Basic properties
| Modulus: | \(8085\) | |
| 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 8085.gz
\(\chi_{8085}(61,\cdot)\) \(\chi_{8085}(271,\cdot)\) \(\chi_{8085}(376,\cdot)\) \(\chi_{8085}(481,\cdot)\) \(\chi_{8085}(556,\cdot)\) \(\chi_{8085}(871,\cdot)\) \(\chi_{8085}(976,\cdot)\) \(\chi_{8085}(1216,\cdot)\) \(\chi_{8085}(1426,\cdot)\) \(\chi_{8085}(1531,\cdot)\) \(\chi_{8085}(1711,\cdot)\) \(\chi_{8085}(1921,\cdot)\) \(\chi_{8085}(2026,\cdot)\) \(\chi_{8085}(2131,\cdot)\) \(\chi_{8085}(2581,\cdot)\) \(\chi_{8085}(2686,\cdot)\) \(\chi_{8085}(2791,\cdot)\) \(\chi_{8085}(2866,\cdot)\) \(\chi_{8085}(3076,\cdot)\) \(\chi_{8085}(3181,\cdot)\) \(\chi_{8085}(3286,\cdot)\) \(\chi_{8085}(3526,\cdot)\) \(\chi_{8085}(3736,\cdot)\) \(\chi_{8085}(3946,\cdot)\) \(\chi_{8085}(4021,\cdot)\) \(\chi_{8085}(4231,\cdot)\) \(\chi_{8085}(4336,\cdot)\) \(\chi_{8085}(4681,\cdot)\) \(\chi_{8085}(4891,\cdot)\) \(\chi_{8085}(4996,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((2696,4852,1816,3676)\) → \((1,1,e\left(\frac{11}{42}\right),e\left(\frac{9}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(13\) | \(16\) | \(17\) | \(19\) | \(23\) | \(26\) | \(29\) |
| \( \chi_{ 8085 }(61, a) \) | \(1\) | \(1\) | \(e\left(\frac{149}{210}\right)\) | \(e\left(\frac{44}{105}\right)\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{88}{105}\right)\) | \(e\left(\frac{68}{105}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{53}{210}\right)\) | \(e\left(\frac{1}{70}\right)\) |