Basic properties
| Modulus: | \(2004\) | |
| 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 \(\chi_{668}(43,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2004.p
\(\chi_{2004}(43,\cdot)\) \(\chi_{2004}(55,\cdot)\) \(\chi_{2004}(67,\cdot)\) \(\chi_{2004}(79,\cdot)\) \(\chi_{2004}(91,\cdot)\) \(\chi_{2004}(103,\cdot)\) \(\chi_{2004}(139,\cdot)\) \(\chi_{2004}(151,\cdot)\) \(\chi_{2004}(163,\cdot)\) \(\chi_{2004}(187,\cdot)\) \(\chi_{2004}(235,\cdot)\) \(\chi_{2004}(247,\cdot)\) \(\chi_{2004}(259,\cdot)\) \(\chi_{2004}(271,\cdot)\) \(\chi_{2004}(307,\cdot)\) \(\chi_{2004}(331,\cdot)\) \(\chi_{2004}(379,\cdot)\) \(\chi_{2004}(403,\cdot)\) \(\chi_{2004}(439,\cdot)\) \(\chi_{2004}(451,\cdot)\) \(\chi_{2004}(463,\cdot)\) \(\chi_{2004}(487,\cdot)\) \(\chi_{2004}(499,\cdot)\) \(\chi_{2004}(511,\cdot)\) \(\chi_{2004}(535,\cdot)\) \(\chi_{2004}(547,\cdot)\) \(\chi_{2004}(571,\cdot)\) \(\chi_{2004}(583,\cdot)\) \(\chi_{2004}(607,\cdot)\) \(\chi_{2004}(619,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{83})$ |
| Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((1003,1337,673)\) → \((-1,1,e\left(\frac{87}{166}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 2004 }(43, a) \) | \(1\) | \(1\) | \(e\left(\frac{87}{166}\right)\) | \(e\left(\frac{57}{166}\right)\) | \(e\left(\frac{29}{166}\right)\) | \(e\left(\frac{163}{166}\right)\) | \(e\left(\frac{129}{166}\right)\) | \(e\left(\frac{149}{166}\right)\) | \(e\left(\frac{32}{83}\right)\) | \(e\left(\frac{4}{83}\right)\) | \(e\left(\frac{51}{83}\right)\) | \(e\left(\frac{111}{166}\right)\) |