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Properties

Label 101.g
Modulus $101$
Conductor $101$
Order $25$
Real no
Primitive yes
Minimal yes
Parity even

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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([12])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(5,101)) 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: \(25\)
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 25 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(11\)
\(\chi_{101}(5,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{3}{25}\right)\) \(1\) \(e\left(\frac{3}{25}\right)\)
\(\chi_{101}(16,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{13}{25}\right)\) \(1\) \(e\left(\frac{13}{25}\right)\)
\(\chi_{101}(19,\cdot)\) \(1\) \(1\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{12}{25}\right)\) \(1\) \(e\left(\frac{12}{25}\right)\)
\(\chi_{101}(24,\cdot)\) \(1\) \(1\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{9}{25}\right)\) \(1\) \(e\left(\frac{9}{25}\right)\)
\(\chi_{101}(25,\cdot)\) \(1\) \(1\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{6}{25}\right)\) \(1\) \(e\left(\frac{6}{25}\right)\)
\(\chi_{101}(31,\cdot)\) \(1\) \(1\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{23}{25}\right)\) \(1\) \(e\left(\frac{23}{25}\right)\)
\(\chi_{101}(37,\cdot)\) \(1\) \(1\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{7}{25}\right)\) \(1\) \(e\left(\frac{7}{25}\right)\)
\(\chi_{101}(52,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{21}{25}\right)\) \(1\) \(e\left(\frac{21}{25}\right)\)
\(\chi_{101}(54,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{1}{25}\right)\) \(1\) \(e\left(\frac{1}{25}\right)\)
\(\chi_{101}(56,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{14}{25}\right)\) \(1\) \(e\left(\frac{14}{25}\right)\)
\(\chi_{101}(58,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{24}{25}\right)\) \(1\) \(e\left(\frac{24}{25}\right)\)
\(\chi_{101}(68,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{4}{25}\right)\) \(1\) \(e\left(\frac{4}{25}\right)\)
\(\chi_{101}(71,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{18}{25}\right)\) \(1\) \(e\left(\frac{18}{25}\right)\)
\(\chi_{101}(78,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{17}{25}\right)\) \(1\) \(e\left(\frac{17}{25}\right)\)
\(\chi_{101}(79,\cdot)\) \(1\) \(1\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{8}{25}\right)\) \(1\) \(e\left(\frac{8}{25}\right)\)
\(\chi_{101}(80,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{16}{25}\right)\) \(1\) \(e\left(\frac{16}{25}\right)\)
\(\chi_{101}(81,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{22}{25}\right)\) \(1\) \(e\left(\frac{22}{25}\right)\)
\(\chi_{101}(88,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{2}{25}\right)\) \(1\) \(e\left(\frac{2}{25}\right)\)
\(\chi_{101}(92,\cdot)\) \(1\) \(1\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{11}{25}\right)\) \(1\) \(e\left(\frac{11}{25}\right)\)
\(\chi_{101}(97,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{19}{25}\right)\) \(1\) \(e\left(\frac{19}{25}\right)\)