Basic properties
| Modulus: | \(633\) | |
| Conductor: | \(211\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{211}(7,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 633.bf
\(\chi_{633}(7,\cdot)\) \(\chi_{633}(22,\cdot)\) \(\chi_{633}(85,\cdot)\) \(\chi_{633}(91,\cdot)\) \(\chi_{633}(106,\cdot)\) \(\chi_{633}(112,\cdot)\) \(\chi_{633}(118,\cdot)\) \(\chi_{633}(127,\cdot)\) \(\chi_{633}(130,\cdot)\) \(\chi_{633}(133,\cdot)\) \(\chi_{633}(142,\cdot)\) \(\chi_{633}(145,\cdot)\) \(\chi_{633}(160,\cdot)\) \(\chi_{633}(166,\cdot)\) \(\chi_{633}(175,\cdot)\) \(\chi_{633}(181,\cdot)\) \(\chi_{633}(187,\cdot)\) \(\chi_{633}(202,\cdot)\) \(\chi_{633}(205,\cdot)\) \(\chi_{633}(214,\cdot)\) \(\chi_{633}(250,\cdot)\) \(\chi_{633}(259,\cdot)\) \(\chi_{633}(268,\cdot)\) \(\chi_{633}(283,\cdot)\) \(\chi_{633}(286,\cdot)\) \(\chi_{633}(319,\cdot)\) \(\chi_{633}(352,\cdot)\) \(\chi_{633}(370,\cdot)\) \(\chi_{633}(373,\cdot)\) \(\chi_{633}(376,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((212,424)\) → \((1,e\left(\frac{139}{210}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 633 }(7, a) \) | \(-1\) | \(1\) | \(e\left(\frac{139}{210}\right)\) | \(e\left(\frac{34}{105}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{1}{210}\right)\) | \(e\left(\frac{69}{70}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{68}{105}\right)\) |