Basic properties
Modulus: | \(712\) | |
Conductor: | \(712\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(88\) | 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 712.bf
\(\chi_{712}(3,\cdot)\) \(\chi_{712}(19,\cdot)\) \(\chi_{712}(27,\cdot)\) \(\chi_{712}(35,\cdot)\) \(\chi_{712}(43,\cdot)\) \(\chi_{712}(51,\cdot)\) \(\chi_{712}(59,\cdot)\) \(\chi_{712}(75,\cdot)\) \(\chi_{712}(83,\cdot)\) \(\chi_{712}(115,\cdot)\) \(\chi_{712}(147,\cdot)\) \(\chi_{712}(155,\cdot)\) \(\chi_{712}(163,\cdot)\) \(\chi_{712}(171,\cdot)\) \(\chi_{712}(211,\cdot)\) \(\chi_{712}(219,\cdot)\) \(\chi_{712}(243,\cdot)\) \(\chi_{712}(291,\cdot)\) \(\chi_{712}(315,\cdot)\) \(\chi_{712}(323,\cdot)\) \(\chi_{712}(363,\cdot)\) \(\chi_{712}(371,\cdot)\) \(\chi_{712}(379,\cdot)\) \(\chi_{712}(387,\cdot)\) \(\chi_{712}(419,\cdot)\) \(\chi_{712}(451,\cdot)\) \(\chi_{712}(459,\cdot)\) \(\chi_{712}(475,\cdot)\) \(\chi_{712}(483,\cdot)\) \(\chi_{712}(491,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{88})$ |
Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\((535,357,537)\) → \((-1,-1,e\left(\frac{85}{88}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 712 }(211, a) \) | \(1\) | \(1\) | \(e\left(\frac{85}{88}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{65}{88}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{63}{88}\right)\) | \(e\left(\frac{7}{88}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{71}{88}\right)\) | \(e\left(\frac{31}{44}\right)\) |