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.ct
\(\chi_{1700}(3,\cdot)\) \(\chi_{1700}(27,\cdot)\) \(\chi_{1700}(63,\cdot)\) \(\chi_{1700}(147,\cdot)\) \(\chi_{1700}(227,\cdot)\) \(\chi_{1700}(303,\cdot)\) \(\chi_{1700}(347,\cdot)\) \(\chi_{1700}(367,\cdot)\) \(\chi_{1700}(403,\cdot)\) \(\chi_{1700}(487,\cdot)\) \(\chi_{1700}(567,\cdot)\) \(\chi_{1700}(583,\cdot)\) \(\chi_{1700}(683,\cdot)\) \(\chi_{1700}(687,\cdot)\) \(\chi_{1700}(827,\cdot)\) \(\chi_{1700}(923,\cdot)\) \(\chi_{1700}(983,\cdot)\) \(\chi_{1700}(1023,\cdot)\) \(\chi_{1700}(1027,\cdot)\) \(\chi_{1700}(1047,\cdot)\) \(\chi_{1700}(1083,\cdot)\) \(\chi_{1700}(1167,\cdot)\) \(\chi_{1700}(1247,\cdot)\) \(\chi_{1700}(1263,\cdot)\) \(\chi_{1700}(1323,\cdot)\) \(\chi_{1700}(1363,\cdot)\) \(\chi_{1700}(1367,\cdot)\) \(\chi_{1700}(1387,\cdot)\) \(\chi_{1700}(1423,\cdot)\) \(\chi_{1700}(1587,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((851,477,1601)\) → \((-1,e\left(\frac{19}{20}\right),e\left(\frac{1}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 1700 }(1363, a) \) | \(-1\) | \(1\) | \(e\left(\frac{17}{80}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{11}{80}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{71}{80}\right)\) | \(e\left(\frac{51}{80}\right)\) | \(e\left(\frac{57}{80}\right)\) |