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.ea
\(\chi_{2624}(13,\cdot)\) \(\chi_{2624}(93,\cdot)\) \(\chi_{2624}(101,\cdot)\) \(\chi_{2624}(117,\cdot)\) \(\chi_{2624}(157,\cdot)\) \(\chi_{2624}(293,\cdot)\) \(\chi_{2624}(309,\cdot)\) \(\chi_{2624}(381,\cdot)\) \(\chi_{2624}(685,\cdot)\) \(\chi_{2624}(805,\cdot)\) \(\chi_{2624}(837,\cdot)\) \(\chi_{2624}(885,\cdot)\) \(\chi_{2624}(909,\cdot)\) \(\chi_{2624}(917,\cdot)\) \(\chi_{2624}(973,\cdot)\) \(\chi_{2624}(1053,\cdot)\) \(\chi_{2624}(1325,\cdot)\) \(\chi_{2624}(1405,\cdot)\) \(\chi_{2624}(1413,\cdot)\) \(\chi_{2624}(1429,\cdot)\) \(\chi_{2624}(1469,\cdot)\) \(\chi_{2624}(1605,\cdot)\) \(\chi_{2624}(1621,\cdot)\) \(\chi_{2624}(1693,\cdot)\) \(\chi_{2624}(1997,\cdot)\) \(\chi_{2624}(2117,\cdot)\) \(\chi_{2624}(2149,\cdot)\) \(\chi_{2624}(2197,\cdot)\) \(\chi_{2624}(2221,\cdot)\) \(\chi_{2624}(2229,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((575,1477,129)\) → \((1,e\left(\frac{15}{16}\right),e\left(\frac{31}{40}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 2624 }(13, a) \) | \(-1\) | \(1\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{79}{80}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{1}{80}\right)\) | \(e\left(\frac{7}{80}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{43}{80}\right)\) | \(e\left(\frac{3}{80}\right)\) |