Basic properties
| Modulus: | \(8085\) | |
| Conductor: | \(1617\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1617}(326,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8085.gn
\(\chi_{8085}(326,\cdot)\) \(\chi_{8085}(431,\cdot)\) \(\chi_{8085}(536,\cdot)\) \(\chi_{8085}(611,\cdot)\) \(\chi_{8085}(821,\cdot)\) \(\chi_{8085}(926,\cdot)\) \(\chi_{8085}(1031,\cdot)\) \(\chi_{8085}(1271,\cdot)\) \(\chi_{8085}(1481,\cdot)\) \(\chi_{8085}(1691,\cdot)\) \(\chi_{8085}(1766,\cdot)\) \(\chi_{8085}(1976,\cdot)\) \(\chi_{8085}(2081,\cdot)\) \(\chi_{8085}(2426,\cdot)\) \(\chi_{8085}(2636,\cdot)\) \(\chi_{8085}(2741,\cdot)\) \(\chi_{8085}(2846,\cdot)\) \(\chi_{8085}(3131,\cdot)\) \(\chi_{8085}(3236,\cdot)\) \(\chi_{8085}(3341,\cdot)\) \(\chi_{8085}(3581,\cdot)\) \(\chi_{8085}(3896,\cdot)\) \(\chi_{8085}(4001,\cdot)\) \(\chi_{8085}(4076,\cdot)\) \(\chi_{8085}(4286,\cdot)\) \(\chi_{8085}(4496,\cdot)\) \(\chi_{8085}(4736,\cdot)\) \(\chi_{8085}(4946,\cdot)\) \(\chi_{8085}(5051,\cdot)\) \(\chi_{8085}(5156,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((2696,4852,1816,3676)\) → \((-1,1,e\left(\frac{2}{21}\right),e\left(\frac{7}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(13\) | \(16\) | \(17\) | \(19\) | \(23\) | \(26\) | \(29\) |
| \( \chi_{ 8085 }(326, a) \) | \(1\) | \(1\) | \(e\left(\frac{71}{105}\right)\) | \(e\left(\frac{37}{105}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{74}{105}\right)\) | \(e\left(\frac{19}{105}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{109}{210}\right)\) | \(e\left(\frac{4}{35}\right)\) |