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Properties

Label 7500.y
Modulus $7500$
Conductor $125$
Order $25$
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(7500, base_ring=CyclotomicField(50)) M = H._module chi = DirichletCharacter(H, M([0,0,18])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(301,7500)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(7500\)
Conductor: \(125\)
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: no, induced from 125.g
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 25 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(7\) \(11\) \(13\) \(17\) \(19\) \(23\) \(29\) \(31\) \(37\) \(41\)
\(\chi_{7500}(301,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{21}{25}\right)\)
\(\chi_{7500}(601,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{17}{25}\right)\)
\(\chi_{7500}(901,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{13}{25}\right)\)
\(\chi_{7500}(1201,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{9}{25}\right)\)
\(\chi_{7500}(1801,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{1}{25}\right)\)
\(\chi_{7500}(2101,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{22}{25}\right)\)
\(\chi_{7500}(2401,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{18}{25}\right)\)
\(\chi_{7500}(2701,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{14}{25}\right)\)
\(\chi_{7500}(3301,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{6}{25}\right)\)
\(\chi_{7500}(3601,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{2}{25}\right)\)
\(\chi_{7500}(3901,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{23}{25}\right)\)
\(\chi_{7500}(4201,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{19}{25}\right)\)
\(\chi_{7500}(4801,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{11}{25}\right)\)
\(\chi_{7500}(5101,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{7}{25}\right)\)
\(\chi_{7500}(5401,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{3}{25}\right)\)
\(\chi_{7500}(5701,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{24}{25}\right)\)
\(\chi_{7500}(6301,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{16}{25}\right)\)
\(\chi_{7500}(6601,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{12}{25}\right)\)
\(\chi_{7500}(6901,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{8}{25}\right)\)
\(\chi_{7500}(7201,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{4}{25}\right)\)