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Properties

Label 373527.sc
Modulus $373527$
Conductor $124509$
Order $16170$
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(373527, base_ring=CyclotomicField(16170)) M = H._module chi = DirichletCharacter(H, M([8085,10175,14994])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(26,373527)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(373527\)
Conductor: \(124509\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(16170\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 124509.hh
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: $\Q(\zeta_{8085})$
Fixed field: Number field defined by a degree 16170 polynomial (not computed)

First 11 of 3360 characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(4\) \(5\) \(8\) \(10\) \(13\) \(16\) \(17\) \(19\) \(20\)
\(\chi_{373527}(26,\cdot)\) \(1\) \(1\) \(e\left(\frac{8119}{16170}\right)\) \(e\left(\frac{34}{8085}\right)\) \(e\left(\frac{2963}{8085}\right)\) \(e\left(\frac{2729}{5390}\right)\) \(e\left(\frac{2809}{3234}\right)\) \(e\left(\frac{5343}{5390}\right)\) \(e\left(\frac{68}{8085}\right)\) \(e\left(\frac{5398}{8085}\right)\) \(e\left(\frac{43}{330}\right)\) \(e\left(\frac{999}{2695}\right)\)
\(\chi_{373527}(152,\cdot)\) \(1\) \(1\) \(e\left(\frac{15997}{16170}\right)\) \(e\left(\frac{7912}{8085}\right)\) \(e\left(\frac{7514}{8085}\right)\) \(e\left(\frac{5217}{5390}\right)\) \(e\left(\frac{2971}{3234}\right)\) \(e\left(\frac{3489}{5390}\right)\) \(e\left(\frac{7739}{8085}\right)\) \(e\left(\frac{1069}{8085}\right)\) \(e\left(\frac{19}{330}\right)\) \(e\left(\frac{2447}{2695}\right)\)
\(\chi_{373527}(278,\cdot)\) \(1\) \(1\) \(e\left(\frac{5101}{16170}\right)\) \(e\left(\frac{5101}{8085}\right)\) \(e\left(\frac{5807}{8085}\right)\) \(e\left(\frac{5101}{5390}\right)\) \(e\left(\frac{109}{3234}\right)\) \(e\left(\frac{1747}{5390}\right)\) \(e\left(\frac{2117}{8085}\right)\) \(e\left(\frac{8017}{8085}\right)\) \(e\left(\frac{157}{330}\right)\) \(e\left(\frac{941}{2695}\right)\)
\(\chi_{373527}(467,\cdot)\) \(1\) \(1\) \(e\left(\frac{3793}{16170}\right)\) \(e\left(\frac{3793}{8085}\right)\) \(e\left(\frac{6911}{8085}\right)\) \(e\left(\frac{3793}{5390}\right)\) \(e\left(\frac{289}{3234}\right)\) \(e\left(\frac{2921}{5390}\right)\) \(e\left(\frac{7586}{8085}\right)\) \(e\left(\frac{1051}{8085}\right)\) \(e\left(\frac{211}{330}\right)\) \(e\left(\frac{873}{2695}\right)\)
\(\chi_{373527}(647,\cdot)\) \(1\) \(1\) \(e\left(\frac{1517}{16170}\right)\) \(e\left(\frac{1517}{8085}\right)\) \(e\left(\frac{6409}{8085}\right)\) \(e\left(\frac{1517}{5390}\right)\) \(e\left(\frac{2867}{3234}\right)\) \(e\left(\frac{4799}{5390}\right)\) \(e\left(\frac{3034}{8085}\right)\) \(e\left(\frac{674}{8085}\right)\) \(e\left(\frac{89}{330}\right)\) \(e\left(\frac{2642}{2695}\right)\)
\(\chi_{373527}(719,\cdot)\) \(1\) \(1\) \(e\left(\frac{15769}{16170}\right)\) \(e\left(\frac{7684}{8085}\right)\) \(e\left(\frac{6668}{8085}\right)\) \(e\left(\frac{4989}{5390}\right)\) \(e\left(\frac{2587}{3234}\right)\) \(e\left(\frac{2853}{5390}\right)\) \(e\left(\frac{7283}{8085}\right)\) \(e\left(\frac{7198}{8085}\right)\) \(e\left(\frac{313}{330}\right)\) \(e\left(\frac{2089}{2695}\right)\)
\(\chi_{373527}(773,\cdot)\) \(1\) \(1\) \(e\left(\frac{8081}{16170}\right)\) \(e\left(\frac{8081}{8085}\right)\) \(e\left(\frac{127}{8085}\right)\) \(e\left(\frac{2691}{5390}\right)\) \(e\left(\frac{1667}{3234}\right)\) \(e\left(\frac{5237}{5390}\right)\) \(e\left(\frac{8077}{8085}\right)\) \(e\left(\frac{5072}{8085}\right)\) \(e\left(\frac{257}{330}\right)\) \(e\left(\frac{41}{2695}\right)\)
\(\chi_{373527}(845,\cdot)\) \(1\) \(1\) \(e\left(\frac{4327}{16170}\right)\) \(e\left(\frac{4327}{8085}\right)\) \(e\left(\frac{2084}{8085}\right)\) \(e\left(\frac{4327}{5390}\right)\) \(e\left(\frac{1699}{3234}\right)\) \(e\left(\frac{439}{5390}\right)\) \(e\left(\frac{569}{8085}\right)\) \(e\left(\frac{3079}{8085}\right)\) \(e\left(\frac{139}{330}\right)\) \(e\left(\frac{2137}{2695}\right)\)
\(\chi_{373527}(1160,\cdot)\) \(1\) \(1\) \(e\left(\frac{15853}{16170}\right)\) \(e\left(\frac{7768}{8085}\right)\) \(e\left(\frac{4001}{8085}\right)\) \(e\left(\frac{5073}{5390}\right)\) \(e\left(\frac{1537}{3234}\right)\) \(e\left(\frac{3371}{5390}\right)\) \(e\left(\frac{7451}{8085}\right)\) \(e\left(\frac{5791}{8085}\right)\) \(e\left(\frac{31}{330}\right)\) \(e\left(\frac{1228}{2695}\right)\)
\(\chi_{373527}(1214,\cdot)\) \(1\) \(1\) \(e\left(\frac{7829}{16170}\right)\) \(e\left(\frac{7829}{8085}\right)\) \(e\left(\frac{43}{8085}\right)\) \(e\left(\frac{2439}{5390}\right)\) \(e\left(\frac{1583}{3234}\right)\) \(e\left(\frac{3683}{5390}\right)\) \(e\left(\frac{7573}{8085}\right)\) \(e\left(\frac{1208}{8085}\right)\) \(e\left(\frac{113}{330}\right)\) \(e\left(\frac{2624}{2695}\right)\)
\(\chi_{373527}(1466,\cdot)\) \(1\) \(1\) \(e\left(\frac{7391}{16170}\right)\) \(e\left(\frac{7391}{8085}\right)\) \(e\left(\frac{1822}{8085}\right)\) \(e\left(\frac{2001}{5390}\right)\) \(e\left(\frac{2207}{3234}\right)\) \(e\left(\frac{4447}{5390}\right)\) \(e\left(\frac{6697}{8085}\right)\) \(e\left(\frac{6812}{8085}\right)\) \(e\left(\frac{287}{330}\right)\) \(e\left(\frac{376}{2695}\right)\)