Properties

Label 151.h
Modulus $151$
Conductor $151$
Order $25$
Real no
Primitive yes
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(151, base_ring=CyclotomicField(50))
 
M = H._module
 
chi = DirichletCharacter(H, M([4]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(9,151))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(151\)
Conductor: \(151\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(25\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{25})\)
Fixed field: Number field defined by a degree 25 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(11\)
\(\chi_{151}(9,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{13}{25}\right)\)
\(\chi_{151}(20,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{23}{25}\right)\)
\(\chi_{151}(29,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{11}{25}\right)\)
\(\chi_{151}(44,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{16}{25}\right)\)
\(\chi_{151}(50,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{6}{25}\right)\)
\(\chi_{151}(68,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{2}{25}\right)\)
\(\chi_{151}(72,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{3}{25}\right)\)
\(\chi_{151}(78,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{8}{25}\right)\)
\(\chi_{151}(81,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{1}{25}\right)\)
\(\chi_{151}(84,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{12}{25}\right)\)
\(\chi_{151}(86,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{22}{25}\right)\)
\(\chi_{151}(91,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{17}{25}\right)\)
\(\chi_{151}(94,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{4}{25}\right)\)
\(\chi_{151}(98,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{21}{25}\right)\)
\(\chi_{151}(110,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{24}{25}\right)\)
\(\chi_{151}(123,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{18}{25}\right)\)
\(\chi_{151}(124,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{7}{25}\right)\)
\(\chi_{151}(125,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{14}{25}\right)\)
\(\chi_{151}(127,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{9}{25}\right)\)
\(\chi_{151}(148,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{19}{25}\right)\)