Basic properties
| Modulus: | \(1169\) | |
| Conductor: | \(167\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(83\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{167}(8,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1169.i
\(\chi_{1169}(8,\cdot)\) \(\chi_{1169}(22,\cdot)\) \(\chi_{1169}(29,\cdot)\) \(\chi_{1169}(36,\cdot)\) \(\chi_{1169}(50,\cdot)\) \(\chi_{1169}(57,\cdot)\) \(\chi_{1169}(64,\cdot)\) \(\chi_{1169}(85,\cdot)\) \(\chi_{1169}(99,\cdot)\) \(\chi_{1169}(127,\cdot)\) \(\chi_{1169}(141,\cdot)\) \(\chi_{1169}(162,\cdot)\) \(\chi_{1169}(169,\cdot)\) \(\chi_{1169}(176,\cdot)\) \(\chi_{1169}(183,\cdot)\) \(\chi_{1169}(211,\cdot)\) \(\chi_{1169}(225,\cdot)\) \(\chi_{1169}(232,\cdot)\) \(\chi_{1169}(239,\cdot)\) \(\chi_{1169}(260,\cdot)\) \(\chi_{1169}(267,\cdot)\) \(\chi_{1169}(274,\cdot)\) \(\chi_{1169}(281,\cdot)\) \(\chi_{1169}(288,\cdot)\) \(\chi_{1169}(295,\cdot)\) \(\chi_{1169}(337,\cdot)\) \(\chi_{1169}(358,\cdot)\) \(\chi_{1169}(365,\cdot)\) \(\chi_{1169}(372,\cdot)\) \(\chi_{1169}(400,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{83})$ |
| Fixed field: | Number field defined by a degree 83 polynomial |
Values on generators
\((836,673)\) → \((1,e\left(\frac{60}{83}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 1169 }(8, a) \) | \(1\) | \(1\) | \(e\left(\frac{76}{83}\right)\) | \(e\left(\frac{79}{83}\right)\) | \(e\left(\frac{69}{83}\right)\) | \(e\left(\frac{60}{83}\right)\) | \(e\left(\frac{72}{83}\right)\) | \(e\left(\frac{62}{83}\right)\) | \(e\left(\frac{75}{83}\right)\) | \(e\left(\frac{53}{83}\right)\) | \(e\left(\frac{20}{83}\right)\) | \(e\left(\frac{65}{83}\right)\) |