Basic properties
| Modulus: | \(8670\) | |
| Conductor: | \(1445\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(68\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1445}(259,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8670.bz
\(\chi_{8670}(259,\cdot)\) \(\chi_{8670}(319,\cdot)\) \(\chi_{8670}(769,\cdot)\) \(\chi_{8670}(1279,\cdot)\) \(\chi_{8670}(1339,\cdot)\) \(\chi_{8670}(1789,\cdot)\) \(\chi_{8670}(1849,\cdot)\) \(\chi_{8670}(2299,\cdot)\) \(\chi_{8670}(2359,\cdot)\) \(\chi_{8670}(2809,\cdot)\) \(\chi_{8670}(2869,\cdot)\) \(\chi_{8670}(3319,\cdot)\) \(\chi_{8670}(3379,\cdot)\) \(\chi_{8670}(3829,\cdot)\) \(\chi_{8670}(3889,\cdot)\) \(\chi_{8670}(4339,\cdot)\) \(\chi_{8670}(4399,\cdot)\) \(\chi_{8670}(4849,\cdot)\) \(\chi_{8670}(4909,\cdot)\) \(\chi_{8670}(5359,\cdot)\) \(\chi_{8670}(5419,\cdot)\) \(\chi_{8670}(5869,\cdot)\) \(\chi_{8670}(5929,\cdot)\) \(\chi_{8670}(6379,\cdot)\) \(\chi_{8670}(6439,\cdot)\) \(\chi_{8670}(6889,\cdot)\) \(\chi_{8670}(6949,\cdot)\) \(\chi_{8670}(7399,\cdot)\) \(\chi_{8670}(7459,\cdot)\) \(\chi_{8670}(7909,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{68})$ |
| Fixed field: | Number field defined by a degree 68 polynomial |
Values on generators
\((2891,6937,6361)\) → \((1,-1,e\left(\frac{3}{68}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 8670 }(259, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{68}\right)\) | \(e\left(\frac{1}{68}\right)\) | \(e\left(\frac{5}{34}\right)\) | \(e\left(\frac{21}{34}\right)\) | \(e\left(\frac{23}{68}\right)\) | \(e\left(\frac{35}{68}\right)\) | \(e\left(\frac{27}{68}\right)\) | \(e\left(\frac{13}{68}\right)\) | \(e\left(\frac{37}{68}\right)\) | \(e\left(\frac{8}{17}\right)\) |