Basic properties
Modulus: | \(2009\) | |
Conductor: | \(2009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(840\) | 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.cl
\(\chi_{2009}(12,\cdot)\) \(\chi_{2009}(17,\cdot)\) \(\chi_{2009}(24,\cdot)\) \(\chi_{2009}(26,\cdot)\) \(\chi_{2009}(47,\cdot)\) \(\chi_{2009}(52,\cdot)\) \(\chi_{2009}(54,\cdot)\) \(\chi_{2009}(75,\cdot)\) \(\chi_{2009}(89,\cdot)\) \(\chi_{2009}(94,\cdot)\) \(\chi_{2009}(101,\cdot)\) \(\chi_{2009}(108,\cdot)\) \(\chi_{2009}(110,\cdot)\) \(\chi_{2009}(136,\cdot)\) \(\chi_{2009}(138,\cdot)\) \(\chi_{2009}(145,\cdot)\) \(\chi_{2009}(152,\cdot)\) \(\chi_{2009}(157,\cdot)\) \(\chi_{2009}(171,\cdot)\) \(\chi_{2009}(192,\cdot)\) \(\chi_{2009}(194,\cdot)\) \(\chi_{2009}(199,\cdot)\) \(\chi_{2009}(220,\cdot)\) \(\chi_{2009}(222,\cdot)\) \(\chi_{2009}(229,\cdot)\) \(\chi_{2009}(234,\cdot)\) \(\chi_{2009}(257,\cdot)\) \(\chi_{2009}(299,\cdot)\) \(\chi_{2009}(304,\cdot)\) \(\chi_{2009}(306,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{840})$ |
Fixed field: | Number field defined by a degree 840 polynomial (not computed) |
Values on generators
\((493,785)\) → \((e\left(\frac{41}{42}\right),e\left(\frac{13}{40}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 2009 }(229, a) \) | \(1\) | \(1\) | \(e\left(\frac{349}{420}\right)\) | \(e\left(\frac{143}{168}\right)\) | \(e\left(\frac{139}{210}\right)\) | \(e\left(\frac{193}{420}\right)\) | \(e\left(\frac{191}{280}\right)\) | \(e\left(\frac{69}{140}\right)\) | \(e\left(\frac{59}{84}\right)\) | \(e\left(\frac{61}{210}\right)\) | \(e\left(\frac{19}{840}\right)\) | \(e\left(\frac{431}{840}\right)\) |