Basic properties
| Modulus: | \(1009\) | |
| Conductor: | \(1009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(112\) | 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 1009.w
\(\chi_{1009}(39,\cdot)\) \(\chi_{1009}(44,\cdot)\) \(\chi_{1009}(59,\cdot)\) \(\chi_{1009}(104,\cdot)\) \(\chi_{1009}(129,\cdot)\) \(\chi_{1009}(141,\cdot)\) \(\chi_{1009}(171,\cdot)\) \(\chi_{1009}(207,\cdot)\) \(\chi_{1009}(212,\cdot)\) \(\chi_{1009}(219,\cdot)\) \(\chi_{1009}(229,\cdot)\) \(\chi_{1009}(231,\cdot)\) \(\chi_{1009}(330,\cdot)\) \(\chi_{1009}(344,\cdot)\) \(\chi_{1009}(376,\cdot)\) \(\chi_{1009}(393,\cdot)\) \(\chi_{1009}(425,\cdot)\) \(\chi_{1009}(428,\cdot)\) \(\chi_{1009}(447,\cdot)\) \(\chi_{1009}(456,\cdot)\) \(\chi_{1009}(457,\cdot)\) \(\chi_{1009}(463,\cdot)\) \(\chi_{1009}(465,\cdot)\) \(\chi_{1009}(488,\cdot)\) \(\chi_{1009}(521,\cdot)\) \(\chi_{1009}(544,\cdot)\) \(\chi_{1009}(546,\cdot)\) \(\chi_{1009}(552,\cdot)\) \(\chi_{1009}(553,\cdot)\) \(\chi_{1009}(562,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{112})$ |
| Fixed field: | Number field defined by a degree 112 polynomial (not computed) |
Values on generators
\(11\) → \(e\left(\frac{51}{112}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1009 }(39, a) \) | \(-1\) | \(1\) | \(e\left(\frac{25}{56}\right)\) | \(e\left(\frac{25}{56}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{1}{56}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{19}{56}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{51}{112}\right)\) |