Basic properties
| Modulus: | \(1601\) | |
| Conductor: | \(1601\) | 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 1601.n
\(\chi_{1601}(32,\cdot)\) \(\chi_{1601}(50,\cdot)\) \(\chi_{1601}(77,\cdot)\) \(\chi_{1601}(122,\cdot)\) \(\chi_{1601}(145,\cdot)\) \(\chi_{1601}(248,\cdot)\) \(\chi_{1601}(265,\cdot)\) \(\chi_{1601}(314,\cdot)\) \(\chi_{1601}(321,\cdot)\) \(\chi_{1601}(399,\cdot)\) \(\chi_{1601}(413,\cdot)\) \(\chi_{1601}(499,\cdot)\) \(\chi_{1601}(510,\cdot)\) \(\chi_{1601}(604,\cdot)\) \(\chi_{1601}(607,\cdot)\) \(\chi_{1601}(748,\cdot)\) \(\chi_{1601}(853,\cdot)\) \(\chi_{1601}(994,\cdot)\) \(\chi_{1601}(997,\cdot)\) \(\chi_{1601}(1091,\cdot)\) \(\chi_{1601}(1102,\cdot)\) \(\chi_{1601}(1188,\cdot)\) \(\chi_{1601}(1202,\cdot)\) \(\chi_{1601}(1280,\cdot)\) \(\chi_{1601}(1287,\cdot)\) \(\chi_{1601}(1336,\cdot)\) \(\chi_{1601}(1353,\cdot)\) \(\chi_{1601}(1456,\cdot)\) \(\chi_{1601}(1479,\cdot)\) \(\chi_{1601}(1524,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\(3\) → \(e\left(\frac{73}{80}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1601 }(1280, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{73}{80}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{29}{80}\right)\) | \(e\left(\frac{51}{80}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{49}{80}\right)\) |