Basic properties
| Modulus: | \(1336\) | |
| Conductor: | \(1336\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(166\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1336.j
\(\chi_{1336}(35,\cdot)\) \(\chi_{1336}(43,\cdot)\) \(\chi_{1336}(51,\cdot)\) \(\chi_{1336}(59,\cdot)\) \(\chi_{1336}(67,\cdot)\) \(\chi_{1336}(83,\cdot)\) \(\chi_{1336}(91,\cdot)\) \(\chi_{1336}(123,\cdot)\) \(\chi_{1336}(131,\cdot)\) \(\chi_{1336}(139,\cdot)\) \(\chi_{1336}(155,\cdot)\) \(\chi_{1336}(163,\cdot)\) \(\chi_{1336}(187,\cdot)\) \(\chi_{1336}(219,\cdot)\) \(\chi_{1336}(227,\cdot)\) \(\chi_{1336}(235,\cdot)\) \(\chi_{1336}(259,\cdot)\) \(\chi_{1336}(307,\cdot)\) \(\chi_{1336}(315,\cdot)\) \(\chi_{1336}(323,\cdot)\) \(\chi_{1336}(331,\cdot)\) \(\chi_{1336}(339,\cdot)\) \(\chi_{1336}(347,\cdot)\) \(\chi_{1336}(371,\cdot)\) \(\chi_{1336}(379,\cdot)\) \(\chi_{1336}(387,\cdot)\) \(\chi_{1336}(403,\cdot)\) \(\chi_{1336}(435,\cdot)\) \(\chi_{1336}(443,\cdot)\) \(\chi_{1336}(451,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{83})$ |
| Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((335,669,673)\) → \((-1,-1,e\left(\frac{87}{166}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 1336 }(43, a) \) | \(1\) | \(1\) | \(e\left(\frac{22}{83}\right)\) | \(e\left(\frac{2}{83}\right)\) | \(e\left(\frac{57}{166}\right)\) | \(e\left(\frac{44}{83}\right)\) | \(e\left(\frac{56}{83}\right)\) | \(e\left(\frac{40}{83}\right)\) | \(e\left(\frac{24}{83}\right)\) | \(e\left(\frac{129}{166}\right)\) | \(e\left(\frac{33}{83}\right)\) | \(e\left(\frac{101}{166}\right)\) |