Basic properties
Modulus: | \(2009\) | |
Conductor: | \(2009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(140\) | 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.bz
\(\chi_{2009}(8,\cdot)\) \(\chi_{2009}(36,\cdot)\) \(\chi_{2009}(43,\cdot)\) \(\chi_{2009}(162,\cdot)\) \(\chi_{2009}(169,\cdot)\) \(\chi_{2009}(225,\cdot)\) \(\chi_{2009}(267,\cdot)\) \(\chi_{2009}(323,\cdot)\) \(\chi_{2009}(330,\cdot)\) \(\chi_{2009}(449,\cdot)\) \(\chi_{2009}(456,\cdot)\) \(\chi_{2009}(484,\cdot)\) \(\chi_{2009}(512,\cdot)\) \(\chi_{2009}(554,\cdot)\) \(\chi_{2009}(582,\cdot)\) \(\chi_{2009}(610,\cdot)\) \(\chi_{2009}(617,\cdot)\) \(\chi_{2009}(743,\cdot)\) \(\chi_{2009}(771,\cdot)\) \(\chi_{2009}(799,\cdot)\) \(\chi_{2009}(841,\cdot)\) \(\chi_{2009}(869,\cdot)\) \(\chi_{2009}(897,\cdot)\) \(\chi_{2009}(904,\cdot)\) \(\chi_{2009}(1023,\cdot)\) \(\chi_{2009}(1058,\cdot)\) \(\chi_{2009}(1086,\cdot)\) \(\chi_{2009}(1156,\cdot)\) \(\chi_{2009}(1184,\cdot)\) \(\chi_{2009}(1191,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{140})$ |
Fixed field: | Number field defined by a degree 140 polynomial (not computed) |
Values on generators
\((493,785)\) → \((e\left(\frac{4}{7}\right),e\left(\frac{7}{20}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 2009 }(267, a) \) | \(1\) | \(1\) | \(e\left(\frac{67}{70}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{109}{140}\right)\) | \(e\left(\frac{61}{70}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{127}{140}\right)\) | \(e\left(\frac{103}{140}\right)\) |