Basic properties
| Modulus: | \(100315\) | |
| Conductor: | \(100315\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(20062\) | 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 100315.v
\(\chi_{100315}(14,\cdot)\) \(\chi_{100315}(34,\cdot)\) \(\chi_{100315}(59,\cdot)\) \(\chi_{100315}(79,\cdot)\) \(\chi_{100315}(84,\cdot)\) \(\chi_{100315}(89,\cdot)\) \(\chi_{100315}(129,\cdot)\) \(\chi_{100315}(139,\cdot)\) \(\chi_{100315}(149,\cdot)\) \(\chi_{100315}(154,\cdot)\) \(\chi_{100315}(164,\cdot)\) \(\chi_{100315}(179,\cdot)\) \(\chi_{100315}(189,\cdot)\) \(\chi_{100315}(204,\cdot)\) \(\chi_{100315}(224,\cdot)\) \(\chi_{100315}(239,\cdot)\) \(\chi_{100315}(254,\cdot)\) \(\chi_{100315}(259,\cdot)\) \(\chi_{100315}(269,\cdot)\) \(\chi_{100315}(309,\cdot)\) \(\chi_{100315}(329,\cdot)\) \(\chi_{100315}(344,\cdot)\) \(\chi_{100315}(354,\cdot)\) \(\chi_{100315}(364,\cdot)\) \(\chi_{100315}(369,\cdot)\) \(\chi_{100315}(374,\cdot)\) \(\chi_{100315}(389,\cdot)\) \(\chi_{100315}(394,\cdot)\) \(\chi_{100315}(399,\cdot)\) \(\chi_{100315}(409,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{10031})$ |
| Fixed field: | Number field defined by a degree 20062 polynomial (not computed) |
Values on generators
\((40127,40131)\) → \((-1,e\left(\frac{14625}{20062}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 100315 }(34, a) \) | \(-1\) | \(1\) | \(e\left(\frac{529}{2866}\right)\) | \(e\left(\frac{8741}{20062}\right)\) | \(e\left(\frac{529}{1433}\right)\) | \(e\left(\frac{6222}{10031}\right)\) | \(e\left(\frac{4689}{10031}\right)\) | \(e\left(\frac{1587}{2866}\right)\) | \(e\left(\frac{8741}{10031}\right)\) | \(e\left(\frac{8208}{10031}\right)\) | \(e\left(\frac{16147}{20062}\right)\) | \(e\left(\frac{9133}{20062}\right)\) |