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 \(\chi_{371}(58,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1113.bu
\(\chi_{1113}(58,\cdot)\) \(\chi_{1113}(67,\cdot)\) \(\chi_{1113}(79,\cdot)\) \(\chi_{1113}(88,\cdot)\) \(\chi_{1113}(109,\cdot)\) \(\chi_{1113}(151,\cdot)\) \(\chi_{1113}(193,\cdot)\) \(\chi_{1113}(214,\cdot)\) \(\chi_{1113}(226,\cdot)\) \(\chi_{1113}(247,\cdot)\) \(\chi_{1113}(268,\cdot)\) \(\chi_{1113}(277,\cdot)\) \(\chi_{1113}(298,\cdot)\) \(\chi_{1113}(310,\cdot)\) \(\chi_{1113}(340,\cdot)\) \(\chi_{1113}(352,\cdot)\) \(\chi_{1113}(373,\cdot)\) \(\chi_{1113}(403,\cdot)\) \(\chi_{1113}(436,\cdot)\) \(\chi_{1113}(445,\cdot)\) \(\chi_{1113}(457,\cdot)\) \(\chi_{1113}(499,\cdot)\) \(\chi_{1113}(508,\cdot)\) \(\chi_{1113}(550,\cdot)\) \(\chi_{1113}(562,\cdot)\) \(\chi_{1113}(571,\cdot)\) \(\chi_{1113}(604,\cdot)\) \(\chi_{1113}(634,\cdot)\) \(\chi_{1113}(655,\cdot)\) \(\chi_{1113}(667,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((743,955,1009)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{47}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 1113 }(58, a) \) | \(-1\) | \(1\) | \(e\left(\frac{89}{156}\right)\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{23}{156}\right)\) | \(e\left(\frac{37}{52}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{29}{78}\right)\) | \(e\left(\frac{17}{156}\right)\) |