Basic properties
| Modulus: | \(85600\) | |
| Conductor: | \(85600\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(2120\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 85600.in
\(\chi_{85600}(13,\cdot)\) \(\chi_{85600}(37,\cdot)\) \(\chi_{85600}(117,\cdot)\) \(\chi_{85600}(197,\cdot)\) \(\chi_{85600}(253,\cdot)\) \(\chi_{85600}(333,\cdot)\) \(\chi_{85600}(413,\cdot)\) \(\chi_{85600}(437,\cdot)\) \(\chi_{85600}(517,\cdot)\) \(\chi_{85600}(597,\cdot)\) \(\chi_{85600}(653,\cdot)\) \(\chi_{85600}(677,\cdot)\) \(\chi_{85600}(813,\cdot)\) \(\chi_{85600}(917,\cdot)\) \(\chi_{85600}(973,\cdot)\) \(\chi_{85600}(997,\cdot)\) \(\chi_{85600}(1053,\cdot)\) \(\chi_{85600}(1213,\cdot)\) \(\chi_{85600}(1317,\cdot)\) \(\chi_{85600}(1373,\cdot)\) \(\chi_{85600}(1453,\cdot)\) \(\chi_{85600}(1477,\cdot)\) \(\chi_{85600}(1533,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{2120})$ |
| Fixed field: | Number field defined by a degree 2120 polynomial (not computed) |
Values on generators
\((26751,32101,82177,16801)\) → \((1,e\left(\frac{7}{8}\right),e\left(\frac{3}{20}\right),e\left(\frac{36}{53}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 85600 }(333, a) \) | \(-1\) | \(1\) | \(e\left(\frac{471}{2120}\right)\) | \(e\left(\frac{75}{106}\right)\) | \(e\left(\frac{471}{1060}\right)\) | \(e\left(\frac{1523}{2120}\right)\) | \(e\left(\frac{1027}{2120}\right)\) | \(e\left(\frac{157}{1060}\right)\) | \(e\left(\frac{1709}{2120}\right)\) | \(e\left(\frac{1971}{2120}\right)\) | \(e\left(\frac{7}{530}\right)\) | \(e\left(\frac{1413}{2120}\right)\) |