Basic properties
| Modulus: | \(8049\) | |
| Conductor: | \(2683\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1341\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2683}(73,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8049.u
\(\chi_{8049}(4,\cdot)\) \(\chi_{8049}(16,\cdot)\) \(\chi_{8049}(25,\cdot)\) \(\chi_{8049}(34,\cdot)\) \(\chi_{8049}(40,\cdot)\) \(\chi_{8049}(58,\cdot)\) \(\chi_{8049}(67,\cdot)\) \(\chi_{8049}(73,\cdot)\) \(\chi_{8049}(85,\cdot)\) \(\chi_{8049}(94,\cdot)\) \(\chi_{8049}(103,\cdot)\) \(\chi_{8049}(106,\cdot)\) \(\chi_{8049}(118,\cdot)\) \(\chi_{8049}(121,\cdot)\) \(\chi_{8049}(124,\cdot)\) \(\chi_{8049}(145,\cdot)\) \(\chi_{8049}(154,\cdot)\) \(\chi_{8049}(157,\cdot)\) \(\chi_{8049}(160,\cdot)\) \(\chi_{8049}(163,\cdot)\) \(\chi_{8049}(166,\cdot)\) \(\chi_{8049}(196,\cdot)\) \(\chi_{8049}(202,\cdot)\) \(\chi_{8049}(241,\cdot)\) \(\chi_{8049}(244,\cdot)\) \(\chi_{8049}(250,\cdot)\) \(\chi_{8049}(253,\cdot)\) \(\chi_{8049}(256,\cdot)\) \(\chi_{8049}(259,\cdot)\) \(\chi_{8049}(262,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1341})$ |
| Fixed field: | Number field defined by a degree 1341 polynomial (not computed) |
Values on generators
\((2684,5368)\) → \((1,e\left(\frac{976}{1341}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 8049 }(73, a) \) | \(1\) | \(1\) | \(e\left(\frac{976}{1341}\right)\) | \(e\left(\frac{611}{1341}\right)\) | \(e\left(\frac{116}{1341}\right)\) | \(e\left(\frac{140}{447}\right)\) | \(e\left(\frac{82}{447}\right)\) | \(e\left(\frac{364}{447}\right)\) | \(e\left(\frac{565}{1341}\right)\) | \(e\left(\frac{6}{149}\right)\) | \(e\left(\frac{55}{1341}\right)\) | \(e\left(\frac{1222}{1341}\right)\) |