{43}{50}\right)\) \(e\left(\frac{3}{50}\right)\) \(e\left(\frac{4}{25}\right)\)
\(\chi_{875}(519,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{50}\right)\) \(e\left(\frac{13}{50}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{27}{50}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{31}{50}\right)\) \(e\left(\frac{1}{50}\right)\) \(e\left(\frac{18}{25}\right)\)
\(\chi_{875}(554,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{50}\right)\) \(e\left(\frac{27}{50}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{33}{50}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{49}{50}\right)\) \(e\left(\frac{29}{50}\right)\) \(e\left(\frac{22}{25}\right)\)
\(\chi_{875}(589,\cdot)\) \(1\) \(1\) \(e\left(\frac{33}{50}\right)\) \(e\left(\frac{31}{50}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{49}{50}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{47}{50}\right)\) \(e\left(\frac{37}{50}\right)\) \(e\left(\frac{16}{25}\right)\)
\(\chi_{875}(659,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{50}\right)\) \(e\left(\frac{9}{50}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{11}{50}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{33}{50}\right)\) \(e\left(\frac{43}{50}\right)\) \(e\left(\frac{24}{25}\right)\)
\(\chi_{875}(694,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{50}\right)\) \(e\left(\frac{33}{50}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{7}{50}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{21}{50}\right)\) \(e\left(\frac{41}{50}\right)\) \(e\left(\frac{13}{25}\right)\)
\(\chi_{875}(729,\cdot)\) \(1\) \(1\) \(e\left(\frac{21}{50}\right)\) \(e\left(\frac{47}{50}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{13}{50}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{39}{50}\right)\) \(e\left(\frac{19}{50}\right)\) \(e\left(\frac{17}{25}\right)\)
\(\chi_{875}(764,\cdot)\) \(1\) \(1\) \(e\left(\frac{43}{50}\right)\) \(e\left(\frac{1}{50}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{29}{50}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{37}{50}\right)\) \(e\left(\frac{27}{50}\right)\) \(e\left(\frac{11}{25}\right)\)
\(\chi_{875}(834,\cdot)\) \(1\) \(1\) \(e\left(\frac{47}{50}\right)\) \(e\left(\frac{29}{50}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{41}{50}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{23}{50}\right)\) \(e\left(\frac{33}{50}\right)\) \(e\left(\frac{19}{25}\right)\)
\(\chi_{875}(869,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{50}\right)\) \(e\left(\frac{3}{50}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{37}{50}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{11}{50}\right)\) \(e\left(\frac{31}{50}\right)\) \(e\left(\frac{8}{25}\right)\)