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.o
\(\chi_{1336}(21,\cdot)\) \(\chi_{1336}(29,\cdot)\) \(\chi_{1336}(61,\cdot)\) \(\chi_{1336}(77,\cdot)\) \(\chi_{1336}(85,\cdot)\) \(\chi_{1336}(93,\cdot)\) \(\chi_{1336}(133,\cdot)\) \(\chi_{1336}(141,\cdot)\) \(\chi_{1336}(157,\cdot)\) \(\chi_{1336}(173,\cdot)\) \(\chi_{1336}(181,\cdot)\) \(\chi_{1336}(189,\cdot)\) \(\chi_{1336}(205,\cdot)\) \(\chi_{1336}(221,\cdot)\) \(\chi_{1336}(229,\cdot)\) \(\chi_{1336}(261,\cdot)\) \(\chi_{1336}(293,\cdot)\) \(\chi_{1336}(317,\cdot)\) \(\chi_{1336}(341,\cdot)\) \(\chi_{1336}(365,\cdot)\) \(\chi_{1336}(381,\cdot)\) \(\chi_{1336}(397,\cdot)\) \(\chi_{1336}(421,\cdot)\) \(\chi_{1336}(461,\cdot)\) \(\chi_{1336}(509,\cdot)\) \(\chi_{1336}(517,\cdot)\) \(\chi_{1336}(525,\cdot)\) \(\chi_{1336}(533,\cdot)\) \(\chi_{1336}(549,\cdot)\) \(\chi_{1336}(557,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{83})$ |
Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((335,669,673)\) → \((1,-1,e\left(\frac{33}{83}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 1336 }(61, a) \) | \(1\) | \(1\) | \(e\left(\frac{145}{166}\right)\) | \(e\left(\frac{149}{166}\right)\) | \(e\left(\frac{76}{83}\right)\) | \(e\left(\frac{62}{83}\right)\) | \(e\left(\frac{105}{166}\right)\) | \(e\left(\frac{75}{166}\right)\) | \(e\left(\frac{64}{83}\right)\) | \(e\left(\frac{6}{83}\right)\) | \(e\left(\frac{93}{166}\right)\) | \(e\left(\frac{131}{166}\right)\) |