Basic properties
| Modulus: | \(1617\) | |
| Conductor: | \(539\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{539}(61,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1617.ck
\(\chi_{1617}(40,\cdot)\) \(\chi_{1617}(52,\cdot)\) \(\chi_{1617}(61,\cdot)\) \(\chi_{1617}(73,\cdot)\) \(\chi_{1617}(94,\cdot)\) \(\chi_{1617}(145,\cdot)\) \(\chi_{1617}(250,\cdot)\) \(\chi_{1617}(271,\cdot)\) \(\chi_{1617}(283,\cdot)\) \(\chi_{1617}(292,\cdot)\) \(\chi_{1617}(304,\cdot)\) \(\chi_{1617}(376,\cdot)\) \(\chi_{1617}(409,\cdot)\) \(\chi_{1617}(481,\cdot)\) \(\chi_{1617}(502,\cdot)\) \(\chi_{1617}(514,\cdot)\) \(\chi_{1617}(523,\cdot)\) \(\chi_{1617}(535,\cdot)\) \(\chi_{1617}(556,\cdot)\) \(\chi_{1617}(640,\cdot)\) \(\chi_{1617}(712,\cdot)\) \(\chi_{1617}(733,\cdot)\) \(\chi_{1617}(745,\cdot)\) \(\chi_{1617}(787,\cdot)\) \(\chi_{1617}(838,\cdot)\) \(\chi_{1617}(871,\cdot)\) \(\chi_{1617}(943,\cdot)\) \(\chi_{1617}(964,\cdot)\) \(\chi_{1617}(976,\cdot)\) \(\chi_{1617}(985,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((1079,199,442)\) → \((1,e\left(\frac{11}{42}\right),e\left(\frac{9}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 1617 }(61, a) \) | \(1\) | \(1\) | \(e\left(\frac{149}{210}\right)\) | \(e\left(\frac{44}{105}\right)\) | \(e\left(\frac{41}{210}\right)\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{88}{105}\right)\) | \(e\left(\frac{68}{105}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{43}{70}\right)\) |