Basic properties
| Modulus: | \(1183\) | |
| Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169}(15,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1183.cf
\(\chi_{1183}(15,\cdot)\) \(\chi_{1183}(50,\cdot)\) \(\chi_{1183}(71,\cdot)\) \(\chi_{1183}(85,\cdot)\) \(\chi_{1183}(106,\cdot)\) \(\chi_{1183}(141,\cdot)\) \(\chi_{1183}(162,\cdot)\) \(\chi_{1183}(176,\cdot)\) \(\chi_{1183}(197,\cdot)\) \(\chi_{1183}(232,\cdot)\) \(\chi_{1183}(253,\cdot)\) \(\chi_{1183}(267,\cdot)\) \(\chi_{1183}(288,\cdot)\) \(\chi_{1183}(323,\cdot)\) \(\chi_{1183}(344,\cdot)\) \(\chi_{1183}(358,\cdot)\) \(\chi_{1183}(379,\cdot)\) \(\chi_{1183}(414,\cdot)\) \(\chi_{1183}(435,\cdot)\) \(\chi_{1183}(449,\cdot)\) \(\chi_{1183}(470,\cdot)\) \(\chi_{1183}(505,\cdot)\) \(\chi_{1183}(540,\cdot)\) \(\chi_{1183}(561,\cdot)\) \(\chi_{1183}(617,\cdot)\) \(\chi_{1183}(631,\cdot)\) \(\chi_{1183}(652,\cdot)\) \(\chi_{1183}(687,\cdot)\) \(\chi_{1183}(708,\cdot)\) \(\chi_{1183}(722,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((339,1016)\) → \((1,e\left(\frac{133}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 1183 }(15, a) \) | \(-1\) | \(1\) | \(e\left(\frac{133}{156}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{35}{52}\right)\) | \(e\left(\frac{89}{156}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{127}{156}\right)\) | \(e\left(\frac{11}{26}\right)\) |