Basic properties
| Modulus: | \(1336\) | |
| Conductor: | \(668\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(166\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{668}(15,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1336.p
\(\chi_{1336}(15,\cdot)\) \(\chi_{1336}(23,\cdot)\) \(\chi_{1336}(39,\cdot)\) \(\chi_{1336}(55,\cdot)\) \(\chi_{1336}(71,\cdot)\) \(\chi_{1336}(79,\cdot)\) \(\chi_{1336}(95,\cdot)\) \(\chi_{1336}(103,\cdot)\) \(\chi_{1336}(111,\cdot)\) \(\chi_{1336}(119,\cdot)\) \(\chi_{1336}(135,\cdot)\) \(\chi_{1336}(143,\cdot)\) \(\chi_{1336}(151,\cdot)\) \(\chi_{1336}(159,\cdot)\) \(\chi_{1336}(207,\cdot)\) \(\chi_{1336}(247,\cdot)\) \(\chi_{1336}(271,\cdot)\) \(\chi_{1336}(287,\cdot)\) \(\chi_{1336}(303,\cdot)\) \(\chi_{1336}(327,\cdot)\) \(\chi_{1336}(351,\cdot)\) \(\chi_{1336}(375,\cdot)\) \(\chi_{1336}(407,\cdot)\) \(\chi_{1336}(439,\cdot)\) \(\chi_{1336}(447,\cdot)\) \(\chi_{1336}(463,\cdot)\) \(\chi_{1336}(479,\cdot)\) \(\chi_{1336}(487,\cdot)\) \(\chi_{1336}(495,\cdot)\) \(\chi_{1336}(511,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{83})$ |
| Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((335,669,673)\) → \((-1,1,e\left(\frac{95}{166}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 1336 }(15, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{166}\right)\) | \(e\left(\frac{95}{166}\right)\) | \(e\left(\frac{5}{166}\right)\) | \(e\left(\frac{49}{83}\right)\) | \(e\left(\frac{87}{166}\right)\) | \(e\left(\frac{157}{166}\right)\) | \(e\left(\frac{72}{83}\right)\) | \(e\left(\frac{55}{166}\right)\) | \(e\left(\frac{115}{166}\right)\) | \(e\left(\frac{27}{83}\right)\) |