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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1336.m
\(\chi_{1336}(5,\cdot)\) \(\chi_{1336}(13,\cdot)\) \(\chi_{1336}(37,\cdot)\) \(\chi_{1336}(45,\cdot)\) \(\chi_{1336}(53,\cdot)\) \(\chi_{1336}(69,\cdot)\) \(\chi_{1336}(101,\cdot)\) \(\chi_{1336}(109,\cdot)\) \(\chi_{1336}(117,\cdot)\) \(\chi_{1336}(125,\cdot)\) \(\chi_{1336}(149,\cdot)\) \(\chi_{1336}(165,\cdot)\) \(\chi_{1336}(197,\cdot)\) \(\chi_{1336}(213,\cdot)\) \(\chi_{1336}(237,\cdot)\) \(\chi_{1336}(245,\cdot)\) \(\chi_{1336}(253,\cdot)\) \(\chi_{1336}(269,\cdot)\) \(\chi_{1336}(277,\cdot)\) \(\chi_{1336}(285,\cdot)\) \(\chi_{1336}(301,\cdot)\) \(\chi_{1336}(309,\cdot)\) \(\chi_{1336}(325,\cdot)\) \(\chi_{1336}(349,\cdot)\) \(\chi_{1336}(357,\cdot)\) \(\chi_{1336}(373,\cdot)\) \(\chi_{1336}(389,\cdot)\) \(\chi_{1336}(405,\cdot)\) \(\chi_{1336}(413,\cdot)\) \(\chi_{1336}(429,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{83})$ |
| Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((335,669,673)\) → \((1,-1,e\left(\frac{133}{166}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 1336 }(1237, a) \) | \(-1\) | \(1\) | \(e\left(\frac{135}{166}\right)\) | \(e\left(\frac{25}{83}\right)\) | \(e\left(\frac{45}{83}\right)\) | \(e\left(\frac{52}{83}\right)\) | \(e\left(\frac{155}{166}\right)\) | \(e\left(\frac{2}{83}\right)\) | \(e\left(\frac{19}{166}\right)\) | \(e\left(\frac{77}{166}\right)\) | \(e\left(\frac{161}{166}\right)\) | \(e\left(\frac{59}{166}\right)\) |