Basic properties
Modulus: | \(1157\) | |
Conductor: | \(89\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(88\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{89}(26,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1157.bq
\(\chi_{1157}(14,\cdot)\) \(\chi_{1157}(27,\cdot)\) \(\chi_{1157}(66,\cdot)\) \(\chi_{1157}(92,\cdot)\) \(\chi_{1157}(118,\cdot)\) \(\chi_{1157}(209,\cdot)\) \(\chi_{1157}(248,\cdot)\) \(\chi_{1157}(261,\cdot)\) \(\chi_{1157}(274,\cdot)\) \(\chi_{1157}(300,\cdot)\) \(\chi_{1157}(313,\cdot)\) \(\chi_{1157}(326,\cdot)\) \(\chi_{1157}(391,\cdot)\) \(\chi_{1157}(404,\cdot)\) \(\chi_{1157}(417,\cdot)\) \(\chi_{1157}(430,\cdot)\) \(\chi_{1157}(469,\cdot)\) \(\chi_{1157}(508,\cdot)\) \(\chi_{1157}(521,\cdot)\) \(\chi_{1157}(547,\cdot)\) \(\chi_{1157}(560,\cdot)\) \(\chi_{1157}(599,\cdot)\) \(\chi_{1157}(638,\cdot)\) \(\chi_{1157}(651,\cdot)\) \(\chi_{1157}(664,\cdot)\) \(\chi_{1157}(677,\cdot)\) \(\chi_{1157}(742,\cdot)\) \(\chi_{1157}(755,\cdot)\) \(\chi_{1157}(768,\cdot)\) \(\chi_{1157}(794,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{88})$ |
Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\((535,92)\) → \((1,e\left(\frac{39}{88}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1157 }(560, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{39}{88}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{47}{88}\right)\) | \(e\left(\frac{79}{88}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{5}{22}\right)\) |