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.ei
\(\chi_{2624}(67,\cdot)\) \(\chi_{2624}(99,\cdot)\) \(\chi_{2624}(147,\cdot)\) \(\chi_{2624}(171,\cdot)\) \(\chi_{2624}(179,\cdot)\) \(\chi_{2624}(235,\cdot)\) \(\chi_{2624}(315,\cdot)\) \(\chi_{2624}(587,\cdot)\) \(\chi_{2624}(667,\cdot)\) \(\chi_{2624}(675,\cdot)\) \(\chi_{2624}(691,\cdot)\) \(\chi_{2624}(731,\cdot)\) \(\chi_{2624}(867,\cdot)\) \(\chi_{2624}(883,\cdot)\) \(\chi_{2624}(955,\cdot)\) \(\chi_{2624}(1259,\cdot)\) \(\chi_{2624}(1379,\cdot)\) \(\chi_{2624}(1411,\cdot)\) \(\chi_{2624}(1459,\cdot)\) \(\chi_{2624}(1483,\cdot)\) \(\chi_{2624}(1491,\cdot)\) \(\chi_{2624}(1547,\cdot)\) \(\chi_{2624}(1627,\cdot)\) \(\chi_{2624}(1899,\cdot)\) \(\chi_{2624}(1979,\cdot)\) \(\chi_{2624}(1987,\cdot)\) \(\chi_{2624}(2003,\cdot)\) \(\chi_{2624}(2043,\cdot)\) \(\chi_{2624}(2179,\cdot)\) \(\chi_{2624}(2195,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((575,1477,129)\) → \((-1,e\left(\frac{3}{16}\right),e\left(\frac{17}{40}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 2624 }(67, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{43}{80}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{57}{80}\right)\) | \(e\left(\frac{79}{80}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{51}{80}\right)\) | \(e\left(\frac{31}{80}\right)\) |