Basic properties
| Modulus: | \(100315\) | |
| Conductor: | \(100315\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(2866\) | 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 100315.p
\(\chi_{100315}(4,\cdot)\) \(\chi_{100315}(64,\cdot)\) \(\chi_{100315}(94,\cdot)\) \(\chi_{100315}(174,\cdot)\) \(\chi_{100315}(199,\cdot)\) \(\chi_{100315}(274,\cdot)\) \(\chi_{100315}(479,\cdot)\) \(\chi_{100315}(584,\cdot)\) \(\chi_{100315}(634,\cdot)\) \(\chi_{100315}(714,\cdot)\) \(\chi_{100315}(754,\cdot)\) \(\chi_{100315}(759,\cdot)\) \(\chi_{100315}(844,\cdot)\) \(\chi_{100315}(899,\cdot)\) \(\chi_{100315}(1024,\cdot)\) \(\chi_{100315}(1124,\cdot)\) \(\chi_{100315}(1254,\cdot)\) \(\chi_{100315}(1329,\cdot)\) \(\chi_{100315}(1394,\cdot)\) \(\chi_{100315}(1504,\cdot)\) \(\chi_{100315}(1539,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{1433})$ |
| Fixed field: | Number field defined by a degree 2866 polynomial (not computed) |
Values on generators
\((40127,40131)\) → \((-1,e\left(\frac{643}{1433}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 100315 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{399}{2866}\right)\) | \(e\left(\frac{2513}{2866}\right)\) | \(e\left(\frac{399}{1433}\right)\) | \(e\left(\frac{23}{1433}\right)\) | \(e\left(\frac{2113}{2866}\right)\) | \(e\left(\frac{1197}{2866}\right)\) | \(e\left(\frac{1080}{1433}\right)\) | \(e\left(\frac{1093}{1433}\right)\) | \(e\left(\frac{445}{2866}\right)\) | \(e\left(\frac{1385}{2866}\right)\) |