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.l
\(\chi_{1336}(3,\cdot)\) \(\chi_{1336}(11,\cdot)\) \(\chi_{1336}(19,\cdot)\) \(\chi_{1336}(27,\cdot)\) \(\chi_{1336}(75,\cdot)\) \(\chi_{1336}(99,\cdot)\) \(\chi_{1336}(107,\cdot)\) \(\chi_{1336}(115,\cdot)\) \(\chi_{1336}(147,\cdot)\) \(\chi_{1336}(171,\cdot)\) \(\chi_{1336}(179,\cdot)\) \(\chi_{1336}(195,\cdot)\) \(\chi_{1336}(203,\cdot)\) \(\chi_{1336}(211,\cdot)\) \(\chi_{1336}(243,\cdot)\) \(\chi_{1336}(251,\cdot)\) \(\chi_{1336}(267,\cdot)\) \(\chi_{1336}(275,\cdot)\) \(\chi_{1336}(283,\cdot)\) \(\chi_{1336}(291,\cdot)\) \(\chi_{1336}(299,\cdot)\) \(\chi_{1336}(355,\cdot)\) \(\chi_{1336}(363,\cdot)\) \(\chi_{1336}(395,\cdot)\) \(\chi_{1336}(411,\cdot)\) \(\chi_{1336}(419,\cdot)\) \(\chi_{1336}(427,\cdot)\) \(\chi_{1336}(467,\cdot)\) \(\chi_{1336}(475,\cdot)\) \(\chi_{1336}(491,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{83})$ |
| Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((335,669,673)\) → \((-1,-1,e\left(\frac{82}{83}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 1336 }(147, a) \) | \(-1\) | \(1\) | \(e\left(\frac{72}{83}\right)\) | \(e\left(\frac{81}{166}\right)\) | \(e\left(\frac{13}{166}\right)\) | \(e\left(\frac{61}{83}\right)\) | \(e\left(\frac{55}{83}\right)\) | \(e\left(\frac{43}{166}\right)\) | \(e\left(\frac{59}{166}\right)\) | \(e\left(\frac{30}{83}\right)\) | \(e\left(\frac{25}{83}\right)\) | \(e\left(\frac{157}{166}\right)\) |