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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1127.z
\(\chi_{1127}(6,\cdot)\) \(\chi_{1127}(13,\cdot)\) \(\chi_{1127}(27,\cdot)\) \(\chi_{1127}(41,\cdot)\) \(\chi_{1127}(55,\cdot)\) \(\chi_{1127}(62,\cdot)\) \(\chi_{1127}(104,\cdot)\) \(\chi_{1127}(118,\cdot)\) \(\chi_{1127}(167,\cdot)\) \(\chi_{1127}(174,\cdot)\) \(\chi_{1127}(188,\cdot)\) \(\chi_{1127}(202,\cdot)\) \(\chi_{1127}(209,\cdot)\) \(\chi_{1127}(216,\cdot)\) \(\chi_{1127}(223,\cdot)\) \(\chi_{1127}(265,\cdot)\) \(\chi_{1127}(279,\cdot)\) \(\chi_{1127}(307,\cdot)\) \(\chi_{1127}(328,\cdot)\) \(\chi_{1127}(335,\cdot)\) \(\chi_{1127}(349,\cdot)\) \(\chi_{1127}(363,\cdot)\) \(\chi_{1127}(370,\cdot)\) \(\chi_{1127}(377,\cdot)\) \(\chi_{1127}(384,\cdot)\) \(\chi_{1127}(426,\cdot)\) \(\chi_{1127}(468,\cdot)\) \(\chi_{1127}(496,\cdot)\) \(\chi_{1127}(510,\cdot)\) \(\chi_{1127}(524,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{77})$ |
Fixed field: | Number field defined by a degree 154 polynomial (not computed) |
Values on generators
\((346,442)\) → \((e\left(\frac{9}{14}\right),e\left(\frac{5}{11}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 1127 }(55, a) \) | \(-1\) | \(1\) | \(e\left(\frac{48}{77}\right)\) | \(e\left(\frac{141}{154}\right)\) | \(e\left(\frac{19}{77}\right)\) | \(e\left(\frac{15}{154}\right)\) | \(e\left(\frac{83}{154}\right)\) | \(e\left(\frac{67}{77}\right)\) | \(e\left(\frac{64}{77}\right)\) | \(e\left(\frac{111}{154}\right)\) | \(e\left(\frac{62}{77}\right)\) | \(e\left(\frac{25}{154}\right)\) |