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.cr
\(\chi_{1375}(38,\cdot)\) \(\chi_{1375}(58,\cdot)\) \(\chi_{1375}(103,\cdot)\) \(\chi_{1375}(137,\cdot)\) \(\chi_{1375}(147,\cdot)\) \(\chi_{1375}(152,\cdot)\) \(\chi_{1375}(267,\cdot)\) \(\chi_{1375}(273,\cdot)\) \(\chi_{1375}(313,\cdot)\) \(\chi_{1375}(333,\cdot)\) \(\chi_{1375}(378,\cdot)\) \(\chi_{1375}(412,\cdot)\) \(\chi_{1375}(422,\cdot)\) \(\chi_{1375}(427,\cdot)\) \(\chi_{1375}(542,\cdot)\) \(\chi_{1375}(548,\cdot)\) \(\chi_{1375}(588,\cdot)\) \(\chi_{1375}(608,\cdot)\) \(\chi_{1375}(653,\cdot)\) \(\chi_{1375}(687,\cdot)\) \(\chi_{1375}(697,\cdot)\) \(\chi_{1375}(702,\cdot)\) \(\chi_{1375}(817,\cdot)\) \(\chi_{1375}(823,\cdot)\) \(\chi_{1375}(863,\cdot)\) \(\chi_{1375}(883,\cdot)\) \(\chi_{1375}(928,\cdot)\) \(\chi_{1375}(962,\cdot)\) \(\chi_{1375}(972,\cdot)\) \(\chi_{1375}(977,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{100})$ |
| Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((1002,376)\) → \((e\left(\frac{33}{100}\right),e\left(\frac{4}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 1375 }(1092, a) \) | \(-1\) | \(1\) | \(e\left(\frac{13}{100}\right)\) | \(e\left(\frac{71}{100}\right)\) | \(e\left(\frac{13}{50}\right)\) | \(e\left(\frac{21}{25}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{39}{100}\right)\) | \(e\left(\frac{21}{50}\right)\) | \(e\left(\frac{97}{100}\right)\) | \(e\left(\frac{67}{100}\right)\) | \(e\left(\frac{39}{50}\right)\) |