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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 561.bl
\(\chi_{561}(29,\cdot)\) \(\chi_{561}(41,\cdot)\) \(\chi_{561}(62,\cdot)\) \(\chi_{561}(74,\cdot)\) \(\chi_{561}(95,\cdot)\) \(\chi_{561}(107,\cdot)\) \(\chi_{561}(116,\cdot)\) \(\chi_{561}(167,\cdot)\) \(\chi_{561}(173,\cdot)\) \(\chi_{561}(182,\cdot)\) \(\chi_{561}(194,\cdot)\) \(\chi_{561}(215,\cdot)\) \(\chi_{561}(227,\cdot)\) \(\chi_{561}(233,\cdot)\) \(\chi_{561}(248,\cdot)\) \(\chi_{561}(260,\cdot)\) \(\chi_{561}(266,\cdot)\) \(\chi_{561}(299,\cdot)\) \(\chi_{561}(326,\cdot)\) \(\chi_{561}(347,\cdot)\) \(\chi_{561}(371,\cdot)\) \(\chi_{561}(380,\cdot)\) \(\chi_{561}(398,\cdot)\) \(\chi_{561}(413,\cdot)\) \(\chi_{561}(431,\cdot)\) \(\chi_{561}(437,\cdot)\) \(\chi_{561}(464,\cdot)\) \(\chi_{561}(470,\cdot)\) \(\chi_{561}(479,\cdot)\) \(\chi_{561}(503,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((188,409,496)\) → \((-1,e\left(\frac{3}{10}\right),e\left(\frac{5}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(19\) |
| \( \chi_{ 561 }(107, a) \) | \(-1\) | \(1\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{21}{80}\right)\) | \(e\left(\frac{43}{80}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{57}{80}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{11}{40}\right)\) |