Basic properties
| Modulus: | \(28900\) | |
| Conductor: | \(7225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(680\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{7225}(2089,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 28900.ff
\(\chi_{28900}(9,\cdot)\) \(\chi_{28900}(189,\cdot)\) \(\chi_{28900}(229,\cdot)\) \(\chi_{28900}(389,\cdot)\) \(\chi_{28900}(529,\cdot)\) \(\chi_{28900}(569,\cdot)\) \(\chi_{28900}(689,\cdot)\) \(\chi_{28900}(729,\cdot)\) \(\chi_{28900}(869,\cdot)\) \(\chi_{28900}(909,\cdot)\) \(\chi_{28900}(1029,\cdot)\) \(\chi_{28900}(1069,\cdot)\) \(\chi_{28900}(1209,\cdot)\) \(\chi_{28900}(1369,\cdot)\) \(\chi_{28900}(1409,\cdot)\) \(\chi_{28900}(1589,\cdot)\) \(\chi_{28900}(1709,\cdot)\) \(\chi_{28900}(1929,\cdot)\) \(\chi_{28900}(2089,\cdot)\) \(\chi_{28900}(2229,\cdot)\) \(\chi_{28900}(2269,\cdot)\) \(\chi_{28900}(2389,\cdot)\) \(\chi_{28900}(2429,\cdot)\) \(\chi_{28900}(2569,\cdot)\) \(\chi_{28900}(2609,\cdot)\) \(\chi_{28900}(2729,\cdot)\) \(\chi_{28900}(2769,\cdot)\) \(\chi_{28900}(2909,\cdot)\) \(\chi_{28900}(3109,\cdot)\) \(\chi_{28900}(3409,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{680})$ |
| Fixed field: | Number field defined by a degree 680 polynomial (not computed) |
Values on generators
\((14451,24277,23701)\) → \((1,e\left(\frac{3}{10}\right),e\left(\frac{107}{136}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 28900 }(2089, a) \) | \(1\) | \(1\) | \(e\left(\frac{603}{680}\right)\) | \(e\left(\frac{61}{136}\right)\) | \(e\left(\frac{263}{340}\right)\) | \(e\left(\frac{609}{680}\right)\) | \(e\left(\frac{77}{85}\right)\) | \(e\left(\frac{141}{340}\right)\) | \(e\left(\frac{57}{170}\right)\) | \(e\left(\frac{509}{680}\right)\) | \(e\left(\frac{449}{680}\right)\) | \(e\left(\frac{643}{680}\right)\) |