Basic properties
Modulus: | \(705\) | |
Conductor: | \(705\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(92\) | 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 705.w
\(\chi_{705}(2,\cdot)\) \(\chi_{705}(8,\cdot)\) \(\chi_{705}(17,\cdot)\) \(\chi_{705}(32,\cdot)\) \(\chi_{705}(53,\cdot)\) \(\chi_{705}(68,\cdot)\) \(\chi_{705}(83,\cdot)\) \(\chi_{705}(98,\cdot)\) \(\chi_{705}(122,\cdot)\) \(\chi_{705}(128,\cdot)\) \(\chi_{705}(143,\cdot)\) \(\chi_{705}(158,\cdot)\) \(\chi_{705}(173,\cdot)\) \(\chi_{705}(197,\cdot)\) \(\chi_{705}(212,\cdot)\) \(\chi_{705}(242,\cdot)\) \(\chi_{705}(263,\cdot)\) \(\chi_{705}(272,\cdot)\) \(\chi_{705}(332,\cdot)\) \(\chi_{705}(338,\cdot)\) \(\chi_{705}(347,\cdot)\) \(\chi_{705}(353,\cdot)\) \(\chi_{705}(383,\cdot)\) \(\chi_{705}(392,\cdot)\) \(\chi_{705}(413,\cdot)\) \(\chi_{705}(437,\cdot)\) \(\chi_{705}(473,\cdot)\) \(\chi_{705}(482,\cdot)\) \(\chi_{705}(488,\cdot)\) \(\chi_{705}(497,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{92})$ |
Fixed field: | Number field defined by a degree 92 polynomial |
Values on generators
\((236,142,616)\) → \((-1,i,e\left(\frac{8}{23}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 705 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{92}\right)\) | \(e\left(\frac{1}{46}\right)\) | \(e\left(\frac{35}{92}\right)\) | \(e\left(\frac{3}{92}\right)\) | \(e\left(\frac{43}{46}\right)\) | \(e\left(\frac{53}{92}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{29}{92}\right)\) | \(e\left(\frac{7}{46}\right)\) |