Basic properties
Modulus: | \(2011\) | |
Conductor: | \(2011\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(134\) | 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 2011.j
\(\chi_{2011}(8,\cdot)\) \(\chi_{2011}(60,\cdot)\) \(\chi_{2011}(97,\cdot)\) \(\chi_{2011}(147,\cdot)\) \(\chi_{2011}(175,\cdot)\) \(\chi_{2011}(213,\cdot)\) \(\chi_{2011}(233,\cdot)\) \(\chi_{2011}(268,\cdot)\) \(\chi_{2011}(307,\cdot)\) \(\chi_{2011}(378,\cdot)\) \(\chi_{2011}(386,\cdot)\) \(\chi_{2011}(410,\cdot)\) \(\chi_{2011}(418,\cdot)\) \(\chi_{2011}(422,\cdot)\) \(\chi_{2011}(450,\cdot)\) \(\chi_{2011}(512,\cdot)\) \(\chi_{2011}(557,\cdot)\) \(\chi_{2011}(572,\cdot)\) \(\chi_{2011}(592,\cdot)\) \(\chi_{2011}(597,\cdot)\) \(\chi_{2011}(609,\cdot)\) \(\chi_{2011}(611,\cdot)\) \(\chi_{2011}(646,\cdot)\) \(\chi_{2011}(678,\cdot)\) \(\chi_{2011}(725,\cdot)\) \(\chi_{2011}(742,\cdot)\) \(\chi_{2011}(767,\cdot)\) \(\chi_{2011}(823,\cdot)\) \(\chi_{2011}(824,\cdot)\) \(\chi_{2011}(835,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{67})$ |
Fixed field: | Number field defined by a degree 134 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{105}{134}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 2011 }(611, a) \) | \(-1\) | \(1\) | \(e\left(\frac{131}{134}\right)\) | \(e\left(\frac{105}{134}\right)\) | \(e\left(\frac{64}{67}\right)\) | \(e\left(\frac{26}{67}\right)\) | \(e\left(\frac{51}{67}\right)\) | \(e\left(\frac{125}{134}\right)\) | \(e\left(\frac{125}{134}\right)\) | \(e\left(\frac{38}{67}\right)\) | \(e\left(\frac{49}{134}\right)\) | \(e\left(\frac{77}{134}\right)\) |