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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1157.cd
\(\chi_{1157}(3,\cdot)\) \(\chi_{1157}(29,\cdot)\) \(\chi_{1157}(35,\cdot)\) \(\chi_{1157}(48,\cdot)\) \(\chi_{1157}(61,\cdot)\) \(\chi_{1157}(74,\cdot)\) \(\chi_{1157}(113,\cdot)\) \(\chi_{1157}(120,\cdot)\) \(\chi_{1157}(152,\cdot)\) \(\chi_{1157}(159,\cdot)\) \(\chi_{1157}(165,\cdot)\) \(\chi_{1157}(172,\cdot)\) \(\chi_{1157}(185,\cdot)\) \(\chi_{1157}(191,\cdot)\) \(\chi_{1157}(204,\cdot)\) \(\chi_{1157}(211,\cdot)\) \(\chi_{1157}(224,\cdot)\) \(\chi_{1157}(237,\cdot)\) \(\chi_{1157}(243,\cdot)\) \(\chi_{1157}(282,\cdot)\) \(\chi_{1157}(295,\cdot)\) \(\chi_{1157}(302,\cdot)\) \(\chi_{1157}(308,\cdot)\) \(\chi_{1157}(315,\cdot)\) \(\chi_{1157}(321,\cdot)\) \(\chi_{1157}(328,\cdot)\) \(\chi_{1157}(341,\cdot)\) \(\chi_{1157}(380,\cdot)\) \(\chi_{1157}(386,\cdot)\) \(\chi_{1157}(399,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{264})$ |
Fixed field: | Number field defined by a degree 264 polynomial (not computed) |
Values on generators
\((535,92)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{81}{88}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1157 }(1075, a) \) | \(-1\) | \(1\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{155}{264}\right)\) | \(e\left(\frac{26}{33}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{259}{264}\right)\) | \(e\left(\frac{235}{264}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{23}{132}\right)\) | \(e\left(\frac{109}{132}\right)\) | \(e\left(\frac{65}{66}\right)\) |