Basic properties
| Modulus: | \(1375\) | |
| Conductor: | \(1375\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(100\) | 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 1375.ck
\(\chi_{1375}(3,\cdot)\) \(\chi_{1375}(27,\cdot)\) \(\chi_{1375}(47,\cdot)\) \(\chi_{1375}(92,\cdot)\) \(\chi_{1375}(148,\cdot)\) \(\chi_{1375}(158,\cdot)\) \(\chi_{1375}(163,\cdot)\) \(\chi_{1375}(262,\cdot)\) \(\chi_{1375}(278,\cdot)\) \(\chi_{1375}(302,\cdot)\) \(\chi_{1375}(322,\cdot)\) \(\chi_{1375}(367,\cdot)\) \(\chi_{1375}(423,\cdot)\) \(\chi_{1375}(433,\cdot)\) \(\chi_{1375}(438,\cdot)\) \(\chi_{1375}(537,\cdot)\) \(\chi_{1375}(553,\cdot)\) \(\chi_{1375}(577,\cdot)\) \(\chi_{1375}(597,\cdot)\) \(\chi_{1375}(642,\cdot)\) \(\chi_{1375}(698,\cdot)\) \(\chi_{1375}(708,\cdot)\) \(\chi_{1375}(713,\cdot)\) \(\chi_{1375}(812,\cdot)\) \(\chi_{1375}(828,\cdot)\) \(\chi_{1375}(852,\cdot)\) \(\chi_{1375}(872,\cdot)\) \(\chi_{1375}(917,\cdot)\) \(\chi_{1375}(973,\cdot)\) \(\chi_{1375}(983,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{100})$ |
| Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((1002,376)\) → \((e\left(\frac{69}{100}\right),e\left(\frac{3}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 1375 }(1087, a) \) | \(-1\) | \(1\) | \(e\left(\frac{29}{100}\right)\) | \(e\left(\frac{63}{100}\right)\) | \(e\left(\frac{29}{50}\right)\) | \(e\left(\frac{23}{25}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{87}{100}\right)\) | \(e\left(\frac{13}{50}\right)\) | \(e\left(\frac{21}{100}\right)\) | \(e\left(\frac{51}{100}\right)\) | \(e\left(\frac{7}{50}\right)\) |