Basic properties
Modulus: | \(1183\) | |
Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1183.cb
\(\chi_{1183}(6,\cdot)\) \(\chi_{1183}(20,\cdot)\) \(\chi_{1183}(41,\cdot)\) \(\chi_{1183}(76,\cdot)\) \(\chi_{1183}(97,\cdot)\) \(\chi_{1183}(111,\cdot)\) \(\chi_{1183}(132,\cdot)\) \(\chi_{1183}(167,\cdot)\) \(\chi_{1183}(202,\cdot)\) \(\chi_{1183}(223,\cdot)\) \(\chi_{1183}(279,\cdot)\) \(\chi_{1183}(293,\cdot)\) \(\chi_{1183}(314,\cdot)\) \(\chi_{1183}(349,\cdot)\) \(\chi_{1183}(370,\cdot)\) \(\chi_{1183}(384,\cdot)\) \(\chi_{1183}(405,\cdot)\) \(\chi_{1183}(440,\cdot)\) \(\chi_{1183}(461,\cdot)\) \(\chi_{1183}(475,\cdot)\) \(\chi_{1183}(496,\cdot)\) \(\chi_{1183}(531,\cdot)\) \(\chi_{1183}(552,\cdot)\) \(\chi_{1183}(566,\cdot)\) \(\chi_{1183}(622,\cdot)\) \(\chi_{1183}(643,\cdot)\) \(\chi_{1183}(678,\cdot)\) \(\chi_{1183}(713,\cdot)\) \(\chi_{1183}(734,\cdot)\) \(\chi_{1183}(748,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((339,1016)\) → \((-1,e\left(\frac{77}{156}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 1183 }(1098, a) \) | \(1\) | \(1\) | \(e\left(\frac{77}{156}\right)\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{31}{156}\right)\) | \(e\left(\frac{25}{52}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{131}{156}\right)\) | \(e\left(\frac{9}{13}\right)\) |