Basic properties
| Modulus: | \(1157\) | |
| Conductor: | \(1157\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(264\) | 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 1157.cb
\(\chi_{1157}(6,\cdot)\) \(\chi_{1157}(28,\cdot)\) \(\chi_{1157}(41,\cdot)\) \(\chi_{1157}(59,\cdot)\) \(\chi_{1157}(63,\cdot)\) \(\chi_{1157}(76,\cdot)\) \(\chi_{1157}(102,\cdot)\) \(\chi_{1157}(115,\cdot)\) \(\chi_{1157}(124,\cdot)\) \(\chi_{1157}(132,\cdot)\) \(\chi_{1157}(145,\cdot)\) \(\chi_{1157}(163,\cdot)\) \(\chi_{1157}(171,\cdot)\) \(\chi_{1157}(175,\cdot)\) \(\chi_{1157}(184,\cdot)\) \(\chi_{1157}(193,\cdot)\) \(\chi_{1157}(201,\cdot)\) \(\chi_{1157}(232,\cdot)\) \(\chi_{1157}(241,\cdot)\) \(\chi_{1157}(253,\cdot)\) \(\chi_{1157}(254,\cdot)\) \(\chi_{1157}(280,\cdot)\) \(\chi_{1157}(293,\cdot)\) \(\chi_{1157}(297,\cdot)\) \(\chi_{1157}(353,\cdot)\) \(\chi_{1157}(370,\cdot)\) \(\chi_{1157}(371,\cdot)\) \(\chi_{1157}(375,\cdot)\) \(\chi_{1157}(379,\cdot)\) \(\chi_{1157}(410,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{264})$ |
| Fixed field: | Number field defined by a degree 264 polynomial (not computed) |
Values on generators
\((535,92)\) → \((e\left(\frac{5}{12}\right),e\left(\frac{45}{88}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1157 }(175, a) \) | \(1\) | \(1\) | \(e\left(\frac{79}{132}\right)\) | \(e\left(\frac{47}{264}\right)\) | \(e\left(\frac{13}{66}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{205}{264}\right)\) | \(e\left(\frac{1}{264}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{47}{132}\right)\) | \(e\left(\frac{19}{132}\right)\) | \(e\left(\frac{115}{132}\right)\) |