Basic properties
| Modulus: | \(100315\) | |
| Conductor: | \(20063\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(20062\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{20063}(21,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 100315.t
\(\chi_{100315}(21,\cdot)\) \(\chi_{100315}(41,\cdot)\) \(\chi_{100315}(51,\cdot)\) \(\chi_{100315}(56,\cdot)\) \(\chi_{100315}(86,\cdot)\) \(\chi_{100315}(91,\cdot)\) \(\chi_{100315}(126,\cdot)\) \(\chi_{100315}(131,\cdot)\) \(\chi_{100315}(136,\cdot)\) \(\chi_{100315}(161,\cdot)\) \(\chi_{100315}(181,\cdot)\) \(\chi_{100315}(191,\cdot)\) \(\chi_{100315}(206,\cdot)\) \(\chi_{100315}(221,\cdot)\) \(\chi_{100315}(231,\cdot)\) \(\chi_{100315}(236,\cdot)\) \(\chi_{100315}(246,\cdot)\) \(\chi_{100315}(266,\cdot)\) \(\chi_{100315}(311,\cdot)\) \(\chi_{100315}(316,\cdot)\) \(\chi_{100315}(326,\cdot)\) \(\chi_{100315}(336,\cdot)\) \(\chi_{100315}(356,\cdot)\) \(\chi_{100315}(366,\cdot)\) \(\chi_{100315}(371,\cdot)\) \(\chi_{100315}(381,\cdot)\) \(\chi_{100315}(391,\cdot)\) \(\chi_{100315}(401,\cdot)\) \(\chi_{100315}(421,\cdot)\) \(\chi_{100315}(451,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{10031})$ |
| Fixed field: | Number field defined by a degree 20062 polynomial (not computed) |
Values on generators
\((40127,40131)\) → \((1,e\left(\frac{4443}{20062}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 100315 }(21, a) \) | \(-1\) | \(1\) | \(e\left(\frac{440}{1433}\right)\) | \(e\left(\frac{9619}{10031}\right)\) | \(e\left(\frac{880}{1433}\right)\) | \(e\left(\frac{2668}{10031}\right)\) | \(e\left(\frac{65}{20062}\right)\) | \(e\left(\frac{1320}{1433}\right)\) | \(e\left(\frac{9207}{10031}\right)\) | \(e\left(\frac{2117}{10031}\right)\) | \(e\left(\frac{5748}{10031}\right)\) | \(e\left(\frac{2948}{10031}\right)\) |