Basic properties
| Modulus: | \(3006\) | |
| Conductor: | \(167\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(83\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{167}(32,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3006.i
\(\chi_{3006}(19,\cdot)\) \(\chi_{3006}(127,\cdot)\) \(\chi_{3006}(181,\cdot)\) \(\chi_{3006}(199,\cdot)\) \(\chi_{3006}(217,\cdot)\) \(\chi_{3006}(289,\cdot)\) \(\chi_{3006}(343,\cdot)\) \(\chi_{3006}(361,\cdot)\) \(\chi_{3006}(397,\cdot)\) \(\chi_{3006}(415,\cdot)\) \(\chi_{3006}(433,\cdot)\) \(\chi_{3006}(505,\cdot)\) \(\chi_{3006}(523,\cdot)\) \(\chi_{3006}(559,\cdot)\) \(\chi_{3006}(577,\cdot)\) \(\chi_{3006}(595,\cdot)\) \(\chi_{3006}(613,\cdot)\) \(\chi_{3006}(631,\cdot)\) \(\chi_{3006}(757,\cdot)\) \(\chi_{3006}(775,\cdot)\) \(\chi_{3006}(847,\cdot)\) \(\chi_{3006}(883,\cdot)\) \(\chi_{3006}(901,\cdot)\) \(\chi_{3006}(919,\cdot)\) \(\chi_{3006}(1009,\cdot)\) \(\chi_{3006}(1027,\cdot)\) \(\chi_{3006}(1063,\cdot)\) \(\chi_{3006}(1099,\cdot)\) \(\chi_{3006}(1117,\cdot)\) \(\chi_{3006}(1135,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{83})$ |
| Fixed field: | Number field defined by a degree 83 polynomial |
Values on generators
\((335,1675)\) → \((1,e\left(\frac{17}{83}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 3006 }(199, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{83}\right)\) | \(e\left(\frac{14}{83}\right)\) | \(e\left(\frac{61}{83}\right)\) | \(e\left(\frac{8}{83}\right)\) | \(e\left(\frac{71}{83}\right)\) | \(e\left(\frac{73}{83}\right)\) | \(e\left(\frac{23}{83}\right)\) | \(e\left(\frac{34}{83}\right)\) | \(e\left(\frac{60}{83}\right)\) | \(e\left(\frac{36}{83}\right)\) |