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.ek
\(\chi_{2624}(37,\cdot)\) \(\chi_{2624}(133,\cdot)\) \(\chi_{2624}(141,\cdot)\) \(\chi_{2624}(221,\cdot)\) \(\chi_{2624}(365,\cdot)\) \(\chi_{2624}(461,\cdot)\) \(\chi_{2624}(469,\cdot)\) \(\chi_{2624}(549,\cdot)\) \(\chi_{2624}(693,\cdot)\) \(\chi_{2624}(789,\cdot)\) \(\chi_{2624}(797,\cdot)\) \(\chi_{2624}(877,\cdot)\) \(\chi_{2624}(1021,\cdot)\) \(\chi_{2624}(1117,\cdot)\) \(\chi_{2624}(1125,\cdot)\) \(\chi_{2624}(1205,\cdot)\) \(\chi_{2624}(1349,\cdot)\) \(\chi_{2624}(1445,\cdot)\) \(\chi_{2624}(1453,\cdot)\) \(\chi_{2624}(1533,\cdot)\) \(\chi_{2624}(1677,\cdot)\) \(\chi_{2624}(1773,\cdot)\) \(\chi_{2624}(1781,\cdot)\) \(\chi_{2624}(1861,\cdot)\) \(\chi_{2624}(2005,\cdot)\) \(\chi_{2624}(2101,\cdot)\) \(\chi_{2624}(2109,\cdot)\) \(\chi_{2624}(2189,\cdot)\) \(\chi_{2624}(2333,\cdot)\) \(\chi_{2624}(2429,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((575,1477,129)\) → \((1,e\left(\frac{11}{16}\right),e\left(\frac{1}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 2624 }(1117, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{7}{80}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{3}{80}\right)\) | \(e\left(\frac{41}{80}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{49}{80}\right)\) | \(e\left(\frac{59}{80}\right)\) |