↑

Properties

Label 101.h
Modulus $101$
Conductor $101$
Order $50$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Downloads

Learn more

Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(101, base_ring=CyclotomicField(50)) M = H._module chi = DirichletCharacter(H, M([1])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(4,101)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(101\)
Conductor: \(101\)
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: yes
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 \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(11\)
\(\chi_{101}(4,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{50}\right)\) \(e\left(\frac{19}{50}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{50}\right)\) \(e\left(\frac{3}{50}\right)\) \(e\left(\frac{19}{25}\right)\) \(-1\) \(e\left(\frac{13}{50}\right)\)
\(\chi_{101}(9,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{50}\right)\) \(e\left(\frac{11}{50}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{21}{50}\right)\) \(e\left(\frac{7}{50}\right)\) \(e\left(\frac{11}{25}\right)\) \(-1\) \(e\left(\frac{47}{50}\right)\)
\(\chi_{101}(13,\cdot)\) \(1\) \(1\) \(e\left(\frac{33}{50}\right)\) \(e\left(\frac{27}{50}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{47}{50}\right)\) \(e\left(\frac{49}{50}\right)\) \(e\left(\frac{2}{25}\right)\) \(-1\) \(e\left(\frac{29}{50}\right)\)
\(\chi_{101}(20,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{50}\right)\) \(e\left(\frac{47}{50}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{17}{50}\right)\) \(e\left(\frac{39}{50}\right)\) \(e\left(\frac{22}{25}\right)\) \(-1\) \(e\left(\frac{19}{50}\right)\)
\(\chi_{101}(21,\cdot)\) \(1\) \(1\) \(e\left(\frac{39}{50}\right)\) \(e\left(\frac{41}{50}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{50}\right)\) \(e\left(\frac{17}{50}\right)\) \(e\left(\frac{16}{25}\right)\) \(-1\) \(e\left(\frac{7}{50}\right)\)
\(\chi_{101}(22,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{50}\right)\) \(e\left(\frac{33}{50}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{13}{50}\right)\) \(e\left(\frac{21}{50}\right)\) \(e\left(\frac{8}{25}\right)\) \(-1\) \(e\left(\frac{41}{50}\right)\)
\(\chi_{101}(23,\cdot)\) \(1\) \(1\) \(e\left(\frac{43}{50}\right)\) \(e\left(\frac{17}{50}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{37}{50}\right)\) \(e\left(\frac{29}{50}\right)\) \(e\left(\frac{17}{25}\right)\) \(-1\) \(e\left(\frac{9}{50}\right)\)
\(\chi_{101}(30,\cdot)\) \(1\) \(1\) \(e\left(\frac{47}{50}\right)\) \(e\left(\frac{43}{50}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{23}{50}\right)\) \(e\left(\frac{41}{50}\right)\) \(e\left(\frac{18}{25}\right)\) \(-1\) \(e\left(\frac{11}{50}\right)\)
\(\chi_{101}(33,\cdot)\) \(1\) \(1\) \(e\left(\frac{41}{50}\right)\) \(e\left(\frac{29}{50}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{19}{50}\right)\) \(e\left(\frac{23}{50}\right)\) \(e\left(\frac{4}{25}\right)\) \(-1\) \(e\left(\frac{33}{50}\right)\)
\(\chi_{101}(43,\cdot)\) \(1\) \(1\) \(e\left(\frac{21}{50}\right)\) \(e\left(\frac{49}{50}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{39}{50}\right)\) \(e\left(\frac{13}{50}\right)\) \(e\left(\frac{24}{25}\right)\) \(-1\) \(e\left(\frac{23}{50}\right)\)
\(\chi_{101}(45,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{50}\right)\) \(e\left(\frac{39}{50}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{29}{50}\right)\) \(e\left(\frac{43}{50}\right)\) \(e\left(\frac{14}{25}\right)\) \(-1\) \(e\left(\frac{3}{50}\right)\)
\(\chi_{101}(47,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{50}\right)\) \(e\left(\frac{1}{50}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{11}{50}\right)\) \(e\left(\frac{37}{50}\right)\) \(e\left(\frac{1}{25}\right)\) \(-1\) \(e\left(\frac{27}{50}\right)\)
\(\chi_{101}(49,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{50}\right)\) \(e\left(\frac{21}{50}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{31}{50}\right)\) \(e\left(\frac{27}{50}\right)\) \(e\left(\frac{21}{25}\right)\) \(-1\) \(e\left(\frac{17}{50}\right)\)
\(\chi_{101}(64,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{50}\right)\) \(e\left(\frac{7}{50}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{27}{50}\right)\) \(e\left(\frac{9}{50}\right)\) \(e\left(\frac{7}{25}\right)\) \(-1\) \(e\left(\frac{39}{50}\right)\)
\(\chi_{101}(70,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{50}\right)\) \(e\left(\frac{23}{50}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{50}\right)\) \(e\left(\frac{1}{50}\right)\) \(e\left(\frac{23}{25}\right)\) \(-1\) \(e\left(\frac{21}{50}\right)\)
\(\chi_{101}(76,\cdot)\) \(1\) \(1\) \(e\left(\frac{49}{50}\right)\) \(e\left(\frac{31}{50}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{41}{50}\right)\) \(e\left(\frac{47}{50}\right)\) \(e\left(\frac{6}{25}\right)\) \(-1\) \(e\left(\frac{37}{50}\right)\)
\(\chi_{101}(77,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{50}\right)\) \(e\left(\frac{9}{50}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{49}{50}\right)\) \(e\left(\frac{33}{50}\right)\) \(e\left(\frac{9}{25}\right)\) \(-1\) \(e\left(\frac{43}{50}\right)\)
\(\chi_{101}(82,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{50}\right)\) \(e\left(\frac{37}{50}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{50}\right)\) \(e\left(\frac{19}{50}\right)\) \(e\left(\frac{12}{25}\right)\) \(-1\) \(e\left(\frac{49}{50}\right)\)
\(\chi_{101}(85,\cdot)\) \(1\) \(1\) \(e\left(\frac{27}{50}\right)\) \(e\left(\frac{13}{50}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{43}{50}\right)\) \(e\left(\frac{31}{50}\right)\) \(e\left(\frac{13}{25}\right)\) \(-1\) \(e\left(\frac{1}{50}\right)\)
\(\chi_{101}(96,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{50}\right)\) \(e\left(\frac{3}{50}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{33}{50}\right)\) \(e\left(\frac{11}{50}\right)\) \(e\left(\frac{3}{25}\right)\) \(-1\) \(e\left(\frac{31}{50}\right)\)