Basic properties
Modulus: | \(1113\) | |
Conductor: | \(371\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{371}(19,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1113.bs
\(\chi_{1113}(19,\cdot)\) \(\chi_{1113}(31,\cdot)\) \(\chi_{1113}(61,\cdot)\) \(\chi_{1113}(73,\cdot)\) \(\chi_{1113}(94,\cdot)\) \(\chi_{1113}(103,\cdot)\) \(\chi_{1113}(124,\cdot)\) \(\chi_{1113}(145,\cdot)\) \(\chi_{1113}(157,\cdot)\) \(\chi_{1113}(178,\cdot)\) \(\chi_{1113}(220,\cdot)\) \(\chi_{1113}(262,\cdot)\) \(\chi_{1113}(283,\cdot)\) \(\chi_{1113}(292,\cdot)\) \(\chi_{1113}(304,\cdot)\) \(\chi_{1113}(313,\cdot)\) \(\chi_{1113}(376,\cdot)\) \(\chi_{1113}(397,\cdot)\) \(\chi_{1113}(451,\cdot)\) \(\chi_{1113}(472,\cdot)\) \(\chi_{1113}(535,\cdot)\) \(\chi_{1113}(544,\cdot)\) \(\chi_{1113}(556,\cdot)\) \(\chi_{1113}(565,\cdot)\) \(\chi_{1113}(586,\cdot)\) \(\chi_{1113}(628,\cdot)\) \(\chi_{1113}(670,\cdot)\) \(\chi_{1113}(691,\cdot)\) \(\chi_{1113}(703,\cdot)\) \(\chi_{1113}(724,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((743,955,1009)\) → \((1,e\left(\frac{5}{6}\right),e\left(\frac{37}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 1113 }(19, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{156}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{95}{156}\right)\) | \(e\left(\frac{7}{52}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{77}{156}\right)\) |