Basic properties
Modulus: | \(2006\) | |
Conductor: | \(1003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(232\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1003}(9,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2006.r
\(\chi_{2006}(9,\cdot)\) \(\chi_{2006}(15,\cdot)\) \(\chi_{2006}(19,\cdot)\) \(\chi_{2006}(25,\cdot)\) \(\chi_{2006}(49,\cdot)\) \(\chi_{2006}(53,\cdot)\) \(\chi_{2006}(87,\cdot)\) \(\chi_{2006}(121,\cdot)\) \(\chi_{2006}(127,\cdot)\) \(\chi_{2006}(145,\cdot)\) \(\chi_{2006}(189,\cdot)\) \(\chi_{2006}(213,\cdot)\) \(\chi_{2006}(223,\cdot)\) \(\chi_{2006}(253,\cdot)\) \(\chi_{2006}(257,\cdot)\) \(\chi_{2006}(263,\cdot)\) \(\chi_{2006}(281,\cdot)\) \(\chi_{2006}(287,\cdot)\) \(\chi_{2006}(315,\cdot)\) \(\chi_{2006}(321,\cdot)\) \(\chi_{2006}(331,\cdot)\) \(\chi_{2006}(359,\cdot)\) \(\chi_{2006}(383,\cdot)\) \(\chi_{2006}(389,\cdot)\) \(\chi_{2006}(399,\cdot)\) \(\chi_{2006}(417,\cdot)\) \(\chi_{2006}(433,\cdot)\) \(\chi_{2006}(461,\cdot)\) \(\chi_{2006}(491,\cdot)\) \(\chi_{2006}(501,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{232})$ |
Fixed field: | Number field defined by a degree 232 polynomial (not computed) |
Values on generators
\((1771,1123)\) → \((e\left(\frac{1}{8}\right),e\left(\frac{21}{29}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
\( \chi_{ 2006 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{77}{232}\right)\) | \(e\left(\frac{225}{232}\right)\) | \(e\left(\frac{95}{232}\right)\) | \(e\left(\frac{77}{116}\right)\) | \(e\left(\frac{227}{232}\right)\) | \(e\left(\frac{5}{58}\right)\) | \(e\left(\frac{35}{116}\right)\) | \(e\left(\frac{31}{116}\right)\) | \(e\left(\frac{43}{58}\right)\) | \(e\left(\frac{171}{232}\right)\) |