Basic properties
Modulus: | \(712\) | |
Conductor: | \(89\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(88\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{89}(43,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 712.be
\(\chi_{712}(33,\cdot)\) \(\chi_{712}(41,\cdot)\) \(\chi_{712}(65,\cdot)\) \(\chi_{712}(113,\cdot)\) \(\chi_{712}(137,\cdot)\) \(\chi_{712}(145,\cdot)\) \(\chi_{712}(185,\cdot)\) \(\chi_{712}(193,\cdot)\) \(\chi_{712}(201,\cdot)\) \(\chi_{712}(209,\cdot)\) \(\chi_{712}(241,\cdot)\) \(\chi_{712}(273,\cdot)\) \(\chi_{712}(281,\cdot)\) \(\chi_{712}(297,\cdot)\) \(\chi_{712}(305,\cdot)\) \(\chi_{712}(313,\cdot)\) \(\chi_{712}(321,\cdot)\) \(\chi_{712}(329,\cdot)\) \(\chi_{712}(337,\cdot)\) \(\chi_{712}(353,\cdot)\) \(\chi_{712}(369,\cdot)\) \(\chi_{712}(385,\cdot)\) \(\chi_{712}(417,\cdot)\) \(\chi_{712}(473,\cdot)\) \(\chi_{712}(505,\cdot)\) \(\chi_{712}(521,\cdot)\) \(\chi_{712}(537,\cdot)\) \(\chi_{712}(553,\cdot)\) \(\chi_{712}(561,\cdot)\) \(\chi_{712}(569,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{88})$ |
Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\((535,357,537)\) → \((1,1,e\left(\frac{29}{88}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 712 }(577, a) \) | \(-1\) | \(1\) | \(e\left(\frac{29}{88}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{61}{88}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{51}{88}\right)\) | \(e\left(\frac{35}{88}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{47}{88}\right)\) | \(e\left(\frac{1}{44}\right)\) |