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.em
\(\chi_{2624}(197,\cdot)\) \(\chi_{2624}(285,\cdot)\) \(\chi_{2624}(333,\cdot)\) \(\chi_{2624}(349,\cdot)\) \(\chi_{2624}(389,\cdot)\) \(\chi_{2624}(405,\cdot)\) \(\chi_{2624}(453,\cdot)\) \(\chi_{2624}(541,\cdot)\) \(\chi_{2624}(853,\cdot)\) \(\chi_{2624}(941,\cdot)\) \(\chi_{2624}(989,\cdot)\) \(\chi_{2624}(1005,\cdot)\) \(\chi_{2624}(1045,\cdot)\) \(\chi_{2624}(1061,\cdot)\) \(\chi_{2624}(1109,\cdot)\) \(\chi_{2624}(1197,\cdot)\) \(\chi_{2624}(1509,\cdot)\) \(\chi_{2624}(1597,\cdot)\) \(\chi_{2624}(1645,\cdot)\) \(\chi_{2624}(1661,\cdot)\) \(\chi_{2624}(1701,\cdot)\) \(\chi_{2624}(1717,\cdot)\) \(\chi_{2624}(1765,\cdot)\) \(\chi_{2624}(1853,\cdot)\) \(\chi_{2624}(2165,\cdot)\) \(\chi_{2624}(2253,\cdot)\) \(\chi_{2624}(2301,\cdot)\) \(\chi_{2624}(2317,\cdot)\) \(\chi_{2624}(2357,\cdot)\) \(\chi_{2624}(2373,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((575,1477,129)\) → \((1,e\left(\frac{1}{16}\right),e\left(\frac{9}{20}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 2624 }(197, a) \) | \(1\) | \(1\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{77}{80}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{53}{80}\right)\) | \(e\left(\frac{71}{80}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{39}{80}\right)\) | \(e\left(\frac{9}{80}\right)\) |