Basic properties
| Modulus: | \(561\) | |
| Conductor: | \(561\) | 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 561.bm
\(\chi_{561}(5,\cdot)\) \(\chi_{561}(14,\cdot)\) \(\chi_{561}(20,\cdot)\) \(\chi_{561}(71,\cdot)\) \(\chi_{561}(80,\cdot)\) \(\chi_{561}(92,\cdot)\) \(\chi_{561}(113,\cdot)\) \(\chi_{561}(125,\cdot)\) \(\chi_{561}(146,\cdot)\) \(\chi_{561}(158,\cdot)\) \(\chi_{561}(218,\cdot)\) \(\chi_{561}(224,\cdot)\) \(\chi_{561}(245,\cdot)\) \(\chi_{561}(269,\cdot)\) \(\chi_{561}(278,\cdot)\) \(\chi_{561}(284,\cdot)\) \(\chi_{561}(311,\cdot)\) \(\chi_{561}(317,\cdot)\) \(\chi_{561}(335,\cdot)\) \(\chi_{561}(350,\cdot)\) \(\chi_{561}(368,\cdot)\) \(\chi_{561}(377,\cdot)\) \(\chi_{561}(401,\cdot)\) \(\chi_{561}(422,\cdot)\) \(\chi_{561}(449,\cdot)\) \(\chi_{561}(482,\cdot)\) \(\chi_{561}(488,\cdot)\) \(\chi_{561}(500,\cdot)\) \(\chi_{561}(515,\cdot)\) \(\chi_{561}(521,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((188,409,496)\) → \((-1,e\left(\frac{2}{5}\right),e\left(\frac{1}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(19\) |
| \( \chi_{ 561 }(71, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{33}{80}\right)\) | \(e\left(\frac{39}{80}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{21}{80}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{3}{40}\right)\) |