Basic properties
| Modulus: | \(2004\) | |
| Conductor: | \(501\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(166\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{501}(29,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2004.n
\(\chi_{2004}(29,\cdot)\) \(\chi_{2004}(65,\cdot)\) \(\chi_{2004}(77,\cdot)\) \(\chi_{2004}(89,\cdot)\) \(\chi_{2004}(137,\cdot)\) \(\chi_{2004}(173,\cdot)\) \(\chi_{2004}(185,\cdot)\) \(\chi_{2004}(209,\cdot)\) \(\chi_{2004}(221,\cdot)\) \(\chi_{2004}(233,\cdot)\) \(\chi_{2004}(281,\cdot)\) \(\chi_{2004}(293,\cdot)\) \(\chi_{2004}(317,\cdot)\) \(\chi_{2004}(329,\cdot)\) \(\chi_{2004}(341,\cdot)\) \(\chi_{2004}(353,\cdot)\) \(\chi_{2004}(365,\cdot)\) \(\chi_{2004}(449,\cdot)\) \(\chi_{2004}(461,\cdot)\) \(\chi_{2004}(509,\cdot)\) \(\chi_{2004}(533,\cdot)\) \(\chi_{2004}(545,\cdot)\) \(\chi_{2004}(557,\cdot)\) \(\chi_{2004}(617,\cdot)\) \(\chi_{2004}(629,\cdot)\) \(\chi_{2004}(653,\cdot)\) \(\chi_{2004}(677,\cdot)\) \(\chi_{2004}(689,\cdot)\) \(\chi_{2004}(701,\cdot)\) \(\chi_{2004}(725,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{83})$ |
| Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((1003,1337,673)\) → \((1,-1,e\left(\frac{75}{83}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 2004 }(29, a) \) | \(-1\) | \(1\) | \(e\left(\frac{67}{166}\right)\) | \(e\left(\frac{52}{83}\right)\) | \(e\left(\frac{133}{166}\right)\) | \(e\left(\frac{6}{83}\right)\) | \(e\left(\frac{65}{166}\right)\) | \(e\left(\frac{34}{83}\right)\) | \(e\left(\frac{159}{166}\right)\) | \(e\left(\frac{67}{83}\right)\) | \(e\left(\frac{7}{166}\right)\) | \(e\left(\frac{27}{83}\right)\) |