Basic properties
Modulus: | \(712\) | |
Conductor: | \(356\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(88\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{356}(35,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 712.bd
\(\chi_{712}(7,\cdot)\) \(\chi_{712}(15,\cdot)\) \(\chi_{712}(23,\cdot)\) \(\chi_{712}(31,\cdot)\) \(\chi_{712}(63,\cdot)\) \(\chi_{712}(95,\cdot)\) \(\chi_{712}(103,\cdot)\) \(\chi_{712}(119,\cdot)\) \(\chi_{712}(127,\cdot)\) \(\chi_{712}(135,\cdot)\) \(\chi_{712}(143,\cdot)\) \(\chi_{712}(151,\cdot)\) \(\chi_{712}(159,\cdot)\) \(\chi_{712}(175,\cdot)\) \(\chi_{712}(191,\cdot)\) \(\chi_{712}(207,\cdot)\) \(\chi_{712}(239,\cdot)\) \(\chi_{712}(295,\cdot)\) \(\chi_{712}(327,\cdot)\) \(\chi_{712}(343,\cdot)\) \(\chi_{712}(359,\cdot)\) \(\chi_{712}(375,\cdot)\) \(\chi_{712}(383,\cdot)\) \(\chi_{712}(391,\cdot)\) \(\chi_{712}(399,\cdot)\) \(\chi_{712}(407,\cdot)\) \(\chi_{712}(415,\cdot)\) \(\chi_{712}(431,\cdot)\) \(\chi_{712}(439,\cdot)\) \(\chi_{712}(471,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{88})$ |
Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\((535,357,537)\) → \((-1,1,e\left(\frac{63}{88}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 712 }(391, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{88}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{43}{88}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{41}{88}\right)\) | \(e\left(\frac{29}{88}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{49}{88}\right)\) | \(e\left(\frac{31}{44}\right)\) |