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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2624.eg
\(\chi_{2624}(107,\cdot)\) \(\chi_{2624}(187,\cdot)\) \(\chi_{2624}(195,\cdot)\) \(\chi_{2624}(291,\cdot)\) \(\chi_{2624}(435,\cdot)\) \(\chi_{2624}(515,\cdot)\) \(\chi_{2624}(523,\cdot)\) \(\chi_{2624}(619,\cdot)\) \(\chi_{2624}(763,\cdot)\) \(\chi_{2624}(843,\cdot)\) \(\chi_{2624}(851,\cdot)\) \(\chi_{2624}(947,\cdot)\) \(\chi_{2624}(1091,\cdot)\) \(\chi_{2624}(1171,\cdot)\) \(\chi_{2624}(1179,\cdot)\) \(\chi_{2624}(1275,\cdot)\) \(\chi_{2624}(1419,\cdot)\) \(\chi_{2624}(1499,\cdot)\) \(\chi_{2624}(1507,\cdot)\) \(\chi_{2624}(1603,\cdot)\) \(\chi_{2624}(1747,\cdot)\) \(\chi_{2624}(1827,\cdot)\) \(\chi_{2624}(1835,\cdot)\) \(\chi_{2624}(1931,\cdot)\) \(\chi_{2624}(2075,\cdot)\) \(\chi_{2624}(2155,\cdot)\) \(\chi_{2624}(2163,\cdot)\) \(\chi_{2624}(2259,\cdot)\) \(\chi_{2624}(2403,\cdot)\) \(\chi_{2624}(2483,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((575,1477,129)\) → \((-1,e\left(\frac{13}{16}\right),e\left(\frac{1}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 2624 }(107, a) \) | \(-1\) | \(1\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{1}{80}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{69}{80}\right)\) | \(e\left(\frac{23}{80}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{7}{80}\right)\) | \(e\left(\frac{77}{80}\right)\) |