Basic properties
| Modulus: | \(1617\) | |
| Conductor: | \(1617\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | 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 1617.cf
\(\chi_{1617}(17,\cdot)\) \(\chi_{1617}(101,\cdot)\) \(\chi_{1617}(173,\cdot)\) \(\chi_{1617}(194,\cdot)\) \(\chi_{1617}(206,\cdot)\) \(\chi_{1617}(248,\cdot)\) \(\chi_{1617}(299,\cdot)\) \(\chi_{1617}(332,\cdot)\) \(\chi_{1617}(404,\cdot)\) \(\chi_{1617}(425,\cdot)\) \(\chi_{1617}(437,\cdot)\) \(\chi_{1617}(446,\cdot)\) \(\chi_{1617}(458,\cdot)\) \(\chi_{1617}(479,\cdot)\) \(\chi_{1617}(530,\cdot)\) \(\chi_{1617}(563,\cdot)\) \(\chi_{1617}(635,\cdot)\) \(\chi_{1617}(677,\cdot)\) \(\chi_{1617}(689,\cdot)\) \(\chi_{1617}(710,\cdot)\) \(\chi_{1617}(761,\cdot)\) \(\chi_{1617}(794,\cdot)\) \(\chi_{1617}(866,\cdot)\) \(\chi_{1617}(887,\cdot)\) \(\chi_{1617}(899,\cdot)\) \(\chi_{1617}(908,\cdot)\) \(\chi_{1617}(920,\cdot)\) \(\chi_{1617}(941,\cdot)\) \(\chi_{1617}(992,\cdot)\) \(\chi_{1617}(1025,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((1079,199,442)\) → \((-1,e\left(\frac{23}{42}\right),e\left(\frac{1}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 1617 }(530, a) \) | \(-1\) | \(1\) | \(e\left(\frac{88}{105}\right)\) | \(e\left(\frac{71}{105}\right)\) | \(e\left(\frac{82}{105}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{37}{105}\right)\) | \(e\left(\frac{19}{210}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{16}{35}\right)\) |