Basic properties
| Modulus: | \(85600\) | |
| Conductor: | \(2675\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(530\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2675}(2254,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 85600.gp
\(\chi_{85600}(129,\cdot)\) \(\chi_{85600}(609,\cdot)\) \(\chi_{85600}(769,\cdot)\) \(\chi_{85600}(929,\cdot)\) \(\chi_{85600}(1409,\cdot)\) \(\chi_{85600}(1569,\cdot)\) \(\chi_{85600}(1729,\cdot)\) \(\chi_{85600}(1889,\cdot)\) \(\chi_{85600}(2369,\cdot)\) \(\chi_{85600}(2529,\cdot)\) \(\chi_{85600}(3169,\cdot)\) \(\chi_{85600}(3489,\cdot)\) \(\chi_{85600}(4129,\cdot)\) \(\chi_{85600}(4609,\cdot)\) \(\chi_{85600}(4929,\cdot)\) \(\chi_{85600}(5089,\cdot)\) \(\chi_{85600}(5409,\cdot)\) \(\chi_{85600}(5569,\cdot)\) \(\chi_{85600}(5729,\cdot)\) \(\chi_{85600}(6529,\cdot)\) \(\chi_{85600}(6689,\cdot)\) \(\chi_{85600}(7009,\cdot)\) \(\chi_{85600}(7969,\cdot)\) \(\chi_{85600}(8129,\cdot)\) \(\chi_{85600}(8289,\cdot)\) \(\chi_{85600}(9569,\cdot)\) \(\chi_{85600}(9889,\cdot)\) \(\chi_{85600}(10369,\cdot)\) \(\chi_{85600}(10529,\cdot)\) \(\chi_{85600}(10689,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{265})$ |
| Fixed field: | Number field defined by a degree 530 polynomial (not computed) |
Values on generators
\((26751,32101,82177,16801)\) → \((1,1,e\left(\frac{1}{10}\right),e\left(\frac{43}{106}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 85600 }(4929, a) \) | \(-1\) | \(1\) | \(e\left(\frac{51}{530}\right)\) | \(e\left(\frac{50}{53}\right)\) | \(e\left(\frac{51}{265}\right)\) | \(e\left(\frac{139}{265}\right)\) | \(e\left(\frac{307}{530}\right)\) | \(e\left(\frac{17}{265}\right)\) | \(e\left(\frac{117}{265}\right)\) | \(e\left(\frac{21}{530}\right)\) | \(e\left(\frac{133}{530}\right)\) | \(e\left(\frac{153}{530}\right)\) |