Basic properties
Modulus: | \(1157\) | |
Conductor: | \(1157\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(88\) | 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.bs
\(\chi_{1157}(31,\cdot)\) \(\chi_{1157}(70,\cdot)\) \(\chi_{1157}(86,\cdot)\) \(\chi_{1157}(112,\cdot)\) \(\chi_{1157}(148,\cdot)\) \(\chi_{1157}(164,\cdot)\) \(\chi_{1157}(213,\cdot)\) \(\chi_{1157}(252,\cdot)\) \(\chi_{1157}(281,\cdot)\) \(\chi_{1157}(330,\cdot)\) \(\chi_{1157}(333,\cdot)\) \(\chi_{1157}(343,\cdot)\) \(\chi_{1157}(359,\cdot)\) \(\chi_{1157}(369,\cdot)\) \(\chi_{1157}(382,\cdot)\) \(\chi_{1157}(460,\cdot)\) \(\chi_{1157}(499,\cdot)\) \(\chi_{1157}(528,\cdot)\) \(\chi_{1157}(541,\cdot)\) \(\chi_{1157}(564,\cdot)\) \(\chi_{1157}(567,\cdot)\) \(\chi_{1157}(580,\cdot)\) \(\chi_{1157}(642,\cdot)\) \(\chi_{1157}(671,\cdot)\) \(\chi_{1157}(681,\cdot)\) \(\chi_{1157}(684,\cdot)\) \(\chi_{1157}(736,\cdot)\) \(\chi_{1157}(772,\cdot)\) \(\chi_{1157}(863,\cdot)\) \(\chi_{1157}(866,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{88})$ |
Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\((535,92)\) → \((-i,e\left(\frac{87}{88}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1157 }(564, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{87}{88}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{49}{88}\right)\) | \(e\left(\frac{29}{88}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{13}{44}\right)\) |