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Properties

Label 373527.sh
Modulus $373527$
Conductor $373527$
Order $16170$
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(373527, base_ring=CyclotomicField(16170)) M = H._module chi = DirichletCharacter(H, M([13475,1595,10878])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(5,373527)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(373527\)
Conductor: \(373527\)
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: 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: $\Q(\zeta_{8085})$
Fixed field: Number field defined by a degree 16170 polynomial (not computed)

First 14 of 3360 characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(4\) \(5\) \(8\) \(10\) \(13\) \(16\) \(17\) \(19\) \(20\)
\(\chi_{373527}(5,\cdot)\) \(1\) \(1\) \(e\left(\frac{3461}{5390}\right)\) \(e\left(\frac{766}{2695}\right)\) \(e\left(\frac{6541}{8085}\right)\) \(e\left(\frac{4993}{5390}\right)\) \(e\left(\frac{1459}{3234}\right)\) \(e\left(\frac{11713}{16170}\right)\) \(e\left(\frac{1532}{2695}\right)\) \(e\left(\frac{7516}{8085}\right)\) \(e\left(\frac{1}{330}\right)\) \(e\left(\frac{754}{8085}\right)\)
\(\chi_{373527}(38,\cdot)\) \(1\) \(1\) \(e\left(\frac{3291}{5390}\right)\) \(e\left(\frac{596}{2695}\right)\) \(e\left(\frac{5216}{8085}\right)\) \(e\left(\frac{4483}{5390}\right)\) \(e\left(\frac{827}{3234}\right)\) \(e\left(\frac{353}{16170}\right)\) \(e\left(\frac{1192}{2695}\right)\) \(e\left(\frac{2006}{8085}\right)\) \(e\left(\frac{71}{330}\right)\) \(e\left(\frac{7004}{8085}\right)\)
\(\chi_{373527}(257,\cdot)\) \(1\) \(1\) \(e\left(\frac{1503}{5390}\right)\) \(e\left(\frac{1503}{2695}\right)\) \(e\left(\frac{3043}{8085}\right)\) \(e\left(\frac{4509}{5390}\right)\) \(e\left(\frac{2119}{3234}\right)\) \(e\left(\frac{12769}{16170}\right)\) \(e\left(\frac{311}{2695}\right)\) \(e\left(\frac{1378}{8085}\right)\) \(e\left(\frac{133}{330}\right)\) \(e\left(\frac{7552}{8085}\right)\)
\(\chi_{373527}(290,\cdot)\) \(1\) \(1\) \(e\left(\frac{3243}{5390}\right)\) \(e\left(\frac{548}{2695}\right)\) \(e\left(\frac{1703}{8085}\right)\) \(e\left(\frac{4339}{5390}\right)\) \(e\left(\frac{2627}{3234}\right)\) \(e\left(\frac{16169}{16170}\right)\) \(e\left(\frac{1096}{2695}\right)\) \(e\left(\frac{6728}{8085}\right)\) \(e\left(\frac{83}{330}\right)\) \(e\left(\frac{3347}{8085}\right)\)
\(\chi_{373527}(383,\cdot)\) \(1\) \(1\) \(e\left(\frac{3779}{5390}\right)\) \(e\left(\frac{1084}{2695}\right)\) \(e\left(\frac{4549}{8085}\right)\) \(e\left(\frac{557}{5390}\right)\) \(e\left(\frac{853}{3234}\right)\) \(e\left(\frac{12037}{16170}\right)\) \(e\left(\frac{2168}{2695}\right)\) \(e\left(\frac{2509}{8085}\right)\) \(e\left(\frac{169}{330}\right)\) \(e\left(\frac{7801}{8085}\right)\)
\(\chi_{373527}(416,\cdot)\) \(1\) \(1\) \(e\left(\frac{1399}{5390}\right)\) \(e\left(\frac{1399}{2695}\right)\) \(e\left(\frac{7559}{8085}\right)\) \(e\left(\frac{4197}{5390}\right)\) \(e\left(\frac{629}{3234}\right)\) \(e\left(\frac{3917}{16170}\right)\) \(e\left(\frac{103}{2695}\right)\) \(e\left(\frac{3524}{8085}\right)\) \(e\left(\frac{269}{330}\right)\) \(e\left(\frac{3671}{8085}\right)\)
