Basic properties
Modulus: | \(2004\) | |
Conductor: | \(2004\) | 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 2004.k
\(\chi_{2004}(23,\cdot)\) \(\chi_{2004}(35,\cdot)\) \(\chi_{2004}(59,\cdot)\) \(\chi_{2004}(71,\cdot)\) \(\chi_{2004}(83,\cdot)\) \(\chi_{2004}(95,\cdot)\) \(\chi_{2004}(119,\cdot)\) \(\chi_{2004}(131,\cdot)\) \(\chi_{2004}(143,\cdot)\) \(\chi_{2004}(155,\cdot)\) \(\chi_{2004}(227,\cdot)\) \(\chi_{2004}(287,\cdot)\) \(\chi_{2004}(323,\cdot)\) \(\chi_{2004}(347,\cdot)\) \(\chi_{2004}(371,\cdot)\) \(\chi_{2004}(407,\cdot)\) \(\chi_{2004}(443,\cdot)\) \(\chi_{2004}(479,\cdot)\) \(\chi_{2004}(527,\cdot)\) \(\chi_{2004}(575,\cdot)\) \(\chi_{2004}(587,\cdot)\) \(\chi_{2004}(611,\cdot)\) \(\chi_{2004}(635,\cdot)\) \(\chi_{2004}(647,\cdot)\) \(\chi_{2004}(659,\cdot)\) \(\chi_{2004}(683,\cdot)\) \(\chi_{2004}(707,\cdot)\) \(\chi_{2004}(719,\cdot)\) \(\chi_{2004}(779,\cdot)\) \(\chi_{2004}(791,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{83})$ |
Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((1003,1337,673)\) → \((-1,-1,e\left(\frac{143}{166}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 2004 }(527, a) \) | \(-1\) | \(1\) | \(e\left(\frac{30}{83}\right)\) | \(e\left(\frac{25}{166}\right)\) | \(e\left(\frac{10}{83}\right)\) | \(e\left(\frac{121}{166}\right)\) | \(e\left(\frac{13}{83}\right)\) | \(e\left(\frac{77}{166}\right)\) | \(e\left(\frac{47}{166}\right)\) | \(e\left(\frac{60}{83}\right)\) | \(e\left(\frac{119}{166}\right)\) | \(e\left(\frac{5}{166}\right)\) |