Basic properties
| Modulus: | \(1169\) | |
| Conductor: | \(1169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(166\) | 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 1169.l
\(\chi_{1169}(6,\cdot)\) \(\chi_{1169}(27,\cdot)\) \(\chi_{1169}(48,\cdot)\) \(\chi_{1169}(62,\cdot)\) \(\chi_{1169}(76,\cdot)\) \(\chi_{1169}(97,\cdot)\) \(\chi_{1169}(132,\cdot)\) \(\chi_{1169}(174,\cdot)\) \(\chi_{1169}(181,\cdot)\) \(\chi_{1169}(188,\cdot)\) \(\chi_{1169}(195,\cdot)\) \(\chi_{1169}(209,\cdot)\) \(\chi_{1169}(216,\cdot)\) \(\chi_{1169}(223,\cdot)\) \(\chi_{1169}(230,\cdot)\) \(\chi_{1169}(244,\cdot)\) \(\chi_{1169}(251,\cdot)\) \(\chi_{1169}(265,\cdot)\) \(\chi_{1169}(279,\cdot)\) \(\chi_{1169}(293,\cdot)\) \(\chi_{1169}(300,\cdot)\) \(\chi_{1169}(314,\cdot)\) \(\chi_{1169}(321,\cdot)\) \(\chi_{1169}(342,\cdot)\) \(\chi_{1169}(356,\cdot)\) \(\chi_{1169}(363,\cdot)\) \(\chi_{1169}(370,\cdot)\) \(\chi_{1169}(384,\cdot)\) \(\chi_{1169}(391,\cdot)\) \(\chi_{1169}(398,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{83})$ |
| Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((836,673)\) → \((-1,e\left(\frac{67}{83}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 1169 }(6, a) \) | \(-1\) | \(1\) | \(e\left(\frac{24}{83}\right)\) | \(e\left(\frac{63}{166}\right)\) | \(e\left(\frac{48}{83}\right)\) | \(e\left(\frac{51}{166}\right)\) | \(e\left(\frac{111}{166}\right)\) | \(e\left(\frac{72}{83}\right)\) | \(e\left(\frac{63}{83}\right)\) | \(e\left(\frac{99}{166}\right)\) | \(e\left(\frac{50}{83}\right)\) | \(e\left(\frac{159}{166}\right)\) |