\(\chi_{373527}(542,\cdot)\) \(1\) \(1\) \(e\left(\frac{3797}{5390}\right)\) \(e\left(\frac{1102}{2695}\right)\) \(e\left(\frac{1487}{8085}\right)\) \(e\left(\frac{611}{5390}\right)\) \(e\left(\frac{2873}{3234}\right)\) \(e\left(\frac{8801}{16170}\right)\) \(e\left(\frac{2204}{2695}\right)\) \(e\left(\frac{1412}{8085}\right)\) \(e\left(\frac{137}{330}\right)\) \(e\left(\frac{4793}{8085}\right)\)
\(\chi_{373527}(698,\cdot)\) \(1\) \(1\) \(e\left(\frac{551}{5390}\right)\) \(e\left(\frac{551}{2695}\right)\) \(e\left(\frac{4786}{8085}\right)\) \(e\left(\frac{1653}{5390}\right)\) \(e\left(\frac{2245}{3234}\right)\) \(e\left(\frac{8443}{16170}\right)\) \(e\left(\frac{1102}{2695}\right)\) \(e\left(\frac{706}{8085}\right)\) \(e\left(\frac{151}{330}\right)\) \(e\left(\frac{6439}{8085}\right)\)
\(\chi_{373527}(731,\cdot)\) \(1\) \(1\) \(e\left(\frac{1591}{5390}\right)\) \(e\left(\frac{1591}{2695}\right)\) \(e\left(\frac{5441}{8085}\right)\) \(e\left(\frac{4773}{5390}\right)\) \(e\left(\frac{3131}{3234}\right)\) \(e\left(\frac{5333}{16170}\right)\) \(e\left(\frac{487}{2695}\right)\) \(e\left(\frac{806}{8085}\right)\) \(e\left(\frac{221}{330}\right)\) \(e\left(\frac{2129}{8085}\right)\)
\(\chi_{373527}(983,\cdot)\) \(1\) \(1\) \(e\left(\frac{4693}{5390}\right)\) \(e\left(\frac{1998}{2695}\right)\) \(e\left(\frac{5078}{8085}\right)\) \(e\left(\frac{3299}{5390}\right)\) \(e\left(\frac{1613}{3234}\right)\) \(e\left(\frac{10019}{16170}\right)\) \(e\left(\frac{1301}{2695}\right)\) \(e\left(\frac{4898}{8085}\right)\) \(e\left(\frac{23}{330}\right)\) \(e\left(\frac{2987}{8085}\right)\)
\(\chi_{373527}(1076,\cdot)\) \(1\) \(1\) \(e\left(\frac{659}{5390}\right)\) \(e\left(\frac{659}{2695}\right)\) \(e\left(\frac{2584}{8085}\right)\) \(e\left(\frac{1977}{5390}\right)\) \(e\left(\frac{1429}{3234}\right)\) \(e\left(\frac{5197}{16170}\right)\) \(e\left(\frac{1318}{2695}\right)\) \(e\left(\frac{2209}{8085}\right)\) \(e\left(\frac{289}{330}\right)\) \(e\left(\frac{4561}{8085}\right)\)
\(\chi_{373527}(1202,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{5390}\right)\) \(e\left(\frac{37}{2695}\right)\) \(e\left(\frac{1192}{8085}\right)\) \(e\left(\frac{111}{5390}\right)\) \(e\left(\frac{499}{3234}\right)\) \(e\left(\frac{13411}{16170}\right)\) \(e\left(\frac{74}{2695}\right)\) \(e\left(\frac{7477}{8085}\right)\) \(e\left(\frac{307}{330}\right)\) \(e\left(\frac{1303}{8085}\right)\)
\(\chi_{373527}(1235,\cdot)\) \(1\) \(1\) \(e\left(\frac{2027}{5390}\right)\) \(e\left(\frac{2027}{2695}\right)\) \(e\left(\frac{4337}{8085}\right)\) \(e\left(\frac{691}{5390}\right)\) \(e\left(\frac{2951}{3234}\right)\) \(e\left(\frac{1811}{16170}\right)\) \(e\left(\frac{1359}{2695}\right)\) \(e\left(\frac{7772}{8085}\right)\) \(e\left(\frac{167}{330}\right)\) \(e\left(\frac{2333}{8085}\right)\)
\(\chi_{373527}(1424,\cdot)\) \(1\) \(1\) \(e\left(\frac{4511}{5390}\right)\) \(e\left(\frac{1816}{2695}\right)\) \(e\left(\frac{2201}{8085}\right)\) \(e\left(\frac{2753}{5390}\right)\) \(e\left(\frac{353}{3234}\right)\) \(e\left(\frac{8003}{16170}\right)\) \(e\left(\frac{937}{2695}\right)\) \(e\left(\frac{1916}{8085}\right)\) \(e\left(\frac{41}{330}\right)\) \(e\left(\frac{7649}{8085}\right)\)