Basic properties
Modulus: | \(8036\) | |
Conductor: | \(2009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(140\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{2009}(169,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8036.dy
\(\chi_{8036}(169,\cdot)\) \(\chi_{8036}(225,\cdot)\) \(\chi_{8036}(449,\cdot)\) \(\chi_{8036}(617,\cdot)\) \(\chi_{8036}(841,\cdot)\) \(\chi_{8036}(869,\cdot)\) \(\chi_{8036}(897,\cdot)\) \(\chi_{8036}(1317,\cdot)\) \(\chi_{8036}(1345,\cdot)\) \(\chi_{8036}(1597,\cdot)\) \(\chi_{8036}(1989,\cdot)\) \(\chi_{8036}(2017,\cdot)\) \(\chi_{8036}(2045,\cdot)\) \(\chi_{8036}(2465,\cdot)\) \(\chi_{8036}(2493,\cdot)\) \(\chi_{8036}(2521,\cdot)\) \(\chi_{8036}(2913,\cdot)\) \(\chi_{8036}(3165,\cdot)\) \(\chi_{8036}(3193,\cdot)\) \(\chi_{8036}(3613,\cdot)\) \(\chi_{8036}(3641,\cdot)\) \(\chi_{8036}(3669,\cdot)\) \(\chi_{8036}(3893,\cdot)\) \(\chi_{8036}(4061,\cdot)\) \(\chi_{8036}(4285,\cdot)\) \(\chi_{8036}(4341,\cdot)\) \(\chi_{8036}(4761,\cdot)\) \(\chi_{8036}(4789,\cdot)\) \(\chi_{8036}(4817,\cdot)\) \(\chi_{8036}(5041,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{140})$ |
Fixed field: | Number field defined by a degree 140 polynomial (not computed) |
Values on generators
\((4019,493,785)\) → \((1,e\left(\frac{4}{7}\right),e\left(\frac{11}{20}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
\( \chi_{ 8036 }(169, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{71}{140}\right)\) | \(e\left(\frac{127}{140}\right)\) | \(e\left(\frac{69}{140}\right)\) | \(e\left(\frac{61}{140}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{12}{35}\right)\) |