Basic properties
Modulus: | \(1336\) | |
Conductor: | \(167\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(83\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{167}(9,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1336.i
\(\chi_{1336}(9,\cdot)\) \(\chi_{1336}(25,\cdot)\) \(\chi_{1336}(33,\cdot)\) \(\chi_{1336}(49,\cdot)\) \(\chi_{1336}(57,\cdot)\) \(\chi_{1336}(65,\cdot)\) \(\chi_{1336}(81,\cdot)\) \(\chi_{1336}(89,\cdot)\) \(\chi_{1336}(97,\cdot)\) \(\chi_{1336}(121,\cdot)\) \(\chi_{1336}(137,\cdot)\) \(\chi_{1336}(169,\cdot)\) \(\chi_{1336}(185,\cdot)\) \(\chi_{1336}(209,\cdot)\) \(\chi_{1336}(217,\cdot)\) \(\chi_{1336}(225,\cdot)\) \(\chi_{1336}(233,\cdot)\) \(\chi_{1336}(265,\cdot)\) \(\chi_{1336}(281,\cdot)\) \(\chi_{1336}(289,\cdot)\) \(\chi_{1336}(297,\cdot)\) \(\chi_{1336}(321,\cdot)\) \(\chi_{1336}(329,\cdot)\) \(\chi_{1336}(337,\cdot)\) \(\chi_{1336}(345,\cdot)\) \(\chi_{1336}(353,\cdot)\) \(\chi_{1336}(361,\cdot)\) \(\chi_{1336}(409,\cdot)\) \(\chi_{1336}(433,\cdot)\) \(\chi_{1336}(441,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{83})$ |
Fixed field: | Number field defined by a degree 83 polynomial |
Values on generators
\((335,669,673)\) → \((1,1,e\left(\frac{11}{83}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 1336 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{38}{83}\right)\) | \(e\left(\frac{11}{83}\right)\) | \(e\left(\frac{53}{83}\right)\) | \(e\left(\frac{76}{83}\right)\) | \(e\left(\frac{59}{83}\right)\) | \(e\left(\frac{54}{83}\right)\) | \(e\left(\frac{49}{83}\right)\) | \(e\left(\frac{2}{83}\right)\) | \(e\left(\frac{57}{83}\right)\) | \(e\left(\frac{8}{83}\right)\) |