Basic properties
| Modulus: | \(1161\) | |
| Conductor: | \(1161\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(126\) | 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 1161.ce
\(\chi_{1161}(106,\cdot)\) \(\chi_{1161}(112,\cdot)\) \(\chi_{1161}(157,\cdot)\) \(\chi_{1161}(202,\cdot)\) \(\chi_{1161}(205,\cdot)\) \(\chi_{1161}(277,\cdot)\) \(\chi_{1161}(292,\cdot)\) \(\chi_{1161}(304,\cdot)\) \(\chi_{1161}(313,\cdot)\) \(\chi_{1161}(319,\cdot)\) \(\chi_{1161}(349,\cdot)\) \(\chi_{1161}(373,\cdot)\) \(\chi_{1161}(493,\cdot)\) \(\chi_{1161}(499,\cdot)\) \(\chi_{1161}(544,\cdot)\) \(\chi_{1161}(589,\cdot)\) \(\chi_{1161}(592,\cdot)\) \(\chi_{1161}(664,\cdot)\) \(\chi_{1161}(679,\cdot)\) \(\chi_{1161}(691,\cdot)\) \(\chi_{1161}(700,\cdot)\) \(\chi_{1161}(706,\cdot)\) \(\chi_{1161}(736,\cdot)\) \(\chi_{1161}(760,\cdot)\) \(\chi_{1161}(880,\cdot)\) \(\chi_{1161}(886,\cdot)\) \(\chi_{1161}(931,\cdot)\) \(\chi_{1161}(976,\cdot)\) \(\chi_{1161}(979,\cdot)\) \(\chi_{1161}(1051,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((947,433)\) → \((e\left(\frac{5}{9}\right),e\left(\frac{37}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 1161 }(106, a) \) | \(-1\) | \(1\) | \(e\left(\frac{43}{126}\right)\) | \(e\left(\frac{43}{63}\right)\) | \(e\left(\frac{101}{126}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{41}{63}\right)\) | \(e\left(\frac{40}{63}\right)\) | \(e\left(\frac{4}{63}\right)\) | \(e\left(\frac{23}{63}\right)\) |