Basic properties
| Modulus: | \(8670\) | |
| Conductor: | \(4335\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(68\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4335}(203,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8670.bv
\(\chi_{8670}(203,\cdot)\) \(\chi_{8670}(407,\cdot)\) \(\chi_{8670}(713,\cdot)\) \(\chi_{8670}(917,\cdot)\) \(\chi_{8670}(1223,\cdot)\) \(\chi_{8670}(1427,\cdot)\) \(\chi_{8670}(1937,\cdot)\) \(\chi_{8670}(2243,\cdot)\) \(\chi_{8670}(2447,\cdot)\) \(\chi_{8670}(2753,\cdot)\) \(\chi_{8670}(2957,\cdot)\) \(\chi_{8670}(3263,\cdot)\) \(\chi_{8670}(3773,\cdot)\) \(\chi_{8670}(3977,\cdot)\) \(\chi_{8670}(4283,\cdot)\) \(\chi_{8670}(4487,\cdot)\) \(\chi_{8670}(4793,\cdot)\) \(\chi_{8670}(4997,\cdot)\) \(\chi_{8670}(5303,\cdot)\) \(\chi_{8670}(5507,\cdot)\) \(\chi_{8670}(5813,\cdot)\) \(\chi_{8670}(6017,\cdot)\) \(\chi_{8670}(6323,\cdot)\) \(\chi_{8670}(6527,\cdot)\) \(\chi_{8670}(6833,\cdot)\) \(\chi_{8670}(7037,\cdot)\) \(\chi_{8670}(7343,\cdot)\) \(\chi_{8670}(7547,\cdot)\) \(\chi_{8670}(7853,\cdot)\) \(\chi_{8670}(8057,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{68})$ |
| Fixed field: | Number field defined by a degree 68 polynomial |
Values on generators
\((2891,6937,6361)\) → \((-1,-i,e\left(\frac{1}{34}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 8670 }(203, a) \) | \(1\) | \(1\) | \(e\left(\frac{21}{68}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{1}{68}\right)\) | \(e\left(\frac{31}{34}\right)\) | \(e\left(\frac{21}{68}\right)\) | \(e\left(\frac{23}{34}\right)\) | \(e\left(\frac{9}{34}\right)\) | \(e\left(\frac{37}{68}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{61}{68}\right)\) |