Basic properties
| Modulus: | \(1127\) | |
| Conductor: | \(1127\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(77\) | 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 1127.y
\(\chi_{1127}(8,\cdot)\) \(\chi_{1127}(29,\cdot)\) \(\chi_{1127}(36,\cdot)\) \(\chi_{1127}(64,\cdot)\) \(\chi_{1127}(71,\cdot)\) \(\chi_{1127}(78,\cdot)\) \(\chi_{1127}(85,\cdot)\) \(\chi_{1127}(127,\cdot)\) \(\chi_{1127}(141,\cdot)\) \(\chi_{1127}(169,\cdot)\) \(\chi_{1127}(190,\cdot)\) \(\chi_{1127}(211,\cdot)\) \(\chi_{1127}(225,\cdot)\) \(\chi_{1127}(232,\cdot)\) \(\chi_{1127}(239,\cdot)\) \(\chi_{1127}(288,\cdot)\) \(\chi_{1127}(302,\cdot)\) \(\chi_{1127}(330,\cdot)\) \(\chi_{1127}(351,\cdot)\) \(\chi_{1127}(358,\cdot)\) \(\chi_{1127}(372,\cdot)\) \(\chi_{1127}(386,\cdot)\) \(\chi_{1127}(400,\cdot)\) \(\chi_{1127}(407,\cdot)\) \(\chi_{1127}(449,\cdot)\) \(\chi_{1127}(463,\cdot)\) \(\chi_{1127}(512,\cdot)\) \(\chi_{1127}(519,\cdot)\) \(\chi_{1127}(533,\cdot)\) \(\chi_{1127}(547,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{77})$ |
| Fixed field: | Number field defined by a degree 77 polynomial |
Values on generators
\((346,442)\) → \((e\left(\frac{3}{7}\right),e\left(\frac{9}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 1127 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{60}{77}\right)\) | \(e\left(\frac{40}{77}\right)\) | \(e\left(\frac{43}{77}\right)\) | \(e\left(\frac{19}{77}\right)\) | \(e\left(\frac{23}{77}\right)\) | \(e\left(\frac{26}{77}\right)\) | \(e\left(\frac{3}{77}\right)\) | \(e\left(\frac{2}{77}\right)\) | \(e\left(\frac{39}{77}\right)\) | \(e\left(\frac{6}{77}\right)\) |