Basic properties
| Modulus: | \(1700\) | |
| Conductor: | \(1700\) | 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 1700.cm
\(\chi_{1700}(23,\cdot)\) \(\chi_{1700}(163,\cdot)\) \(\chi_{1700}(167,\cdot)\) \(\chi_{1700}(267,\cdot)\) \(\chi_{1700}(283,\cdot)\) \(\chi_{1700}(363,\cdot)\) \(\chi_{1700}(447,\cdot)\) \(\chi_{1700}(483,\cdot)\) \(\chi_{1700}(503,\cdot)\) \(\chi_{1700}(547,\cdot)\) \(\chi_{1700}(623,\cdot)\) \(\chi_{1700}(703,\cdot)\) \(\chi_{1700}(787,\cdot)\) \(\chi_{1700}(823,\cdot)\) \(\chi_{1700}(847,\cdot)\) \(\chi_{1700}(887,\cdot)\) \(\chi_{1700}(947,\cdot)\) \(\chi_{1700}(963,\cdot)\) \(\chi_{1700}(1127,\cdot)\) \(\chi_{1700}(1163,\cdot)\) \(\chi_{1700}(1183,\cdot)\) \(\chi_{1700}(1187,\cdot)\) \(\chi_{1700}(1227,\cdot)\) \(\chi_{1700}(1287,\cdot)\) \(\chi_{1700}(1303,\cdot)\) \(\chi_{1700}(1383,\cdot)\) \(\chi_{1700}(1467,\cdot)\) \(\chi_{1700}(1503,\cdot)\) \(\chi_{1700}(1523,\cdot)\) \(\chi_{1700}(1527,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((851,477,1601)\) → \((-1,e\left(\frac{19}{20}\right),e\left(\frac{11}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 1700 }(1163, a) \) | \(-1\) | \(1\) | \(e\left(\frac{67}{80}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{41}{80}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{21}{80}\right)\) | \(e\left(\frac{41}{80}\right)\) | \(e\left(\frac{67}{80}\right)\) |