Basic properties
Modulus: | \(1011\) | |
Conductor: | \(1011\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(168\) | 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 1011.bk
\(\chi_{1011}(14,\cdot)\) \(\chi_{1011}(50,\cdot)\) \(\chi_{1011}(86,\cdot)\) \(\chi_{1011}(95,\cdot)\) \(\chi_{1011}(107,\cdot)\) \(\chi_{1011}(113,\cdot)\) \(\chi_{1011}(149,\cdot)\) \(\chi_{1011}(155,\cdot)\) \(\chi_{1011}(167,\cdot)\) \(\chi_{1011}(170,\cdot)\) \(\chi_{1011}(182,\cdot)\) \(\chi_{1011}(188,\cdot)\) \(\chi_{1011}(224,\cdot)\) \(\chi_{1011}(230,\cdot)\) \(\chi_{1011}(242,\cdot)\) \(\chi_{1011}(251,\cdot)\) \(\chi_{1011}(287,\cdot)\) \(\chi_{1011}(323,\cdot)\) \(\chi_{1011}(365,\cdot)\) \(\chi_{1011}(428,\cdot)\) \(\chi_{1011}(431,\cdot)\) \(\chi_{1011}(437,\cdot)\) \(\chi_{1011}(449,\cdot)\) \(\chi_{1011}(452,\cdot)\) \(\chi_{1011}(482,\cdot)\) \(\chi_{1011}(527,\cdot)\) \(\chi_{1011}(548,\cdot)\) \(\chi_{1011}(566,\cdot)\) \(\chi_{1011}(596,\cdot)\) \(\chi_{1011}(611,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{168})$ |
Fixed field: | Number field defined by a degree 168 polynomial (not computed) |
Values on generators
\((338,10)\) → \((-1,e\left(\frac{43}{168}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 1011 }(983, a) \) | \(-1\) | \(1\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{53}{56}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{43}{168}\right)\) | \(e\left(\frac{15}{56}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{59}{84}\right)\) | \(e\left(\frac{5}{21}\right)\) |