Basic properties
| Modulus: | \(100315\) | |
| Conductor: | \(20063\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1433\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{20063}(16,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 100315.m
\(\chi_{100315}(16,\cdot)\) \(\chi_{100315}(146,\cdot)\) \(\chi_{100315}(211,\cdot)\) \(\chi_{100315}(256,\cdot)\) \(\chi_{100315}(281,\cdot)\) \(\chi_{100315}(376,\cdot)\) \(\chi_{100315}(446,\cdot)\) \(\chi_{100315}(696,\cdot)\) \(\chi_{100315}(726,\cdot)\) \(\chi_{100315}(796,\cdot)\) \(\chi_{100315}(891,\cdot)\) \(\chi_{100315}(941,\cdot)\) \(\chi_{100315}(971,\cdot)\) \(\chi_{100315}(981,\cdot)\) \(\chi_{100315}(1096,\cdot)\) \(\chi_{100315}(1201,\cdot)\) \(\chi_{100315}(1226,\cdot)\) \(\chi_{100315}(1301,\cdot)\) \(\chi_{100315}(1311,\cdot)\) \(\chi_{100315}(1461,\cdot)\) \(\chi_{100315}(1506,\cdot)\) \(\chi_{100315}(1751,\cdot)\) \(\chi_{100315}(1801,\cdot)\) \(\chi_{100315}(1826,\cdot)\) \(\chi_{100315}(1916,\cdot)\) \(\chi_{100315}(1981,\cdot)\) \(\chi_{100315}(2086,\cdot)\) \(\chi_{100315}(2126,\cdot)\) \(\chi_{100315}(2166,\cdot)\) \(\chi_{100315}(2181,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1433})$ |
| Fixed field: | Number field defined by a degree 1433 polynomial (not computed) |
Values on generators
\((40127,40131)\) → \((1,e\left(\frac{1286}{1433}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 100315 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{399}{1433}\right)\) | \(e\left(\frac{1080}{1433}\right)\) | \(e\left(\frac{798}{1433}\right)\) | \(e\left(\frac{46}{1433}\right)\) | \(e\left(\frac{680}{1433}\right)\) | \(e\left(\frac{1197}{1433}\right)\) | \(e\left(\frac{727}{1433}\right)\) | \(e\left(\frac{753}{1433}\right)\) | \(e\left(\frac{445}{1433}\right)\) | \(e\left(\frac{1385}{1433}\right)\) |