Basic properties
Modulus: | \(2624\) | |
Conductor: | \(2624\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(80\) | 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)
|
Galois orbit 2624.ej
\(\chi_{2624}(11,\cdot)\) \(\chi_{2624}(19,\cdot)\) \(\chi_{2624}(35,\cdot)\) \(\chi_{2624}(75,\cdot)\) \(\chi_{2624}(211,\cdot)\) \(\chi_{2624}(227,\cdot)\) \(\chi_{2624}(299,\cdot)\) \(\chi_{2624}(603,\cdot)\) \(\chi_{2624}(723,\cdot)\) \(\chi_{2624}(755,\cdot)\) \(\chi_{2624}(803,\cdot)\) \(\chi_{2624}(827,\cdot)\) \(\chi_{2624}(835,\cdot)\) \(\chi_{2624}(891,\cdot)\) \(\chi_{2624}(971,\cdot)\) \(\chi_{2624}(1243,\cdot)\) \(\chi_{2624}(1323,\cdot)\) \(\chi_{2624}(1331,\cdot)\) \(\chi_{2624}(1347,\cdot)\) \(\chi_{2624}(1387,\cdot)\) \(\chi_{2624}(1523,\cdot)\) \(\chi_{2624}(1539,\cdot)\) \(\chi_{2624}(1611,\cdot)\) \(\chi_{2624}(1915,\cdot)\) \(\chi_{2624}(2035,\cdot)\) \(\chi_{2624}(2067,\cdot)\) \(\chi_{2624}(2115,\cdot)\) \(\chi_{2624}(2139,\cdot)\) \(\chi_{2624}(2147,\cdot)\) \(\chi_{2624}(2203,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((575,1477,129)\) → \((-1,e\left(\frac{5}{16}\right),e\left(\frac{3}{40}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 2624 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{77}{80}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{23}{80}\right)\) | \(e\left(\frac{1}{80}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{29}{80}\right)\) | \(e\left(\frac{9}{80}\right)\) |