Basic properties
| Modulus: | \(9317\) | |
| Conductor: | \(9317\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(3630\) | 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 9317.bu
\(\chi_{9317}(17,\cdot)\) \(\chi_{9317}(19,\cdot)\) \(\chi_{9317}(24,\cdot)\) \(\chi_{9317}(52,\cdot)\) \(\chi_{9317}(61,\cdot)\) \(\chi_{9317}(68,\cdot)\) \(\chi_{9317}(73,\cdot)\) \(\chi_{9317}(96,\cdot)\) \(\chi_{9317}(101,\cdot)\) \(\chi_{9317}(117,\cdot)\) \(\chi_{9317}(129,\cdot)\) \(\chi_{9317}(138,\cdot)\) \(\chi_{9317}(145,\cdot)\) \(\chi_{9317}(150,\cdot)\) \(\chi_{9317}(171,\cdot)\) \(\chi_{9317}(173,\cdot)\) \(\chi_{9317}(178,\cdot)\) \(\chi_{9317}(194,\cdot)\) \(\chi_{9317}(206,\cdot)\) \(\chi_{9317}(222,\cdot)\) \(\chi_{9317}(227,\cdot)\) \(\chi_{9317}(248,\cdot)\) \(\chi_{9317}(250,\cdot)\) \(\chi_{9317}(255,\cdot)\) \(\chi_{9317}(271,\cdot)\) \(\chi_{9317}(283,\cdot)\) \(\chi_{9317}(292,\cdot)\) \(\chi_{9317}(299,\cdot)\) \(\chi_{9317}(304,\cdot)\) \(\chi_{9317}(325,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1815})$ |
| Fixed field: | Number field defined by a degree 3630 polynomial (not computed) |
Values on generators
\((2663,7988)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{359}{1210}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
| \( \chi_{ 9317 }(325, a) \) | \(1\) | \(1\) | \(e\left(\frac{2287}{3630}\right)\) | \(e\left(\frac{151}{330}\right)\) | \(e\left(\frac{472}{1815}\right)\) | \(e\left(\frac{1543}{3630}\right)\) | \(e\left(\frac{53}{605}\right)\) | \(e\left(\frac{1077}{1210}\right)\) | \(e\left(\frac{151}{165}\right)\) | \(e\left(\frac{20}{363}\right)\) | \(e\left(\frac{521}{726}\right)\) | \(e\left(\frac{502}{605}\right)\) |