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.el
\(\chi_{2624}(45,\cdot)\) \(\chi_{2624}(189,\cdot)\) \(\chi_{2624}(269,\cdot)\) \(\chi_{2624}(277,\cdot)\) \(\chi_{2624}(373,\cdot)\) \(\chi_{2624}(517,\cdot)\) \(\chi_{2624}(597,\cdot)\) \(\chi_{2624}(605,\cdot)\) \(\chi_{2624}(701,\cdot)\) \(\chi_{2624}(845,\cdot)\) \(\chi_{2624}(925,\cdot)\) \(\chi_{2624}(933,\cdot)\) \(\chi_{2624}(1029,\cdot)\) \(\chi_{2624}(1173,\cdot)\) \(\chi_{2624}(1253,\cdot)\) \(\chi_{2624}(1261,\cdot)\) \(\chi_{2624}(1357,\cdot)\) \(\chi_{2624}(1501,\cdot)\) \(\chi_{2624}(1581,\cdot)\) \(\chi_{2624}(1589,\cdot)\) \(\chi_{2624}(1685,\cdot)\) \(\chi_{2624}(1829,\cdot)\) \(\chi_{2624}(1909,\cdot)\) \(\chi_{2624}(1917,\cdot)\) \(\chi_{2624}(2013,\cdot)\) \(\chi_{2624}(2157,\cdot)\) \(\chi_{2624}(2237,\cdot)\) \(\chi_{2624}(2245,\cdot)\) \(\chi_{2624}(2341,\cdot)\) \(\chi_{2624}(2485,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((575,1477,129)\) → \((1,e\left(\frac{7}{16}\right),e\left(\frac{3}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 2624 }(45, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{3}{80}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{7}{80}\right)\) | \(e\left(\frac{69}{80}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{61}{80}\right)\) | \(e\left(\frac{71}{80}\right)\) |