Basic properties
| Modulus: | \(2004\) | |
| Conductor: | \(167\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(83\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{167}(25,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2004.i
\(\chi_{2004}(25,\cdot)\) \(\chi_{2004}(49,\cdot)\) \(\chi_{2004}(61,\cdot)\) \(\chi_{2004}(85,\cdot)\) \(\chi_{2004}(97,\cdot)\) \(\chi_{2004}(121,\cdot)\) \(\chi_{2004}(133,\cdot)\) \(\chi_{2004}(157,\cdot)\) \(\chi_{2004}(169,\cdot)\) \(\chi_{2004}(181,\cdot)\) \(\chi_{2004}(205,\cdot)\) \(\chi_{2004}(217,\cdot)\) \(\chi_{2004}(229,\cdot)\) \(\chi_{2004}(265,\cdot)\) \(\chi_{2004}(289,\cdot)\) \(\chi_{2004}(337,\cdot)\) \(\chi_{2004}(361,\cdot)\) \(\chi_{2004}(397,\cdot)\) \(\chi_{2004}(409,\cdot)\) \(\chi_{2004}(421,\cdot)\) \(\chi_{2004}(433,\cdot)\) \(\chi_{2004}(481,\cdot)\) \(\chi_{2004}(505,\cdot)\) \(\chi_{2004}(517,\cdot)\) \(\chi_{2004}(529,\cdot)\) \(\chi_{2004}(565,\cdot)\) \(\chi_{2004}(577,\cdot)\) \(\chi_{2004}(589,\cdot)\) \(\chi_{2004}(601,\cdot)\) \(\chi_{2004}(613,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{83})$ |
| Fixed field: | Number field defined by a degree 83 polynomial |
Values on generators
\((1003,1337,673)\) → \((1,1,e\left(\frac{1}{83}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 2004 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{83}\right)\) | \(e\left(\frac{35}{83}\right)\) | \(e\left(\frac{28}{83}\right)\) | \(e\left(\frac{20}{83}\right)\) | \(e\left(\frac{53}{83}\right)\) | \(e\left(\frac{58}{83}\right)\) | \(e\left(\frac{16}{83}\right)\) | \(e\left(\frac{2}{83}\right)\) | \(e\left(\frac{67}{83}\right)\) | \(e\left(\frac{7}{83}\right)\) |