Basic properties
Modulus: | \(1048\) | |
Conductor: | \(131\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(130\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{131}(17,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1048.bf
\(\chi_{1048}(17,\cdot)\) \(\chi_{1048}(57,\cdot)\) \(\chi_{1048}(97,\cdot)\) \(\chi_{1048}(137,\cdot)\) \(\chi_{1048}(145,\cdot)\) \(\chi_{1048}(153,\cdot)\) \(\chi_{1048}(161,\cdot)\) \(\chi_{1048}(185,\cdot)\) \(\chi_{1048}(241,\cdot)\) \(\chi_{1048}(249,\cdot)\) \(\chi_{1048}(257,\cdot)\) \(\chi_{1048}(329,\cdot)\) \(\chi_{1048}(345,\cdot)\) \(\chi_{1048}(377,\cdot)\) \(\chi_{1048}(401,\cdot)\) \(\chi_{1048}(433,\cdot)\) \(\chi_{1048}(449,\cdot)\) \(\chi_{1048}(465,\cdot)\) \(\chi_{1048}(481,\cdot)\) \(\chi_{1048}(489,\cdot)\) \(\chi_{1048}(497,\cdot)\) \(\chi_{1048}(513,\cdot)\) \(\chi_{1048}(521,\cdot)\) \(\chi_{1048}(553,\cdot)\) \(\chi_{1048}(561,\cdot)\) \(\chi_{1048}(609,\cdot)\) \(\chi_{1048}(617,\cdot)\) \(\chi_{1048}(657,\cdot)\) \(\chi_{1048}(665,\cdot)\) \(\chi_{1048}(681,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{65})$ |
Fixed field: | Number field defined by a degree 130 polynomial (not computed) |
Values on generators
\((263,525,657)\) → \((1,1,e\left(\frac{43}{130}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 1048 }(17, a) \) | \(-1\) | \(1\) | \(e\left(\frac{53}{65}\right)\) | \(e\left(\frac{14}{65}\right)\) | \(e\left(\frac{49}{65}\right)\) | \(e\left(\frac{41}{65}\right)\) | \(e\left(\frac{34}{65}\right)\) | \(e\left(\frac{62}{65}\right)\) | \(e\left(\frac{2}{65}\right)\) | \(e\left(\frac{29}{130}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{37}{65}\right)\) |