Basic properties
Modulus: | \(2009\) | |
Conductor: | \(2009\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2009.cb
\(\chi_{2009}(3,\cdot)\) \(\chi_{2009}(38,\cdot)\) \(\chi_{2009}(96,\cdot)\) \(\chi_{2009}(150,\cdot)\) \(\chi_{2009}(208,\cdot)\) \(\chi_{2009}(243,\cdot)\) \(\chi_{2009}(290,\cdot)\) \(\chi_{2009}(355,\cdot)\) \(\chi_{2009}(383,\cdot)\) \(\chi_{2009}(437,\cdot)\) \(\chi_{2009}(465,\cdot)\) \(\chi_{2009}(495,\cdot)\) \(\chi_{2009}(530,\cdot)\) \(\chi_{2009}(577,\cdot)\) \(\chi_{2009}(612,\cdot)\) \(\chi_{2009}(642,\cdot)\) \(\chi_{2009}(670,\cdot)\) \(\chi_{2009}(724,\cdot)\) \(\chi_{2009}(752,\cdot)\) \(\chi_{2009}(782,\cdot)\) \(\chi_{2009}(817,\cdot)\) \(\chi_{2009}(899,\cdot)\) \(\chi_{2009}(929,\cdot)\) \(\chi_{2009}(957,\cdot)\) \(\chi_{2009}(1039,\cdot)\) \(\chi_{2009}(1069,\cdot)\) \(\chi_{2009}(1104,\cdot)\) \(\chi_{2009}(1151,\cdot)\) \(\chi_{2009}(1186,\cdot)\) \(\chi_{2009}(1216,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{168})$ |
Fixed field: | Number field defined by a degree 168 polynomial (not computed) |
Values on generators
\((493,785)\) → \((e\left(\frac{23}{42}\right),e\left(\frac{7}{8}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 2009 }(530, a) \) | \(1\) | \(1\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{113}{168}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{37}{56}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{89}{168}\right)\) | \(e\left(\frac{109}{168}\right)\) |