Basic properties
| Modulus: | \(1127\) | |
| Conductor: | \(1127\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(154\) | 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.ba
\(\chi_{1127}(20,\cdot)\) \(\chi_{1127}(34,\cdot)\) \(\chi_{1127}(76,\cdot)\) \(\chi_{1127}(83,\cdot)\) \(\chi_{1127}(90,\cdot)\) \(\chi_{1127}(111,\cdot)\) \(\chi_{1127}(125,\cdot)\) \(\chi_{1127}(132,\cdot)\) \(\chi_{1127}(153,\cdot)\) \(\chi_{1127}(181,\cdot)\) \(\chi_{1127}(237,\cdot)\) \(\chi_{1127}(251,\cdot)\) \(\chi_{1127}(258,\cdot)\) \(\chi_{1127}(272,\cdot)\) \(\chi_{1127}(286,\cdot)\) \(\chi_{1127}(314,\cdot)\) \(\chi_{1127}(356,\cdot)\) \(\chi_{1127}(398,\cdot)\) \(\chi_{1127}(405,\cdot)\) \(\chi_{1127}(412,\cdot)\) \(\chi_{1127}(419,\cdot)\) \(\chi_{1127}(433,\cdot)\) \(\chi_{1127}(447,\cdot)\) \(\chi_{1127}(454,\cdot)\) \(\chi_{1127}(475,\cdot)\) \(\chi_{1127}(503,\cdot)\) \(\chi_{1127}(517,\cdot)\) \(\chi_{1127}(559,\cdot)\) \(\chi_{1127}(566,\cdot)\) \(\chi_{1127}(573,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{77})$ |
| Fixed field: | Number field defined by a degree 154 polynomial (not computed) |
Values on generators
\((346,442)\) → \((e\left(\frac{11}{14}\right),e\left(\frac{9}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 1127 }(356, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{77}\right)\) | \(e\left(\frac{51}{154}\right)\) | \(e\left(\frac{38}{77}\right)\) | \(e\left(\frac{15}{77}\right)\) | \(e\left(\frac{89}{154}\right)\) | \(e\left(\frac{57}{77}\right)\) | \(e\left(\frac{51}{77}\right)\) | \(e\left(\frac{34}{77}\right)\) | \(e\left(\frac{17}{154}\right)\) | \(e\left(\frac{127}{154}\right)\) |