Basic properties
| Modulus: | \(1000\) | |
| Conductor: | \(125\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(100\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{125}(17,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1000.bg
\(\chi_{1000}(17,\cdot)\) \(\chi_{1000}(33,\cdot)\) \(\chi_{1000}(73,\cdot)\) \(\chi_{1000}(97,\cdot)\) \(\chi_{1000}(113,\cdot)\) \(\chi_{1000}(137,\cdot)\) \(\chi_{1000}(153,\cdot)\) \(\chi_{1000}(177,\cdot)\) \(\chi_{1000}(217,\cdot)\) \(\chi_{1000}(233,\cdot)\) \(\chi_{1000}(273,\cdot)\) \(\chi_{1000}(297,\cdot)\) \(\chi_{1000}(313,\cdot)\) \(\chi_{1000}(337,\cdot)\) \(\chi_{1000}(353,\cdot)\) \(\chi_{1000}(377,\cdot)\) \(\chi_{1000}(417,\cdot)\) \(\chi_{1000}(433,\cdot)\) \(\chi_{1000}(473,\cdot)\) \(\chi_{1000}(497,\cdot)\) \(\chi_{1000}(513,\cdot)\) \(\chi_{1000}(537,\cdot)\) \(\chi_{1000}(553,\cdot)\) \(\chi_{1000}(577,\cdot)\) \(\chi_{1000}(617,\cdot)\) \(\chi_{1000}(633,\cdot)\) \(\chi_{1000}(673,\cdot)\) \(\chi_{1000}(697,\cdot)\) \(\chi_{1000}(713,\cdot)\) \(\chi_{1000}(737,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{100})$ |
| Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((751,501,377)\) → \((1,1,e\left(\frac{73}{100}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 1000 }(17, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{100}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{11}{50}\right)\) | \(e\left(\frac{12}{25}\right)\) | \(e\left(\frac{47}{100}\right)\) | \(e\left(\frac{29}{100}\right)\) | \(e\left(\frac{7}{50}\right)\) | \(e\left(\frac{4}{25}\right)\) | \(e\left(\frac{63}{100}\right)\) | \(e\left(\frac{33}{100}\right)\) |